Edward W Said

Thomas Piketty

Hubert Jayet

Claire Naiditch

Fabien Tripier

Marco Casiraghi

Jakob De Haan

Céline Poilly

Nordine Abidi

Sahra I Sakha

El Fouad

Corentin La Haddad

Ulugbek Tte

Gaston Aminjonov

Yassine Van Der Meulen

Dallal Esmili

Marijn Bendjellal

Laura Ton

Meryem Duthilleul

Amara Rhouzlane

Zongo

Exile is strangely compelling to think about but terrible to experience. It is the unhealable rift forced between a human being and a native place, between the self and its true home: its essential sadness can never be surmounted. "

Introduction

This thesis aims to contribute to the empirical analysis of the distributional consequences of monetary policies and the macroeconomic implications of rising income inequality. The interest in studying the relationship between monetary policy and inequality relates to a speci c context in the advanced economies. Following the Global Financial Crisis (GFC) of 2008 and the recession that ensued, the economic debate among academics and policymakers in developed countries has separately focused on two burgeoning topics: monetary policy alongside the moves of central banks and the worrying level of income and wealth inequality. On the one hand, central banks have been on the frontline to prop up their economies by engaging in massive cuts of their policy rates. In the meantime, they mobilized a toolkit of Unconventional Monetary Policies (UMPs henceforth) that sought to ease nancial conditions and guide agents' expectations. These exceptional measures ranged from negative interest rates to forward guidance and asset purchase programs. On the other hand, the noteworthy contributions in public debate of [START_REF] Piketty | Capital in the 21st century[END_REF] made a strong argument concerning the troubling state of inequality in the advanced economies and its potential impact on growth and social cohesion. Consequently, it fostered wide discussions on how to mitigate the disparities within societies and create more inclusive growth.

In the aftermath of the GFC, policymakers neglected to focus on how far monetary policy could shape income distribution. This is logical as long as the main priority back then was to restore growth. As a matter of fact, central banks were subject to an intertemporal bias where long-term consequences of their decisions are sacri ced in favor of short-term objectives. Nevertheless, it is only recently that we observed a resurgence of interest for the potential links between monetary policy and inequality. In the United States (U.S.) and Europe, the (un)conventional measures implemented by central banks have been blamed for causing distributional consequences. In fact, there is increasing concern that monetary authorities

In the meantime, central bankers did not take long to make a stand in this debate. [START_REF] Draghi | Stability, equity and monetary policy[END_REF], the former President of the European Central Bank (ECB), claimed that UMPs have prevented the Eurozone from falling into a deep recession. Moreover, he asserted that the criticism levelled at the ECB ignores what would have been the state of monetary union without such exceptional measures, arguing that:

"Those who claim that monetary policy worsens inequality typically do not consider the counterfactual. They take the distributional situation as given, but forget that monetary policy is acting precisely because the macroeconomic situation was at risk of changing. In fact, according to ECB simulations, Euro area GDP would be cumulatively at least 1.5 percent lower between 2015 and 2018 without the expansionary policy measures we have adopted. "

Central bankers argue that their post-crisis decisions produced positive outcomes on the macroeconomy. That is, they have relatively succeeded in stabilizing output, enhancing employment and making debt service less painful. However, this reading grid conceals an important part of the puzzle. It is actually feared that these measures and particularly Quantitative Easing programs (QE henceforth) push asset prices up, resulting in wider income dispersion. This is likely to happen, especially if the distribution of nancial assets ownership is highly skewed towards top-income households. In this context, it is necessary to take a step back and ask some questions: is the non-neutrality of monetary policy with respect to the income and wealth distributions an important feature of central banks interventions? Inasmuch as top incomes have signi cantly contributed to the upward trend of inequality, how does changes in monetary conditions a ect this part of the income ladder? Ultimately, what is the impact of in ation -which constitutes nowadays the core mandate of central banks and certainly overlaps with monetary policy decisions -on top incomes?

The rise of income and wealth inequality witnessed in most of the advanced countries is not without consequences on the economy, and even questions the virtues of modern capitalism.

The general public across the world has become aware of the rising inequality problem and the risks that it carries for liberal democracies. As a case in point, movements like "Occupy Wall Street" in the U.S. or "15-M" in Spain have clearly identi ed rising economic inequality as a rst-order issue. From an economic perspective, several research contributions have already stressed the side e ects of inequality on growth and social mobility (see [START_REF] Stiglitz | The Price of Inequality: How Today's Divided Society Endangers Our Future[END_REF] The introduction of this thesis carries on with a general overview of the determinants of inequality. Second, I discuss the mechanisms underlying the distributional e ects of monetary policy as well as the inequality-credit nexus. Finally, I brie y present the interest and motives, the contributions and results of each chapter.

Stylized facts on income and wealth inequality

Concerns on rising economic inequalities in the advanced world have fostered a research agenda on its determinants in two speci c directions. The rst one focused on documenting the factors that widened wage and earning disparities within developed societies in the early 1980s (see e.g. [START_REF] Acemoglu | Why do new technologies complement skills? directed technical change and wage inequality[END_REF], [START_REF] Askenazy | Trade, services, and wage inequality[END_REF], [START_REF] Card | Skill-biased technological change and rising wage inequality: Some problems and puzzles[END_REF], [START_REF] Feenstra | Foreign direct investment and relative wages: Evidence from Mexico's maquiladoras[END_REF], among others). The second strand adopted a political economy approach and attempted to historically dissect the drivers of income and wealth inequality (see e.g. [START_REF] Alvaredo | The top 1 percent in international and historical perspective[END_REF], [START_REF] Atkinson | Top incomes in the long run of history[END_REF] and [START_REF] Piketty | Capital in the 21st century[END_REF]).

Three factors are generally invoked in the rst strand of the literature: skill-biased technological progress, globalization and institutional change. The rst factor put forward the idea that technology is the main driver of the recent increases in inequality. Technological changes have been pointed out as responsible for increasing skill-premium and then wage inequality between skilled and unskilled workers. In fact, the outbreak of Information and communications technology (ICT) revolution favored activities that require speci c skills. In return, this put unskilled workers at a disadvantage, while it has signi cantly contributed to increasing the wages of highly skilled workers. The advent of robots and automation is likely to intensify these dynamics as routine jobs are eliminated and demand for new skills increases. As discussed in [START_REF] Brynjolfsson | The Second Machine Age -Work, Progress, and Prosperity in a Time of Brilliant Technologies[END_REF]'s book, a technology-based economy promotes the emergence of entrepreneurs or "superstars", who derive their incomes directly from the rewards of new technologies they come up with. This implies that as the pace of innovation accelerates, a small group of successful people would be favored against the rest of the population left behind, leading as a consequence to a systematic rise in inequality.

The second factor relates to globalization and how the development of north-south trade recon gured international specializations schemes in terms of skill endowments. This echoes to the idea that greater economic integration via openness to trade has destroyed employment in rich countries, while it has bene ted the developing world's poor, due to the jobs outsourced.

Given that the developed economies have specialized in producing high-skilled goods, wage inequality consequently increased. Such a view is embodied in the elephant curve of [START_REF] Milanovic | Global Inequality : A New Approach for the Age of Globalization[END_REF] presented below, which illustrates the unequal global distribution of income growth for individuals across the income ladder. On the one side, this curve suggests that the lower-middle class in the advanced economies -located at the 80th percentile -has experienced small income gains over the period 1988-2008. On the other side, the middle section of the graph -10th percentile to the 50th percentile -represents the global middle-class and speaks to the fast growth that middle-income countries, like China or India, have achieved over the past decades. Although these changes cannot be directly linked to globalization, they do indicate that the expected gains from economic integration on the rich world's middle-class have not compensated its potential negative e ects.

Figure 0.1: The elephant curve of [START_REF] Milanovic | Global Inequality : A New Approach for the Age of Globalization[END_REF] As far as institutional factors are concerned, they relate, among others, to the erosion of labor market institutions and more particularly, to union density and the minimum wage. These factors reduce the bargaining power of unskilled workers and, in turn, impact inequalities. This relationship is illustrated in Figure 0.2, which depicts the evolution of union membership and the top 10% income share in the U.S. over the period 1913-2012. [START_REF] Jaumotte | Inequality and labor market institutions[END_REF] further provide cross-country evidence showing that the decline in unionization rates is related to the rise of top income shares, while the erosion of minimum wages is associated with signi cant increases in overall inequality. Similarly, [START_REF] Farbe | Unions and inequality over the twentieth century: New evidence from survey data[END_REF] use U.S. microdata on union membership dating back to 1936 and nd consistent evidence that unions reduce inequality and account for a signi cant share of the dramatic fall in inequality between the mid-1930s and late 1940s. Other aspects linked to labor markets such as pay-setting institutions and corporate governance can also explain some deal of inequality. Besides, it is important to underline that institutional factors are somehow tied up to globalization. For instance, the increasing capital and labor mobility across borders strongly pushed towards lower top marginal tax rates and consequently favored rich households. Piketty et al. (2014) con rm this intuition and document that top tax rate cuts in the U.S. are associated with top one percent pretax income shares increases but not higher economic growth. In the same spirit, the loosening of inheritance taxation can give rise to wealth concentration and extends inequality across generations. From a historical perspective, the literature on inequality has more leaned on capital and income than wages. On the very long-run, the determinants of inequality at a point of time seem to be the outcome of political and power struggles between social groups. As a matter of fact, throughout the 19th and 20th centuries, major shocks commonly shaped income and wealth distributions in the advanced economies. Shocks such as world wars resulted in a massive destruction of capital and private wealth, and signi cantly decreased the shares of top deciles in national income. In the same way, transformations in the political process and spread of liberal democracy in the western economies forced the elites to accept social and scal reforms. This resulted in a relatively low income and wealth inequalities in the post-WWII period and allowed the advanced countries to become, to a certain extent, egalitarian societies. These dynamics are quite noticeable in Figure 0.3 below, which traces out for 5 advanced economies, the national income share held by the top 10% richest. However, a trend reversal has been experienced in the evolution of inequalities by the end of 1970s. In fact, the political benchmark, particularly in Anglo-Saxon countries, shifted with the advent of the Washington consensus economic policy prescriptions. The latter has reduced the scope of the traditional instruments used to mitigate inequalities (top marginal taxation and redistribution via the welfare-state, among others) and featured other measures that have pushed up economic disparities (privatization of state-owned enterprises, nancial deregulation, etc.). This change of direction in the dynamics of inequality contrasts with the [START_REF] Kuznets | Economic growth and income inequality[END_REF] curve, which predicts that while economic growth may have a negative impact on inequalities early in a country's economic development, market forces would ultimately push them down.

Monetary policy, in ation and inequality: channels and mechanisms

If distributional questions remain rst and foremost long-run issues, what role can economic policies play? And how central banks' measures to ensure price stability can a ect income inequality? [START_REF] Haldane | How monetary policy a ects your gross domestic product[END_REF] from the Bank of England provides a preliminary answer, arguing that:

"All public policy is distributional, be it monetary, scal, structural or social. The reason I know this is because redistribution is the way public policy works; it is what policy does for a living. Some policies redistribute resources between agents at a point in time. Others redistribute resources between agents over time. If policy is not working through one of these channels, it is not working. "

The distributional implications of monetary policy were, until recently, not considered in the macroeconomic literature. This follows the conventional wisdom, according to which monetary policy is neutral with regard to redistributive issues. As a result, the role of inequality is not examined in most of the macroeconomic models that are used for public policy evaluation. But more recently, several research contributions suggested that the income distribution matters for the transmission of monetary policy. In this respect, [START_REF] Auclert | Monetary policy and the redistribution channel[END_REF] considers the role of redistribution in the transmission mechanism of monetary policy to consumption and conclude that impact on inequality rest upon the extent to which households -with high Marginal Propensity to Consume (MPC) -could bene t from monetary expansions. In a similar vein, [START_REF] Voinea | The impact of inequality on the transmission of monetary policy[END_REF] introduce a model to analyze the relationship between household debt and the transmission of monetary policy. Their results suggest that "the transmission of monetary policy is more e ective for middle income households, which are more indebted and have adjustable rates, as lower policy rates ease the consumption constraints on these households". Therefore, higher inequality can impede the e ectiveness of monetary policy.

In view of this evidence, central bankers should take inequality more seriously. Whether or not monetary policy actions produce distributional e ects remains an empirical question, but it is essential to understand the channels through which these e ects operate. [START_REF] Coibion | Innocent bystanders? monetary policy and inequality[END_REF] list various channels linking monetary policy and inequality. The latter can be distinguished between income and wealth channels. Following this categorization, income channels can be summarized as follows:

• Individuals primarily di er in terms of income composition. While some substantially rely on labor income, others may receive other forms of revenue (dividends, profits, rents, etc.). Therefore, if monetary policy largely favors pro ts over wages, income inequality is likely to increase.

• Business cycles a ect labor incomes heterogeneously. Workers located at the bottom of the skill distribution are generally the most exposed to unexpected shocks. Hence, given earnings heterogeneity in the labor market, a monetary policy that would secure jobs and reduce unemployment will lower income inequality.

As far as wealth channels are concerned, one can think of how people closely operating with central banks can be a ected by monetary policy decisions:

• Individuals primarily dealing with central banks, particularly in nancial markets, tend to respond instantaneously to monetary policy decisions. In such a case, nancial markets segmentation leads the operators who are best connected to a given market to experience positive wealth e ects.. In ation shocks, which happen sometimes to be the consequence of monetary policy actions, can have distributional consequences. First, an expansionary monetary policy, which aims at targeting higher in ation, typically redistributes wealth from savers to borrowers. Hence, the savings redistribution channel reduces wealth inequality. Second, If individuals hold assets that are less protected against in ation, wealth redistribution can occur. As a case in point, given that poor households hold assets mainly in cash, portfolio e ects in consequence of in ation are likely to increase wealth inequality. The redistributive e ect of in ation on wealth can also spill on income dynamics via real asset returns: if in ation a ects asset prices (stock), it will inevitably have an e ect on their returns ( ow). Therefore, the net e ect will depend on the type of asset that is a ected (housing, equity, etc.) and the income percentile to which the asset holder belongs.

In ation is often assumed to a ect households across the income ladder in the same way.

But as put by [START_REF] Hobijn | In ation inequality in the united states[END_REF]: "di erences in spending patterns across households and di erences in price increases across goods and services lead to unequal levels of in ation for di erent households". While the empirical literature on this topic is still developing, [START_REF] Jaravel | The unequal gains from product innovations: Evidence from the u.s. retail sector[END_REF] is the rst contribution that analyzes how product innovations led to in ation inequality in the U.S. from 2004 to 2015. Using data recorded by the retailers when consumers make purchases, he nds that annual in ation for retail products was 0.67 percentage points higher for the bottom income quintile relative to the top income quintile. In explaining the mechanisms behind this result, the author suggests that because of rising inequality, the demand for products consumed by high-income households has increased. Consequently, competition became more intense in these goods segments as rms introduced more new products catering to high-income households. Another dimension worth noticing is the fact that ination nowadays no longer occurs in the market for goods and services but seems to have moved to nancial markets. In this context, asset price in ation, which could partly result from monetary policy decisions such as QE programs, will inevitably favor the rich. The standard view attempting to explain the rise in total debt and household debt ignores the role of inequality, and put forward the idea that there was a misguided attempt to redistribute from the nancial system by encouraging lending to poorer households. It follows that at some point things went out of control in terms of regulation and the behavior ofnancial institutions, leaving out low-income households with unsustainable amounts of debt to payback. While this view has some credence, the distributional angle has attracted more attention in the last decades. Furthermore, the focus has been on the drivers of aggregate credit and household debt as long as the existing literature shows that other forms of credit, such as business credit, are much weaker predictors of nancial crises (see [START_REF] Buyukkarabacak | The role of household and business credit in banking crises[END_REF], for instance). In the aftermath of the 2008 GFC, the potential relationship between rising inequality and leverage has been scrutinized from two points of view. The rst interpretation, notably pioneered by [START_REF] Mian | The saving glut of the rich and the rise in household debt[END_REF], argues that the rise in income inequality leads to essentially more savings entering the nancial system -i.e. the saving glut of the rich -and this money ultimately goes to household and government borrowing. In such a case, permanent positive shocks a ecting top incomes trigger credit supply expansions and increase the loanable funds to poor and middle-income households (see [START_REF] Kumhof | Inequality, leverage, and crises[END_REF], among others). The saving glut of the rich has been initially described by [START_REF] Bernanke | The global saving glut and the us current account de cit[END_REF] to account for the fact that sluggish growth can be the outcome of a situation in which desired saving exceeds desired investment; but according to [START_REF] Mian | Indebted demand[END_REF], the inequalitycredit (or debt) nexus operating via the savings of the rich has important implications for the macroeconomy. In a context of greater saving rates by the rich, rising inequality leads to a downward pressure on aggregate demand that could only be avoided if the non-rich continue to borrow and interest rates keep falling over time. [START_REF] Mian | Indebted demand[END_REF] describe, however, this support to aggregate demand as "indebted" because low-income households indebtedness in the present means less spending in the future, as non-rich debt has to be paid back to the rich.

The inequality-credit nexus

Consequently, rising inequality generates a reliance on credit to sustain aggregate demand, leading, in turn, to persistent decline in long-term interest rates.

The second interpretation of the inequality-credit nexus is a credit-demand side view, which suggests that households are borrowing to sustain their living standards, and thus debt acts as a substitute for wages. Di erent theoretical frameworks have been developed to explain how households can increase their indebtedness to keep up with their peers; but the common feature of these contributions is that a household's attitude to consumption and saving does not depend only on its absolute income but rather on its level of income relative to others. [START_REF] Veblen | The Theory of the Leisure Class. An Economic Study of Institutions[END_REF] is the rst to have introduced the idea that consumption has a social component as it serves to display economic power and signal a speci c social status i.e. conspicuous consumption. Similarly, [START_REF] Duesenberry | Income, Saving and the Theory of Consumer Behavior[END_REF]' contributions to the understanding of consumer behavior are very relevant for the demand channel of the inequality-debt nexus. As a matter of fact, Duesenberry rst acknowledges that the neoclassical consumer theory has not considered how consumption habits are established and the e ects that these habits may have on spending patterns. It follows then two mechanisms addressing these limitations: the "demonstration e ect" and the relative income hypothesis. While the former considers that individuals change their spending behavior by witnessing the consumption habits of others that they are in contact with; the latter links individuals' consumption and saving rates to their income relative to those of people they spend time with. This interpretation implies that rising inequality, whether observed at the local level (state, county, city) or at more disaggregated levels (workplace, neighborhood, etc.), shapes households' consumption patterns and may push them to take on debt to "Keep up with the Joneses".

Outline of the thesis

This thesis consists of four chapters; each can be read separately from the others, except that the rst half analyzes the relationship between monetary policy, in ation and income inequality, while the second half studies the macroeconomic consequences of rising inequality. Speci cally, the rst and second chapters deal with the distributional e ects of monetary policy and in ation on top incomes from a historical perspective. The third and fourth chapters take an interest in the relationship between rising inequality and aggregate credit at the macro-level as well as household debt from a micro-level perspective. Albeit addressing di erent research questions, the rst, second and third chapters mobilize top income data from the latest release of the World Inequality Database (WID) and long macroeconomic series from the Jorda-Schularick-Taylor (JST) Macrohistory Database.

Monetary policy and the top 1%

The rst chapter relates to the distributional implications of monetary policies. This topic has become popular following the measures taken by central banks in the aftermath of the 2008 GFC and, as a consequence, a growing empirical literature has emerged to quantify the side e ects of monetary policy decisions on the income distribution. The search for a causal link between monetary policy shocks and inequality faces, however, some challenges. First, data on income inequality are at best available at the annual level, which can be problematic in view of the high-frequency of monetary policy decisions. Second, granular data on households' income and wealth obtained from micro surveys often omit the tails of the distribution, which can underestimate the e ects of monetary policy on income inequality. In dealing with these limitations, as noticed by [START_REF] Colciago | Central bank policies and income and wealth inequality: A survey[END_REF], the existing literature has addressed the question of monetary policy and inequality either by: (i) using mixed-frequency methods (Samarina and Nguyen (2019a)), (ii) considering a panel of countries over a short period of time [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF]) or relying on (iii) micro-simulations to replicate the wealth distribution from household surveys [START_REF] Adam | Distributional consequences of asset price in ation in the euro area[END_REF]).

The distributional e ects of monetary policies on rich households have received relatively less attention, although it is commonly agreed that top incomes have contributed signicantly to the rise in inequality since 1980s. Chapter 1 is primarily concerned with estimating the dynamic causal e ect of monetary policy shocks on top incomes shares, and the top 1% in particular, for a panel of 12 OECD countries. This chapter is also characterized by the adoption of a historical perspective as it analyzes the relationship between exogenous changes in monetary conditions and top incomes over the 1920-2016 period, thereby covering several exceptional macroeconomic events. Furthermore, the used identi cation strategy of monetary policy shocks is adapted to the historical context of the empirical analysis conducted. In fact, [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF] builds on the macroeconomic policy trilemma as an external instrument -a country cannot simultaneously achieve an independent monetary policy with a xed exchange rate and openness to capital mobility -to provide variations in the short-term interest rates that are exogenous to domestic economic conditions.

The results show that contractionary monetary policy shocks persistently and signi cantly decrease the national income share held by the top 1% and vice-versa for monetary expansions.

The historical data makes it complicated to investigate the underlying mechanisms at work but evidence suggests that the baseline e ect on top incomes is partly channeled through the dynamics of asset returns and the negative e ect of restrictive monetary policy on the capital income share. Two important policy implications can be drawn from chapter 1. First, monetary policy is not neutral vis-a-vis the income distribution, and coordination with other economic policies may be necessary to mitigate potential negative distributional e ects, if any.

Second, although the post-crisis monetary policy toolkit prevented a prolonged recession and massive unemployment, rich households -who own large nancial portfolios -may have bene ted more.

In ation and the income share of the rich

Chapter 2 contributes to the in ation-inequality nexus literature from an empirical perspective. In ation has always been at the heart of the economic policy debate and has given rise to several controversies regarding its impact on households and businesses. For instance, in his essay on The Economic Consequences of the Peace, [START_REF] Keynes | The Economic Consequences of the Peace[END_REF] argues that:

"By a continuing process of in ation, governments can con scate, secretly and unobserved, an important part of the wealth of their citizens. By this method they not only con scate, but they con scate arbitrarily; and, while the process impoverishes many, it actually enriches some".

The existing empirical evidence documents that the relationship between in ation and income inequality is positive (see [START_REF] Easterly | In ation and the poor[END_REF], among others). But a recent work of [START_REF] Binder | Inequality and the in ation tax[END_REF] questions such a stylized fact and nds that the sign of the correlation depends on the time period and sample of countries. Most importantly, what are the transmission channels behind this nexus? The mechanisms underlying the link between in ation and inequality are indeed better known in the literature for wealth inequality -savings redistribution channel and portfolio e ects -than income inequality. This chapter revisits the distributional consequences of in ation, with a focus on top incomes, and introduces a new transmission mechanism based on the e ect of in ation on the dynamics of asset returns. The empirical analysis is based on a panel of 14 OECD countries (Australia, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, Sweden, Switzerland, the U.K. and the U.S.) over the 1920-2016 period.

The main result shows that in ation shocks persistently reduce the national income share held by the top 1% richest. This impact is rationalized in the context of the following mechanism: unexpected in ation reduces real interest rates, which negatively spills on the asset returns that are held by top income households (equity shares, bonds, housing , etc.). Similarly to the rst chapter, this channel also assumes that the very wealthy receive most of their income not from labor but from asset holdings. To make sure that this channel is the prime responsible for the decline in the income share of the rich, it is necessary to confront it with another channel potentially capturing the e ects of in ation on the economy, i.e. output. One way to do this consists of estimating the e ect of an in ation shock on the gap between the real return to capital and the growth rate of output, i.e. r -g. The ndings show that unexpected in ation reduces the r -g gap, thereby demonstrating the prevalence of the real return on assets transmission channel. Furthermore, because unanticipated changes in in ation can depart from the long-run in ation rate, we also estimate the correlations between in ation and top incomes over ve-year averaged periods and conclude that expected and unexpected in ation both reduce the income share of the rich. In view of the de ationary risks that some advanced countries have faced in the last decade (especially in Japan and the Eurozone), the results of this chapter imply that de ation favors top income shares.

Do rising top incomes fuel credit expansions?

Chapter 3 takes on the inequality-credit nexus at the macro-level. The interest in this topic stems from the objective of understanding the factors a ecting credit booms, whose negative consequences on the macroeconomy are now well established in the literature. [START_REF] Bordo | Does inequality lead to a nancial crisis[END_REF], for instance, nd that credit booms heighten the probability of a banking crisis, but there is no evidence that a rise in top income shares leads to credit booms. This chapter challenges the latter nding by establishing a direct causal relationship between top incomes and credit booms. The transmission channel linking top incomes to credit expansions is straightforward: an increase in top incomes leads the rich to save more out of their income, which triggers credit supply shocks. The identi cation of such a causal link is, however, subject to various empirical hurdles, especially related to endogeneity issues: both top incomes and credit dynamics are simultaneously a ected by common shocks (omitted variables bias), and credit booms may also have an impact the income distribution (reverse causality).

One contribution of this chapter is to establish a causal link using an external instrument, which is more convincing than the use of internal instruments and GMM method as in [START_REF] Perugini | Inequality, credit and nancial crises[END_REF] or [START_REF] Gu | Inequality, leverage and crises: Theory and evidence revisited[END_REF]. This chapter follows [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF] by testing two instrumentation strategies in order to exploit di erent sources of the exogenous shocks to inequality. In the rst place, the foreign Communist in uence developed by [START_REF] Madsen | Inequality, nancial development and economic growth in the oecd, 1870-2011[END_REF][START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF] is used as the baseline instrument for inequality and top incomes. This IV can be considered as a cultural-distance index, which tracks overtime the proximity of a domestic country to a potential regime change (i.e. from a market economy to communism) coming from abroad. The index relies on the basic idea that if the foreign communist threat increases, it will likely encourage the national government to implement policies that reduce income inequality, without directly a ecting credit dynamics. The second instrument is based on the idea that changes in policy preferences in neighboring countries -regarding taxation by way of illustration -eventually produce changes in domestic policy as well. The IV considered here is the average top marginal tax rates of neighboring countries in the sample and particularly countries sharing a common language. These instruments are used in the context of a panel of 12 OECD economies over the 1948-2015 period.

The main results suggest that top income shocks persistently increase the credit-to-GDP ratio. This evidence can support the supply-side channel of the inequality-credit nexus. But the ndings show that exogenous increases in synthetic inequality measures, i.e. the Gini coe cients for market and disposable incomes, also lead to credit booms. Furthermore, when decomposing the responses of di erent credit component to an inequality shock, we nd that both business and mortgage loans increase. This makes it di cult to clearly identify the mechanism at play and leads to conclude that both demand and supply side factors are contributing to the relationship between inequality and credit.

Local inequality and household debt in the U.S.

Chapter 4 complements the research question asked in the previous chapter and evaluates the relationship between local inequality and household debt in the U.S. over the 1999-2015 period. Since the 1980s, the U.S. have experienced a considerable rise in debt, which has been concentrated primarily in household debt and government debt. Rising income inequality has notably emerged as a solid explanation of the excessive household debt pattern. A rst strand of the empirical literature is using cross-country macro-economic data to assess the e ects of inequality on household debt. But the move towards individual data is a necessary step to deepen the understanding of underlying mechanisms. This chapter examines the relationship between household income rank, income inequality at the state-level and their interaction on household's participation in the debt market. To do so, several datasets are mobilized but the main structure relies on household-level data from the Panel Study of Income Dynamics (PSID), which is a bi-annual nationally representative survey. There is clearly a trade-o in the choice of the data because, for instance, the Survey of Consumer Finances (SCF) o ers detailed information on households' assets and liabilities but it is only a cross-sectional survey and households' states of residence are omitted. Therefore, the PSID is the only survey in the U.S. featuring decent data on debt status while providing information on households states of residence, along with a strong panel component that will serve to control for unobserved heterogeneity and track changes in borrowing decisions. The contributions of this chapter to the literature are threefold. First, unlike most the existing papers on this topic, the empirical analysis of this chapter focuses on household borrowing decisions instead of debt accumulation per se. Second, previous works had to develop imputation methods to obtain household income information, while in this chapter, I rely directly on households' self-reported income information. Third, I exploit the panel component of the survey and the advantage it o ers in terms of a low attrition bias

The ndings suggest that higher income inequality at the state-level is associated with a lower frequency of household debt. However, the most important result is that this baseline e ect is heterogeneous across the income ladder: low and middle-class income households living in high inequality states are more likely to hold debt than similar households living in low inequality states. Such an evidence points that credit demand is the driving force behind household borrowing decisions and supports, overall, the "Keeping Up with the Joneses" hypothesis: rising local inequality exposes bottom-income households to given consumption standards, which they emulate through increased loan demand.

Part I

Monetary policy, in ation and top incomes C 1 Monetary policy and the top 1% *

Introduction

The global nancial crisis and subsequent central bank measures raised important questions about the side e ects of accommodative monetary policies. In a context already marked by rising income and wealth inequality, the distributional e ects of monetary policy have become an increasingly popular topic in policymaking circles. This is unusual because it is widely accepted that central banks should not be concerned about inequality: they are independent of the political process, and dealing with distributional matters goes beyond their mandate. Nevertheless, the combination of an ultra-low interest rate environment and large asset purchase programs is argued to have reduced modest household savings and driven up asset prices, which are mainly held by rich households. Are these e ects only linked to the context of unconventional measures or do they constitute a structural feature of monetary policy?

This chapter presents new empirical evidence regarding the distributional consequences of monetary policy using annual data from 12 OECD economies over the period 1920-2016. 1 The pre-tax national income share held by the top one percent (P1) is used as a benchmark top income measure. 2 The adopted identi cation scheme of monetary policy shocks particularly relates to the historical context of this study and uses a quasi-natural experiment approach to estimate how exogenous changes in monetary conditions a ect the top 1%. To understand how monetary policy interacts with the rest of the income distribution, we draw on di erent distributional measures of the top decile and standard indicators of income inequality. Furthermore, we exploit the importance of nancial assets and capital returns for top income households to provide insights into some of the underlying transmission mechanisms of mon-etary policy. Finally, state-dependent e ects of interest rate shocks are estimated to study the non-linear e ects of monetary policy on top incomes.

