Vivien Georges
email: gvivienh@psemail.eu

Julienne Houngbonon

Liang

Georges V Houngbonon
email: georges-vivien.houngbonon@ecp.fr

Julienne Liang
email: julienne.liang@orange.com

Broadband Internet and Income Inequality *

Keywords: Broadband Internet, Income Inequality, Telecommunications. JEL Classification: D31, L96, O15

published or not. The documents may come

Introduction

Broadband Internet is a more advanced telecommunications technology that provides faster access to the Internet. It enables users to access information online and communicate with other users at lower cost. Within a decade, it has been adopted by the vast majority of households in developed economies. According to the Organization for Economic Co-operation and Development (OECD), up to 90% of households in its region have access to fixed broadband Internet in 2016.1 This massive adoption have been associated with a dramatic spread of online services, among which job search and posting. According to a nationwide survey conducted in France, a growing share of broadband users, particularly in the low-income segment, rely on their household's Internet connection to search for jobs. This usage pattern is likely to affect household's income, as suggested by [START_REF] Roller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF] and [START_REF] Czernich | Broadband Infrastructure and Economic Growth[END_REF], and more specifically its distribution.

In the meantime, full coverage of faster broadband Internet has become an important policy objective in several countries. The European Commission has designed a "Digital Agenda for Europe" targeting large coverage of high-speed broadband Internet access. This agenda has been declined into national policies. In France for instance, the government is aiming for full coverage of the territory by 2020. Similar objectives have been set in the United States "National Broadband Plan". However, there is still a lack of evidence about the effects of broadband Internet on the distribution of income, and particularly at the household level.

In this paper, we take advantage of a unique town-level data to investigate the effects of broadband adoption and quality on the distribution income using data from France. Our data set provides information about the yearly number of fixed broadband subscribers and the distribution of download speed per town, from 2009 to 2013. We complement these data with town-level distribution of income as well as socio-demographic characteristics. Broadband adoption is measured by the penetration rate, that is the ratio of the number of users to the number of households. Broadband quality is measured by the median download speed. We use the Gini index as well as inter-decile ratios as measures of income inequality. Ordinary Least Squares (OLS) estimates suggest that broadband adoption and quality raise mean income and lower income inequality. However, these effects could be biased by the endogeneity of broadband Internet diffusion.

We rely on measures of signal attenuation of broadband Internet, a time-invariant variable which strongly determines the trend in broadband adoption and quality. Interestingly, signal attenuation is predetermined by the initial deployment of the historical telephony network, and does not directly affect the distribution of income. In addition, this variable is a better measure of the distance between users and local exchanges, a typical instrument for broadband adoption [START_REF] Czernich | Broadband Infrastructure and Economic Growth[END_REF][START_REF] Czernich | Does broadband internet reduce the unemployment rate? Evidence for Germany[END_REF]. Following [START_REF] Duflo | Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment[END_REF], we implement a Wald Difference-in-Difference (Wald-DiD) estimation strategy, whereby the interaction between time and signal attenuation serves as an instrument for both broadband penetration and download speed.

The Wald-DiD estimates confirm the sign of the OLS estimates. More specifically, both broadband adoption and quality raise mean income, and lower income inequality. A percentage point increase in broadband penetration raises mean income by 0.14% and lowers the Gini index by 0.0005 unit, that is 1% of standard deviation. Likewise, 1 megabit per second (Mbps) additional increase in download speed raises mean income by 0.04% and lowers the Gini index by 0.0002 unit, that is 0.4% of standard deviation. Using the inter-decile ratios as measures of income inequality, we find that the positive effects of broadband Internet on income inequality is driven by a relatively greater benefit