Our methodology primarily relies on local projections (LPs) à la [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF]. The latter generates dynamic responses of top income shares to an exogenous perturbation in the short-term interest rate. The identi cation of such shocks is based on the approach recently proposed by [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF], which responds to the fact that the short-term interest rate and top income shares are potentially in uenced by common unobserved factors, biasing the empirical e ect of interest. Precisely, our approach exploits an instrumental variable in the context of a local projection-instrumental variable (LP-IV) framework (see, [START_REF] Jordà | Betting the house[END_REF]; [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF]; [START_REF] Ramey | Government spending multipliers in good times and in bad: evidence from us historical data[END_REF]) to isolate exogenous uctuations in the short-term interest rate, which are drawn from the well-known macroeconomic policy trilemma. The trilemma states that movements in the base country's short-term interest rate provide exogenous variations in the domestic short-term rate for an open peg. As a result, policy choices regarding capital mobility, exchange rates and interest rates provide a natural experiment to analyse the e ect of monetary policy on top income shares. Finally, because LPs easily accommodate non-linearities, we test our model in a state-dependent setting, where we allow the response of top income shares to depend on the regime of a speci c variable (i.e., business cycle, the in ation regime, credit cycles, cycles and monetary policy stance).

The empirical literature on the e ects of monetary policy on the income distribution is growing rapidly but remains inconclusive. Country-level studies using household-level data suggest that conventional monetary tightening increases income and consumption inequality (see [START_REF] Coibion | Innocent bystanders? monetary policy and inequality[END_REF] for the U.S. and [START_REF] Mumtaz | The impact of monetary policy on inequality in the UK. An empirical analysis[END_REF] for the U.K.). [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF] documents a similar e ect while stressing that its magnitude depends on the share of labor income and extent of redistribution policies.

Cross-country evidence by

Other studies argue that expansionary monetary policy may also have negative distributional implications (see [START_REF] Cloyne | Monetary policy when households have debt: New evidence on the transmission mechanism[END_REF] for the U.K. and U.S. and [START_REF] Inui | E ects of monetary policy shocks on inequality in japan[END_REF] for Japan).

In contrast, most recent research on the distributional e ects of unconventional monetary policy shows that the relationship between monetary expansions and inequality is negative but small in magnitude (see, e.g., [START_REF] Casiraghi | A "reverse robin hood"? the distributional implications of non-standard monetary policy for italian households[END_REF] for Italy, [START_REF] Guerello | Conventional and unconventional monetary policy and households income distribution. an empirical analysis for the euro area[END_REF] and Samarina and Nguyen (2019b) for the Eurozone). Most important, the existing evidence features survey-based estimates of income inequality and mostly focuses on a short time span.

The contribution of this chapter departs from the existing literature in two important respects.

First, we use tax-based estimates of top income shares from the World Inequality Database (WID) because, as shown by [START_REF] Atkinson | Top incomes in the long run of history[END_REF] and [START_REF] Burkhauser | Recent trends in top income shares in the united states: Reconciling estimates from march cps and irs tax return data[END_REF], such data allow for (i) better coverage of business and capital returns, which constitute the bulk of top incomes, and (ii) provide a more accurate picture of the trend of income inequality since the 1980s. In fact, as noted by [START_REF] Roine | Long-run trends in the distribution of income and wealth[END_REF], rich households are underrepresented in income and wealth surveys, which leaves out an essential piece of the income distribution for understanding the e ects of monetary policy on inequality. We extend the empirical analysis by comparing the e ect of monetary policy on the top 1% income share (P1) to other top income indicators, i.e., the share of national income held by the lower 9 percent of the top decile (P09) and the top 0.1% and 0.01% (P01 and P001, respectively) along with a standard income inequality measure, i.e., the Gini index (for market and disposable incomes). While P09 consists of highly salaried workers, the right-tail percentile shares (P01 and P001) could be considered the ultra-rich, for whom capital income matters most (see [START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF] on the heterogeneity underlying incomes at the top). Second, this chapter features a historical analysis covering a century of modern economic history. This approach has the advantage of dealing with several macroeconomic occurrences and covers important events experienced in the developed world, such as the Great Depression and the post-war boom, hence providing more variation in the data and, in particular, top income shares. For this purpose, long series of macroeconomic variables are extracted from the Jordà-Schularick-Taylor Macrohistory Database, developed by Jordà et al. (2016). Using such data is of great interest because they o er a rich set of control variables that could enter as potential determinants of top incomes.

Our main results are easily summarized. First, monetary policy has a signi cant and persistent e ect on top income shares: monetary tightening decreases the share of national income held by the top one percent (P1), while expansionary monetary policy has the opposite e ect.

A normalized +100 b.p. exogenous increase in the short-term interest rate via the external instrument reduces P1 by 0.45 percentage points over a ve-year horizon for the full sample, although the e ects on top incomes are smaller during the post-WWII era (0.3 percentage points decline in P1 over a ve-year horizon). Second, in line with [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF], we nd evidence of considerable attenuation bias in policy responses when we estimate the responses to monetary policy using traditional OLS selection-on-observables versus IV identi cation. Third, it is shown that the e ects of monetary policy on top incomes are (i) heterogeneous and (ii) not necessarily mirrored over the entire income distribution. On the one hand, a positive interest rate shock reduces the shares of national income held by the top 1, 0.1 and 0.01 percent, while its e ect on the bottom 9 percent of the top decile is positive (although not statistically signi cant). On the other hand, monetary tightening increases the Gini index for market and disposable incomes. Fourth, with respect to the literature, we take several steps to explain that our di erence with [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF] is not driven by our sample and is even less tied to the identi cation strategy; rather, it is very likely due to the di erent economies considered in our respective panels. Finally, we demonstrate that our baseline nding is arguably channeled via lower (real) asset returns, which is consistent with the income composition channel of [START_REF] Coibion | Innocent bystanders? monetary policy and inequality[END_REF]. The results are valid regardless of the state of the economy and hold under a battery of robustness checks.

These ndings contribute to [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF] and highlight that the e ects of monetary policy on inequality crucially rely on the distributional indicator examined (tax-based estimates of income shares or synthetic inequality measures), the macroeconomic occurrences covered (historical data vs short period samples) and most important the countries considered along with the identi cation strategy adopted for monetary surprises.

Chapter 1 is structured as follows. Section 2 discusses the estimation methodology and the identi cation strategy. Section 3 thoroughly describes the data. The fourth section presents the LP results, while the fth and nal section concludes the chapter.

Local projections

We follow the general method proposed by [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF] and its very recent application to our context in [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF] by estimating impulse response functions (IRFs) from local projections (LPs). In its basic form, LP consists of a sequence of regressions of the endogenous variable shifted several steps ahead. As a result, the approach consists of estimating the following equation:

∆ h y i,t+h = α h i + β h ∆r i,t + θ h X i,t + ε h i,t (1.1)
where ∆ h y i,t+h = y i,t+h -y i,t and corresponds to the change in the top income variable from the base year t 0 up to year t + h, with h = 1, ..., H; ∆r i,t denotes the change in the short-term interest rate; and X i,t refers to a vector containing a set of control variables. The latter includes the lags of the rst di erence of y i,t and r i,t , together with additional controls that could theoretically explain top income shares and, simultaneously, be correlated with monetary conditions.

It is important to note that each step of the local IRF is obtained from a di erent equation and directly corresponds to the estimates of β h . Thus, unlike in a VAR approach, the estimated coe cients contained in θ h are not used to build the IRF. Instead, they only serve as controls and cleanse the β h of the e ects of past top income and monetary policy changes, in addition to contemporaneous and past changes in other macroeconomic variables (output and CPI, for instance). Moreover, the LP approach is intentionally "model-free" and therefore imposes fewer restrictions -with respect to VARs --when calculating IRFs. As shown by [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF], such an approach confers numerous advantages. This estimation technique is actually (i) more robust to model misspeci cation, (ii) does not su er from the curse of dimensionality, (iii) can more easily accommodate non-linearities and (iv) can also be estimated with simple regression techniques. 3 In what follows, we describe the bene ts of LP with respect to our research question.

First, LPs allow for the addition of several control variables -before encountering dimensionality problems -that may in uence top income shares and, simultaneously, be correlated with monetary policy actions. The X i,t vector includes the rst di erence up to two lags of the log of the CPI, real GDP, real consumption, real investment, the government expenditure-to-GDP ratio, house prices, stock prices, total factor productivity, the total loans-to-GDP ratio and a trade openness ratio. In addition to these country-time variables, we include world real GDP growth to parsimoniously remove global business cycle e ects. 4The second bene t of LP is that it o ers an original identi cation strategy to estimate dynamic causal e ects. To build shock series, our strategy relies on external instruments, i.e., variables correlated with changes in short-term interest rates but not with the other macroeconomic shocks a ecting the economy. Our aim is to obtain external sources of variation in shortterm interest rates to provide quasi-random experiments and thereby more clearly identify causal e ects. These types of strategies have recently attracted growing interest in applied macroeconomics [START_REF] Jordà | Betting the house[END_REF][START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF]Jordà and Taylor, 2016;[START_REF] Ramey | Government spending multipliers in good times and in bad: evidence from us historical data[END_REF][START_REF] Stock | Identi cation and estimation of dynamic causal e ects in macroeconomics using external instruments[END_REF]. Regarding our research question, monetary policy is unlikely to be driven by top incomes; therefore, the dynamic causal e ect is clear (no simultaneity bias).

However, even if the income distribution is not a target of central banks, both top incomes and monetary policy decisions depend on economic conditions, which may be improperly measured by the set of control variables in our regressions (omitted variable bias) [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF]. Accordingly, this situation calls for the use of exogenous shocks to domestic monetary conditions rather than short-term interest rates. As is widely agreed upon in the literature, the challenge is to nd external factors that would make the variations in monetary conditions a random treatment.

In this chapter, we use the local projection-instrumental variable (LP-IV) method proposed by [START_REF] Jordà | Betting the house[END_REF], [START_REF] Ramey | Macroeconomic shocks and their propagation[END_REF], and [START_REF] Stock | Identi cation and estimation of dynamic causal e ects in macroeconomics using external instruments[END_REF]. We couple this method with the identi cation strategy for external variations in monetary conditions based on [START_REF] Jordà | Betting the house[END_REF] and [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF]. The purpose here is to use the macroeconomic policy trilemma to nd external variations in monetary conditions. The latter states that a country cannot simultaneously achieve free capital mobility, a xed exchange rate and independent monetary policy. When pursuing any two of these goals, it is necessary to abandon the third.

Building on the trilemma [START_REF] Obstfeld | Monetary sovereignty, exchange rates, and capital controls: the trilemma in the interwar period[END_REF][START_REF] Obstfeld | The trilemma in history: tradeo s among exchange rates, monetary policies, and capital mobility[END_REF][START_REF] Shambaugh | The e ect of xed exchange rates on monetary policy[END_REF], we trace out episodes where monetary policy is not autonomous and external conditions from the base country can generate perturbations to the domestic short-term interest rate. Such perturbations are considered to be exogenous because the base country, for example, the U.S. during the Bretton Woods era, does not internalize the externalities of its own policy choices on partner countries.

This makes the trilemma a source of natural experiments for domestic monetary policy.

The trilemma links the domestic interest rate to the base country's interest rate through the exchange rate regime and the intensity of nancial openness. A suitable expression for such an instrumental approach is given by: (KOP EN i,t = 0) to international capital markets; ∆r base i,t denotes the monetary policy change in the base country; and C i,t is a vector of macroeconomic controls in country i at time t. 5 Equation 1.2 corresponds to the rst-stage IV approach adopted by [START_REF] Jordà | Betting the house[END_REF] with the term [P EG i,t * KOP EN i,t * ∆r base i,t ] referring to the external instrument (z i,t ).

∆r i,t = a + b[P EG i,
The instrument has to ful l two usual criteria. First, z i,t must have a signi cant in uence on the endogenous variable. In practice, when there is perfect capital mobility and a xed exchange rate regime, the home country's monetary conditions (∆r i,t ) are perfectly related to those of the base country (∆ base r i,t ), which theoretically ensures the relevance of our instrument. 6 Second, z i,t should a ect home monetary policy without in uencing top incomes.

This condition implies that only the international interest rate channel is at play. However, base monetary conditions may impact domestic outcomes other than interest rates. For instance, an increase of the base country's policy rate decreases its real GDP, which can have consequences for the peg countries and, in ne, a ect top incomes. Such spillover e ects lead to failure of the exclusion restriction. To control for such spillover confounding, we follow [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF] and consider base country policy surprises rather than the change in its interest rate. Therefore, the corresponding two-stage least squares (2SLS) model we estimate is given by:

∆r i,t = a + b[P EG i,t * KOP EN i,t * ∆ M S base i,t ] + ΘC i,t + µ i,t (1.3) ∆ h y i,t+h = α h i + β h ∆r i,t + θ h X i,t + ε h i,t (1.4)
where ∆ M S base i,t corresponds to movements in base country rates unexplained by observable controls. The latter include the current and lagged values of macroeconomic aggregates and the lagged values of the policy rates. 7 The third motivation for using LP is that it easily accommodates non-linearities. 8 This feature 5 The controls include the contemporaneous and two lags of real per capita GDP growth; the CPI in ation growth rate; real consumption growth; government expenditure growth; real investment growth, stock price growth; house price growth; total factor productivity growth; the change in commercial openness; the change in the ratio of loans to the non-nancial private sector to GDP; and world GDP growth. 6 We discuss in subsection 3.3 the adopted base countries, which are allowed to vary over time. 7 ∆ M S base i,t = ∆i base i,t -∆ îbase i,t , where îbase i,t is the tted value of a simple linear model estimated by OLS. 8 The VAR literature also o ers some solutions to deal with non-linearities. However, the richer structure of the VAR model entails several complications in computing IRFs, which often makes the estimation intractable in practice if we are outside the baseline framework.

allows us to enrich our analysis by checking whether the IRFs of the top income share to a short-term rate shock are state-dependent. This is of great interest because (i) we use historical data that cover di erent monetary policy regimes, and (ii) it also follows many studies that highlight that the e ects of monetary policy vary over the business cycle. In practice, we extend equation 1.4 and condition the e ect of interest rates on the top income variable by a state variable:

∆ h y i,t+h = α h i + β h 1 ∆r i,t * State i,t + β h 2 ∆r i,t * (1 -State i,t ) + θ h X i,t + ε h i,t (1.5)
where State i,t is a variable indicating a speci c regime (i.e., business cycle, the in ation regime, credit cycles, stock return cycles and monetary policy stance).

Data description 1.3.1 Top income shares

Top income data are extracted from the World Inequality Database (WID, 2019).9 Speci cally, the main variable of interest is operationalized by the top one percent's pre-tax national income share (P1) in 12 OECD economies over the 1920-2016 period. 10 The countries considered include Australia, Canada, Italy, Germany, Denmark, France, the U.K., Japan, the Netherlands, Norway, Sweden and the U.S. As noted by [START_REF] Roine | Long-run trends in the distribution of income and wealth[END_REF], [START_REF] Leigh | Top incomes[END_REF] and [START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF] 2016)), we extend our analysis by checking how changes in monetary conditions a ect the ultra-rich. To do so, we mobilize data on the share of national income held by the top 0.1% and 0.01% from [START_REF] Atkinson | Top Incomes: A Global Perspective[END_REF]. Another important exer-cise consists of comparing the e ect of monetary policy on top income shares with the entire income distribution using a synthetic measure of inequality, i.e., the Gini index, which is obtained from the Standardized World Income Inequality Database (SWIID) of Solt (2020).11 A notable di erence between WID and SWIID is that the latter o ers data based on disposable income, thereby allowing us to account for redistributive transfers. Finally, we also check how monetary policy a ects changes within the top of the distribution using the P1/P09 ratio.

Macroeconomic variables

We exploit the Jordà while trade globalization is associated with a reduction in inequality, nancial globalization is associated with its increase. We control for the rst using the ratio of imports and exports to GDP. The ratio of government expenditure to GDP is also included in our control variables. In fact, based on a political economy model and an empirical analysis using data on OECD countries, [START_REF] Azzimonti | Financial globalization, inequality, and the rising public debt[END_REF] show that governments choose higher levels of public spending when inequality increases. Moreover, technological change has been repeatedly identi ed in the literature as playing a potent role in widening the gap between top and bottom income earners (see [START_REF] Acemoglu | Why do new technologies complement skills? directed technical change and wage inequality[END_REF] and [START_REF] Card | Skill-biased technological change and rising wage inequality: Some problems and puzzles[END_REF], among others). A standard way to control for this factor consists of mobilizing data on total factor productivity (TFP) per hour worked, which are obtained from [START_REF] Bergeaud | Productivity trends in advanced countries between 1890 and 2012[END_REF]. Finally, we include world real GDP growth to account for global business cycle e ects.

External instruments

As discussed above, our IV strategy -based on the trilemma faced by policymakers -identi es exogenous changes in domestic monetary conditions resulting from estimated surprise movements in the base country interest rate (∆ M S base i,t ). Therefore, our sample implicitly includes three subpopulations: the rst group concerns base countries whose monetary policy is relatively autonomous; the second group contains pegs, that is, economies that import monetary policy and for which the base country's currency serves a focal anchor; and the last group relates to oats, which are the economies allowing their currency to be determined freely in the market. This subsection brie y discusses the de nition of base countries, the source for applicable exchange rate regimes and the adopted capital mobility index.

Local projection results

Baseline

Our empirical setup builds primarily on LP estimation, along with an identi cation strategy of monetary surprises that is consistent with the historical context of this study. The rst step is to assess the strength of our instrument. To do so, we estimate, in the context of equation 1.3, a rst-stage regression of changes in the short-term interest rate on the instrument z i,t and the aforementioned macroeconomic controls, including country xed e ects. The rststage regression results are reported in Table 1.1 and underline the importance of the passthrough from base to home interest rates over several periods. The coe cient estimates of the instrument z i,t are statistically signi cant at the 1% level and range between 0.52 and 0.58 from year 0 up to year 5, both across the full and post-WWII samples. Similarly, the F -statistics feature high values across samples. Note that [START_REF] Stock | A survey of weak instruments and weak identi cation in generalized method of moments[END_REF] recommend a threshold of 10 for the rst-stage F -statistic. Thus, we can now proceed to analyse the LP responses of the top one percent income share to exogenous uctuations in the short-term interest rate.

The results obtained from the estimation of equation 1.4 by LPs are presented in Figure 1.1.

The four graphs illustrate IRFs (in percentage points) of P1 -relative to their initial value in year 0 -to a normalized +100 b.p. increase in the short-term interest rate, with the associated 90% con dence bands, which are constructed from clustered-robust standard errors. The impulse responses of P1 are reported using both the instrumental variable and OLS for the full and post-WWII samples.

An initial glance at the IRFs suggests that monetary tightening signi cantly and durably decreases the share of national income held by the top one percent. 13 Inasmuch as our empirical model is linear, the exact opposite e ect holds with respect to monetary easing. Precisely, an exogenous increase of +100 b.p. in the short-term interest rate via the instrument (graph (a) on the left) reduces P1 by 0.4 percentage points three years after the shock. This e ect is economically considerable, given that the average of P1 across the sample over the studied period amounts to 10 percent. The post-WWII sample follows a similar path, but the e ect on P1 over a ve-year horizon is smaller (graph (b) on the right). 14 The negative e ect on P1 is, interestingly, more than halved across both samples when using an OLS estimation: a short-term interest rate shock in graph (c) reduces P1 by 0.19 and 0.16 percentage points four and ve years following the shock, respectively. These di erences are clearer in Table 1.2, which jointly reports coe cient estimates of OLS and LP-IV. We compare the results obtained by the two methods to assess the degree of attenuation bias in the OLS estimation. In doing so, we notice that the impulse responses under both methods exhibit relatively similar patterns. However, the coe cient estimates obtained via OLS are less statistically signi cant and substantially smaller than those produced by the IV. Note that [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF] document the same observation and of a fairly similar magnitude. How should one account for such discrepancy between the OLS and LP-IV coe cient estimates? Some limitations of OLS regression may be at work and explain this contrast. As noted in section 2, given that monetary policy is not driven by top incomes, simultaneity bias is not a concern. However, both variables are a ected by economic conditions, some of which may be omitted from the set of control variables.

Finding that monetary tightening decreases P1 over a long time span sets our contribution apart from the literature. Particularly, our baseline result contradicts the cross-country evidence of [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF], who document that contractionary monetary policy has negative distributional e ects for a panel of 32 advanced and emerging market countries over the period 1990-2013. 15 Hence, it is important to understand what explains such di erences. First, we demonstrate that our result holds for a shorter sample period (see Figure A.4 in the Appendix). 16 Second, we estimate equation 1.4 using the benchmark income inequality indicator considered by [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF], i.e., the Gini index. Graphs (a) and (b) in Figure 1.2 indicate -as in [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF] -that contractionary monetary policy increases the Gini index for market and disposable incomes. This is a fairly standard result, but it has two important implications: (i) our di erence with respect to [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF] does not depend on the sample period or the identi cation strategy, but it is most likely driven by the sample of economies considered; (ii) the impact of monetary policy on P1 is not necessarily mirrored on the entire income distribution. On the one hand, this is perhaps because the Gini index attaches greater importance to households in the middle of the distribution, who are likely to become unemployed following monetary tightening. On the other hand, unlike tax-based estimates from WID, SWIID relies on survey data and therefore features a lower representation of top income households.

Given the heterogeneity in the top decile, we decompose the e ect of monetary policy on three distributional indicators presented in the data section: the national income shares held by the top 9% (P09), 0.1% (P01) and 0.01% (P001). The impulse responses displayed in graphs (c) and (d) are in sharp contrast to the baseline result, as they report a positive, albeit not statistically signi cant, e ect on P09.17 A plausible explanation for this nding is that provided by [START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF], who nd that changes in per capita GDP growth yield opposite e ects for the top percentile (P1) and the bottom of the top decile (P09). In this respect, it can be assumed that output losses following monetary tightening strongly spill over onto capital income and performance-related payments (stock options, bonus programs, etc. ), which constitute a signi cant share of P1's total income -this assertion is also con rmed for the ultra-rich, where capital income is bound to be larger (see the responses of P01 and P001 shown in graphs (e) to (h)). In contrast, P09 is much less linked to developments in the economy because highly salaried workers hold smaller capital shares and are arguably more protected by labor market settings, which makes such income groups less sensitive to unanticipated changes in the monetary policy stance. Hence, our empirical analysis reveals that the e ect of monetary policy on top income shares would depend on the segment that is examined: income shares going from the top 1 to 0.01 percentiles or the residual part of the top decile (P09). Another useful exercise on distributional measures can check how monetary policy a ects income changes within the top of the distribution.

Robustness checks

The identi cation strategy adopted to estimate dynamic causal e ects obviously requires checking the reliability of the instrument z i,t . In the rst step, we overidentify the estimated model by including the lag of z i,t as an additional instrument. The IRFs presented in graphs (a) and (b) of Figure 1.3 are consistent and con rm that the maximum impact on P1 is smaller for the post-WWII sample. Furthermore, the related estimations fail to reject the null hypothesis of the Hansen-Sargan over-identi cation test, hence suggesting that the exclusion restriction holds. Second, the instrumental variable is constructed using the base country de nitions of [START_REF] Ilzetzki | Exchange arrangements entering the 21st century: Which anchor will hold?[END_REF], which allows us to exploit di erent sources of changes in monetary conditions. In fact, [START_REF] Ilzetzki | Exchange arrangements entering the 21st century: Which anchor will hold?[END_REF] do not consider, for instance, Norway as belonging to the dollar bloc during the post Bretton Woods era. Graphs (c) and (d) show that the negative effect of monetary tightening on P1 is still robust to a di erent base country de nition for both samples. Finally, we control for potential spatial correlations in the residuals by including the jackknifed average of P1 as a control variable. The estimated IRFs are depicted in graphs (e) and (f) of Figure 1.3 and con rm the stability of our baseline estimate.

Having assessed the strength of our instrumental variable, we perform additional sensitivity analyses on the full and post-WWII samples. These are shown in Figure 1.4 and include di erent model speci cations plus a pre-crisis analysis. The rst test consists of estimating equation 1.4 with country xed e ects while omitting the rich set of control variables. This exercise is valuable because it is also a way to assess whether the IV exclusion restriction is violated. In fact, a correctly speci ed instrument would be su cient to avoid potential endogeneity bias.

The evidence depicted in graphs (a) and (b) does not contradict our main result. The second test presented in graphs (c) and (d) reduces the lag number of equation 1.4 and suggests that the LP framework remains robust to di erent lag numbers. The third test excludes the base countries from the sample and retains only observations from pegged regimes. The IRFs displayed in graphs (e) and (f) are in line with the main result. Another concern that may arise relates to the fact that our sample period covers episodes where the short-term interest rate reaches the lower bound and becomes inadequate to measure the monetary policy stance. To address this issue, we perform two robustness checks: rst, we use long-term interest rates as the monetary policy instrument, and second, the Great Recession period is omitted from the sample. The results are reported from graphs (g) to (j) and show strong consistency with the LP-IV baseline nding. We note, however, that the impact on P1 is not statistically signi cant in the short run when considering the post-WWII sample.

Insights on the income composition channel

Our baseline result suggested that monetary tightening lowers the share of national income held by the top one percent (P1). That said, it is relevant to investigate one of the underlying transmission mechanisms of monetary policy towards top income shares. Speci cally, we demonstrate here that our evidence can support the income composition channel introduced by [START_REF] Coibion | Innocent bystanders? monetary policy and inequality[END_REF]. That is, considering the heterogeneity in income sources between households, monetary policy will probably a ect the income distribution if it disadvantages some types of income. With respect to the top percentile, the idea we would like to support in this chapter is straightforward: if the top 1% receive an important share of their total income from capital, then the e ect of monetary policy is likely to be channeled through one or several assets' returns. For this purpose, we estimate the e ect of monetary tightening on the (real) returns of di erent nancial and real assets. The latter consists of returns on (i) total wealth (weighted average of housing, equity, bonds and bills) and (ii) risky assets (weighted average of housing and equity). 18 We prefer capital returns over stock prices because the former include dividends and rents while the latter are expected to have more impact -through asset valuations -on wealth than on income. The impulse responses depicted in graphs (a) and (b) show that the (real) total return on wealth is lowered by 3.7 percentage points in the full sample, while this reduction is slightly stronger during the post-WWII period. It is also worth noting that unexpected monetary tightening induces a more sizeable reduction in risky asset returns (see graphs (c) and (d) in section 6). This means that monetary policy shocks will have a stronger e ect on top income households if they hold a large share of risky assets in their portfolios. 19 This magnitude of such a channel is obviously related to the assets ownership shares in each country. In fact, the OECD (2018) documents substantial variation in nancial asset holdings across countries and deciles. For example, the share of bonds, equity and voluntary pensions in the total nancial assets of the top decile in France is higher than that in Germany or the Netherlands (see Figure A.9 in the Appendix).

Another way to investigate the income composition channel is to estimate the impact of monetary policy on the gap between returns on capital r and the real GDP growth rate of the economy g, i.e., r -g.20 Such an approach makes it possible to appraise whether the negative e ect of monetary tightening on (real) asset returns is more than proportional to that on growth. The results reported in Figure 1.6 yield similar outcomes to the IRFs previously discussed: regardless of whether r is approached through total wealth or only risky assets, a positive interest rate shock narrows the gap r -g for the full and post-WWII samples. 21

State-dependent e ects

The results we have reported thus far support that monetary policy tightening decreases P1 and vice versa. There is, however, a potential pitfall because our sample encompasses very di erent economic regimes. Moreover, several studies indicate that some economic variables, such as the short-term interest rate, may, for instance, behave very di erently during economic downturns. To overcome this limitation, we take advantage of the fact that the LP-IV framework easily accommodates non-linearities. It is convenient to explore whether the effects of changes in monetary conditions on top income shares are state-dependent. Thus, we allow the impact of monetary policy on the top income variable to depend upon the state of another variable (see equation 1.5). In this way, we can compute conditional impulse responses in a particular regime to a normalized +100 b.p. increase in the short-term rate.

We consider ve factors that potentially lead to di erent IRFs of monetary policy: the state of the economy over the business cycle, the in ation regime, credit cycles, stock market cycles and the monetary policy stance. The episodes of the business cycle are identi ed using the HP lter and take value one in the case of an economic expansion and value zero during recessions. The same approach is adopted to identify credit and stock market surges/slowdowns.

With respect to in ation, a high-in ation episode is de ned as a period during which in ation is above its country-speci c fourth quartile. Conversely, a country features a low-in ation regime when in ation is below its rst quartile. With regard to the monetary policy stance, we de ne a binary variable taking value one when there is positive variation in the short-term interest rate (i.e., monetary tightening) and 0 in the case of negative variation (i.e., monetary easing). Finally, we check whether the responses in the aforementioned regimes are signicantly di erent from each other by conducting a Wald Chi-squared test.

Figure 1.7 reports the IRFs estimated with the state-dependent e ect model and the instrumental variable (equation 1.5) for the rst 4 factors previously described. Overall, the displayed 21 It should be noted that a positive shock a ecting the gap r -g increases P1 in our sample. This contradicts Acemoglu and Robinson (2015), who nd no correlation between r -g and the top one percent share, which could be explained by the fact that they proxy returns on capital by the yields of long-term government bonds, while we adopt a measure that is more relevant to top incomes (returns on equity, housing, bills and bonds).

IRFs do not con ict with the previous results: the e ect of monetary policy on P1 continues to hold, irrespective of the state of the economy. As shown in graphs (a) and (b), monetary policy has more immediate e ects on P1 during expansions than during recessions. This is an expected outcome, as [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF] nd that the e ect of monetary policy on output is quite strong in booms but considerably weaker in slumps. Interestingly, it also appears from graphs (c) and (d) that monetary tightening has a strong e ect in the medium run under a high-in ation regime. This makes sense considering that in ation itself is a redistributive tool, which, according to Paarlberg (1993) "...steals from widows, orphans, bondholders, retirees, annuitants, bene ciaries of life insurance, and those on xed salaries, decreases the value of their incomes".

In addition, the impulse responses presented in graphs (e) and (f) show that the impact of changes in short-term rates on P1 is not a ected by credit cycles. In fact, during episodes of credit booms and slumps, restrictive monetary policy produces very similar impacts on P1. Another non-linear experiment addresses the idea that during periods of high volatility in stock markets, investors are less willing to hold stocks, and the e ects of monetary policy shocks could be limited. That is why we test the state-dependent e ect on P1 in the context of stock market booms/slumps. Graphs (g) and (h) of Figure 1.7 show that there is no di erence in the response to monetary policy regardless of whether stock prices experience a boom or bust episode. However, the response of P1 during stock market slowdowns is not statistically signi cant, thereby lending some credence to this assumption. Finally, Figure A.10 in the Appendix supports our baseline result when considering potential asymmetries between expansionary and contractionary monetary policies. Table A.5 in the Appendix, which reports the Wald test results for each regime along with their respective p-values, indicates that the responses in the respective regimes are not signi cantly di erent from each other. Overall, this con rms that monetary tightening reduces the national income share of P1 and vice versa for a monetary expansion, regardless of how the economy behaves.22

Conclusion

This chapter sought to investigate the distributional consequences of monetary policy via top income shares between 1920 and 2016 in 12 OECD economies. The central idea that guided our argument is that the existing empirical literature on the distributional e ects of monetary policy mainly uses survey-based estimates of income inequality and covers a shorter period. This approach translates into lower inequality estimates -particularly due to the underestimation of business and capital incomes of rich households -and a lower coverage of exceptional macroeconomic occurrences (recessions, sovereign defaults, etc.). We address these shortcomings by studying how changes in the short-term interest rate over a century impacted the share of national income held by the top one percent while controlling for the determinants of inequality and top incomes. To do so, we combined two large datasets: (i) the World Inequality Database (WID) to extract tax-based data on top income shares and the Jordà-Schularick-Taylor (JST) Macrohistory Database, which allows us to access a large series of macroeconomic and nancial variables.

Our empirical strategy is based on local projections (LPs) to obtain the impulse responses of top income shares to a normalized +100 b.p. exogenous increase in the short-term interest rate via the instrument. The motivation for this empirical setup is threefold: (i) LP is a "model-free" approach, which allows us to control for several factors that may a ect top income shares and, simultaneously, be correlated with monetary policy actions; (ii) it o ers a quasi-natural experiment as an identi cation strategy, where exogenous perturbations to the short-term rate are driven by factors unrelated to domestic economic conditions; and (iii) it easily accommodates non-linearities, thereby allowing us to estimate potential state-dependent e ects of monetary policy on the top one percent.

The results obtained from the LP estimates indicate that tight monetary conditions strongly decrease the top one percent's income share and vice versa for an expansionary monetary policy.

Following a positive perturbation to the domestic short-term rate via the external instrument, the share of national income held by the richest one percent decreases by 0.13 to 0.44 percentage points. This e ect is economically sizeable and statistically signi cant in the medium run. It is also shown that changes in monetary conditions produce a stronger e ect on righttail percentile shares (P1, P01 and P001) than the bottom 9 percent of the top decile. We also demonstrate that this negative e ect on top incomes is not re ected in the whole income distribution, as the Gini index (for market and disposable incomes) responds positively to monetary policy shocks. Furthermore, regarding the transmission mechanism of this e ect, the reduction in the top one percent's share is arguably the consequence of lower (real) asset returns (on equity, housing and other safe assets), which is consistent with the income composition and indirect income channels. On top of that, there may be other mechanisms than the one we put forward and and further research is needed in this direction.

The baseline results hold under a battery of robustness checks, which (i) introduce an empirical setting that is similar to that of [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF], (ii) overidentify the estimated model using the lagged term of the instrument, (iii) change the base country de nition, (iv) control for spatial correlations in the residuals, (v) remove the rich set of control variables, (vi) test di erent lag numbers, (vii) estimate the empirical model only on pegged regimes, (viii) use long-term interest rates as the monetary policy instrument and (ix) omit the Great Recession from the sample. Finally, the state-dependent e ects version of our model suggests that our conclusions are robust, regardless of the state of the economy.

In future research, we would like to test the e ects of monetary policy on di erent income deciles to focus exclusively on poor and middle-class households (i.e., the bottom 5% or 1% with the lowest market incomes). From the same perspective, are the results obtained here also valid for wealth inequality? This aspect is important because wealth is more unevenly distributed than income. Moreover, while we use pre-tax data, policymakers may be interested in the e ects of monetary policy on the income distribution net of the contribution of scal policy. Finally, in the spirit of the corresponding literature, the empirical approach adopted in this chapter considers only the global e ects of monetary policy on the income distribution.

That is, we do not identify all the transmission channels through which monetary policy a ects top incomes. Ultimately, what policy implications can we draw from these ndings for the ongoing debate on monetary policy and the income distribution? Central bankers need to be attentive not only to the aggregate consequences of monetary policy but also to their side e ects. Notes: *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively. Country-based cluster-robust standard errors in parentheses. The rst di erence of the short-term interest rate is regressed on the instrumental variable, using country xed e ects and macroeconomic controls (the change in the short-term interest rate; real per capita GDP growth; the CPI in ation growth rate; real consumption growth; government expenditure growth; real investment growth; stock price growth; house price growth; the level of commercial openness; the change in the loans to non-nancial private sector to GDP ratio; total factor productivity growth; and world GDP growth). We include contemporaneous terms and two lags. Notes: Country-based cluster-robust standard errors are reported in parentheses below the coe cient estimates. The controls include the twice-lagged terms of (i) the change in the short-term interest rate; (ii) the change in top income share; and the contemporaneous and twice-lagged terms of (iii) real per capita GDP growth; In ation and the income share of the rich †

Main gures and tables

Introduction

Rising income and wealth inequality over the past 40 years in many advanced economies has led to renewed interest in the drivers of the income and wealth distributions, inspired by the work of [START_REF] Piketty | Income inequality in France, 1901-1998[END_REF], [START_REF] Piketty | Capital in the 21st century[END_REF] and [START_REF] Atkinson | Top incomes in the long run of history[END_REF]. One of the drivers of inequality that received considerable attention is in ation. Although [START_REF] Piketty | Capital in the 21st century[END_REF] argues that "the redistributions induced by in ation are always complex, multidimensional, and largely unpredictable and uncontrollable" (p. 575), most previous research suggests that in ation increases inequality and is bad for low-income households because they typically hold a disproportionate share of their assets in cash (see [START_REF] Colciago | Central bank policies and income and wealth inequality: A survey[END_REF]). However, Binder (2019) challenges this view, arguing that the correlation between in ation and income inequality depends on the time period and sample of countries considered.

Previous research paid only limited attention to the e ect of (un)expected in ation on the right tail of the income distribution. This chapter aims to quantify the distributional consequences of in ation on top income shares. 1 While the income of poor households primarily consists of labor income or transfers, the income of the rich mainly comes from business, capital incomes and rents [START_REF] Atkinson | Top Incomes over the Twentieth Century: A Contrast between continental European and English-Speaking Countries[END_REF]). This implies that the top income shares may be a ected di erently by in ation than income shares at the lower end of the distribution.

Using the pre-tax national income share held by the top 1% richest (P1) from the World Inequality Database (WID), we examine how in ation shocks and long-run in ation a ect rich households using data over the 1920-2016 period for a sample of 14 advanced economies (Australia, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, Sweden, Switzerland, the U.K. and the U.S.). Data on tax-based top income shares has two advantages: (i) unlike survey-based estimates, the data provide a better coverage of business and capital incomes [START_REF] Atkinson | Top incomes in the long run of history[END_REF], and (ii) they re ect the trend of income inequality since the 1980s more accurately. Using long-run data allows to cover major events, such as the Great Depression and the post-war boom, hence giving more variation in the data and in particular the top income variable.

Our empirical strategy is as follows. We rst quantify the impact of an in ation shock on the income share of the top 1% richest and then investigate the relationship between in ation and top income shares in the long run. In the former part, we estimate the dynamic e ects of changes of the in ation rate that are orthogonal to contemporaneous and lagged monetary policy decisions, aggregate demand or past and anticipated in ation, while in the latter we evaluate how long-term in ation shapes top income shares. The rationale behind this dual approach is to account for the possible contrasting e ects between unexpected and longrun in ation on the top income distribution. We employ di erent methodologies in both analyses. In the rst part, we use the Local Projection (LP) method proposed by [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF] to generate Impulse Response Functions (IRFs) of top income shares to an in ation shock, taking into account that the relationship between the in ation shock and top incomes may be statedependent. To be more precise, we allow the response of the top-one-percent income share to an in ation shock to depend on the regime of a speci c variable (i.e., the business cycle, the in ation regime, nancial openness and political institutions). This is particularly relevant in view of our use of a long sample period with various economic and monetary arrangements in place. In the second part of our analysis, we use panel regressions in which all variables are de ned as ve-year averages. By doing so, we eliminate business-cycle uctuations, which allows us to examine the impact of in ation on the income share of the top-one-percent in the long term. Here, we control for structural factors driving top incomes, such as globalization, technological progress, education and labor market institutions.

Our evidence suggests that in ation reduces the share of national income held by the top one percent (P1). In particular, a 100 bps in ation shock reduces P1 by around 0.12 percentage points over a ve year horizon. This baseline nding is robust to alternative top income measures (i.e. the shares of national income held by the top 10% and top 0.1%) and also holds for sub-periods covering di erent monetary regimes. We demonstrate that insofar as in ation shocks reduce real interest rates, the negative e ect of in ation on top incomes is likely to be channeled via lower real assets returns (housing, equity, bonds and bills). On top of that, the state-dependent version of our LP estimation indicates that the distributional consequences of in ation shocks on P1 are stronger for low levels of nancial openness. As to long-term in ation, our ndings indicate that a high average in ation rate is associated with lower top income shares: a one percent increase of in ation reduces the income share of the top 1% and top 10% by 0.05 and 0.085 percentage points in the long run, respectively.

The chapter is structured as follows. Section 2 reviews the theoretical and empirical literature on the e ects of in ation on income and wealth distribution. Next, section 3 describes the data while section 4 presents the empirical strategy. Section 5 highlights key results from the LP estimations and the panel regressions. The nal section draws conclusions and outlines a road-map for future research.

Related literature

This section reviews previous studies -both theoretical and empirical -on the in ationinequality nexus. The distributional e ects of in ation have attracted a great deal of interest [START_REF] Baumol | The transactions demand for cash: An inventory theoretic approach[END_REF], [START_REF] Tobin | The interest-elasticity of transactions demand for cash[END_REF]), particularly in terms of its welfare implications (see e.g., [START_REF] Lucas | In ation and welfare[END_REF] and [START_REF] Ireland | On the welfare cost of in ation and the recent behavior of money demand[END_REF]). Recent theoretical models have contributed to this literature by studying the e ects of (un)anticipated in ation on income and wealth distributions.

The rst strand of theoretical contributions relied on cash-in-advance models in which lowincome households are assumed to hold a disproportionate share of their assets in cash, while rich households have more diversi ed portfolios. In this context, [START_REF] Erosa | On in ation as a regressive consumption tax[END_REF] and [START_REF] Kakar | Role of cash and costs of in ation for di erent income groups in the U[END_REF] study the asymmetric incidence of the in ation tax and derive a positive correlation between in ation and inequality. [START_REF] Albanesi | In ation and inequality[END_REF] uses a similar model to analyze the distributional e ects of expected in ation from a political economy perspective.

In the model, the in ation rate is the outcome of a bargaining game between households with uneven economic attributes. The rich exert pressure for monetary nancing of public spending rather than tax nancing, which leads to higher in ation and more inequality.

In another strand of the literature, models have been developed with incomplete markets and/or heterogeneous agents, calibrated using household wealth surveys. A good example is the work by [START_REF] Gottlieb | On the distributive e ects of in ation[END_REF], who introduces portfolio choice in his model and nds that the welfare costs of in ation in the U.S. are low. He also departs from the literature discussed above as he concludes that expected in ation may act as a progressive tax. Boel (2018) also nds a non-linear relationship between in ation and inequality in a matching model where agents di er in their consumption risk: inequality declines for low to moderate in ation rates while the opposite is true when in ation moves from moderate to high levels. [START_REF] Menna | Optimal in ation to reduce inequality[END_REF] reconsider in ation optimality in a DSGE model with limited access to the market for interest bearing assets. Interestingly, they demonstrate that higher in ation together with lower income taxes reduce inequality: nontaxable monopoly pro ts shift the nancial burden of the in ation tax towards asset holders. Finally, Camera and Chien (2014) specify that three features of an economy determine the extent of the in ation-inequality nexus, namely: nancial structure, elasticity of labor supply, and the process underlying earnings shocks.

Scenario analysis has been used for studying the impact of unexpected in ation on wealth distribution through the Fisher channel (i.e. the revaluation of nominal balance sheets due to in ation shocks). Speci cally, household's balance sheet exposures under di erent in ation scenarios are estimated, which allows identifying potential winners and losers from an ination shock. [START_REF] Doepke | In ation and the redistribution of nominal wealth[END_REF] Early empirical country-level investigations of income inequality mainly covered advanced economies and reported mixed ndings. For instance, while [START_REF] Blinder | Macroeconomic activity and income distribution in the postwar United States[END_REF] and [START_REF] Mocan | Structural unemployment, cyclical unemployment, and income inequality[END_REF] nd that in ation increased quintile shares of bottom income families in the U.S., [START_REF] Yoshino | Macroeconomic activity and income distribution in the postwar United States[END_REF] documents the opposite e ect for Japan. Cross-country studies frequently point to a positive correlation between in ation and inequality (see [START_REF] Colciago | Central bank policies and income and wealth inequality: A survey[END_REF]).

For instance, based on a large panel of developed economies, [START_REF] Romer | Monetary policy and the well-being of the poor[END_REF] show that long-run in ation reduces the average income of the bottom quintile. Similarly, [START_REF] Bulíř | In ation and income distribution: Further evidence on empirical links[END_REF] nd that in ation tends to be a regressive tax, particularly in lower-income countries with a relatively unsophisticated nancial sector. [START_REF] Easterly | In ation and the poor[END_REF] argue that in ation hurts poor households, which are more reliant on state-determined income that is not fully indexed to in ation. In ation reduces the real minimum wage and transfers to the bottom quintiles of the income distribution, whereas rich households are less a ected. Other research suggests that the relationship between in ation and income inequality is U-shaped. [START_REF] Bulíř | Income inequality: Does in ation matter?[END_REF] reports for 75 economies that a reduction in in ation from hyper-in ationary levels signi cantly lowers income inequality, while a further reduction towards a very low level of in ation has little e ects. [START_REF] Galli | Is in ation bad for income inequality: The importance of the initial rate of in ation[END_REF] and Monnin (2014) also report a non-linear relationship for panels of OECD countries. However, [START_REF] Binder | Inequality and the in ation tax[END_REF] concludes that the correlation between in ation and inequality has fallen most notably in European countries. Her regression analysis suggests that the association of in ation and inequality depends on the interaction of political regime and central bank independence; the in ation-inequality nexus becomes more negative as central bank independence increases in democratic countries.

Thus, although theoretical studies have managed to identify various transmission channels of in ation towards inequality, the empirics of the link between in ation and income distribution remain ambiguous. Most importantly, as Binder (2019) noticed, the sign of the correlation between in ation and inequality depends on the sample of countries, the time period and also the measure for inequality used. In this respect, our contribution departs from previous studies as it (i) focuses on the top of the distribution using income tax-based data and (ii) covers a century of modern economic history.

Data

Our empirical analysis relies on a country-level yearly dataset for 14 advanced economies over the period 1920-2016 for top income shares, in ation and macroeconomic controls. 2 The 14 countries examined in our analysis include: Australia, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, Sweden, Switzerland, the U.K. and the U.S.

Top income shares

We rely on top income data, which are extracted from the World Inequality Database (WID).

To compute top income shares, the WID uses national accounts together with census data and as explained by [START_REF] Roine | Long-run trends in the distribution of income and wealth[END_REF], it subsequently matches tax units in the top and their incomes with the reference tax population and reference total income. The share of pre-tax national income held by the richest one percent (P1) is used as the main variable of interest. The top one percent are generally considered as very rich because they receive a signi cant share of their income in the form of rents, dividends and capital gains [START_REF] Atkinson | Top Incomes over the Twentieth Century: A Contrast between continental European and English-Speaking Countries[END_REF]). As an alternative, we test our empirical models using the top 10 percent's pre-tax national income share (P10). [START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF] demonstrate that P10 includes the upper middle class, i.e. the lower 9 percent of the top decile. Our empirical analysis introduces percentile ratios to provide insights into how in ation a ects the gap between top incomes and the rest of the population. The latter is approached by the residual share received by the lowest 90 percent of the population (B90). Our percentile ratios, i.e., P1/B90 and P10/B90, can serve as proxies for assessing the impact of in ation on income inequality. Finally, we estimate the e ect of in ation within top income earners using the P1/P10 and P1/P9 ratios, de ned as the share of the top percentile in relation to the top decile.

Determinants of top income shares

Some studies on the drivers of income inequality consider the role of economic factors, such as technological progress and international competition, while others emphasize the importance of institutional and political factors. We try to control for these factors where the challenge is to nd data measuring them for the long time span we consider. For this purpose, we primarily use the Jordà-Schularick-Taylor Macrohistory Database.

2 We omit World War II covering the period from 1939 to 1945.

Addressing globalization through the volume of economic ows is relatively common in the literature. We opt here for a de facto measure of openness by using the ratio of trade (i.e.

the sum of exports and imports) to GDP. Alternatively, we use the capital account openness measure proposed by [START_REF] Quinn | Assessing measures of nancial openness and integration[END_REF] [START_REF] Galor | Income distribution and macroeconomics[END_REF] and [START_REF] Piketty | The dynamics of the wealth distribution and the interest rate with creditrationing[END_REF]) there is growing evidence that more nance only bene ts top incomes (see De Haan and Sturm (2017b) and [START_REF] Bazillier | The circular relationship between inequality, leverage, and nancial crises[END_REF] for reviews of the literature).

Following most empirical studies on the drivers and consequences of nancial development (see [START_REF] Doucouliagos | What drives nancial development? a meta-regression analysis[END_REF]), we employ private credit (as a share to GDP) to assess the impact of nancial development.

Redistribution policies, labor market institutions, the political regime in place, and education may also a ect the income distribution in the long run. We proxy redistribution policy by the ratio of government expenditures to GDP and through top marginal tax rates. As proxies for labor market institutions re ecting the power of workers, we use the number of labor con icts (strikes and lockouts) and trade union density. The political regime in place is assessed by the Polyarchy Index of [START_REF] Teorell | Measuring polyarchy across the globe, 1900-2017[END_REF] from the V-Dem database, and communist in uence from [START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF]. The former evaluates the extent to which the ideal of electoral democracy in its fullest sense is achieved, while the latter measures foreign communist inuence and is constructed as the cultural distance fraction of the world population having communist governance. As stated by [START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF], a rise of the communist threat may in uence the stance of non-communist governments regarding workers' wage aspirations.

Finally, the level of human capital is taken into account by the share of the population with secondary education from the Barro and Lee Educational Attainment Dataset [START_REF] Lee | Human capital in the long run[END_REF]). Table A1 in the Appendix provides an overview of the data used. cies and the oil crises, while P1 dropped from 10 to 6 percent. In the 1980s, a considerable trend reversal took place. Wealth-income ratios in rich countries jumped back to pre-war levels [START_REF] Piketty | Capital is back: Wealth-income ratios in rich countries 1700-2010[END_REF]) and also income inequality increased. This shift in inequality dynamics came along with a new paradigm in monetary economics that emphasizes the welfare gains from low in ation and supports credible and predictable monetary policies.

Top income shares and in ation in the twentieth century

Average in ation gradually fell to even below 2%.

Empirical methodology

Our empirical strategy accounts for the possible contrasting e ects between unexpected ination and long-run in ation on the income share of the rich. Speci cally, we are considering two di erent empirical approaches. First, we use the Local Projection method proposed by [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF] to estimate the dynamic e ects of in ation shocks on the income share of top income earners. Second, we analyze the long-run e ect of in ation on P1 using a standard panel-data approach for non-overlapping ve year sub-periods.

Local projection

Impulse responses are common means to assess the dynamic empirical regularities between two variables. We use the Local Projection (LP) method introduced by Jordà (2005) to compute Impulse Response Functions (IRFs). 3 The LP method requires to estimate a sequence of projections of the endogenous variable shifted forward in time onto its lags and a set of real and monetary controls. The baseline regression equation is:

∆ h y i,t+h = α h i + γ h t + β h π i,t + θ h X i,t + ε h i,t (2.1)
where ∆ h y i,t+h = y i,t+h -y i,t-1 and corresponds to a change in the top income variable from the base year t -1 up to year t + h, with h = 0, ..., H; π i,t denotes the change in the (log) consumer price index; and X i,t refers to a vector of control variables. The latter includes two lags of ∆ t y i,t , π i,t , and the contemporaneous value and two lags of the rst-di erence of additional macroeconomic controls that could theoretically explain top income shares. 4 The list of the additional controls includes the log of real GDP per capita, real consumption per capita, real investment, Total Factor Productivity (TFP) along with the level of the credit-to-GDP ratio, trade openness, central government expenditure ratio, the long-term interest rate and the variation of the short-term interest rate. Finally, time xed e ects are included to control for common trends in the evolution of top incomes.

Equation 2.1 is estimated by a xed e ects estimator that accounts for heteroscedasticity with [START_REF] Stock | Heteroskedasticity-robust standard errors for xed e ects panel data regression[END_REF]'s robust standard errors for each h = 0, ..., 4 in our analysis. As

shown by [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF], the sequence of estimates β h gives an accurate estimate of the local IRF, while the respective standard errors can be used to build con dence bands. This means that, unlike in a VAR approach, the estimated coe cients contained in θ h are not used to build the IRF. Instead, they only serve as controls and cleanse the β h from the e ects of past top income shares and consumer price changes, as well as contemporaneous and past changes in other macroeconomic variables. Our rich set of controls ensures that the estimated dynamic e ect of in ation is orthogonal to contemporaneous and lagged e ects of monetary policy decisions, aggregate demand or past and anticipated in ation.

LP can easily accommodate state-dependence. This is a great advantage, as our analysis covers a long time span encompassing di erent monetary regimes and economic situations. To test for state-dependent e ects in the response of the top income variable to an in ation shock, we consider the following regression model:

∆ h y i,t = α h i + γ h t + β h 1 π i,t * State i,t + β h 2 π i,t * (1 -State i,t ) + θ h X i,t + ε h i,t (2.2)
where State i,t is a variable indicating a speci c state (i.e. business cycle, in ation regime, the level of nancial openness5 and the type of political regime).

The long-term inequality process

Responses of in ation shocks may provide misleading results about the e ect of in ation in the long term. A positive in ation shock might be o set by a negative one and therefore be only a source of short and medium-run uctuations in the top income variable. In order to explore the long-run relationship between in ation and top incomes, we have to eliminate uctuations at the business-cycle frequency.

Using n-year averages is an easy and standard way to identify long-run relationships. Averaging our variables of interest over a given time window allows estimating the e ect of in ation on top income shares in the long run. This is also a method to reduce the impact of measurement errors (provided that measurement errors are not perfectly correlated over time).

However, averaging has some limitations as well. In particular, averaging may not fully eliminate business cycle uctuations because the length of business cycles may vary over time and across countries. Following previous studies like De Haan and Sturm (2017b), we use 5-year averages (and 10-year averages as a robustness check). We particularly extend the model of [START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF] and add in ation as a determinant of the share of top incomes:

ȳi,p = α i + γ t + β πi,p + θ Xi,p + ε i,t (2.3)
This standard regression includes time xed e ects γ t and country-speci c trends (here captured by a country speci c e ect α i ). Further, p refers to an interval of ve years and ȳ, π, X refer to the average over ve years of the top income variable, the in ation rate and the set of control variables, respectively.6

We estimate equation 2.3 using an OLS estimator that accounts for potential country-speci c serial correlation in the error terms. The control variables in equation 2.3 slightly di er from those used in equation 2.1. We add other factors that account for the dynamics of long-run inequality. The vector of control variables in our baseline model consists of the log of average real GDP per capita and population size along with the level of education (proxied by school enrollment ratios for the secondary level), trade openness, the credit-to-GDP ratio, central government expenditures (as share of GDP) and the top marginal tax rate.7

Results

This section reports results for the e ects of in ation on top income shares. We rst discuss the LP estimates, then we examine the relationship between in ation and the share of top incomes in the long run.

Local projections 2.5.1.1 Baseline results

The baseline result is displayed in Figure 2.1, which depicts the cumulated IRF of P1 to a 100 bps increase in the in ation rate. It shows that in ation has an e ect on incomes at the very top: P1 declines by 0.05 and 0.08 percentage points at the impact and two years following the shock, respectively. Over the horizon of 5 years, the impact amounts to 0.12 percentage points.

This e ect is economically signi cant, given that the average of P1 across the sample over the studied period is 10 percent. 8 This nding is consistent with the strand of the literature that documents the negative implications of unexpected in ation on rich households via the revaluation of nominal balance sheets (see [START_REF] Doepke | In ation and the redistribution of nominal wealth[END_REF], among others). The key di erence between this literature and this chapter is that the former deals with wealth distribution.

We perform several sensitivity analyses to check the robustness of our result. These are shown in Figure 2.2. In the rst set of checks, we use alternative measures for top income shares.

Graph (a) reports the impulse response of P10 and suggests that the baseline e ect of in ation seems to hold for the entire top decile. However, the response of P10 hides a contrasting e ect between P1 and the upper middle-class, P9 (i.e. P10-P1): while the decline of P1 is still strong 4 years after the shock, the response of P9 becomes non-signi cant in later periods (see graph In the second set of robustness tests, we examine several sample splits of the data, bearing in mind the obvious di erences in monetary arrangements before and after WW2. Graph (e)

shows that the response of P1 does not depart from the baseline estimation when we only consider the post-WW2 period. Similarly, the negative e ect of unexpected in ation on P1 continues to hold when the sample starts from the 1970s. Furthermore, our nding is not impacted when (i) the episode of the Great Recession is omitted (Graph g) and (ii) the vector of control variables is removed (Graph h). 9

Transmission channel

We explore one of the transmission mechanisms of in ation towards top incomes. Speci cally, we test the following hypothesis: an in ation shock reduces real interest rates, which can have a negative impact on the (real) rate of return on capital. Rich households would then be worse-o given that capital and business incomes account for a large share of their total income. To this end, we estimate impulse responses of returns on various nancial and real assets to surprise in ation. Graph (a) in Figure 2.3 depicts the cumulated IRF of total returns on assets -i.e., the weighted average of real returns on housing, equity, bonds and bills 10to a 100 bps in ation shock. The latter reduces real asset returns by 0.6 percentage points immediately. The same exercise is conducted using real returns on housing and equity.

From a historical perspective, the dynamics of housing returns are as important as those of other assets. Jordà et al. (2019) document that: "although aggregate total returns on equities 9 We also estimated our model with a mean group (MG) estimator to assess whether our results are a ected by the slope homogeneity assumption of the pooled models. The results (available on request) show that allowing all parameters to di er across group does not change our main conclusion: in ation shocks matter for the income of the rich.

10 Information on how the weighting of assets is done can be found in Jordà et al. (2019).

exceed those on housing for certain countries and time periods, equities do not outperform housing in simple risk-adjusted terms" (p. 1274). In particular, real estate tends to be less tradable at the global level than nancial assets and is more exposed to idiosyncratic country-level shocks. Graph (b) in Figure 2.3 indicates that following an in ation shock, housing real returns decrease by 0.6 and 0.9 percentage points in year 0 and year 4, respectively. Further, Graph (c) in Figure 2.3 shows that in ation shocks also lower real returns on equity by a similar magnitude.

Our statement about the transmission channel operating through lower real asset returns may be only part of the story if an in ation shock would also compress real wages. In such a case, the nal outcome on income inequality would depend on which of the two e ects dominate. Unfortunately, data on the distribution of wages are not widely available. As an alternative, we consider Piketty's "r -g" concept, i.e. the di erence between the real return to capital and the growth rate of output. A decrease of "r -g" following an in ation shock

indicates that the real return on assets transmission channel dominates the wage channel.

The impulse response shown in Graph (d) supports this view as it suggests that an in ation shock signi cantly reduces the r -g gap.

State-dependent e ects

Are the e ects of surprise in ation on top incomes state-dependent? This question is relevant in view of our historical sample that covers several economic and monetary regimes. We estimate equation 2.2 that allows the response of P1 to depend upon four speci c regimes/factors: business cycle, in ation regime, nancial openness and political institutions. Business cycle episodes are identi ed using the Hodrick-Prescott (HP) lter -with λ=6.25 -and take the value of one when the output gap is positive and zero when it is negative. With respect to the in ation regime, high-in ation refers to a period during which in ation is above its countryspeci c median. Conversely, a country features a low-in ation regime when the in ation rate is below its median. As for nancial openness, we compare the states of incomplete and full capital liberalization (index of capital mobility lower and equal to 100, respectively). Finally, we de ne for the political regime two states of democratic intensity, based on the median sample of our Polyarchy Index.

The impulse responses based on the state-dependent models are displayed in Figure 2 [START_REF] Lahiri | A political economy perspective on persistent inequality, in ation, and redistribution[END_REF] suggests that the in ation-inequality nexus "within any period or over time depends on institutional and preference related parameters" (p. 1199). However, the IRFs depicted in graphs (g) and (h) suggest that the political regime in place does not matter.

Long-run in ation and top incomes

Our second empirical model focuses on the inequality e ects of in ation in the long run. It employs variables averaged over a xed-length interval in order to eliminate business-cycle e ects and to identify long-run e ects of in ation on top-income shares. This contrasts with the previous section where we focused on in ation shocks.

The baseline estimates of equation 2.3, which are displayed in Table 2.1, indicate that longrun in ation has a negative e ect on top income shares. This is consistent with the results reported in the previous section. The results in column (1) show that a 100 bps increase in the long-run in ation rate decreases P1 by 0.05 percentage points. The magnitude of the e ect is twice smaller than the estimated e ect of an unexpected in ation shock. The same holds for P10 in column (2). In addition, the percentile ratios (P1/B90 and P10/B90) shown in columns

(3) and ( 4), respectively, suggest that in ation also reduces the gap between top incomes and the rest of the population. By contrast, the estimated (negative) coe cient of in ation is not signi cant for P01. This discrepancy does not appear when we consider 10-year averages instead of 5-year averages (see Table B.3).

Our regressions provide also some evidence for other determinants of top income shares. We nd that education, measured by the secondary school enrollment rate for the total population, is associated with lower top income shares (this holds for P1, P10 and P01). The same e ect is found for the top marginal tax rate. The latter nding is not the result of redistributive tax policies because our dependent variables refer to gross (i.e. market) national income

shares; yet, top marginal tax rates could a ect incentives and individual market opportunities.

Finally, trade openness is positively associated with top income shares. This result contributes to the literature on the globalization-inequality nexus and supports the ndings of [START_REF] Dreher | Has globalization increased inequality?[END_REF], [START_REF] Bergh | Do liberalization and globalization increase income inequality?[END_REF] and [START_REF] Lang | The distribution of gains from globalization[END_REF].

The results for nancial development, government spending, GDP per capita and population are rather mixed. We observe that nancial development is negatively associated with top income shares, yet the e ect is not statistically signi cant. This contrasts with the result of [START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF] showing that nancial development is "pro-rich" over the long run. By contrast, we obtain similar mixed results as [START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF] regarding government spending.

The estimated coe cients are positive but insigni cant. Besides, a higher GDP per capita increases the concentration of the income at the top of the distribution. Finally, while there is no well-established literature on the relationship between population and income inequality, we nd a positive but insigni cant e ect of population size on top income shares.

The robustness of our results is assessed in multiple ways. Table 2.2 displays the outcomes of several tests using 5-year averages.12 First, we estimate our empirical model using trend in ation instead of 5-year averages and show that our results are not impacted (column (1)).

Second, focusing only on the post-war era or the post-Bretton Woods period does not change our ndings (columns (2) and (3), respectively). Further, columns (4) and ( 5) of Table 2.2 report estimates using the sample period before the 2008 nancial crisis and without control variable, respectively, con rming our main result.

Finally, we include covariates related to several country-level characteristics. We do so by adding the corresponding variables one-by-one. As the sample size of these covariates varies considerably, we maximize the size of our estimation sample by adding them sequentially.

Speci cally, we test the confounding e ects of the Kuznets curve, nancial openness, labor disputes, trade union density, communist in uence, democracy and technical progress. The results for our augmented baseline models as displayed in Table 2.3 con rm our previous result

for the e ect of long-term in ation on P1: the coe cients on in ation remain negative and highly signi cant. 13 We also establish that an increase in labor con icts and more communist in uence are associated with a lower top one percent's income share, which is in line with our expectations.

Conclusion

This chapter attempted to quantify the distributional consequences of in ation on top income shares using a sample spanning 97 years and 14 advanced economies. While it is commonly accepted that in ation harms the poor, much is less known about how it interacts with top income households. We combined tax-based top income shares from the World Inequality Database (WID) with other macroeconomic variables from the Jordà-Schularick-Taylor Macrohistory Database. Our empirical strategy featured a dual approach with two aims: (i)

estimate the e ects of in ation shocks on the share of national income held by the top one percent (P1) and (ii) study the relationship between long-run in ation and top income shares.

The rst part is based on the LP method proposed by [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF] to generate IRFs of P1 to an in ation shock, while the second part is based on panel regressions using ve-year averages of all variables to evaluate the long-run dynamics between in ation and P1.

Our ndings suggest that in ation reduces the share of national income held by the top one percent. LP estimates show that an in ation shock negatively a ects P1, with an accumulated decrease of 0.12 percentage points. This e ect also holds for other top income measures (P10, P09, P01) and sub-periods. The impulse responses of percentile ratios (i.e. P1/B90, P10/B90 and P9/B90) and top decile ratios (i.e. P1/P9 and P1/P10) show that in ation shocks reduce the gap between top income shares and the rest of the population as well as among the top of the distribution. Next, we demonstrate that in ation shocks are likely to a ect P1 via lower real asset returns, especially because top income households receive considerable amounts of business income and capital gains. As for the state-dependent e ects, our results indicate that the e ect of in ation on P1 holds, irrespective of the state of the economy. Nonetheless, this e ect is stronger for a low level of capital mobility. Further, results from our panel regressions yield similar results as the LP approach. An increase in the average long-run in ation rate is associated with lower top income shares. This correlation is robust when we: (i) use 10-year averaged variables, (ii) consider only the post-war and post-Bretton Woods periods and (iii) estimate the baseline model using trend in ation. Because our empirical models are linear, our results mean that de ation shocks and a low in ation regime are likely to favor top incomes.

Our empirical evidence is consistent with the scenario analyses conducted by [START_REF] Doepke | In ation and the redistribution of nominal wealth[END_REF] for the U.S. and [START_REF] Adam | Price-level changes and the redistribution of nominal wealth across the Euro area[END_REF] for the Eurozone with respect to the e ects of in ation on di erent groups of households, and in particular for the richest ones.

However, while these studies quantify the implications of in ation on the wealth distribution, our chapter focuses on the income distribution. Our results challenge the widely accepted predictions of the in ation tax literature developed by [START_REF] Erosa | On in ation as a regressive consumption tax[END_REF] and [START_REF] Albanesi | In ation and inequality[END_REF]. Although portfolio holdings and transaction patterns are di erent across households, we show that top incomes might be as much worse-o from in ation as households belonging to another tail of the income distribution. For future research, the challenge would be to deepen -from a historical perspective -our understanding about how in ation a ects the other tails of the income distribution and poverty. Note: This table shows baseline results from panel regressions with country and time xed e ects for the top 1% income share using trend in ation (column (1)), the top 1% income share post-WWII (column (2)), the top 1% income share post-Bretton Woods (column (3)), the top 1% income share before the 2008 nancial crisis (column (4)) and the top 1% income share in a speci cation without control variables (column (5)). HAC standard errors are reported in parentheses. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively. Explanatory variables are de ned in Table B.1 in the Appendix.

Main gures and tables

Chapter 2. In ation and the income share of the rich that greater inequality hampers economic growth and reduces social mobility (see (Chetty and Hendren, 2018a,b;OECD, 2015)). In the meantime, the subprime mortgage crisis in 2007 has raised an interest for the drivers of household debt and leverage in the economy as well as the role of income and wealth distributions in shaping these dynamics. The contribution of Rajan (2010)'s book highlights that rising inequality in the past decades led to excessive indebtedness and eventually fueled nancial instability, especially because credit growth is a strong predictor of nancial crises (see [START_REF] Gourinchas | Stories of the twentieth century for the twenty-rst[END_REF][START_REF] Schularick | Credit booms gone bust: Monetary policy, leverage cycles, and nancial crises, 1870-2008[END_REF], for instance). But how does an unequal income distribution produce credit expansions, and above all, following which transmission channels? [START_REF] Bazillier | The circular relationship between inequality, leverage, and nancial crises[END_REF] distinguish between demand and supply mechanisms through which a rise in income inequality endogenously a ects credit. First, low-and middle-income households may perceive a permanent decline in their relative income as transitory, which encourages them to borrow more in order to smooth consumption over time. 1 Second, the rise ‡ This chapter is co-authored with Aurélien Leroy and is published in Economics Letters.

1 From a behavioral perspective, Veblen (1899) has introduced the concept of "conspicuous consumption". It consists of overspending from the rich to display their wealth that could translate into envy and push the poor to increase their credit demand. Similarly, [START_REF] Frank | Expenditure cascades[END_REF] have put forward a theory of "expenditure cascades", where the consumption standards of a household group follow those of the group just above on the income scale. Consequently, an income change in one household group a ects the consumption of the group just below and so on, leading to expenditure cascades (and to more debt accumulation). Both theories support the notion of "Keeping up with the Joneses".

in top incomes pushes savings upwards (and reduces the equilibrium interest rate), which in turn favors a credit boom. This intuition has been rationalized in a theoretical framework by [START_REF] Kumhof | Inequality, leverage, and crises[END_REF] in which higher leverage and crises are the endogenous result of a growing income share of high-income households. In such a case, changes in the income distribution produce higher indebtedness through credit supply.

Recent research by [START_REF] Mian | The saving glut of the rich and the rise in household debt[END_REF] gives credence to the supply-side of the inequality-credit nexus as it highlights that the large rise in savings by the top 1% of the income or wealth distribution in the U.S. for the last 35 years has not been associated with an increase in investment.

Instead, they note that "rich households have accumulated substantial nancial assets that are direct claims on household and government debt". In other words, the signi cant reductions in top income taxation since the 1980s did not increase the productive capacity of the U.S. economy but only contributed to substantial dissaving by the non-rich and the government.

Hence, on top of being one of the main contributing factors to inequality for the past decades [START_REF] Piketty | The evolution of top incomes: A historical and international perspective[END_REF]), top incomes are also at the heart of the debt accumulation process. This chapter quanti es the causal impact of rising top incomes and speci cally the top 1% income share on credit dynamics. Using data on top income distribution from the World Inequality Database (WID) over the period 1948-2015 for a sample of 12 advanced economies2 , we study how exogenous variations in top income shares a ect the path of credit over GDP.

Our empirical strategy relies on the Local Projections (LP) method by [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF] to estimate the dynamic e ects of an unanticipated increase in the top 1% income share on the creditto-GDP ratio. The empirical e ect of interest entails, however, endogeneity issues stemming from two distinct sources: reverse causality and confounding factors. While the former relates to the impact that nancial development may have on the income distribution (see De Haan and Sturm (2017b) for a review), the latter refers to the fact that both inequality and credit are potentially in uenced by common unobserved factors (monetary environment, banking crises, etc.). To overcome these issues, instrumental variables (IV) constitute a serious option, as long as they are able to explain inequality and top income shares without directly a ecting credit growth.

In this context, we mobilize the foreign Communist in uence of [START_REF] Madsen | Inequality, nancial development and economic growth in the oecd, 1870-2011[END_REF][START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF] as an IV for exogenous shifts in the top income distribution. The foreign Communist in uence is constructed as the cultural distance-weighted fraction of the world population that has Communist governance, and may be relevant in accounting for inequality dynamics. It assumes that the workers' economic and political claims are more seriously taken on board when policymakers are facing the external "threat" of Communism as a credible political alternative. This is consistent in view of several existing historical events, where a general discontent in one country sets o -in culturally neighboring countries -an important regime change (decolonization waves, Arab Spring, etc.). Therefore, to avoid potential turmoils, governments and employers implement pro-labor policies that are likely to reduce inequality, without impacting the dynamics of credit directly. In practice, our baseline instrument is coupled with the Local Projection-Instrumental variable (LP-IV) approach of Jordà et al. ( 2020) (a sequence of 2SLS predictive regressions of the variable of interest on a structural shock for di erent projection horizons) to obtain impulse responses of credit over GDP to an exogenous variation in top 1% income share.

Cross-country empirical evidence on the e ect of inequality on credit is relatively scarce and remains inconclusive. Based on a sample of 14 advanced economies between 1920 and 2008, [START_REF] Bordo | Does inequality lead to a nancial crisis[END_REF] nd no signi cant e ect of the top 1% income share on credit growth. However, relying on a panel of 18 OECD countries over the period 1970[START_REF] Albanesi | In ation and inequality[END_REF][START_REF] Perugini | Inequality, credit and nancial crises[END_REF] document that income inequality and total credit are positively related.

Recent evidence by [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF] and [START_REF] Gu | Inequality, leverage and crises: Theory and evidence revisited[END_REF] con rm this positive relationship and nd that it is mainly driven by household credit. 3 However, most of the existing cross-country contributions did not manage to provide strong causal evidence. To the best of our knowledge, [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF] is the only contribution to have introduced an empirical strategy that relies on instrumental variables to identify exogenous variations in inequality.

Speci cally, the authors use the number of rati cations of International Labor Organization (ILO) conventions at the country-year level. In fact, the ILO strategies to promote common labor standards as such -through the process of country-level rati cations over time -are orthogonal to country-speci c developments.

3 van Treeck (2014) provides a detailed survey on the e ects of inequality on household behavior.

The contributions of this chapter to the literature are three-fold. First, we follow [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF] in using a credible instrument to properly identify the impact of inequality on credit.

Second, while the empirical literature featured static regressions, we focus on the dynamic e ects of top incomes on credit growth using the LP method of [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF]. Third, we do not solely focus on total credit but also examine how di erent components of total credit (mortgage, business and household loans) respond to a top income shock.

We nd that a positive top income shock persistently increases the ratio of credit over GDP.

Precisely, a 100 b.p. increase in the top 1% income share via the instrument produces a positive impact on credit growth that amounts to 3.12% over a ve year horizon. The baseline estimates underline the relevance of our identi cation strategy because the opposite e ect of a top income shock is obtained with a standard OLS estimation. Furthermore, the positive inequality-credit nexus in our empirical setting especially holds for mortgage and business loans, thereby pointing to a potential interplay between supply and demand mechanisms. It is also shown that these results are robust to (i) di erent shares of the top income distribution, (ii) inequality measures and (iii) alternative instruments. Our ndings contribute to [START_REF] Kumhof | Inequality, leverage, and crises[END_REF] and [START_REF] Mian | The saving glut of the rich and the rise in household debt[END_REF] as they o er a cross-country perspective of the importance of rising top incomes in relation to the leverage of the economy.

The chapter is structured as follows. Section 2 introduces the data. Section 3 discusses the identi cation strategy along with the empirical methodology. Section 4 presents the results while section 5 concludes.

Data

The data we use cover 12 advanced countries over the period 1948-2015, based on three building blocks: top income shares and credit along with macroeconomic controls. The 12-country panel consists of: Australia, Canada, Denmark, France, Germany, Italy, Japan, the Netherlands, Norway, Sweden, the U.K. and the U.S. Top income shares are extracted from the World Inequality Database (WID (2020)). The pre-tax national income share held by the top 1% (P1) is considered the main top income variable. Further, bearing in mind the heterogeneity underlying incomes at the top, we conduct our empirical analysis using the share of national income held by the lower 9% (P9) of the top decile. Given that top percentile shares grew even faster in the last decades (see [START_REF] Saez | Wealth inequality in the United States since 1913: Evidence from capitalized income tax data[END_REF], for instance), the national income share held by the top 0.1% and top 0.01% -obtained from [START_REF] Atkinson | Top incomes in the long run of history[END_REF] Credit and macroeconomic data mainly come from the Jordà-Schularick-Taylor (JST) Macrohistory Database. We use the ratio of total credit over GDP as the main dependent variable because it is line with the literature stressing that nancial risks may emerge from excessive levels of credit compared to output and not as a result of credit expansion (see e.g., [START_REF] Morelli | Inequality and crises revisited[END_REF]). Alternatively, we estimate the dynamic response of mortgage, business and household loans to a top income shock. 6 Figure C.4 in the Appendix displays the evolution of credit-to-GDP ratio over time as well as the other components of total loans.

In addition, we introduce a set of control variables that may in uence credit while being, at the same time, correlated with income dynamics, namely, per capita GDP growth, consumption growth, the level of trade openness, government expenditure growth, variation in the shortterm interest rate, the CPI in ation rate, population growth, variation in the investment-to-GDP ratio, stock price growth, house price growth and real broad money growth. Information on nancial openness and top marginal tax rates is obtained from the well-known database of [START_REF] Chinn | What matters for nancial development? capital controls, institutions, and interactions[END_REF] and [START_REF] Rubolino | Trends and gradients in top tax elasticities: crosscountry evidence, 1900-2014[END_REF], respectively. Table C.1 in the Appendix lists all the variables and their sources.

Empirical approach

Baseline speci cation

Our research objective is to identify and estimate the dynamic e ect of rising top incomes on the path of credit. However, in order to have an initial glance at how income inequality and 4 Data on the Gini coe cients are available starting from the 1960s. [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF] provide a discussion on the di erences in terms of comparability and measurement methods between the SWIID and WID databases. 5 The dynamics of top income shares and inequality can be classi ed into three stages: increasing top income shares on the eve of the two world wars before these gains were then eliminated; a post-war era when top marginal taxation contained the accumulation of private wealth; and then the return of a patrimonial society at the beginning of the 1980s, which largely favored top-income households.

6 Figure C.5 depicts the share of mortgage, business and household loans in total credit.

credit are related, we begin with a basic speci cation of the following form:

Credit i,t = α i + γ t + βIneq i,t + θX i,t + εh i,t (3.1)
where Credit i,t and Ineq i,t are respectively total credit over GDP and inequality in country i during year t. To assess the impact of inequality, we primarily focus on top income shares (the national income shares held by the richest 1% and lower 9% of the top decile, i.e. P1

and P9) and use in addition standard inequality measures (i.e. Gini coe cients for market and disposable incomes). X i,t is a vector of controls including the log of GDP per capita, real broad money and real house prices. Finally, α i denotes country xed e ects and γ t refers to time xed e ects that capture common trends and shocks.

Table 3.1 reports the results obtained when equation 3.1 is estimated using a standard OLS estimator. Columns (1) and ( 2) show the estimated coe cients when inequality is approached through top income shares (represented by P1 and P9), while columns ( 2) and ( 4) rely on Gini coe cients before and after redistribution. As long as we are interested in the relationship between inequality and credit, the coe cient of interest is β: if the latter is positive, this would suggest that an increase in inequality (or top incomes in particular) is associated with a higher share of credit in the economy.

The correlations between credit and inequality shown in Table 3.1 are largely insigni cant, regardless of the considered inequality measure. Such a result notably speaks to the nding documented by Bordo and Meissner (2012) -using credit growth as a dependent variable.

However, for several reasons, these OLS estimates are likely to be biased. First, top income earners and the leverage of the economy are potentially jointly determined. In fact, nancial development is likely to increase top executive compensation in the nance industry (Philippon and Reshef, 2012) but, in the other direction, improve economic opportunities -through a better access to credit markets for the poor -and favor a more egalitarian society [START_REF] Beck | Big bad banks? the winners and losers from bank deregulation in the united states[END_REF]. Second, there are several unobservable determinants of credit dynamics that are correlated with top incomes. For instance, the waves of nancial deregulation experienced in most of the advanced economies during the 1980s a ected credit but also had non-negligible distributional impacts (see [START_REF] Bazillier | The circular relationship between inequality, leverage, and nancial crises[END_REF] for a survey).

Identi cation strategy

The issues entailed by the standard OLS estimation could be addressed through the use of external instruments. To allow for causal inference, such instruments must induce variations in inequality and top incomes that are exogenous to other macroeconomic shocks a ecting the economy. To the best of our knowledge, only a single contribution in the literature on the inequality-credit nexus identi ed causality through an instrumental variable strategy, Bazillier et al. ( 2021), who mobilized the total number of rati ed International Labour Organization (ILO) conventions and factor endowments at the country-level as an IV for inequality.

In this chapter, we follow [START_REF] Madsen | Inequality, nancial development and economic growth in the oecd, 1870-2011[END_REF][START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF] and use foreign Communist in uence as a quasi-natural experiment. The latter is de ned as the cultural distance-weighted fraction of the world population that has Communist governance. The argument put forward in [START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF] assumes that Communist in uence has historically been a source of income redistribution within OECD countries as a way to accommodate workers' wage claims, which are associated with lower income inequality. They further note that: "ruling elites and employers' concessions to improve workers'relative and absolute standard of living, and attempts to mitigate their various grievances, were one practical, e ective, and potentially lower-cost option to stem the spread of communism". In other words, such an in uence is actually perceived as an external threat that should be avoided domestically by implementing pro-labor public policies. More importantly, the extent to which the foreign Communist in uence is likely to produce domestic shifts in the income distribution and labor market outcomes will ultimately depend on cultural distance to communism, which is proxied by geographical and linguistic proximities.

Following [START_REF] Madsen | Inequality, nancial development and economic growth in the oecd, 1870-2011[END_REF][START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF] notations, the foreign Communist in uence from country i to country j is constructed as follows:

ComInf = i,t Σ 12 j=1 (P op ijt D Com jt /Dis Lin ij ) Σ 12 j=1 (P op ijt /Dis Lin ij ) (3.2)
where

Dis Lin ij = 1 - ω ij [0.5(ω j + ω i )] λ (3.3)
Dis Lin refers to linguistic distance and D Com is a dummy variable that is equal to 1 if the government is communist and 0 otherwise; P op denotes the population size while ω ij represents the number of common nodes between country i's and j's languages. The main idea behind equation 3.2 is that the social movement in the country i is in uenced by communist regimes in other countries. This external in uence is weighted by the linguistic distance, which is used as a proxy for cultural proximity between two countries. According to [START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF]: "linguistic distance gives a more plausible account of the spread of political ideas than geographic proximity". As a matter of fact, Australia and New Zealand are culturally (i.e. in terms of values) and linguistically closer to the U.S., U.K. and western Europe than East and South Asian countries.

To summarize, this instrument may produce external variation in the income distribution, as elites, governments and employers have an interest in avoiding the spread of foreign Communist revolutions and, therefore, in responding to workers' wage aspirations. Thus, the rise of a Communist alternative as a serious political threat should lead to exogenous shifts in public policies and inequality, with plausibly no direct impact on credit dynamics. 7 It is worth noting that none of the countries of our sample had experienced a communist regime, although some have had a long standing tradition of communist parties (e.g., France or Italy).

The Communist in uence IV embodies therefore an in uence that is external to the domestic country. Figures C.6 and C.7 in the Appendix trace out the evolution of the foreign Communist in uence index overtime. The index replicates relatively well the major political events in the industrialized economies that shaped the external communist in uence: following the WWII and the emergence of a bipolar world, the index substantially increases, then remains stable over the 1950-1990 period before declining amid the fall of the Soviet union.

The validity of our identi cation strategy is, however, threatened if unobserved factors correlated with foreign Communist in uence have an impact on credit dynamics. To address this issue, we rst control in our rst-stage regression for numerous variables that may potentially be correlated with the intensity of foreign Communist in uence and the credit market.

The latter include the twice lagged terms of (i) the log of the credit-to-GDP ratio, and the contemporaneous terms of (ii) real GDP per capita growth; Then, a second attempt to assess the robustness of our identi cation strategy consists of introducing an additional instrument. In this respect, recent evidence by [START_REF] Rubolino | Tax progressivity and top incomes evidence from tax reforms[END_REF] shows -for a panel of 18 countries over the period 1960-2010 -that reductions in tax progressivity had large and lasting positive impacts on top income shares, especially for the top percentile. This e ect seems to operate mainly through reductions in top marginal tax rates that increase the share of capital income going to rich households. This is why we use foreign income tax in uence as a second instrument for top income shocks. The latter is de ned as the average top marginal tax rates of neighboring countries in the sample and countries sharing a common language. 8 The evolution of top marginal taxation abroad could indeed signal a shift in ideology regarding the acceptance of inequality, which is likely to spread to other countries and impact their domestic public policies. Having two di erent external instruments o ers two advantages. First, it allows us to check whether our results are a ected when we identify di erent external sources of top income uctuations. Second, the exclusion restriction can be assessed via the Sargan-Hansen test by pairing the two instruments (foreign Communist in uence and top marginal tax rates), as the empirical model becomes overidenti ed in such cases.

To estimate the dynamic causal e ect of top incomes on credit, we pair the external instrument with the LP method of Jordà (2005) (LP-IV). Such an application has recently been proposed in the literature [START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF]) and is a direct (or semiparametric) approach to obtaining impulse response functions (IRFs). Using this method allows us to estimate dynamic e ects and therefore to depart from the existing literature, which mainly featured static regressions.

In practice, the LP-IV approach consists of estimating through 2SLS a sequence of predictive regressions of the variable of interest on a structural shock for di erent projection horizons.

Then, the IRF is obtained directly from the sequence of regression coe cients of the structural shock. Hence, we estimate the following equation:

∆ h Cred i,t+h = α h i + γ h t + β h Îneq i,t + θ h X i,t + ε h i,t (3.4)
where ∆ h Cred i,t+h = Cred i,t+h -Cred i,t and corresponds to the log change in the creditto-GDP ratio from base year t up to year t + h, with h = 0, ..., H; α h i and γ h t refer to country and time xed e ects, respectively; X i,t is a vector containing a set of control variables. They include the twice-lagged terms of (i) the log of the credit-to-GDP ratio and the contemporaneous terms of (ii) real GDP per capita growth, (iii) real consumption growth, (iv) the change in the investment-to-GDP ratio, (v) government expenditure growth, (vi) the CPI in ation rate, (vii) the change in the short-term interest rate, (viii) real broad money growth, (ix) stock price growth, (x) house price growth, (xi) the level of trade openness, (xii) population growth, (xiii) the degree of capital account openness and (xiv) the top marginal tax rate; and Îneq i,t denotes the tted value of the top income variable (or inequality measure) obtained from the following rst-stage regression:

Ineq i,t = a i + b t + φX i,t + ζZ i,t + η i,t (3.5)
where Z i,t refers to the foreign Communist in uence variable. 9 The rst-stage includes country and time xed e ects as well as a vector of control variables.

As long as the usual IV conditions (relevance and exclusion restriction) are met, an accurate estimate of the local credit impulse response to a top income shock is given by the sequence of estimates β h , while the respective standard errors can be used to build con dence bands.10

Results

Baseline results

The basic idea of this chapter is to estimate the dynamic causal e ect of rising top incomes on credit dynamics. To do so, we build on an instrumental variable approach and mobilize the foreign Communist in uence to identify exogenous variations in inequality and top incomes in particular. Table 3.2 reports the rst-stage regression results. Several income inequality measures (P1, P9 and the net-Gini) are regressed on the instrument Z i,t with the aforemen-tioned controls X i,t , country and time xed e ects and robust standard errors. The rst-stage regression of our second instrumental variable, i.e. top marginal taxation, is shown in the last column of Table 3.2. The coe cient estimates con rm the predicted negative relationship between income inequality and the foreign Communist in uence. Put di erently, an increase in the foreign Communist in uence decreases top income shares as well as the Gini coe cient for disposable income.11 Furthermore, the F -statistics are well above 10, illustrating that the instrument is not weak.

The baseline result, obtained from the estimation of equation 3.4 by LPs, is displayed in Figure 3.1. It depicts the accumulated impulse responses of total credit over GDP to a shock to the top 1% income share. The reported IRs concern both the IV setting and the standard OLS estimation, with the associated 90% con dence bands that are constructed from Driscoll-Kraay robust standard errors. Figure 3.1 indicates that a 100 b.p. exogenous increase in P1 via the instrument has a positive and long-lasting e ect on the growth of the credit-to-GDP ratio. This positive e ect amounts to 1.4% and 2.1% two and three years after the shock, with a maximum impact of 3.1% over 5 years.12 Interestingly, the opposite e ect of a similar top income shock is detected with a standard OLS estimation. This discrepancy is also noticeable in Table 3.3, which reports coe cient estimates from the IV and OLS estimations. In fact, a 100 b.p. increase in P1 lowers credit growth by 1.3% ve years after the shock. This obviously points to the existence of important endogeneity bias in the standard OLS regression stemming from omitted variables that are determinants of top incomes. It also con rms that the identi cation strategy is key to understand how inequality shapes credit dynamics.

Our baseline result con rms the theoretical predictions of [START_REF] Kumhof | Inequality, leverage, and crises[END_REF], stressing the role of top incomes in fueling credit expansions. It is also consistent with the cross-country evidence provided by [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF], [START_REF] Perugini | Inequality, credit and nancial crises[END_REF] and [START_REF] Gu | Inequality, leverage and crises: Theory and evidence revisited[END_REF]. It contradicts, however, earlier contributions on the inequality-credit nexus that documents an insigni cant relationship between inequality and credit growth, i.e. [START_REF] Bordo | Does inequality lead to a nancial crisis[END_REF].

While our nding primarily deals with the total credit-to-GDP ratio, it is worth assessing which component of credit is the most relevant to study the impact of inequality on the leverage of the economy.

Recently, [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF] have focused on household leverage and demonstrated that exogenous variations in inequality have a positive impact on household credit. In the same spirit, we explore how di erent types of credit respond to a top income shock. To do so, we separately focus on three components of credit: business, mortgage and household loans.

While the e ects of inequality on household nances have been studied both at the macro and all credit components when we consider the response of the (log of) real total credit instead of the credit-to-GDP ratio.

The fact that business, mortgage and household credit positively respond to a top income shock prevents us from clearly establishing the mechanism driving the causal e ect of top incomes on credit over GDP. As previously discussed, the channels inducing a causal impact of inequalities on our variable of interest may be either demand or supply sided. On the demand side, higher income and wealth dispersion is likely to spur conspicuous consumption from the rich, and thereby push low-income households to borrow more in order to "Keep up with the Joneses" (Veblen (1899)). On the supply side, more credit in the economy is the consequence of higher credit supply triggered by the increased saving of the rich as a result of higher inequality [START_REF] Kumhof | Inequality, leverage, and crises[END_REF]). The evidence from Figure 3.2 is inconclusive in determining the relevant transmission channel and rather supports the idea that there is an interplay between demand and supply channels in shaping the e ect of inequality on credit dynamics. For example, mortgage loans can be also acquired by low-income households, who are a ected by the inequality shock.

Robustness checks

We examine the reliability of our baseline result to a variety of robustness checks. First, inasmuch as our main contribution to the literature is to focus on top income shares and the top 1% in particular, it is important to evaluate how exogenous shocks on other parts of the top decile a ect the credit-to-GDP ratio. The rationale for doing so stems from the fact that households at the top of the income distribution may exhibit strong heterogeneity in terms of income sources. In this respect, [START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF] highlight that the lower 9 percent of the top decile consists of highly salaried workers with little capital holdings, while top percentiles' income is mainly composed of dividends and nancial returns. For that purpose, we rst estimate the impulse response of credit-to-GDP ratio to a shock to the top 10% and then to an exogenous increase in the bottom share of the top decile (P9). Next, we focus on the right tail of the top percentile and estimate the dynamic e ects of an exogenous shock to the top 0.1% and 0.01% income shares on the credit-to GDP ratio. The impulse responses shown in Figure 3.3 con rm that a top income shock has positive and persistent e ects on the path of credit, irrespective of the considered top income measure. The magnitude of the e ect for the alternative top income measures is comparable to the baseline impact of the top 1% income shock. As a case in point, exogenous shocks to the top 9 percent and top 0.1 percent richest increase the credit-to-GDP ratio by 4.8% and 5%, respectively. Interestingly, a shock to the top 0.1% and top 0.01% income shares produces a more sizable e ect when using the (log of) real total credit (see Figure C.10 in the Appendix).

A relevant limitation that one could claim relates to the choice of exclusively focusing on the top income distribution. This is problematic because it does not allow us to make statements about the e ects of inequality on credit dynamics since that would require looking also at the median (or inter-quartile range) and at the left tail of the income distribution. As data on bottom income shares are not available over the studied period, an alternative way to address this point consists of working with the Gini coe cients for market and disposable incomes.

In addition, percentile ratios are also good proxies for income inequality as they illustrate how a higher gap between top incomes and the lowest 90 percent of the population (B90) a ects total credit over GDP. induces a positive impact on credit that amounts to 1.5% ve years after the shock. However, we notice that the impact on the credit-to-GDP ratio is not statistically signi cant in the short run when using the net Gini. Similarly, the responses of the percentile ratios (P1/B90 and P9/B90) shown in graphs (c) and (d) do not con ict with our baseline nding. Furthermore, these results also speak to the interplay between supply and demand channels as they show that the positive response of credit could be driven by an increase in top income shares or a decline in the residual share received by the lowest 90 percent of the population (B90).

We perform additional sensitivity analyses that are shown in in Figure 3.5 below. In graphs In graph (e), we conduct the empirical analysis until 2006 and con rm that our results are not a ected by the period following the 2007-2008 nancial crisis. 14 Afterwards, to assess whether the instrument satis es the exclusion restriction, we estimate equation 3.4 without the vector of control variables. The impulse response depicted in graph (f) is consistent with the baseline nding and shows that the e ect of top incomes on credit over GDP is slightly higher (a maximum impact of 6.2% over a 5 year horizon). On top of that, the robustness of the instrumental variable is assessed by (i) using foreign top income taxation as an instrument and (ii) pairing the latter with the initial foreign Communist in uence instrument. The impulse response displayed in graph (g) shows that our results are robust to another external source of variations in inequality. 15 Finally, the estimations related to graph (f) fail to reject the null hypothesis of the Hansen-Sargan overidenti cation test, meaning that the exclusion restriction holds.

14 Figure C.12 in the Appendix shows that all these tests produce the same outcome when using the real credit growth as the dependent variable. 15 One remaining concern is that the potential role of the Foreign communist in uence index may be seen as irrelevant after the 1980s. That is why the empirical model is estimated using the two instruments for the post-1980s period. The results are reported in Figure 3.6.

Conclusion

This chapter sought to provide an empirical assessment of the inequality-credit nexus, focusing on top incomes for a panel of 12 advanced economies over the period 1948-2015. To this end, we extract top income shares from the World Inequality Database (WID) and macroeconomic data from the Jordà-Schularick-Taylor (JST) Macrohistory Database. The cross-country empirical literature on the relationship between inequality and the leverage of the economy lacked strong causal evidence and primarily relied on static regressions. We depart from the existing contributions in two important respects. First, the dynamic e ects of a top income shock on credit growth are estimated using the LP method of [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF]. Second, we exploit foreign Communist in uence, following [START_REF] Madsen | Inequality, nancial development and economic growth in the oecd, 1870-2011[END_REF][START_REF] Madsen | The creation of e ective states in the oecd since 1870: The role of inequality[END_REF], as an instrumental variable to identify exogenous variations in inequality. Communism has constituted throughout history a serious external political threat, against which governments and elites in non-Communist countries implemented pro-labor policies. This historical mechanism is therefore perceived as a good predictor of income distribution that contributed to reduce inequality, without directly a ecting credit dynamics.

The results show that income inequality and, in particular, the evolution of top incomes have a non-negligible impact on credit expansion. An exogenous shock to the top 1% income share via the instrument increases credit growth by 2.16% and 2.85% three and four years after the shock, respectively. The positive response of business and mortgage loans to a top income shock prevents, however, to clearly determine the underlying mechanism. This supports, to say the least, that there is an inter-play between demand and supply channels in accounting for such an e ect. Part of the intuition behind our ndings is that an increase in top incomes leads to more savings entering the nancial system, which triggers credit expansions via loan supply. We also demonstrate that the inequality-credit nexus crucially relies on the adopted identi cation strategy. In fact, a similar top income shock has the opposite e ect on credit growth when using a standard OLS estimator. Our baseline nding is line with the recent contributions of [START_REF] Perugini | Inequality, credit and nancial crises[END_REF] and [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF] documenting the positive impact of inequality on credit. It also holds for di erent shares of the top income distribution (top 10%, 9%, 0.1% and 0.01% of national income) as well as income inequality measures (pre and post redistribution Gini coe cients along with percentile ratios). Our results are also robust to (i) alternative instruments (foreign top marginal taxation), (ii) shorter period samples and (iii) various model speci cations. One limitation that should be acknowledged is that most of the inequality measures mobilized in this chapter are pre-tax indices. Because credit is more likely to be a ected by disposable income than by gross income, further research should be conducted in this direction.

For future research, the challenge would be to re ect on new empirical strategies along with the various institutional settings underlying such relationships. Assessment of the transmission mechanisms -using more granular data -would also contribute to a better understanding of what channels drive the causal e ect of inequality on nance. Note: The table reports the coe cient estimates for the IV and OLS settings. Driscoll-Kraay robust standard errors are reported in parentheses below the coe cient estimates. Coe cient estimates of controls and xed e ects are not reported. Controls include the twice-lagged terms of (i) the log of the credit-to-GDP ratio and the contemporaneous terms of (ii) real GDP per capita growth, (iii) real consumption growth, (iv) the change in the investment-to-GDP ratio, (v) government expenditure growth, (vi) the CPI in ation rate, (vii) the change in the short-term interest rate, (viii) real broad money growth, (ix) stock price growth, (x) house price growth, (xi) the level of trade openness, (xii) population growth, (xiii) the degree of capital account openness and (xiv) the top marginal tax rate. We report the Kleibergen and Paap (2006) Local Inequality and household debt in the U.S.

Main gures and tables

Introduction

Policymakers have long focused attention on public debt and its implications for macroeconomic stability. But following the subprime mortgage crisis, private debt and household debt in particular have also become a major concern in the advanced economies. This is especially the case in the United States where household debt is the largest component of national debt and it has been on an upward trend since the 1980s. 1 In discussing these dynamics, a distributional angle has been introduced by [START_REF] Stiglitz | The Price of Inequality: How Today's Divided Society Endangers Our Future[END_REF] and [START_REF] Galbraith | Inequality and Instability: A Study of the World Economy Just Before the Great Crisis[END_REF], arguing that household debt has gone up over the past decades as a response to rising inequalities and stagnant wages.

In the post-crisis period, several contributions took an interest in empirically exploring the relationship between inequality and household leverage. On the one hand, most recent crosscountry evidence focused on documenting the existence of a (causal) relationship and concluded to a positive impact of income inequality on household credit (see [START_REF] Bazillier | Structure of income inequality and household leverage: Theory and cross-country evidence[END_REF], [START_REF] Gu | Inequality, leverage and crises: Theory and evidence revisited[END_REF] and [START_REF] Perugini | Inequality, credit and nancial crises[END_REF]; [START_REF] Bazillier | The circular relationship between inequality, leverage, and nancial crises[END_REF] for a review of the literature). On the other hand, country-level studies are inconclusive and have yet to reach a consensus on the underlying mechanism, through which a rise in income inequality a ects household debt. In this respect, one strand of the literature argues that households care about their social status and "Keep up with the Joneses" by taking on debt i.e. through credit demand (see [START_REF] Georgarakos | Household debt and social interactions[END_REF] for The Netherlands and [START_REF] Berlemann | The joneses' income and debt market participation: Empirical evidence from bank account data[END_REF] for Germany). Another strand emphasizes the role of factors in uencing credit supply such as nancial deregulation, the saving glut, and bank screening procedures (see [START_REF] Kumhof | Inequality, leverage, and crises[END_REF] and [START_REF] Loschiavo | Household debt and income inequality: Evidence from italian survey data[END_REF], among others).

In the U.S. context, the existence of both demand and supply mechanisms in shaping household debt has been well documented. For instance, Drechsel-Grau and Greimel (2020) nd that "Keeping up with the Joneses and rising income inequality generate 60% of the observed boom in mortgage debt and 50% of the house price boom". Similarly, [START_REF] Carr | Relative income and indebtedness: Evidence from panel data[END_REF] focus on the period surrounding the housing bubble and show that "leverage grew faster for households with lower relative income compared to other households in similar demographic groups or within a state". By contrast, [START_REF] Coibion | Greater inequality and household borrowing: New evidence from household data[END_REF] challenge the notion of "Keep up with the Joneses", demonstrating that when inequality rises, banks increasingly rely on household's income as a signal regarding its solvency and would consequently grant more credit to high income households. This results in credit rationing, which rationalizes why they nd that low-income households living in high-inequality areas accumulated relatively less debt than similar households in low-inequality areas.

This chapter evaluates the impact of income inequality on household borrowing decisions in the U.S. over the period 1999-2015. It examines how local inequality, as measured by the state-level Gini coe cients, a ects the likelihood of household's participation in the debt market. To achieve this, I use nationally representative household-level data from the Panel Study of Income Dynamics (PSID), which is thought to be the longest running longitudinal household survey in the world. States are considered the "local" unit of analysis, which allows (i) studying heterogeneous regions, while (ii) separating the e ect of local inequality on the frequency of debt from important institutional factors that arise in a cross-country analysis.

Speci cally, I exploit information on household income rank in order to assess (i) how rising local inequality a ects the frequency of household debt across di erent income groups and

(ii) provide insight into the relevant transmission channel. The adopted empirical approach borrows from Georgarakos et al. ( 2014), [START_REF] Coibion | Greater inequality and household borrowing: New evidence from household data[END_REF][START_REF] Loschiavo | Household debt and income inequality: Evidence from italian survey data[END_REF] as it mobilizes well-established (non)-linear probability models to estimate the impact of household rank, local inequality and their interaction on the likelihood of holding debt.

The contributions of this chapter to the growing literature of the inequality-debt nexus are threefold. First, unlike most of the existing works on the U.S. using granular data (see [START_REF] Bartscher | Modigliani meets minsky: Inequality, debt, and nancial fragility in america[END_REF], for instance), I focus on household participation in the debt market i.e. the decision to take on debt, instead of household debt accumulation. Second, while Coibion et al.

(2020) develop an income imputation procedure to match credit data, I rely directly on house-holds' self-reported income information. Third, I exploit the panel feature of the PSID to account for unobserved heterogeneity and track shifts in households borrowing decisions over time. This chapter also o ers a regional dimension to the notion of "Keeping up with the Joneses", which is documented by [START_REF] Carr | Relative income and indebtedness: Evidence from panel data[END_REF] at the national level.

The ndings suggest that local inequality is negatively associated with the probability of household's participation in the debt market, which is consistent with [START_REF] Coibion | Greater inequality and household borrowing: New evidence from household data[END_REF].

In view of the e ect of local inequality across income groups, the results depart, however, from the aforementioned paper, as the negative e ect of income inequality at the state-level on household frequency of debt is found to be stronger for high-income households. In other words, low-and middle income households living in high-inequality states are more likely to be indebted than similar households living in low-inequality states and vice-versa for rich households. This e ect especially holds for mortgage loans and is more potent for the 1999-2005 period and supports, overall, the "Keeping up with the Joneses" narrative: as inequality within states increases, bottom income households emulate their peers' living standards through credit demand.

The chapter is structured as follows: section 4.2 discusses the existing literature. Sections 4.3 and 4.4 describe the data and introduce the empirical speci cation, respectively. Section 4.5

presents empirical evidence on the relationship between local inequality and household debt.

Related literature

How does rising inequality a ect households debt? The existing literature has put forward several mechanisms that either (i) account for households borrowing behavior or (ii) trace out how nancial institutions increased credit supply.

The rst strand of the literature echoes to the "Keeping up with the Joneses" notion, referring to the fact that one's compares to some reference group as a benchmark for social class (i.e. status concerns). In this context, relative income and interpersonal comparisons shape households consumption and investment decisions. This reading grid can be traced back to the concept of "conspicuous consumption" formulated by [START_REF] Veblen | The Theory of the Leisure Class. An Economic Study of Institutions[END_REF], where overspending serves to display -or achieve -a given social status. Based on similar arguments, the relative income hypothesis of [START_REF] Duesenberry | Income, Saving and the Theory of Consumer Behavior[END_REF] and theory of "expenditure cascade" by [START_REF] Frank | Expenditure cascades[END_REF] suggest that household consumption depends not only on its income but follows as well that of other reference groups across the income scale.2

The empirical importance of such a mechanism on household behavior has been well documented in the literature. With respect to consumption, [START_REF] Bertrand | Trickle-down consumption[END_REF] nd that non-rich households in the U.S. "consume a larger share of their current income when exposed to higher top income and consumption levels". [START_REF] Bowles | Emulation, inequality, and work hours: Was thorsten veblen right?[END_REF] and [START_REF] Oh | Veblen e ects, political representation, and the reduction in working time over the 20th century[END_REF] demonstrate how the desire to emulate the rich could also a ect the "labor-leisure" trade-o and result in longer work hours. Speaking of the e ect of social status-signaling on household intendedness, two contributions stand out. First, [START_REF] Georgarakos | Household debt and social interactions[END_REF] mobilize Dutch micro data over the period 2001-2008 and document that "the higher the average income in the social circle, as perceived by a household, the more this household tends to borrow". Second, [START_REF] Carr | Relative income and indebtedness: Evidence from panel data[END_REF] exploit the PSID waves around the 1999-2009 period to examine the idea that rising indebtedness in the 2000s is linked with rising inequality in the U.S. 3 Their results

suggest that household leverage grew faster as the "distance" between a household and the reference group above it in the income distribution (i.e. inequality) increased. In this chapter, I extend [START_REF] Carr | Relative income and indebtedness: Evidence from panel data[END_REF] as I explore how the interaction between local inequality and income rank at the state-level impacts U.S. households' participation in the debt market.

The second strand of the literature takes an interest in understanding how shifts in the institutional environment and bank lending behavior have resulted in an increase of credit supply.

Banking deregulation spanning the 1980s is thought to have intensi ed competition, which allowed banks to grant more loans. Speci cally, the relaxation of geographical restrictions on bank expansion in the US (suppression of both intrastate and interstate branching) had positive e ects on credit supply (see e.g., [START_REF] Cetorelli | Finance as a barrier to entry: Bank competition and industry structure in local u.s. markets[END_REF], [START_REF] Rice | Does credit competition a ect small-rm nance?[END_REF] and [START_REF] Favara | Credit supply and the price of housing[END_REF], among others). In addition, accommodative monetary policy conditions encouraged nancial institutions to increase lending to riskier households. 4 This momentum reached its height in 2007 following the burst of the housing bubble triggered by sub-prime loans. What role has inequality played in these dynamics? [START_REF] Rajan | How Hidden Fractures still Threaten the World Economy[END_REF] argues that rising income disparities magni ed banks' risk-taking behavior and created political pressure to facilitate low-income households' credit access. [START_REF] Kumhof | Inequality, leverage, and crises[END_REF] uncover another mechanism linking inequality to leverage through credit supply. In fact, if the rise in the income share of the rich is associated with higher savings, credit supply would increase, which positively spills on the debt leverage of low-and middle-income households.

Coibion et al. ( 2020) support as well a supply-side interpretation of the inequality-leverage nexus. Using data from the New York Federal Reserve Consumer Credit Panel (CCP), their main nding points that low-income households in high-inequality regions accumulated less debt than similar households in low-inequality regions. To unveil the underlying transmission channel, the authors exploit information on both credit-card balances and credit-card limits, which could be re ecting loan demand and credit supply, respectively. The evidence shows that low-income households in high-inequality regions saw their credit limits rise by less than those in lower-inequality regions, thereby giving credence to supply-side factors in driving household debt. To illustrate the mechanism, the authors develop a model in which they explain how borrowing patterns are a ected by regional inequality. The model introduces two regions (high and low inequality) composed of two types of households (with high and low incomes), while assuming that banks observe the level of local inequality and use it to screen applicants' creditworthiness. The model then predicts that as local inequality rises, banks will increasingly rely on household income as a precise signal about their risk pro le, thereby pushing them to increase lending towards high-income households.

The present chapter departs from Coibion et al. ( 2020) by (i) studying the e ect of local inequality on the likelihood of being indebted, (ii) using households' self-reported income information so that no imputation is needed and (iii) exploiting the panel feature of PSID survey.

Data description

The household-level data used in the empirical analysis come from the main survey of the Panel Study of Income Dynamics (PSID) over the period 1999-2015. The PSID is a nationally and Lehnert (2010) nd that deregulation explains at least 10% of the rise in bankruptcy rates.

representative longitudinal dataset of U.S. households that was conducted yearly since 1968 and changed to be a biannual survey in 1999. It initially started with a sample of over 18,000 individuals living in 5,000 families and information on these individuals and their descendants has been collected continuously. Unlike other U.S. household surveys (the Survey of Consumer Finances (SCF), for instance), the PSID has particularly the advantage of tracking as many households as possible over time. Besides a wide range of socio-economic variables -age, gender, marital status, number of children, geographical location, etc. -the dataset also provides information on household indebtedness. Two main categories of debt are available:

(i) mortgage debt and (ii) consumer debt (vehicle, student and other loans).5

Several steps are undertaken to re ne the dataset. First, because of the large number of households appearing in the PSID for only one wave, I consider in the sample households that participated at least in two consecutive waves of the survey. Second, households where the age of the head is younger than 20 years or older than 70 years are excluded as well as those who report a negative or a zero income. Finally, I trim total family income at the 1st and 99th percentiles to ensure that estimates are not biased by outliers. 6 The nal sample used in baseline estimations consists of 62,016 observations (8,359 households in the panel analysis).

The social interactions driving the demand for credit and banks' signaling procedures that a ect credit supply are more likely to occur at the local level. The role of income inequality in shaping household borrowing behavior should accordingly be considered at a dimension that would allow to test such economic mechanisms. Inasmuch as the PSID features information on households state of residence, I opt for income distribution at the state-level to measure local inequality. This level of spatial aggregation is relevant because households compare themselves to others around an area whose social characteristics (including inequality) are well-known. [START_REF] Coibion | Greater inequality and household borrowing: New evidence from household data[END_REF] and [START_REF] Loschiavo | Household debt and income inequality: Evidence from italian survey data[END_REF] note that studying inequality at the regional (or state) level also contributes to (i) avoiding measurement issues associated with comparing incomes across very di erent regions and minimize the risk of (ii) sampling error as well as (iii) confounding factors that determine household debt and its selection into a geographical area.

However, because the PSID was not designed to be representative at the state-level, I rely on the updated Gini coe cients of the Frank-Sommeiller-Price series. The latter are obtained from the U.S. State-Level Income Inequality Database of [START_REF] Frank | Inequality and growth in the united states: Evidence from a new statelevel panel of income inequality measures[END_REF] and use individual tax ling data available from the Internal Revenue Service (IRS). To construct households position over the income distribution, I use historical income tables from the United States Census Bureau, which de ne household income at selected percentiles. Income ranks are thus determined by the income deciles limits for each wave of the survey. With respect to location controls, data on housing prices and non-performing loans at the state-level are obtained from the Federal Housing Finance Agency (FHFA) and the Federal Reserve Bank of St. Louis, respectively. Local inequality and regional controls are afterwards merged using households' state of residence.

Table 4.1 reports total family income and total debt by percentiles. The median income of $63,470 is lower than the mean one (see Table D.1 in the Appendix), re ecting the positive skewness of the income distribution. In line with [START_REF] Carr | Relative income and indebtedness: Evidence from panel data[END_REF], total debt of lower percentiles is $0, suggesting that a large number of families report zero debt. Table D.2 in the Appendix presents summary statistics by income class using the deciles computed for income ranks. All household-level statistics are calculated with household weights provided by the PSID. Notes: Author's calculations based on PSID (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). Statistics are weighted using PSID household weights. estingly, it appears that states featuring on average high income inequality levels also have the highest debt-to-income ratios, although this observation does not hold for all states. This chapter o ers an analysis that goes beyond these maps as it explores -within states -how relative income rank and inequality shape household indebtedness.

Econometric speci cation

The baseline model estimates the e ect of local income inequality on the probability of holding debt and de nes itself with the terms of [START_REF] Georgarakos | Household debt and social interactions[END_REF] and [START_REF] Loschiavo | Household debt and income inequality: Evidence from italian survey data[END_REF].

Speci cally, I consider household's participation in the debt market as a function of its relative income rank, conditional on the level of local income inequality. The basic relationship is given by the following equation:

Debt ist = α i +γ t +β 0 IncDec ist +β 1 Gini st +β 2 IncDec ist * Gini st +δX ist +φZ st-1 +ε ist (4.1)
where Debt ist is the binary outcome variable that is equal to one if a household i living in state s report positive debt and zero otherwise 7 ; IncDec ist refers to household's income rank as expressed by income deciles; Gini st is the U.S. state's Gini coe cient 8 ; X ist and Z st-1

indicate, respectively, a set of household-speci c and location-speci c controls. The household characteristics in the X vector include head of household information such as age, age squared, ethnicity, marital status, educational achievement as well as total family income and the household size, i.e. number of persons living in the family unit at the time of the interview.

The location controls in the Z vector include the growth rate of housing prices and the ratio of non-performing loans at the state-level. These controls are one year lagged as it is unlikely that the latter have a contemporaneous impact on household indebtedness. α i and γ t denote macro-region and time xed e ects, while ε ist is the error term. Table D.3 in the Appendix shows correlation coe cients among the regressors.

The main coe cient of interest is IncDec ist * Gini st , which illustrates how the interaction between household income rank and state-level inequality a ects household debt. To allow for 7 The binary ownership indicator of debt is constructed from the amount of reported debt. This is done to avoid potential measurement errors stemming from answering random questions concerning household debt status. 8 The Gini index measures the dispersion of the income distribution and illustrates how a country (region in this case) is far from perfect equality.

an interpretation of coe cients that makes sense, I rst center both IncDec and Gini by subtracting their respective median value before computing the interaction term. 9 As discussed by [START_REF] Loschiavo | Household debt and income inequality: Evidence from italian survey data[END_REF], the coe cient β 0 of equation 4.1 represents -after having centered the two covariates -the marginal e ect of household income position on its probability to hold debt when the state-level Gini coe cient is equal to its median value. 10 Similarly, β 1 should indicate the e ect of local inequality on household indebtedness when its rank over the income distribution corresponds to its median level.

The baseline speci cation allows to test di erent mechanisms. First, β 0 links household's frequency of debt with its income rank. Table D.2 in the Appendix shows -at the national level -that household debt is positively correlated with income deciles, leading to expect that such a relationship is likely hold within U.S. states. Second, β 1 evaluates whether local inequality is relevant for households' participation in the debt market. The question of how inequality shapes household borrowing decisions remains unanswered in the empirical literature. For example, while Loschiavo (2020) documents for Italy that inequality in the regional income distribution has a negative e ect on the probability of being indebted, Jestl (2019) nds a positive impact of income inequality on consumption-related household indebtedness in a small sample of European countries. Finally, the coe cient β 2 of the interaction term captures the incidence of local inequality on household borrowing across income deciles. The interaction between state-level Gini coe cients and household income deciles further provides insights into the transmission mechanism of inequality towards household debt.

On the one hand, if β 2 > 0, the e ect of local inequality on the probability to hold debt strengthens as household moves up in the income distribution. In other words, low-income households living in high-inequality states are less likely to access credit markets. Such an interpretation echoes to the ndings of [START_REF] Coibion | Greater inequality and household borrowing: New evidence from household data[END_REF] and [START_REF] Loschiavo | Household debt and income inequality: Evidence from italian survey data[END_REF], where supplyside factors matter the most in household indebtedness. This reading grid actually builds on adverse selection models (see [START_REF] Stiglitz | Credit rationing in markets with imperfect information[END_REF] and [START_REF] Bester | Screening vs. rationing in credit markets with imperfect information[END_REF], among others) and assumes that when inequality increases, nancial institutions treat household's income as a 9 In the context of equation 4.1, without centering the variables, β 1 would be interpreted as the marginal e ect of income inequality on the probability of being indebted when the income decile is zero and vice-versa in the case of β 0 , which are not plausible cases, i.e. perfect inequality or a null income decile simply do not exist.

10 Such a procedure also participates in mitigating the collinearity that is likely to arises when computing an interaction term from two variables that are not centered.

strong signal of its solvency and therefore, grant more funding to high income households (i.e. credit rationing). On the other hand, if β 2 < 0, the e ect of rising local inequality on the probability to hold debt weakens as household moves up in the income distribution, that is, low-income income households living in a high-inequality state are more likely indebted than similar households living in a low-inequality state. This is consistent with the "Keeping up with the Joneses" notion and suggests that credit demand drives household borrowing decisions. Put di erently, rising local inequality favors new consumption standards that lowand middle income households attempt to emulate through loan demand.

To establish which transmission channel is at play, we need to separately assess the contribution of demand and supply factors as they are likely to jointly determine household's borrowing decision. While the PSID does not provide information on households that were denied credit or have been discouraged from applying, I exploit information about the year during which a household obtained its mortgage or consumer loan to study the credit demand channel. The following equation is estimated:

Dem ist = α i +γ t +β 0 IncDec ist +β 1 Gini st +β 2 IncDec ist * Gini st +δX ist +φZ st-1 +ε ist (4.2)
where Dem ist is a dummy variable indicating whether or not the household head obtained a mortgage and/or consumer loan for each survey wave, meaning Dem ist is equal to one if household i living in state s has obtained a loan in year t, given that 1999≤t≤201511 ; household-speci c and location-speci c controls are unchanged with respect to equation 4.1.

As discussed earlier, the relevance of interpersonal comparisons in household indebtedness would be veri ed if β 2 <0, that is, the e ect of rising local inequality on credit demand is stronger for bottom income deciles.

To estimate equations 4.1 and 4.2, three di erent but complementary regression approaches are mobilized, namely the (i) Linear Probability Model (LPM), (ii) pooled probit and (iii) random e ects panel probit. The standard LPM regression o ers an easier interpretation of the coe cients as it assumes that the probability to hold debt is a linear function of the independent variables. In contrast, the interpretation of coe cients estimates in non-linear models is more challenging as it requires computing marginal e ects. The latter are interpreted as the change in (conditional) probability of holding debt following, for instance, an increase in local inequality, holding all other variables constant at some values. Additionally, by exploiting the panel feature of the PSID, the random e ects panel probit controls for unobserved household heterogeneity and takes into account potential changes in household characteristics over time. Finally, it is important to acknowledge the literature stressing that interpreting interaction terms in non-linear models is tricky (see [START_REF] Ai | Interaction terms in logit and probit models[END_REF]). For this reason, I follow [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]'s methodology and compute a consistent estimator for the interaction e ect (cross-derivative) that is reported for pooled and panel probit models.

Empirical results

Baseline

The baseline results of equation 4.1, estimated at the state-level over the period 1999-2015, are reported in Table 4.2. The impact of household income rank, local inequality and their interaction on the frequency of debt are rst discussed before turning to the e ects of other household-speci c and location-speci c variables.

[Insert Table 4.2 here] Column (1) presents the estimated coe cients from the standard LPM regression on pooled data (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015), with robust standard errors clustered at the household level to account for the panel structure of the data and deal with auto-correlation. The rst nding is that the coe cient of household's position (β 0 ) in the income distribution is signi cantly positive. As expected from Table D.2 in the Appendix, the probability to hold debt increases as household's rank moves up in the income ladder, which suggests that high-income households are likely to be more indebted than low-income groups. Second, the coe cient of local inequality at the state-level (β 1 ) is consistently negative, implying -ceteris paribus -that households living in high-inequality states are less likely to hold debt than those living in low-inequality states. Finally, the interaction term between household income rank and local inequality (β 2 ) is negative. This suggests that the negative e ect of rising local inequality on the probability to hold debt is stronger for high-income households. Precisely, the sign of β 2 means that there is a crossing point such that to the right, high-income households hold less debt as state inequality increases. To the left of this crossing, low-income households are likely to hold more debt as local inequality increases. Precisely, gure 4.1 illustrates that this crossing point lies between the 5th and 6th decile, meaning that low and middle-income households living in high inequality states feature a higher predicted debt than similar households living in low inequality states. Although the sign and contribution of income rank and local inequality to household debt are consistent with [START_REF] Coibion | Greater inequality and household borrowing: New evidence from household data[END_REF] for a cross-sectional sample of U.S. households and [START_REF] Loschiavo | Household debt and income inequality: Evidence from italian survey data[END_REF] in the case of Italy, this is not the case when interacting income deciles with state-level inequality. In fact, while the aforementioned chapters document the prevalence of supply-side factors in shaping household borrowing decisions, while the evidence presented in Table 4.2 points that the demand-side hypothesis also matters.

To further grasp the empirical ndings, I estimate equation 4.1 using a pooled probit model with robust standard errors clustered at the household level. Column (2) reports the computed marginal e ects and shows that the sign and magnitude of the estimated coe cients are similar to those reported for the LPM regression. 12 Furthermore, Column (3) presents the results from a random e ects panel probit. 13 The coe cient estimates from the panel data speci cation con rm the e ects of income rank and local inequality on the probability to hold debt but also the relevance of credit demand as a driver of household indebtedness. To formally compare the pooled probit model with the panel estimator, I report in the bottom of Table 4.2 a Likelihood-Ratio test. The latter rejects the null hypothesis under which the inclusion of random e ect does not change the coe cient estimates with respect to the former model, suggesting that the panel probit model ts signi cantly better than the pooled one.

In order to con rm the reliability of the panel probit estimates, some additional speci cations are introduced. First, Column (4) demonstrates that the random e ect panel probit is not sensitive to the exclusion of total family income. Second, more granular regional xed e ects levels are used in order to rule out regional time-invariant e ects that are likely to a ect both local inequality and household borrowing decisions. 14 In this respect, Columns ( 5) and ( 6) 12 It is worth noticing that marginal e ects of the estimated probability models are computed at the means of the independent variables. This is more appropriate because household income rank and state-level Gini coe cients were centered. However, using average marginal e ects instead do not impact the results. 13 The random-e ects estimator is preferred over the population-averaged model because the latter does not fully specify the distribution of the population. 14 In order to distinguish the e ect of regional income inequality from other state characteristics, I follow Loschiavo (2020) and use in the baseline speci cation xed e ects at one level of aggregation (macro-region) that is higher than the geographic area (state) used to construct the income distribution and the income inequality measure.

mobilize Census Bureau-designated divisions and state-level xed e ects, respectively. The coe cients in Column (5) show that when regional xed e ects are considered using the census regions classi cation, the contribution of local inequality to debt likelihood is statistically signi cant but its magnitude is relatively smaller than previous estimations. In Column (6), the introduction of state-level xed e ects cancels out the e ect of local inequality on household probability to hold debt. However, the coe cient of the interaction term in both settings remains signi cant and comparable to those obtained in previous panel estimates.

Regarding the set of control variables mobilized in equation 4.1, the main results in Table 4.2 show that they are broadly consistent with expectations. First, household size and the frequency of debt are positively related. Second, the relationship between aging and the probability to hold debt is non-linear: debt increases with household's age up to a given threshold and then declines. Third, single and divorced households are less likely to be indebted than married households. Fourth, the probability to hold debt increases with the level of educational achievement while it decreases when the household head is an African-American. Finally, a higher ratio of non-performing loans at the state-level is associated with a lower frequency of debt while the e ect of housing prices is insigni cant across all the speci cations.

Demand for credit

The interaction between income rank and local inequality suggested that household indebtedness is likely to be driven by credit demand, which stems from comparisons with peers and social-status concerns. In an attempt to further assess this hypothesis, I estimate in equation 4.2 the probability of household obtaining a loan for each survey wave over the period 1999-2015.

[Insert Table 4

.3 here]

The results are reported in Table 4.3. The important nding is that the coe cient of the interaction term IncDec ist * Gini st is signi cantly negative, indicating that the negative effect of rising local inequality on the frequency of obtaining a loan is weaker for low-income households, which supports the "Keep up with the Joneses" notion. The fact that the interaction term is negative also points that rich households living in low-inequality states are more likely to obtain a loan than similar households living in high-inequality states. Furthermore, while the outcome variable in equation 4.2 is equal to one only for households who obtained a loan at a given survey wave, the coe cient signs of household-speci c controls in Table 4.3 show, nonetheless, that some demand mechanisms are captured. For instance, married and less educated households are more likely to apply for a loan.

Loan decomposition

In order to disentangle which debt component contributes the most to household's frequency of debt, I separate in equation 4.1 mortgage debt from consumer loans. This is done because (i) the maturity of both types of debt is not equivalent and (ii) motives to hold a mortgage or a consumer loans can be di erent. The empirical approaches used in the baseline estimations are therefore replicated for each type of loan. The results are reported in Table 4.4.

[Insert Table 4.4 here]

Columns (1) to (3) show that the baseline results are sensitive to the di erences across types of debt and they are primarily driven by mortgages. Household income rank, local inequality as well as their interaction have a statistically signi cant impact on the probability to hold a mortgage debt, while they do not a ect the frequency of consumer loans across all specications (Columns 4 to 6). Such an evidence is consistent in the U.S. context: (i) mortgages account for a large share of total debt and (ii) households accumulated high-risk mortgage loans, especially during the pre-crisis period. [START_REF] Bartscher | Modigliani meets minsky: Inequality, debt, and nancial fragility in america[END_REF] trace back even further the role played by mortgage debt in the U.S. as they document that it explains a substantial share of the increase in household debt since the 1970s.

Pre-crisis, crisis and post-crisis sub-samples

How do the ndings on the frequency of total debt and its component t with di erent subsamples? To answer this question, I exploit the time span covered by the dataset to draw comparisons with respect to the periods before (1999-2005), during (2007-2009) and after (2011-2015) the 2008 nancial crisis. In this respect, I take advantage of the low attrition bias featured in the PSID data in order to keep track of as much households as possible, although the sample periods are signi cantly reduced. 15 The results concerning the pre-crisis, crisis and post-crisis periods are reported in Tables 4. 5,4.6 and 4.7,respectively. [Insert Tables 4.5,4.6 and 4.7 here] The coe cient estimates presented in the previous subsection provided evidence that household participation in the credit market is primarily driven by mortgage debt. Table 4.5 shows, however, that during the pre-crisis period, both mortgage and consumer loans contributed to the total debt pattern; albeit the parameter β 2 for consumer loans is statistically signi cant only at a 10 percent level for the pooled probit and random e ects panel probit (see Columns ( 8) and ( 9) of Table 4.5). The crisis period estimates presented in Table 4.6 cover the PSID waves of 2007 and 2009 and show that local inequality and its interaction with income rank had no signi cant impact on either total household debt or its components. This demonstrates above all that in the aftermath of the Great Recession, banks signi cantly reduced credit supply, while households were forced to deleverage. In the post-crisis sub-period, although the e ect of state-level income inequality is not signi cant, the interaction term IncDec ist * Gini st still negatively a ected the probability of holding a debt, while being primarily driven by mortgages. Overall, before the crisis, rising local inequality is associated with lower frequency of debt, driven by both of its components (mortgages and consumer loans); the 2008 nancial crisis and the turmoil it ensued ruled out the e ect of inequality, while the post-crisis period recovered the pattern described before 2007.

Endogeneity issues

Although the adopted empirical analysis does not feature a fully identi ed estimation that allows to assert causality, it is still important to discuss potential endogeneity issues. The latter may arise if they a ect income rank and/or local inequality that build the main variable of interest IncDec ist * Gini st .

[Insert Tables 4.8 and 4.9 here] As far as household's rank is concerned, income decile is constructed from family income series that are net of imputed home equity and gross of debt-service. Therefore, holding a debt does not a ect total income -and by extension IncDec ist -through home/car ownership or payable interests on a mortgage or other debts. However, to ensure that a simultaneitybias does not stem from contemporaneous household controls, I replace the latter with their respective value at previous PSID wave into equation 4.1. The results are reported in Table 4.8 and show strong consistency with the baseline ndings. Furthermore, Table 4.9 con rms that the e ect of local inequality on the frequency to hold debt is mainly driven by mortgage loans, in line with evidence presented in the debt decomposition subsection.

[Insert Tables 4.10 and4.11 here] Second, while household-speci c and location-speci c controls reduce the omitted variable bias on the interaction term, endogeneity may a ect state-level Gini coe cient if it is jointly determined with the frequency to hold debt. In such a case, to reduce concerns about a potential simultaneity bias, I follow [START_REF] Coibion | Greater inequality and household borrowing: New evidence from household data[END_REF] and [START_REF] Loschiavo | Household debt and income inequality: Evidence from italian survey data[END_REF] and estimate the baseline speci cation with Gini coe cients as well as household and locations controls being xed at their respective value at the PSID wave of 1999. Doing so contributes to alleviate simultaneity with regard to local inequality but also isolate the contemporaneous e ect of controls on the probability to hold debt. The evidence displayed in Table 4.10 does not depart from the baseline results, albeit the e ect of the interaction term in the panel probit is not signi cant. Interestingly, conducting the same procedure on mortgage and consumer loans reveal that they both contribute to total debt, which is in line with the pattern described for the pre-crisis analysis (see Table 4.11).

Sensitivity analysis

Additional robustness checks are performed to assess the reliability of the results. First, regarding the binary variable for mortgages, its construction is such that it equals one if the remaining principal on the loan is positive for each survey wave. In this context, one can raise the point that household decision to take up a mortgage may occur at a previous date, which casts doubt on the accuracy of the outcome variable. To deal with this drawback, I estimate equation 4.1 for mortgage loans while restricting the sample to only households that had no outstanding mortgage in 1999. The results reported in Table 4.12 suggest that the baseline evidence is una ected by this issue. Second, I interact macro-area and time xed e ects, thereby allowing the latter to have disperse e ects on U.S. states. In fact, state-speci c time trends linked, for instance, to the nancial crisis may impact households' participation in the debt market. The results presented in Table 4.13 show that the main result is not sensitive either to this issue. Third, as previously described, standard errors in pooled speci cations were clustered at the household level to account for the panel component of the data and deal with serial correlation. However, there may still be within-cluster error correlation, which can produce misleading standard errors. That is why we cluster standard errors at the state-level for pooled speci cations. Table 4.14 shows that while the negative e ect of local inequality on the probability to hold debt turns insigni cant, its impact across income groups remains intact. To further minimize the potential omitted variable bias, the LPM speci cation is preferred, to which additional constraints are introduced, consisting of state xed e ects and an interaction term between state xed e ects and year xed e ects along with standard errors clustered at the state-level. The results are reported in Tables D.4 to D.7 in the Appendix and show that the coe cients of the interaction term remain signi cant, which strengthens the argument of the "Keeping up with the Joneses" notion. Fourth, I estimate the baseline specication using the level of income itself instead of household income ranks as one can be also interested in the conditional e ect of state-level inequality and individual income. Table 4.16 suggests that the main results across the LPM, pooled probit and panel probit are not impacted when using the level of income. Finally, I show in Table 4.15 that the baseline results are not a ected when measuring households income rank with quantiles instead of deciles.

Conclusion

This chapter studied the relationship between income inequality and household debt in the United States. The subprime mortgage crisis demonstrated how excessive household indebtedness can be a source of nancial instability. In the U.S. case, the rise of household debt relative to income since the 1980s occurred at a time where the American society was becoming increasingly unequal. In the aftermath of the 2008 Global Financial Crisis (GFC), an economic literature emerged that highlighted income inequality as one of the potential explanations for the increase in household debt. In this context, two strands of this literature are pushing in opposite directions: the rst insists on how social interactions and interpersonal comparisons drive demand for credit, while the second gives more weight to supply-side factors related, for instance, to nancial deregulation or excess savings by the rich. This chapter contributed to this debate by examining the extent to which local inequality in the U.S. is associated with household borrowing decisions over the period 1999-2015. To do so, I mobilized state-level Gini coe cients provided by Frank-Sommeiller-Price Series and household-level data from the Panel Study of Income Dynamics (PSID), in addition to other location-speci c information on housing prices and non-performing loans. This allows to study how income inequality in the household's state of residence is related to its decisions to take on debt over time. Speci cally, the empirical analysis also enables to have a glance at how rising local inequality a ects the frequency of debt across income groups. The adopted econometric speci cation builds on (non)-linear probability models to estimate the association between household income rank, local inequality and their interaction with the probability to hold debt.

The empirical evidence suggests that rising inequality at the state-level is associated with a decrease in the probability to hold debt. However, analyzing this e ect across income groups reveals that when local inequality increases, high-income households are less likely to be indebted than low-income households. To put it di erently, high-income households living in high-inequality states are less likely indebted than similar household living in low inequality states and vice-versa for poor households. This nding is in line with the "Keeping up with the Joneses" narrative documented by [START_REF] Drechsel-Grau | Falling behind: Has rising inequality fueled the american debt boom?[END_REF] at the macro-level and provides a local perspective to the Veblen e ects found by [START_REF] Carr | Relative income and indebtedness: Evidence from panel data[END_REF]. However, three limitations should be kept in mind. First, the evidence on the credit demand channel is only partial as PSID data lacks precision. Second, one should note that -in the spirit of the existing literature -the empirical analysis conducted here is not able to assert causality, hence more e ort should be conducted in this direction. Third, national inequality still matters because individuals are exposed to the same national TV and consequently, people in West Virginia can be in uenced by the consumption habits of high-income people in New York or elsewhere. In such a case, it is not just "Keeping up with the Joneses" but also "Keeping up with the Kardashians". Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to obtain a loan from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in nonlinear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to hold a mortgage or consumer loan from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. (1999)(2000)(2001)(2002)(2003)(2004)(2005) from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. [2007][2008][2009] from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. [2011][2012][2013][2014][2015] from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. 0.00

Main tables and gures

Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in nonlinear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. All householdspeci c controls are two-year lagged and replaced with their value at previous PSID wave. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to hold a mortgage or consumer loan from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. All household-speci c controls are two-year lagged and replaced with their value at previous PSID wave. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. 0.00

Main tables and gures 123

Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in nonlinear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. State-level Gini coe cients and household-level controls are replaced with their values at 1999 PSID wave. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to hold a mortgage or consumer loan from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. State-level Gini coe cients and household-level controls are replaced with their values at 1999 PSID wave. Robust standard errors clustered at the householdlevel (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. 0.00

Note: The table presents coe cient estimates for the probability to hold a mortgage from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. The sample is restricted to household who did not have an outstanding mortgage by 1999. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Area and time xed e ects are interacted to allow the latter to have disperse e ects across regions. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Robust standard errors clustered at the state-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS and marginal e ectscalculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Income ranks are measured by qunatiles. Robust standard errors clustered at the household (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. 0.00

Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS and marginal e ects -calculated at the mean value of the independent variables -from nonlinear probability models, estimated via pooled probit and panel probit random e ect estimation. A consistent estimator is computed for interaction terms in nonlinear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Income ranks are replaced by the levels of family incomes. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively.

Conclusions

This thesis aims to answer two research questions: (i) how do monetary policy decisions and in ation a ect income inequality? and (ii) what is the impact of rising inequality on credit dynamics? First, the interest in studying the side e ects of monetary policies on the income distribution stems from concerns raised by central banks interventions in the advanced economies following the 2008 nancial crisis. As a matter of fact, large asset purchase programs ultimately push up asset prices and favor the very wealthy, while the prevailing low interest rate environment has a negative impact on xed returns assets, which are typically held by modest households. The rst and second chapters of this thesis take a closer look at the distributional consequences of monetary policy and in ation. They depart from the existing research by particularly focusing on top incomes -which have largely contributed to the rising inequality pattern in most of the OECD economies -and adopting a historical analysis.

Second, growing inequalities have fostered a new stream of empirical research studying their macroeconomic consequences. Speci cally, the contribution of inequality to credit booms and the likelihood of nancial crises have received particular attention. The third and fourth chapters empirically focus on the inequality-credit nexus. Chapter 3 assesses the causal effect of rising top incomes on credit growth at the macro level, while chapter 4 examines the relationship between local inequality and household debt using U.S. micro-level data.

The purpose of this thesis is empirical hence several datasets are used. Data measuring the top of the income distribution are obtained from the World Inequality Database (WID). Other cross-country income inequality measures are mobilized from the Standardized World Income Inequality Database (SWIID) of [START_REF] Solt | Measuring income inequality across countries and over time: The standardized world income inequality database[END_REF]; and macroeconomic variables are extracted from the Jorda-Schularick-Taylor (JST) Macrohistory Database, which features data spanning more than a century of modern economic history. The rst, second and third chapters of this thesis build on these databases. Chapter 4 uses U.S. household-level data from the Panel Study of Income Dynamics (PSID), which is the longest running longitudinal household survey in the world. The adopted empirical methods borrow both from the most recent causal identi cation strategies in applied macroeconomics and standard (non)linear probability models. For instance, Chapter 1 and 3 use instrumental variables to estimate dynamic causal e ects by Local Projections, while chapter 4 relies on marginal e ects from probability models.

Speaking of the rst part of this thesis, the main empirical results document that exogenous changes in monetary conditions are not neutral with respect to the income distribution, which should make central bankers attentive to the fact that their policies may increase inequality. Furthermore, higher in ation is found to persistently and signi cantly reduce the national income share of the rich. Inasmuch as the empirical analysis here is linear, this evidence also echoes to the assertion that de ation is pro-inequality given that it favors the top of the income distribution. The second part, which focuses on the inequality-credit (debt) nexus, comes up with two important results: (i) top income shocks positively a ect the credit-to-GDP ratio and (ii) an increase in state-level inequality leads low and middle-income households living in high-inequality states to borrow more in comparison to similar households living in lowinequality states. In view of the extensive body of works showing the positive relationship between credit expansions and nancial stability, these results demonstrate that combating inequality should not only be motivated by social cohesion objectives but also by macroeconomic stability concerns. This thesis has also opened several questions that should be further investigated in future research. First, regarding the distributive e ects of monetary policy, more e orts should be conducted to understand how central banks' measures a ect other parts of the income distribution, especially poor and middle-class households. Although some recent research contributions have addressed this issue using household-level data over a short period of time, the historical approach should be preferred. The extension of the historical series on top incomes to middle and bottom income shares would be very welcome. Second, as in ation has now moved from the goods and services market to nancial markets, it is important to analyze how asset price in ation -which is at the heart of the transmission mechanism of unconventional monetary policies -impacts households balance sheets. In addition, there is now a consensus that greater inequality can lead to uncontrolled credit expansion and excessive household indebtedness. But more needs to be known about the relevant transmission mechanisms as well as the empirics underlying a direct causal relationship. Finally, the works featured in this thesis have mainly relied on pre-tax inequality measures. Further analyses involving inequality measures based on disposable income can improve our understanding of these issues. Notes: There are some years with missing values in each subperiod. As previously mentioned, the identi cation using an external instrument involves two stages.

Empirical results

The rst stage consists of regressing the residuals computed from the short-term interest rate equation of the panel-SVAR (equation A.1) on our external instrument. Table A.6 veri es if z i,t has the potential to be a valid instrument. The correlation between the instrument and the innovation in the short-term interest rate is perceived to be strong: the coe cient is signi cant at the 1% level and the F-statistic exceeds 22. Con dent in our instrument choice, we can now proceed to the second stage and comment on the panels presented in Note: This table shows baseline results from panel regressions with country and time xed e ects for the top 1% income share (column (1)), the top 10% income share (column (2)), the P1/B90 (column (3)), P10/B90 ratios (column (4)), the top 0.1% income share (column (5)). HAC standard errors are reported in parentheses. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively. Explanatory variables are de ned in Table B.1 in the Appendix. Note: This table shows results from panel regressions with country and time xed e ects for the top 1% income share using: Kuznets curve (column (1)), nancial openness (column (2)), labor disputes (column(3)), trade union (column (4), the communist in uence (column(5)), democracy (column ( 6)) and TFP (column ( 7)). HAC standard errors are reported in parentheses. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively. Explanatory variables are de ned in Table B.1 in the Appendix. Notes: Statistics are calculated from the cross-section sample of PSID waves (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). Statistics are weighted using PSID household weights. Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS with state-xed effects and standard errors clustered at the state-level. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Income ranks are replaced by the levels of family incomes. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS with state-xed effects and standard errors clustered at the state-level. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Income ranks are replaced by the levels of family incomes. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS with state-xed effects and standard errors clustered at the state-level. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Income ranks are replaced by the levels of family incomes. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively. Note: The table presents coe cient estimates for the probability to hold debt from a linear probability model, estimated via OLS with state-xed effects and standard errors clustered at the state-level. A consistent estimator is computed for interaction terms in non-linear models using the methodology of [START_REF] Ai | Computing interaction e ects and standard errors in logit and probit models[END_REF]. Income ranks are replaced by the levels of family incomes. Robust standard errors clustered at the household-level (in pooled estimations) are in parentheses. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively.

List of Figures

List of Tables

Figure 0 . 2 :

 02 Figure 0.2: Union membership and the top 10% income share in the U.S.

Figure 0 . 3 :

 03 Figure 0.3: The top decile income share: Europe and the U.S., 1900-2010

Figure 0 .

 0 Figure 0.4 depicts the evolution of the credit-to-GDP ratio in 12 advanced economies over the period 1980-2015. Over several decades, credit with respect to output has increased and seems to move with inequality mostly in the same direction, especially in the Anglo-Saxon countries. How can growing income inequality a ect credit dynamics?

Figure 0

 0 Figure 0.4: Credit-to-GDP ratio, 1980-2015

  Figure A.5 in the Appendix depicts the responses of the P1/P09 ratio for the full and post-WWII samples, suggesting that monetary tightening narrows the gap among top decile households.

Figure 1 .

 1 Figure 1.5 reports the non-cumulated IRFs of asset returns to a normalized +100 b.p. exogenous increase in the short-term interest rate via the instrument for the full and post-WWII samples.

Figure 1 . 1 :

 11 Figure 1.1: Top one percent LPs to a positive short-term interest rate shock

  (iv) the CPI in ation rate;(v) stock price growth; (vi) real per capita consumption growth; (vii) the level of nancial development; (viii) the level of commercial openness; (ix) house price growth; (x) government expenditure; (xi) real investment growth; (xii) total factor productivity growth; and (xiii) world GDP growth. We report the Kleibergen and Paap (2006) statistic for weak instruments. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively.

Figure 1 . 2 :

 12 Figure 1.2: Alternative distributional indicator responses to an interest rate shock

Figure 1 . 3 :

 13 Figure 1.3: Top one percent LP-IV responses to interest rates: Instrument robustness

Figure

  Figure 1.4: Sensitivity tests

Figure

  Figure 1.5: Insights on the income composition channel Total return on wealth

Figure

  Figure 1.6: r -g evidence Total wealth

Figure 1 . 7 :

 17 Figure 1.7: Top one percent LP responses to a positive short-term interest rate shock: statedependent e ects

Figure

  Figure B.1 in the Appendix shows the average income share of the top one percent and the in ation rate. The 1925-1939 period is characterized by both a de ationary environment and a high share of national income going to the top. During the inter-war period, in ation settled around 1 percent and P1 slightly decreased. The two world wars and the political transformations that followed resulted in relatively low income inequality (Piketty (2014) and Acemoglu et al. (2015)). Under the Bretton Woods system, in ation was moderate up to the latter half of the 1960s. During the 1970, average in ation rate drifted, fueled by in ationary U.S. poli-

  (a) of Figure B.2 in the Appendix).[START_REF] Saez | Wealth inequality in the United States since 1913: Evidence from capitalized income tax data[END_REF] have noticed for the last decades in the U.S. that the share of national income held by the top 0.1% grew even faster than that of P1. That is why we are interested in understanding the e ect of unexpected in ation on the ultra-rich. The impulse response shown in Graph (b) demonstrates that in ation reduces the top 0.1%'s income share. Although the coe cient estimates are noticeably lower than those obtained for P1, the semi-elasticity is comparable and slightly higher than 1. Besides that, the responses of percentile ratios (P1/B90 and P10/B90) in graphs (c) and (d) provide a picture of how in ation lowers the gap between top incomes and the rest of the population. Using the P1/P10 and P1/P9 ratios, we nd that in ation shocks also reduce inequality within the top of the distribution (see IRFs reported in FigureB.3 in the Appendix).

  .4. The e ect of unexpected in ation on P1 as found in the baseline model continues to hold, irrespective of the state of the economy. Particularly, business cycle uctuations (graphs (a) and (b)) and di erent in ation regimes (graphs (c) and (d)) do not change the response of P1 to an in ation shock. Interestingly, graph (e) shows that the negative e ect of surprise in ation is stronger when there are restrictions on capital mobility: the maximum impact on P1 is two times higher than that obtained when the economy is fully open. 11 This may unveil how top income households use arbitrage strategies and trade across global equity markets to diversify risk and avoid lower (real) asset returns due to in ation. Finally, we analyze how a country's political regime shapes the e ect of in ation on top incomes. The political economy model of

Figure 2 . 1 :

 21 Figure 2.1: Local Projection response of top 1% income share to a 100 bps in ation shock

Figure 2 . 2 :

 22 Figure 2.2: Local Projection responses of top 1% income share to a 100 bps in ation shock -Robustness checks

Figure 2 . 3 :

 23 Figure 2.3: Insights on the transmission channel

Figure 2 . 4 :

 24 Figure 2.4: Local Projection responses of top 1% income share to a 100 bps in ation shock: state-dependent e ects

  Growing income and wealth inequalities have recently become one of the de ning characteristics of the advanced economies. The notable work of[START_REF] Piketty | Capital in the 21st century[END_REF] has documented the lasting stagnation of median wages, and especially the expanding share in national income held by top income households. Such a pattern has prompted academic attention to study the potential consequences of inequality for the economy. Accordingly, it has been demonstrated

  -are used as additional indicators of top incomes. In robustness, we consider synthetic pre and post-tax measures of inequality over the whole income distribution, i.e., the Gini and net-Gini indices, which are obtained from the Standardized World Income Inequality Database (SWIID) of Solt (2020). 4 Figures C.1, C.2 and C.3 in the Appendix plot the sample-mean of top income shares and inequality measures over the studied period. 5

  (iii) real consumption growth; (iv) the change of the investment to GDP ratio; (v) government expenditures growth ; (vi) the CPI in ation rate; (vii) the change of the short-term interest rate; (viii) real broad money growth; (ix) stock price growth; (x) house price growth; (xi) the level of trade openness; (xii) the population growth, (xiii) the degree of capital account openness and (xiv) the top marginal tax rate.

  Figure C.8 in the Appendix show that top incomes have a positive and signi cant impact on

Figure 3 .

 3 Figure 3.4 depicts the impulse responses of the credit-to-GDP ratio to an exogenous inequality shock. First, a 100 b.p. increase in the gross and net Gini coe cients (graphs (a) and (b))

  (a) and (b), we consider time-varying coe cients for the post-1980 and 1990 periods, which coincide with nancial deregulation across OECD economies. The results indicate that the e ect of a top income shock on credit over GDP are stronger for periods during which the institutional environment has provided nancial institutions with the possibility to increase loan supply (the IRs in Figure C.9 of the Appendix also demonstrate that our main nding remains intact for shorter sample periods starting from the 1960s and 1970s). The IRs displayed in graphs (c) and (d) highlight that our empirical set-up is robust to di erent numbers of lags.

Figure 3

 3 Figure 3.1: Top 1% income share and total credit

Figure 3 . 2 :

 32 Figure 3.2: Top incomes and credit -Decomposition of total loans

  statistic for weak instruments. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively.

Figure 3 . 3 :

 33 Figure 3.3: Top incomes and credit -Di erent shares of the income distribution

Figure

  Figure 3.4: Top incomes and credit -Inequality measures

Figure

  Figure 3.5: Top incomes and credit -Robustness checks

Figure 3

 3 Figure 3.6: Top incomes and credit: post-1980s

Figure D. 1

 1 Figure D.1 takes a snapshot of income inequality across U.S. states using state-level Gini coe cients. Income inequality is on average highest in Southern states -with an average Gini coe cient of 60.77 -as well as in California and the Paci c Northwest i.e. Idaho, Oregon and Washington. While inequality at the national level in the U.S. substantially increased, Midwestern states stand out as they present the lowest levels of average inequality over the period 1999-2015. Figure D.2 depicts the debt-to-income ratio by state in the same way as the previous graph. One may be tempted to draw a comparison between the two maps. Inter-

Figure 4 . 1 :

 41 Figure 4.1: Local inequality and household's frequency of debt

Figure A. 2 :

 2 Figure A.2: Top income shares over time -12 countries

Figure A. 5 :

 5 Figure A.5: LPs to a positive short-term interest rate shock: P1/P09 ratio

Figure A. 6 :

 6 Figure A.6: LPs to a positive short-term interest rate shock: Post Korean-war sample

Figure A. 7 :

 7 Figure A.7: LPs to a positive short-term interest rate shock: capital income share

Figure A. 8 :

 8 Figure A.8: LPs to a positive short-term interest rate shock: labor income share

Figure A. 10 :

 10 Figure A.10: LP state-dependent e ects: monetary policy stance

Figure A. 11 :

 11 Figure A.11: LPs to a positive short-term interest rate shock: P10 income share response

Figure A. 12

 12 Figure A.12 presents impulse responses of the top one percent's income share and standard macroeconomic variables to a shock in the short-term rate. The left-hand panels display impulse responses when structural monetary shocks are identi ed using external instruments.The right-hand panels show the case where the standard Cholesky decomposition of the residuals is used to identify structural shocks. The presented panels feature the estimated impulse responses with 90% con dence bands, generated by bootstrapping methods.6

  Figure B.1: Average top 1% income share and in ation over time

Figure B. 2 :

 2 Figure B.2: Top income shares LPs to an in ation shock (P9 and P9/B90)

Figure B. 3 :

 3 Figure B.3: Top income shares LPs to an in ation shock (P1/P10 and P1/P9)

Figure C. 3 :

 3 Figure C.3: Percentile ratios -Average for 12 countries

Figure C. 9 :

 9 Figure C.9: Top incomes and credit -Shorter sample periods

Figure

  Figure C.11: Top incomes and (real) credit growth -Inequality measures

Figure 1 .

 1 Figure 1.1 Top one percent LPs to a positive short-term interest rate shock . . . .

  Figure 1.1 Top one percent LPs to a positive short-term interest rate shock . . . .

Figure 1 . 2

 12 Figure 1.2 Alternative distributional indicator responses to an interest rate shock .

Figure 1 . 3

 13 Figure 1.3 Top one percent LP-IV responses to interest rates: Instrument robustness Figure 1.4 Sensitivity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 . 5

 15 Figure 1.5 Insights on the income composition channel . . . . . . . . . . . . . . . .

Figure 1 .

 1 Figure 1.6 r -g evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 . 7

 17 Figure 1.7 Top one percent LP responses to a positive short-term interest rate shock: state-dependent e ects . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2 . 1

 21 Figure 2.1 Local Projection response of top 1% income share to a 100 bps in ation shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2 . 2

 22 Figure 2.2 Local Projection responses of top 1% income share to a 100 bps in ation shock -Robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2 . 3

 23 Figure 2.3 Insights on the transmission channel . . . . . . . . . . . . . . . . . . .

Figure 2 . 4

 24 Figure 2.4 Local Projection responses of top 1% income share to a 100 bps in ation shock: state-dependent e ects . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3 .

 3 Figure 3.1 Top 1% income share and total credit . . . . . . . . . . . . . . . . . . .

Figure 3 . 2

 32 Figure 3.2 Top incomes and credit -Decomposition of total loans . . . . . . . . .

Figure 3 . 3

 33 Figure 3.3 Top incomes and credit -Di erent shares of the income distribution . .

Figure 3 . 4

 34 Figure 3.4 Top incomes and credit -Inequality measures . . . . . . . . . . . . . .

Figure 3 . 5

 35 Figure 3.5 Top incomes and credit -Robustness checks . . . . . . . . . . . . . . .

Figure 3 . 6

 36 Figure 3.6 Top incomes and credit: post-1980s . . . . . . . . . . . . . . . . . . . .

Figure 4 . 1

 41 Figure 4.1 Local inequality and household's frequency of debt . . . . . . . . . . .

Figure A. 1

 1 Figure A.1 Sample mean of top income shares (P1 and P09) . . . . . . . . . . . . .

Figure A. 2

 2 Figure A.2 Top income shares over time -12 countries . . . . . . . . . . . . . . . .

Figure A. 3

 3 Figure A.3 Jorda, Schularick and Taylor-based IV: change in short-term interest rate in home and base countries . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure A. 4

 4 Figure A.4 LPs to a positive short-term interest rate shock: post-1980 . . . . . . . .

Figure A. 5

 5 Figure A.5 LPs to a positive short-term interest rate shock: P1/P09 ratio . . . . . .

Figure A. 6

 6 Figure A.6 LPs to a positive short-term interest rate shock: Post Korean-war sample Figure A.7 LPs to a positive short-term interest rate shock: capital income share .

Figure A. 8

 8 Figure A.8 LPs to a positive short-term interest rate shock: labor income share . .

Figure A. 9

 9 Figure A.9 Breakdown of nancial assets, as a share of total nancial assets, by income deciles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure

  Figure A.10 LP state-dependent e ects: monetary policy stance . . . . . . . . . . .

Figure A. 11

 11 Figure A.11 LPs to a positive short-term interest rate shock: P10 income share response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure

  Figure A.12 Top one percent Panel-SVAR-IV responses to a short-term interest rate shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure B. 1

 1 Figure B.1 Average top 1% income share and in ation over time . . . . . . . . . .

Figure B. 2

 2 Figure B.2 Top income shares LPs to an in ation shock (P9 and P9/B90) . . . . . .

Figure B. 3

 3 Figure B.3 Top income shares LPs to an in ation shock (P1/P10 and P1/P9) . . . .

Figure C. 1

 1 Figure C.1 Top incomes: Average for 12 countries . . . . . . . . . . . . . . . . . . .

Figure C. 2

 2 Figure C.2 Gini coe cients: Average for 12 countries . . . . . . . . . . . . . . . . .

Figure C. 3

 3 Figure C.3 Percentile ratios -Average for 12 countries . . . . . . . . . . . . . . . .

Figure C. 4

 4 Figure C.4 Credit-to-GDP ratio -Average for 12 countries . . . . . . . . . . . . . .

Figure C. 5

 5 Figure C.5 Loans share of total credit -Average for 12 countries . . . . . . . . . . .

Figure C. 6

 6 Figure C.6 Foreign Communist in uence index -Average for 12 countries . . . . .

Figure C. 7

 7 Figure C.7 Country-level foreign Communist in uence index . . . . . . . . . . . .

Figure C. 8

 8 Figure C.8 Top incomes and credit -Decomposition of (real) total loans . . . . . .

Figure C. 9

 9 Figure C.9 Top incomes and credit -Shorter sample periods . . . . . . . . . . . . .

Figure C. 10

 10 Figure C.10 Top incomes and (real) credit growth -Di erent shares of the income distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure C. 11

 11 Figure C.11 Top incomes and (real) credit growth -Inequality measures . . . . . . .

Figure C. 12

 12 Figure C.12 Top incomes and (real) credit growth -Robustness checks . . . . . . .

Figure D. 1

 1 Figure D.1 Income inequality across US states -Gini coe cient . . . . . . . . . . .

Figure D. 2

 2 Figure D.2 Debt-to-income ratio across US states . . . . . . . . . . . . . . . . . . .

Table 1 .

 1 1: Local projection-IV: First-stage results ∆ Short-term interest rate Year 0 Year 1 Year 2 Year 3 Year 4

	Full sample -IV	0.57*** 0.58*** 0.55*** 0.55*** 0.56***
		(0.12)	(0.12)	(0.12)	(0.13)	(0.13)
	F-statistic	21.97	23.06	19.94	18.25	18.01
	Observations	633	619	607	595	582
	Post-WWII sample -IV	0.53*** 0.53*** 0.52*** 0.52*** 0.52***
		(0.10)	(0.10)	(0.10)	(0.11)	(0.11)
	F-statistics	27.06	27.03	24.90	23.42	21.38
	Observations	565	552	540	528	515

Table 1

 1

	.2: Local projection: OLS and IV estimation results
	IV estimates -P1	Year 1 Year 2 Year 3 Year 4	Year 5
	Full sample
	∆ î	-0.13** -0.28** -0.39** -0.47** -0.44**
		(0.06) (0.11) (0.17)	(0.23)	(0.19)
	R 2	0.119	0.115	0.124	0.147	0.161
	Kleibergen-Paap	4.89	4.89	4.66	4.54	4.47
	Observations	633	619	607	595	582
	Post-WWII sample
	∆ î	-0.1111)	(0.10)	(0.11)
	R 2	0.118	0.139	0.168	0.174	0.186
	Kleibergen-Paap	4.46	4.49	4.35	4.30	4.11
	Observations	565	552	540	528	515
	OLS estimates -P1
	Full sample
	∆i	-0.04** -0.07** -0.13*	-0.19*	-0.16**
		(0.02) (0.03) (0.07)	(0.10)	(0.08)
	R 2	0.119	0.125	0.136	0.173	0.211
	Observations	656	641	629	617	604
	Post-WWII sample
	∆i	-0.02	-0.04	-0.07*	-0.12* -0.09***
		(0.02) (0.03) (0.04)	(0.07)	(0.03)
	R 2	0.130	0.158	0.178	0.188	0.206
	Observations	565	552	540	528	515

* -0.17** -0.19* -0.27*** -0.29** (0.06) (0.09) (0.

  as an indicator of nancial openness. Recently, Helpman (2018) argued that international trade is responsible for only a small part of the inequality increase: the skill-premium stemming from skill-biased technological change appears to have contributed more to the increase of inequality than trade liberalization (see[START_REF] Acemoglu | Skills, tasks and technologies: Implications for employment and earnings[END_REF] for a review). Total Factor Productivity (TFP) is the usual way to measure technological progress. We draw on the productivity database constructed byBergeaud et al.

(2016) that o ers estimates of TFP per hour worked over a long period. Financial development is another potential driver of inequality. The interaction between nance and inequality remains an open question. Although nancial development could make access to credit easier for nancially constrained households thereby reducing inequality (see

Table 2 .

 2 1: Long-run in ation and top income shares (Baseline) This table shows baseline results from panel regressions with country and time xed e ects for the top 1% income share (column (1)), the top 10% income share (column (2)), the P1/B90 (column (3)) and P10/B90 ratios (column (4)), the top 0.1% income share (column (5)). HAC standard errors are reported in parentheses. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively. Explanatory variables are de ned in TableB.1 in the Appendix.

		(1)	(2)	(3)	(4)	(5)
		P1	P10	P1/B90	P10/B90	P01
	In ation	-0.050*** -0.085*** -0.054** -0.195***	-0.011
		(0.016)	(0.024)	(0.023)	(0.059)	(0.008)
	GDPpc	0.542	0.734	3.085**	0.721	0.029
		(1.163)	(1.461)	(1.464)	(3.493)	(0.574)
	Education	-0.043*** -0.102*** -0.098*** -0.258*** -0.017*
		(0.012)	(0.024)	(0.028)	(0.059)	(0.009)
	Openness	7.366*** 9.563*** 12.863*** 22.673** 5.643***
		(2.273)	(3.589)	(4.898)	(8.910)	(1.236)
	Government spending	4.110	-7.434	-6.101	-17.139	3.677*
		(4.084)	(5.449)	(7.727)	(13.876)	(2.219)
	Fin. development	-0.639	-1.978	-4.530** -7.219**	-0.062
		(1.003)	(1.406)	(1.945)	(3.447)	(0.874)
	Population	2.283	-0.842	0.742	-3.497	0.451
		(1.953)	(2.023)	(3.562)	(5.534)	(1.030)
	Marg. tax	-6.175*** -6.743*** -8.148*** -12.133** -3.311***
		(1.285)	(2.055)	(2.353)	(5.046)	(0.639)
	Observations	210	191	191	191	164
	N countries	14	14	14	14	11

Note:

Table 2

 2

	.2: Long-run in ation and top income shares (Robustness checks 1)
		(1)	(2)	(3)	(4)	(5)
		Trend in ation Post-45	Post-70 Pre-2007 Without controls
	In ation	-0.046***	-0.033** -0.184*** -0.045**	-0.039***
		(0.007)	(0.015)	(0.065)	(0.017)	(0.013)
	GDPpc	1.053*	2.314**	5.206**	1.186
		(0.60)	(1.040)	(2.270)	(1.161)
	Education		-0.031*** -0.047*** -0.036***
			(0.010)	(0.018)	(0.012)
	Openness	7.33***	5.544***	1.589	10.379***
		(1.44)	(2.073)	(2.084)	(2.349)
	Government spending	5.23**	11.472***	5.773	1.997
		(2.29)	(3.791)	(4.333)	(3.998)
	Fin. development	-1.20**	-0.752	-1.501*	-0.287
		(0.51)	(0.845)	(0.779)	(1.255)
	Population	4.82***	6.385***	5.225**	1.703
		(0.97)	(1.511)	(2.511)	(2.053)
	Marg. tax	-5.58***	-6.644***	2.058	-5.824***
		(0.72)	(1.170)	(2.594)	(1.263)
	Observations	936	183	112	182	225
	N countries	14	14	14	14	14

Table 2 .

 2 3: Long-run in ation and top income shares (Robustness checks 2)

	(1)	(2)	(3)	(4)	(5)	(6)	(7)

Note: This table shows results from panel regressions with country and time xed e ects for the top 1% income share using: Kuznets curve (column (1)), nancial openness (column (2)), labor disputes (column(3)), trade union (column (4), the communist in uence (column(5)), democracy (column (

6

)) and TFP (column (

7

)). HAC standard errors are reported in parentheses. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively. Explanatory variables are de ned in Table

B

.1 in the Appendix.

Table 3

 3

			.1: OLS estimates
		(1)	(2)	(3)	(4)
	Dep. variable		Total Credit/GDP
		P1	P9	Gini	Net Gini
	Inequality measure	-0.30	-0.37	-0.21	-0.62
		(1.52)	(1.53)	(1.15)	(1.22)
	GDP per capita	-1.24 * * *	-1.21 * * *	-1.17 * * *	-1.18 * * *
		(0.26)	(0.26)	(0.35)	(0.33)
	Real Broad Money 0.66 * * *	0.70 * *	0.53 *	0.58 * *
		(0.21)	(0.23)	(0.24)	(0.22)
	Real House prices	0.17	0.13	0.38 * * *	0.36 * * *
		(0.16)	(0.16)	(0.08)	(0.08)
	R 2	0.878	0.873	0.812	0.812
	Countries	12	12	12	12
	Observations	717	679	607	607

All estimations include country and time xed e ects. Robust standard errors in parentheses.

* p < 0.10, * * p < 0.05, * * * p < 0.01

Table 3

 3

		.2: Local projection -IV: First-stage results
	Inequality	P1	P9	Net Gini P1 -Top marginal tax
	IV	-39.01*** -30.94*** -50.49***	-2.01***
		(3.47)	(5.05)	(4.90)	(0.57)
	Observations	662	654	546	654
	F	126.32	136.12	105.88	12.34

Note: Driscoll-Kraay robust standard errors are reported in parentheses below the coe cient estimates. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively.

Table 3

 3

	.3: Local projection: IV and OLS estimation results
	IV estimates -P1	Year 0 Year 1	Year 2	Year 3	Year 4	Year 5
	P1	0.37	0.93*	1.39**	2.16*** 2.85*** 3.12***
		(0.30)	(0.52)	(0.67)	(0.83)	(0.96)	(1.03)
	R 2	0.321	0.364	0.356	0.325	0.315	0.313
	Kleibergen-Paap	19.65	19.65	19.65	19.65	19.65	19.65
	Observations	662	662	662	662	662	662
	OLS estimates -P1
	P1	-0.19* -0.48*** -0.72*** -0.92*** -1.02*** -1.28***
		(0.10)	(0.16)	(0.20)	(0.24)	(0.29)	(0.33)
	R 2	0.346	0.424	0.435	0.441	0.449	0.446
	Observations	676	676	675	674	668	662

Table 4

 4

			.1: Average family income and total debt
				Percentiles
		10	25	50	75	90	95
	Family income 18,330	35,000	63,470	103,000	152,006	190,400
	Total debt	0	0	20,500	100,000	180,000	235,000

Table 4

 4

				.2: Estimates of Pr(Debt>0) -Baseline
		(1)	(2)	(3)	(4)	(5)	(6)
		LPM	Pooled Probit RE Panel Probit RE Panel Probit RE Panel Probit RE Panel Probit
	Income Decile	0.05 * * *	0.04 * * *	0.18 * * *	0.095 * * *	0.094 * * *	0.096 * * *
		(0.00)	(0.04)	(0.00)	(0.01)	(0.01)	(0.01)
	Gini	-0.25 * * *	-0.31 * * *	-0.87 * * *	-0.87 * * *	-0.70 * *	-0.23
		(0.09)	(0.10)	(0.30)	(0.30)	(0.31)	(0.39)
	Inc.Dec*Gini	-0.10 * * *	-0.14 * * *	-0.10 * * *	-0.11 * * *	-0.11 * * *	-0.12 * * *
		(0.025)	(0.03)	(0.03)	(0.03)	(0.03)	(0.03)
	Family income	0.05 * * *	0.09 * * *		0.30 * * *	0.303 * * *	0.30 * * *
		(0.00)	(0.01)		(0.04)	(0.04)	(0.039)
	Household size	0.004 *	0.005 * *	0.042 * * *	0.041 * * *	0.041 * * *	0.042 * * *
		(0.002)	(0.006)	(0.007)	(0.007)	(0.007)	(0.007)
	Age	0.016 * * *	0.019 * * *	0.078 * * *	0.08 * * *	0.08 * * *	0.079 * * *
		(0.00)	(0.00)	(0.00)	(0.00)	(0.005)	(0.005)
	Age 2	-0.00 * * *	-0.00 * * *	-0.001 * * *	-0.001 * * *	-0.001 * * *	-0.001 * * *
		(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
	African-American -0.06 * * *	-0.07 * * *	-0.34 * * *	-0.388 * * *	-0.39 * * *	-0.38 * * *
		(0.007)	(0.00)	(0.032)	(0.032)	(0.032)	(0.034)
	Single	-0.17 * * *	-0.19 * * *	-0.64 * * *	-0.63 * * *	-0.634 * * *	-0.63 * * *
		(0.01)	(0.01)	(0.03)	(0.032)	(0.03)	(0.03)
	Divorced	-0.1 * * *	-0.11 * * *	-0.41 * * *	-0.411 * * *	-0.412 * * *	-0.41 * * *
		(0.00)	(0.00)	(0.027)	(0.027)	(0.02)	(0.02)
	High-school	0.04 * * *	0.05 * * *	0.2 * * *	0.19 * * *	0.19 * * *	0.187 * * *
		(0.00)	(0.03)	(0.01)	(0.03)	(0.03)	(0.03)

Table 4 . 2 Table 4

 424

		.3: Estimates of Pr(Demand>0) -Demand channel
		(1)	(2)	(3)	(4)
		LPM	Pooled Probit RE Panel Probit RE Panel Probit
	Income Decile	0.00	-0.00	0.04 * * *	-0.00
		(0.00)	(0.01)	(0.00)	(0.01)
	Gini	-0.12 * *	-0.11 * *	-0.54 * *	-0.54 * *
		(0.05)	(0.05)	(0.23)	(0.25)
	Inc.Dec*Gini	-0.04 * *	-0.03 * *	-0.04 * *	-0.035 * *
		(0.02)	(0.02)	(0.01)	(0.02)
	Family income	0.03 * * *	0.03 * * *		0.16 * * *
		(0.01)	(0.00)		(0.03)
	Household size	0.01 * * *	0.00 * * *	0.04 * * *	0.04 * * *
		(0.00)	(0.00)	(0.01)	(0.01)
	Age	-0.01 * * *	-0.00 * * *	-0.03 * * *	-0.03 * * *
		(0.00)	(0.00)	(0.00)	(0.00)
	Age 2	0.00 * * *	0.00 * * *	0.00 * * *	0.00 * * *
		(0.00)	(0.00)	(0.00)	(0.00)
	African-American -0.02 * * *	-0.01 * * *	-0.09 * * *	-0.09 * * *
		(0.00)	(0.00)	(0.02)	(0.02)
	Single	-0.02 * * *	-0.02 * * *	-0.08 * * *	-0.08 * * *
		(0.01)	(0.00)	(0.02)	(0.02)
	Divorced	-0.04 * * *	-0.05 * * *	-0.30 * * *	-0.30 * * *
		(0.01)	(0.00)	(0.06)	(0.06)
	High-school	-0.02 * * *	-0.02 * * *	-0.08 * * *	-0.08 * * *
		(0.00)	(0.00)	(0.02)	(0.02)

Table 4

 4

			.4: Estimates of Pr(Debt>0) -Debt Decomposition
			Mortgages			Consumer Loans
		(1)	(2)	(3)	(4)	(5)	(6)
		LPM	Pooled Probit RE Panel Probit LPM Pooled Probit RE Panel Probit
	Income Decile	0.08 * * *	0.07 * * *	0.17 * * *	0.01 * * *	0.00	0.00
		(0.00)	(0.00)	(0.02)	(0.00)	(0.01)	(0.01)
	Gini	-0.33 * * *	-0.38 * * *	-1.60 * * *	-0.09	-0.09	-0.18
		(0.10)	(0.13)	(0.38)	(0.07)	(0.07)	(0.23)
	Inc.Dec*Gini	-0.12 * * *	-0.16 * * *	-0.14 * *	-0.03	-0.03	-0.03
		(0.03)	(0.04)	(0.05)	(0.02)	(0.02)	(0.07)
	Family income	0.06 * * *	0.02	0.15 * * *	0.06 * * *	0.10 * * *	0.35 * * *
		(0.01)	(0.01)	(0.05)	(0.01)	(0.00)	(0.03)
	Household controls	Yes	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.28	0.23		0.06	0.05
	Observations	62016	62016	62016	62016	62016	62016
	LR test (p -value)			0.00			0.00

Table 4 .

 4 5: Estimates of Pr(Debt>0) -Pre-crisis analysis(1999)(2000)(2001)(2002)(2003)(2004)(2005) The table presents coe cient estimates for the probability to hold debt during the pre-crisis period

			Total Debt			Mortgages			Consumer Loans
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
		LPM	Pooled Probit RE Panel Probit	LPM	Pooled Probit RE Panel Probit	LPM	Pooled Probit RE Panel Probit
	Income Decile	0.04 * * *	0.04 * * *	0.12 * * *	0.08 * * *	0.08 * * *	0.25 * * *	0.01 * *	0.00	0.00
		(0.00)	(0.00)	(0.02)	(0.00)	(0.00)	(0.03)	(0.00)	(0.00)	(0.02)
	Gini	-0.48 * * *	-0.58 * * *	-2.09 * * *	-0.48 * * *	-0.60 * * *	-2.74 * * *	-0.30 * * *	-0.30 * * *	-1.10 * * *
		(0.12)	(0.14)	(0.51)	(0.13)	(0.17)	(0.67)	(0.10)	(0.11)	(0.35)
	Inc.Dec*Gini	-0.12 * * *	-0.15 * * *	-0.19 * * *	-0.13 * * *	-0.18 * * *	-0.26 * * *	-0.07 * *	-0.06 *	-0.07 *
		(0.04)	(0.045)	(0.06)	(0.04)	(0.06)	(0.09)	(0.03)	(0.03)	(0.04)
	Family income	0.06 * * *	0.08 * * *	0.33 * * *	-0.07 * * *	-0.00	0.03	0.06 * * *	0.10 * * *	0.33 * * *
		(0.01)	(0.02)	(0.07)	(0.01)	(0.02)	(0.09)	(0.01)	(0.01)	(0.05)
	Household controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.24	0.20		0.28	0.23		0.054	0.048
	Observations	27596	27596	27596	27596	27596	27596	27596	27596	27596
	Nbr Individuals			7916			7916			7916
	LR Test (p -value)			0.00			0.00			0.00

Note:

Table 4 .

 4 6: Estimates of Pr(Debt>0) -Crisis analysis(2007)(2008)(2009) The table presents coe cient estimates for the probability to hold debt during the crisis period (

			Total Debt			Mortgages			Consumer Loans
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
		LPM Pooled Probit RE Panel Probit LPM Pooled Probit RE Panel Probit LPM Pooled Probit RE Panel Probit
	Income Decile	0.05 * * *	0.04 * * *	0.14 * * *	0.07 * * *	0.05 * * *	0.22 * * *	0.02 * * *	0.01 * *	0.04
		(0.01)	(0.00)	(0.03)	(0.01)	(0.00)	(0.06)	(0.01)	(0.00)	(0.02)
	Gini	0.02	0.00	-0.55	-0.09	-0.04	-0.04	0.27 * *	0.25 *	0.83 *
		(0.14)	(0.18)	(0.77)	(0.15)	(0.20)	(1.34)	(0.14)	(0.13)	(0.48)
	Inc.Dec*Gini	-0.08 * *	-0.11 * *	-0.12	-0.07 *	-0.10	-0.08	0.04	0.03	0.04
		(0.04)	(0.05)	(0.08)	(0.04)	(0.04)	(0.16)	(0.04)	(0.04)	(0.05)
	Family income	0.06 * * *	0.11 * * *	0.53 * * *	-0.03 * *	0.08 * * *	0.82 * * *	0.03 * *	0.06 * * *	0.24 * * *
		(0.02)	(0.03)	(0.11)	(0.02)	(0.03)	(0.20)	(0.01)	(0.06)	(0.07)
	Household controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.236	0.186		0.280	0.232		0.075	0.065
	Observations	13627	13627	13627	13627	13627	13627	13627	13619	13619
	Nbr Individuals			7617			7617			7617
	LR Test (p -value)			0.00			0.00			0.00

Note:

Table 4

 4 The table presents coe cient estimates for the probability to hold debt during the post-crisis period (

			.7: Estimates of Pr(Debt>0) -Post-Crisis (2011-2015)
			Total Debt			Mortgages			Consumer Loans
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
		LPM	Pooled Probit RE Panel Probit	LPM	Pooled Probit RE Panel Probit LPM Pooled Probit RE Panel Probit
	Income Decile	0.05 * * *	0.04 * * *	0.15 * * *	0.08 * * *	0.07 * * *	0.33 * * *	0.02 * * *	0.00	0.02
		(0.00)	(0.00)	(0.02)	(0.00)	(0.00)	(0.04)	(0.00)	(0.00)	(0.02)
	Gini	-0.19	-0.23	-0.91	-0.24 *	-0.27	-3.06 * *	-0.21 *	-0.22 *	-0.77 *
		(0.13)	(0.16)	(0.68)	(0.14)	(0.418)	(1.22)	(0.12)	(0.12)	(0.44)
	Inc.Dec*Gini	-0.10 * * *	-0.12 * *	-0.13 *	-0.14 * * *	-0.17 * * *	-0.50 * * *	-0.06 *	-0.05	-0.04
		(0.04)	(0.05)	(0.20)	(0.04)	(0.06)	(0.13)	(0.03)	(0.04)	(0.04)
	Family income	0.05 * * *	0.08 * * *	0.32 * * *	-0.06 * * *	0.01	0.12	0.06 * * *	0.11 * * *	0.40 * * *
		(0.01)	(0.02)	(0.08)	(0.01)	(0.02)	(0.13)	(0.01)	(0.02)	(0.06)
	Household controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.235	0.186		0.278	0.232		0.075	0.064
	Observations	20793	20780	20780	20793	20780	20780	20793	20780	20780
	Nbr Individuals			7680			7680			7680
	LR Test (p -value)			0.00			0.00			0.00

Note:

Table 4

 4

		.8: Estimates of Pr(Debt>0)
	Fully lagged controls -Total debt
		(1)	(2)	(3)
		LPM	Pooled Probit RE Panel Probit
	Income Decile	0.06 * * *	0.07 * * *	0.22 * * *
		(0.00)	(0.00)	(0.00)
	Gini	-0.21 * *	-0.28 * *	-0.80 * *
		(0.09)	(0.11)	(0.32)
	Inc.Dec*Gini	-0.12 * * *	-0.15 * * *	-0.14 * * *
		(0.03)	(0.04)	(0.04)
	Fam income	0.05 * * *	0.06 * * *	0.16 * * *
		(0.00)	(0.00)	(0.02)
	Household controls	Yes	Yes	Yes
	State controls	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.234	0.186
	Observations	53657	53657	53657
	Nbr Individuals			8220
	LR Test (p -value)

Table 4

 4

			.9: Estimates of Pr(Debt>0)
		Fully lagged controls -Mortgages and Consumer Loans
			Mortgage Debt			Consumer Loans
		(1)	(2)	(3)	(4)	(5)	(6)
		LPM	Pooled Probit RE Panel Probit LPM Pooled Probit RE Panel Probit
	Income Decile	0.06 * * *	0.07 * * *	0.27 * * *	0.03 * * *	0.03 * * *	0.10 * * *
		(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
	Gini	-0.35 * * *	-0.40 * * *	-1.86 * * *	0.02	0.02	0.24
		(0.10)	(0.13)	(0.41)	(0.07)	(0.23)	(0.24)
	Inc.Dec*Gini	-0.14 * * *	-0.19 * * *	-0.27 * * *	-0.02	-0.00	-0.02
		(0.03)	(0.04)	(0.05)	(0.03)	(0.08)	(0.03)
	Family income	0.05 * * *	0.07 * * *	0.28 * * *	0.01 * * *	0.01 * * *	0.05 * * *
		(0.00)	(0.00)	(0.02)	(0.00)	(0.01)	(0.01)
	Household controls	Yes	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	No	Yes	No
	Year FE	No	Yes	No	No	Yes	Yes
	R 2 /Pseudo R 2	0.274	0.223		0.058	0.05
	Observations	53657	53657	53657	53657	53657	53657
	LR Test (p -value)			0.00			0.00

Table 4

 4

		.10: Estimates of Pr(Debt>0)
	All controls from year 1999 -Total debt
		(1)	(2)	(3)
		LPM	Pooled Probit RE Panel Probit
	Income Decile	0.07 * * *	0.08 * * *	0.23 * * *
		(0.00)	(0.00)	(0.00)
	Gini	-0.52 * * *	-0.61 * * *	-1.65 * * *
		(0.13)	(0.15)	(0.56)
	Inc.Dec*Gini	-0.07 * *	-0.10 * *	-0.02
		(0.03)	(0.04)	(0.12)
	Household controls	Yes	Yes	Yes
	State controls	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.23	0.18
	Observations	58492	58492	58492
	LR Test (p -value)

Table 4

 4

			.11: Estimates of Pr(Debt>0)
		All controls from year 1999 -Mortgages and Consumer Loans
			Mortgage Debt			Consumer Loans
		(1)	(2)	(3)	(4)	(5)	(6)
		LPM	Pooled Probit RE Panel Probit	LPM	Pooled Probit RE Panel Probit
	Income Decile	0.07 * * *	0.09 * * *	0.28 * * *	0.03 * * *	0.03 * * *	0.11 * * *
		(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
	Gini	-0.42 * * *	-0.51 * * *	-2.05 * *	-0.57 * * *	-0.60 * * *	-1.91 * * *
		(0.15)	(0.18)	(0.81)	(0.1)	(0.11)	(0.34)
	Inc.Dec*Gini	-0.09 * * *	-0.12 * *	0.00	-0.11 * * *	-0.08 * * *	-0.18 * *
		(0.03)	(0.05)	(0.06)	(0.02)	(0.03)	(0.09)
	Household controls	Yes	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.26	0.21		0.054	0.05
	Observations	58492	58492	58492	58492	58492	58492
	LR Test (p -value)			0.00			0.00

Table 4

 4

	.12: Estimates of Pr(Mortgage>0)
	Households without outstanding mortgage in 1999
		(1)	(2)	(3)
		LPM	Pooled Probit RE Panel Probit
	Income Decile	0.08 * * *	0.07 * * *	0.17 * * *
		(0.00)	(0.01)	(0.02)
	Gini	-0.34 * *	-0.35 * * *	-1.80 * * *
		(0.1)	(0.29)	(0.42)
	Inc.Dec*Gini	-0.13 * * *	-0.16 * * *	-0.15 * * *
		(0.03)	(0.04)	(0.05)
	Family income	0.05 * * *	0.02	0.18 * * *
		(0.01)	(0.02)	(0.04)
	Household controls	Yes	Yes	Yes
	State controls	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.30	0.23
	Observations	58591	55064	55064
	LR Test (p -value)

Table 4

 4

			.13: Estimates of Pr(Debt>0)
			AreaxYear Fixed E ects
			Total Debt		Mortgages	Consumer Loans
		(1)	(2)	(3)	(4)	(5)
		LPM	Pooled Probit RE Panel Probit RE Panel Probit RE Panel Probit
	Income Decile	0.06 * * *	0.04 * * *	0.10 * * *	0.16 * * *	0.00
		(0.00)	(0.00)	(0.01)	(0.02)	(0.01)
	Gini	-0.30 * * *	-0.38 * * *	-1.23 * * *	-1.75 * * *	-0.31
		(0.10)	(0.12)	(0.34)	(0.43)	(0.25)
	Inc.Dec*Gini	-0.10 * * *	-0.14 * * *	-0.11 * * *	-0.15 * * *	-0.00
		(0.03)	(0.03)	(0.03)	(0.05)	(0.02)
	Family income	0.06 * * *	0.09 * * *	0.30 * * *	0.15 * * *	0.34 * * *
		(0.00)	(0.01)	(0.04)	(0.05)	(0.03)
	Household controls	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.236	0.187
	Observations	62016	62016	62016	62016	62016
	LR Test (p -value)			0.00	0.00	0.00

Table 4

 4

			.14: Estimates of Pr(Debt>0)
			State-clusters
		Total Debt	Mortgages	Consumer Loans
		(1)	(2)	(3)	(4)	(5)	(6)
		LPM	Pooled Probit	LPM	Pooled Probit LPM Pooled Probit
	Income Decile	0.05 * * *	0.04 * * *	0.08 * * *	0.17 * * *	0.01 * * *	0.00
		(0.01)	(0.00)	(0.01)	(0.01)	(0.00)	(0.02)
	Gini	-0.25	-0.31	-0.33	-0.38	-0.09	-0.10
		(0.17)	(0.21)	(0.20)	(0.27)	(0.15)	(0.16)
	Inc.Dec*Gini	-0.10 * * *	-0.14 * * *	-0.12 * *	-0.16 * *	-0.03	-0.03
		(0.03)	(0.04)	(0.05)	(0.07)	(0.04)	(0.04)
	Family income	0.06 * *	0.09 * * *	-0.06 * * *	0.02	0.06 * * *	0.10 * * *
		(0.02)	(0.03)	(0.02)	(0.04)	(0.01)	(0.02)
	Household controls	Yes	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.235	0.187	0.279	0.228	0.058	0.051
	Observations	62016	62016	62016	62016	62016	62016

Table 4

 4

				.15: Estimates of Pr(Debt>0)
				Income Quantiles
			Total Debt		Mortgages	Consumer Loans
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
		LPM	Pooled Probit RE Panel Probit Pooled Probit RE Panel Probit Pooled Probit RE Panel Probit
	Income Quantile	0.11 * * *	0.11 * * *	0.22 * * *	0.12 * * *	0.25 * * *	0.05 * * *	0.11 * * *
		(0.00)	(0.00)	(0.01)	(0.00)	(0.02)	(0.00)	(0.012)
	Gini	-0.31 * * *	-0.30 * * *	-0.84 * * *	-0.37 * * *	-1.57 * * *	0.10 * * *	-0.19
		(0.09)	(0.11)	(0.30)	(0.13)	(0.38)	(0.08)	(0.22)
	Inc.Dec*Gini	-0.19 * * *	-0.25 * * *	-0.19 * * *	-0.32 * * *	-0.27 * * *	-0.05	0.01
		(0.05)	(0.07)	(0.07)	(0.09)	(0.10)	(0.05)	(0.05)
	Family income	0.04 * * *	-0.07 * * *	-0.29 * * *	-0.06 * * *	-0.32 * * *	0.04 * * *	0.20 * * *
		(0.00)	(0.01)	(0.03)	(0.01)	(0.04)	(0.00)	(0.02)
	Household controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	State controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.24	0.19		0.23		0.05
	Observations	62016	62016	62016	62016	62016	62016	62016
	LR Test (p -value)			0.00		0.00		0.00

Note:

Table 4

 4

		.16: Estimates of Pr(Debt>0)
		Levels of income
		(1)	(2)	(3)
		LPM	Pooled Probit RE Panel Probit
	Gini	-0.56 * * *	-0.33 * * *	-0.91 * * *
		(0.14)	(0.11)	(0.31)
	Family income*Gini -0.35 * * *	-0.49 * * *	-0.37 * * *
		(0.07)	(0.124)	(0.12)
	Family income	0.19 * * *	0.23 * * *	0.61 * * *
		(0.00)	(0.01)	(0.01)
	Household controls	Yes	Yes	Yes
	State controls	Yes	Yes	Yes
	Macro-region FE	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes
	R 2 /Pseudo R 2	0.24	0.20
	Observations	62016	62016	62016
	LR Test (p -value)

Table A .

 A 1: Data sources and periods of top income shares

	Country	Period	Details
	Australia	1921-2015	WID (2019)
	Canada	1920-2010	WID (2019)
	Germany	1925-2013	WID (2019)
	Denmark	1920-2016	WID (2019)
	France	1920-2014	WID (2019)
	U.K.	1951-2014	WID (2019)
	Italy	1974-2009	WID (2019)
	Japan	1920-2010	WID (2019)
	Netherlands 1920-2012	WID (2019)
	Norway	1948-2011	WID (2019)
	Sweden	1943-2013	WID (2019)
	U.S.	1920-2016 WID (2019), Atkinson et al. (2015)

Table A .

 A 6: SVAR-IV -First-stage results

		Short-term interest rate
	IV	0.10***
		(0.02)
	R 2	0.04
	F-statistic	22.05
	Observations	707

Note: *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively.

Table B .

 B 3: Long-run in ation and top income shares (10-year average -Baseline)

		(1)	(2)	(3)	(4)	(5)
		P1	P10	P1/B90 P10/B90	P01
	In ation	-0.028*** -0.032*** -0.061*** -0.089*** -0.013***
		(0.008)	(0.008)	(0.014)	(0.022)	(0.004)
	GDPpc	0.160	0.904	2.575	0.603	0.072
		(1.539)	(2.256)	(1.754)	(5.619)	(0.778)
	Education	-0.050*** -0.100*** -0.092*** -0.251***	-0.016
		(0.016)	(0.026)	(0.032)	(0.068)	(0.011)
	Openness	5.725**	8.848** 10.662** 20.969** 6.200***
		(2.877)	(4.330)	(5.265)	(10.620)	(1.780)
	Government spending	4.532	-0.615	-0.247	0.774	3.253
		(6.193)	(7.226)	(11.659) (18.587)	(3.896)
	Fin. development	-0.950	-2.242	-5.180** -8.697**	-0.669
		(1.139)	(1.661)	(2.302)	(4.115)	(1.012)
	Population	4.148*	1.241	4.840	2.108	0.906
		(2.226)	(2.719)	(4.709)	(7.404)	(1.133)
	Marg. tax	-5.649*** -7.454*** -8.088*** -13.351* -3.478***
		(1.683)	(2.829)	(3.032)	(6.853)	(0.805)
	Observations	110	101	101	101	81
	N countries	14	14	14	14	11

Table B .

 B 4: Long-run in ation and top income shares (10-year average -Robustness 1) : This table shows baseline results from panel regressions with country and time xed e ects for the top 1% income share post-WWII (column (1)), the top 1% income share post-Bretton Woods (column (2)) and the top 1% income share in a speci cation without control variables (column (3)). HAC standard errors are reported in parentheses. *, ** and *** indicate statistical signi cance at the 10%, 5% and 1% levels, respectively. Explanatory variables are de ned in TableB.1 in the Appendix.

		Post-45	Post-70 Without controls
	In ation	0.019	-0.354***	-0.022***
		(0.095)	(0.086)	(0.004)
	GDPpc	1.978	7.825**
		(1.382)	(3.121)
	Education	-0.036*** -0.064**
		(0.013)	(0.032)
	Openness	4.416*	1.174
		(2.440)	(1.728)
	Government spending 13.916*** 9.058**
		(5.121)	(3.662)
	Fin. development	-0.857	-0.659
		(0.996)	(0.838)
	Population	7.427***	2.673
		(2.090)	(2.692)
	Marg. tax	-6.583***	6.119*
		(1.657)	(3.198)
	Observations	95	56	111
	N countries	14	14	14

Note

Table B .

 B 5: Long-run in ation and top income shares (10-year average -Robustness 2)

		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	In ation	-0.028*** -0.030*** -0.019*** -0.352*** -0.025*** -0.031*** -0.028***
		(0.008)	(0.006)	(0.006)	(0.084)	(0.008)	(0.005)	(0.008)
	GDPpr	-2.098	-0.168	1.361	10.383***	1.421	-0.387
		(6.869)	(1.807)	(1.440)	(3.147)	(1.383)	(1.755)
	GDPpc 2	0.357
		(0.940)
	Financial openness		0.023
			(0.021)
	Labour disputes			0.112
				(0.174)
	Trade union				0.110**
					(0.045)
	Communist in uence					-17.640**
						(6.882)
	Political institutions						7.501**
							(3.625)
	Technical progress							0.134
								(0.135)
	Observations	110	104	88	56	110	110	110
	N countries	14	13	12	14	14	14	14

Table C

 C The table presents coe cient estimates of the e ect of inequality on credit dynamics using the foreign communist in uence as an IV. Robust standard errors are in parentheses. All speci cations include country xed-e ects. Statistical signi cance at the 1%, 5%, and 10% levels are indicated by ***, **, and * respectively.

	.3: Second-stage estimates : Total Credit/GDP -static regressions
		(1)	(2)	(3)	(4)	(5)	(6)
		P1	P9	P01	Gini	Net Gini P1/B90
	Inequality measure	7.06 * * * 12.66 * * * 0.181 * * * 5.26 * * *	5.37 * * * 4.81 * * *
		(1.67)	(1.80)	(0.03)	(0.00)	(0.01)	(0.67)
	Real GDP	0.007	0.009	0.003	0.013	0.012	0.006
		(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.009)
	Government expenditures -0.05	0.13	0.09	0.05	0.11	-0.09
		(0.04)	(0.18)	(0.19)	(0.22)	(0.23)	(0.18)
	Real broad money	0.64 * *	0.94 * * *	0.41	0.44 *	0.52 * * * 0.90 * * *
		(0.26)	(0.3)	(0.27)	(0.24)	(0.23)	(0.29)
	Interest rate	0.00	-0.01	0.012	-0.001	-0.001	-0.007
		(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.009)
	Commercial Openness	0.55 * *	0.49 * *	-0.58 * *	-0.55 * *	-0.14	0.29
		(0.22)	(0.21)	(0.23)	(0.22)	(0.23)	(0.19)
	Population	-0.98	10.79 *	-10.40 *	-0.04	0.19	6.53
		(0.64)	(6.08)	(5.16)	(0.55)	(0.72)	(5.70)
	Financial openness	0.002 * *	0.001	0.003 * * * 0.003 * * * 0.003 * * * 0.002 *
		(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
	Consumption	-0.006	0.003	-0.002	-0.004	-0.004	0.003
		(0.00)	(0.00)	(0.00)	(0.008)	(0.00)	(0.007)
	Year dummies	Yes	Yes	Yes	Yes	Yes	Yes
	Observations	686	604	560	546	546	604
	Countries	12	12	12	12	12	12

Note:

Table D

 D

	.1: Summary statistics -Mean values
	Variables	Mean Std. Dev.
	Households with debt 0.59	0.48
	Family income	76,860	57,050
	Age	44.47	12.01
	Household size	3.18	1.55
	Sex	0.72	0.44
	African-American	0.37	0.48
	Married	0.60	0.48
	Non-educated	0.12	0.32
	Observations	62,016

Table D

 D Statistics are calculated from the cross-section sample of PSID waves(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). Statistics are weighted using PSID household weights. Table D.4: State-xed e ects, StatexYear xed e ects and clusters at the state-level (Baseline)

			(1)	(2)	(3)
		Total debt Mortgages Consumer loans
	Income Decile	0.05 * * *	0.08 * * *	0.01 * * *
			(0.01)	(0.01)	(0.00)
	Inc.Dec*Gini	-0.11 * * *	-0.12 * *	-0.05
			(0.04)	(0.05)	(0.04)
	Family income	0.05 * *	-0.06 * * *	0.05 * * *
			(0.02)	(0.02)	(0.01)
	Household controls	Yes	Yes	Yes
	State FE		Yes	Yes	Yes
	Year FE		Yes	Yes	Yes
	StatexYear FE		Yes	Yes	Yes
	R 2	.2: Summary statistics -Mean values 0.257 0.291 0.076
	Observations		62016	62016	62016
	Variables	Low (D1-D4) Middle (D5-D8) High (D9 + Top 10%)
	Family income	21,596.77	62,603.35	145,452
	Total debt	14,120.83	56,556.21	110,090
	Debt-to-income	0.52		0.86	0.82
	Age	40.94		44.74	48.53
	Household size	2.97		3.21	3.38
	Sex	0.37		0.48	0.96
	Married	0.24		0.69	0.91
	Non-educated	0.23		0.09	0.02
	Observations	19,644		27,016	15,356

Notes:

Table D .

 D 5: State-xed e ects, StatexYear xed e ects and clusters at the state-level (pre-crisis period: 1999-2005)

		(1)	(2)	(3)
		Total debt Mortgages Consumer loans
	Income Decile	0.05 * * *	0.08 * * *	0.01 * *
		(0.01)	(0.01)	(0.00)
	Inc.Dec*Gini	-0.04 * *	-0.14 * *	-0.08
		(0.06)	(0.07)	(0.05)
	Family income	0.06 * *	-0.07 * *	0.06 * * *
		(0.03)	(0.03)	(0.02)
	Household controls	Yes	Yes	Yes
	State FE	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes
	StatexYear FE	Yes	Yes	Yes
	R 2	0.25	0.3	0.07
	Observations	13627	13627	13627

Table D .

 D 6: State-xed e ects, StatexYear xed e ects and clusters at the state-level (crisis period: 2007-2009)

		(1)	(2)	(3)
		Total debt Mortgages Consumer loans
	Income Decile	0.04 * * *	0.07 * * *	0.02 * * *
		(0.01)	(0.01)	(0.00)
	Inc.Dec*Gini	-0.04	-0.03	-0.07
		(0.05)	(0.06)	(0.06)
	Family income	0.06 *	-0.03	0.03 * * *
		(0.03)	(0.03)	(0.02)
	Household controls	Yes	Yes	Yes
	State FE	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes
	StatexYear FE	Yes	Yes	Yes
	R 2	0.25	0.3	0.07
	Observations	13627	13627	13627

Table D .

 D 7: State-xed e ects, StatexYear xed e ects and clusters at the state-level (post-crisis period: 2011-2015)

		(1)	(2)	(3)
		Total debt Mortgages Consumer loans
	Income Decile	0.04 * * *	0.08 * * *	0.01 * * *
		(0.01)	(0.01)	(0.00)
	Inc.Dec*Gini	-0.14 * * *	-0.15 * * *	-0.09 * *
		(0.03)	(0.05)	(0.05)
	Family income	0.03	-0.06 * * *	0.06 * * *
		(0.02)	(0.02)	(0.01)
	Household controls	Yes	Yes	Yes
	State controls	Yes	Yes	Yes
	State FE	Yes	Yes	Yes
	Year FE	Yes	Yes	Yes
	StatexYear FE	Yes	Yes	Yes
	R 2	0.26	0.29	0.07
	Observations	20793	20793	20793

Table 1 .

 1 1 Local projection-IV: First-stage results . . . . . . . . . . . . . . . . . . . Table 1.2 Local projection: OLS and IV estimation results . . . . . . . . . . . . . . Table 2.1 Long-run in ation and top income shares (Baseline) . . . . . . . . . . . Table 2.2 Long-run in ation and top income shares (Robustness checks 1) . . . . . Table 2.3 Long-run in ation and top income shares (Robustness checks 2) . . . . . Table 3.1 OLS estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 3.2 Local projection -IV: First-stage results . . . . . . . . . . . . . . . . . . Table 3.3 Local projection: IV and OLS estimation results . . . . . . . . . . . . . . Table 4.1 Average family income and total debt . . . . . . . . . . . . . . . . . . . . Table 4.2 Estimates of Pr(Debt>0) -Baseline . . . . . . . . . . . . . . . . . . . . . Table 4.3 Estimates of Pr(Demand>0) -Demand channel . . . . . . . . . . . . . . . Table 4.4 Estimates of Pr(Debt>0) -Debt Decomposition . . . . . . . . . . . . . . . Table 4.5 Estimates of Pr(Debt>0) -Pre-crisis analysis (1999-2005) . . . . . . . . . Table 4.6 Estimates of Pr(Debt>0) -Crisis analysis (2007-2009) . . . . . . . . . . . Table 4.7 Estimates of Pr(Debt>0) -Post-Crisis (2011-2015) . . . . . . . . . . . . . Table 4.8 Estimates of Pr(Debt>0) Fully lagged controls -Total debt . . . . . . . . Table 4.9 Estimates of Pr(Debt>0) Fully lagged controls -Mortgages and Consumer Loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 4 .

 4 10 Estimates of Pr(Debt>0) All controls from year 1999 -Total debt . . . . .

Table 4 .

 4 11 Estimates of Pr(Debt>0) All controls from year 1999 -Mortgages and Consumer Loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Table 4.12 Estimates of Pr(Mortgage>0) Households without outstanding mortgage in 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 4.13 Estimates of Pr(Debt>0) AreaxYear Fixed E ects . . . . . . . . . . . . . . Table 4.14 Estimates of Pr(Debt>0) State-clusters . . . . . . . . . . . . . . . . . . . Table 4.15 Estimates of Pr(Debt>0) Income Quantiles . . . . . . . . . . . . . . . . . Table 4.16 Estimates of Pr(Debt>0) Levels of income . . . . . . . . . . . . . . . . . .

However, it also has some drawbacks in terms of e ciency (see[START_REF] Ramey | Macroeconomic shocks and their propagation[END_REF] on the e ciency/ exibility trade-o of LP).

As noted by[START_REF] Jordà | The e ects of quasi-random monetary experiments[END_REF], adding time xed e ects would require almost one hundred additional parameter estimates.

The de nition of income includes labor as well as business and capital incomes.

We conduct our empirical analysis while excluding the years of WWII from the sample. TableA.1 in the Appendix traces out the data sources and their availability for each country.

The time coverage of the Gini coe cients is fairly shorter than that of our baseline top income variable.

Our sample is restricted only because of the limited availability of top income data.

The persistence of our results is particularly consistent with the recent evidence ofJordà et al. (2019) indicating that monetary policy -based on a historical panel data for 17 advanced economies and using the macroeconomic policy trilemma to identify monetary surprises -a ects TFP, capital accumulation, and output for a very long

time. 14 This result also holds for the post-Korean war sample presented in Figure A.6 of the Appendix, which corresponds to the last episode of large spikes in government spending due to wars.

The identi cation shock scheme adopted by[START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF] is di cult to replicate in the context of our study because (i) our country sample is much smaller than theirs (ii) and macroeconomic forecasts o ered by Consensus Economics are only available as of the 1990s.

Such evidence should be cautiously interpreted, as[START_REF] Herbst | Bias in local projections[END_REF] recently nd that impulse responses from LPs can be severely biased in the context of small sample sizes.

This contrasts with the responses of the top 10% income share (P10), which are likely to be driven by that of P1 (see IRFs reported in Figure A.11 of the Appendix).

These variables are obtained from the Jordà-Scularick-Taylor (JST) Macrohistory database. Their construction and historical dynamics are lengthily discussed inJordà et al. (2019).

 19 The IRFs of the capital income and labor income shares to an exogenous monetary policy shock -depicted in Figures A.7 and A.8 of the Appendix -are also consistent with this interpretation of the income composition

channel.20 The main idea of[START_REF] Piketty | Capital in the 21st century[END_REF] states that inequality and the capital share of national income systematically move up as r -g grows. However, Piketty considers this gap to have a more potent e ect on wealth inequality.

We are unable to conduct such a test for the monetary policy stance because the e ect of each regime (i.e., monetary tightening/easing) is estimated in a separate LP speci cation.

† This chapter is co-authored with Jakob de Haan and Aurélien Leroy. It is under review in the Review of Income and Wealth.1 The evolution of top income shares as such has received signi cant attention in the literature on inequality since the seminal works of[START_REF] Piketty | Capital in the 21st century[END_REF] and[START_REF] Piketty | Income inequality in the United States, 1913-1998[END_REF]. In fact, it is now well established that the growing income inequality witnessed since the 1980s in the developed world is, to a large extent, the result of a sharp increase of top incomes (see e.g.,[START_REF] Alvaredo | The top 1 percent in international and historical perspective[END_REF] and[START_REF] Alvaredo | Global inequality dynamics: New ndings from WID.world[END_REF]).

The LP approach has several advantages over VARs. LP is (i) more robust to model misspeci cation, (ii) does not su er from the curse of dimensionality, (iii) can more easily accommodate non-linearities and (iv) can also be estimated with simple regression techniques.

By considering contemporaneous macroeconomic variables, our identifying assumption is equivalent to a Cholesky identi cation whereby P1 would be ordered at the top.

International nancial openness is approached by the capital mobility index (which ranges from 0 to 100) introduced by[START_REF] Quinn | Assessing measures of nancial openness and integration[END_REF].

In our robustness analysis, we also estimate equation 2.3 using trend in ation. The latter is obtained from a standard Hodrick-Prescott lter.

Note that these controls are the same as in[START_REF] Roine | The long-run determinants of inequality: What can we learn from top income data[END_REF] with the exception of education.

The sample standard deviation of in ation amounts to 4.

Tables B.3, B.4 and B.5 in the Appendix report the same tests using 10-year averages.

The size of the coe cient of the foreign Communist in uence variable could be explained by the fact that this variable is capturing several historical and institutional arrangements, which are instrumental for the dynamics of inequality.

The countries are: Australia, Canada, Denmark, France, Germany, Italy, Japan, the Netherlands, Norway, Sweden, the U.K. and the U.S.

This instrument assumes that there are potential contagion of political changes, of which politicians are aware, and that the probability of contagion depends on the cultural proximity between the countries, which seems to be reasonable assumptions.

This means, for instance, that the Australian foreign income tax in uence corresponds to the average top marginal tax rates of the U.K., the U.S. and Canada. For Germany, the instrument is the average of the French, Danish and Dutch top marginal tax rates.

We thank Jakob B. Madsen for providing us with data on the foreign communist in uence.

We use Driscoll-Kraay standard errors that account for heteroskedasticity as well as for temporal and spatial dependence in the residuals.

The strength of the instrument is similar during the periods1950-1970 and 1980-2010.

The results are unchanged when using a simple IV regression instead of Local Projections (see TableC.3 in the Appendix).

The increase in business loans does not, however, indicate whether it favors small or large rms. Recent evidence by[START_REF] Doerr | Income inequality, nancial intermediation, and small rms[END_REF] shows that a higher share of income accruing to top earners reduces deposits that banks use to fund small businesses and depresses job creation.

See Flow of Funds (2020), Board of Governors of the Federal Reserve System (U.S.).

It is important to note that other factors contribute to reinforce the "Keep up with the Joneses" behavior. For instance,[START_REF] Schor | The Overspent American: Why We Want What We Don't Need[END_REF] emphasizes the role played by television and other medias in providing individuals with di erent consumption standards than they have experienced.

The authors rely on the index developed by[START_REF] Brown | Does wage rank a ect employees' well-being? Industrial Relations[END_REF] as a measure of relative income. It assumes that social comparisons are made with reference to some outside group above the income scale rather than the entire distribution. In practice, the index computes -at the household level -the share of families with income greater than a given family (either by state of residence, education level or race group) and is regressed afterwards on the change in the debt-to-income ratio.

Banking deregulation is also associated with an increase in banks risk-taking behavior. For instance Dick

Information on student loans and other debts are only available from the 2011 wave.

Total income is considered in the PSID as the sum of wages and salaries plus income from professional practice and self-employment, rental income, interest, dividends, and transfer payments, as well as business and farm income.

This is obviously a partial way to assess the credit demand channel. Ideally, one should mobilize data on households who applied for a loan, regardless of whether they got it or not. However, such an information is not available in the PSID questionnaire.

The number of panel units, i.e. household heads followed for each sample period are reported in the bottom of corresponding tables.

Given that we estimate the VAR in levels, we marginally change the construction of our instrumental variable by considering the level of the interest rate of the base country rather than its rst-di erence.

 5 Because we are interested only in the e ects of exogenous uctuations in monetary conditions, we do not have to identify all the coe cients of B.

In the same way as[START_REF] Mertens | The dynamic e ects of personal and corporate income tax changes in the united states[END_REF] and[START_REF] Gertler | Monetary policy surprises, credit costs, and economic activity[END_REF], we use wild bootstrap with 1000 draws.

Acknowledgments A D Appendix of Chapter 4

In robustness to the LPs setting, we consider a panel-SVAR to generate the IRF of the top one percent's income share following an exogenous shock to the short-term rate. 1 Structural VARs are the traditional approach to identify structural monetary policy shocks and simultaneously trace out the corresponding impulse responses. We assume that our multicountry panel can be described by a small monetary SVAR extended to include the top income variable. Hence, our VAR contains six endogenous variables: the (log) WTI annual price (W T I t ), the top one percent's share of national income (P 1), the (log) real GDP (y i,t ), the (log) CPI (π i,t ), the nominal short-term interest rate (r i,t ) and the (log) of stock prices (s i,t ). 2 Let X i,t = (W T I t , P 1 i,t , y i,t , π i,t , r i,t , s i,t ) be a vector of the six endogenous variables.

The reduced form of the model can be represented as follows:

where the indices t and i relate to years and countries; µ i corresponds to country xed e ects; L represents the number of lags on the endogenous variables included in the model, set at two according to the Akaike information criterion; A l are 6 * 6 matrices of unrestricted coe cients;

and nally, ν i,t is a vector of reduced form residuals related to a set of structural shocks as follows:

where B is an invertible matrix of coe cients and ε i,t a vector of structural shocks.

To disentangle the causal chain of events and identify structural shocks of interest, di erent approaches exist. The standard one is Cholesky decomposition: it considers timing assumptions based on contemporaneous restrictions among the shocks in the VAR, which is typically done by assuming that B is a lower triangular matrix. 3 In particular, monetary policy shocks 1 We thank Ambrogio Cesa-Bianchi for providing his MATLAB toolbox for VAR analysis. 2 The VAR is estimated in log-levels, which allows for possible co-integration relationships between the variables [START_REF] Sims | Inference in linear time series models with some unit roots[END_REF].

3 Another common way to identify exogenous changes in the short-term rate is the narrative approach of [START_REF] Romer | A new measure of monetary shocks: Derivation and implications[END_REF]. This is the strategy adopted, for instance, by [START_REF] Coibion | Innocent bystanders? monetary policy and inequality[END_REF] and [START_REF] Furceri | The e ects of monetary policy shocks on inequality[END_REF] to study the distributional e ects of monetary policy. Nonetheless, this identi cation strategy is not tractable in our case because it requires (at least) forecasts of short-term interest rates, in ation and GDP growth, are identi ed as innovations to the short-term interest rate, which do not contemporaneously a ect macroeconomic conditions. However, when using annual data, this identi cation scheme is questionable at best. Therefore, to identify the coe cients of matrix B, we consider a di erent strategy and adopt an external instrument approach. The latter replicates the work of [START_REF] Mertens | A reconciliation of svar and narrative estimates of tax multipliers[END_REF], [START_REF] Gertler | Monetary policy surprises, credit costs, and economic activity[END_REF] and [START_REF] Stock | Identi cation and estimation of dynamic causal e ects in macroeconomics using external instruments[END_REF]. In practice, this identi cation strategy is implemented in three steps. First, the reduced form of the panel-SVAR model (eq. A.1) is estimated equation-by-equation with a xed e ect estimator, which allows us to obtain the reduced-form residuals (ν X i,t ) along with an estimate of unrestricted coe cients (A l ). Then, the reduced-form residual of the short-term interest rate equation (ν r i,t ) is regressed on the instrumental variable (z i,t ) as de ned for local projections (i.e., rst-stage regression). 4 Finally, the tted value of the short-term interest rate ( νr i,t ) is regressed by OLS on the reduced-form residual (ν i,t ).

Because the instrument z i,t is supposed to be orthogonal to all structural shocks with the exception of innovations to monetary conditions, equation A.3 below provides contemporaneous responses of the endogenous variables to a one-unit interest rate shock. The dynamic response is then obtained by A i and forward iteration.

where b denotes the column of interest in matrix B, which corresponds to the impact of the structural interest-rate shock (ζ r i,t ) on each element of the vector ν i,t . 5

We compare between this external instrument identi cation strategy and the standard Cholesky decomposition. In such case, the vector of endogenous variables has the following order: W T I t , P 1 i,t , GDP i,t , CP I i,t , r i,t and s i,t .

which are not available over the long run.

negative shocks to the short-term interest rate, which implies that monetary policy loosening increases the top one percent's income share. A typical concern in the monetary VAR literature is the nding of a price puzzle, i.e., the fact that unexpected monetary tightening leads to increased in ation. Hence, a necessary requirement is to check the consistency of our external instrument with standard macroeconomic predictions. First, we observe that the estimated shape of the in ation response to an exogenous perturbation in monetary conditions does not exhibit counter-intuitive e ects. Indeed, the estimated impulse response is negative, even though it is not statistically signi cant at the 90% con dence level (which is in line with the nding of [START_REF] Gertler | Monetary policy surprises, credit costs, and economic activity[END_REF]). Second, the dynamic e ects of monetary policy on real GDP and stock prices are fairly standard. Two years after the shock, monetary tightening induces a reduction in GDP of approximately 1.5% and a decline in stock prices of more than 2% (since both variables enter the VAR in log-level).

A B

Appendix of Chapter 2 (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). This doctoral thesis contributes to the empirical analysis of the distributional effects of monetary policies and the macroeconomic implications of rising inequality. The monetary policy measures implemented in the advanced economies following the 2008 financial crisis have raised several concerns regarding their potential side effects on the income and wealth distributions. In addition, the context of growing inequality since the 1980s raises questions about its consequences on credit dynamics and macroeconomic stability. The first and second chapters of this thesis examine the distributional implications of monetary policy and inflation on top incomes from a historical perspective. The third and fourth chapters focus on understanding the impact of rising inequality on credit expansions and household debt, both at the macro level and from a granular perspective.

List of Tables

Keywords:

Monetary policy; Credit and household debt; Top incomes; Income inequality Titre : Dynamiques de crédit, politique monétaire et inégalités Résumé:

Cette thèse de doctorat contribue à l'analyse empirique des effets distributifs des politiques monétaires et des conséquences macroéconomiques de l'augmentation des inégalités. Les mesures de politiques monétaires mises en oeuvre dans les économies avancées suite à la crise financière de 2008 ont soulevé plusieurs inquiétudes quant à leurs effets indésirables sur les distributions de revenus et de patrimoine. En outre, le contexte d'inégalité croissante depuis les années 1980 soulève des questions quant à ses conséquences sur les dynamiques du crédit et la stabilité macroéconomique.

Les premier et deuxième chapitres de cette thèse s'intéressent aux effets distributifs de la politique monétaire et de l'inflation sur les hauts revenus dans une perspective historique. Les troisième et quatrième chapitres s'attachent à comprendre l'impact de la hausse des inégalités sur l'expansion du crédit et l'endettement des ménages, tant au niveau macroéconomique que dans une perspective granulaire.

Mots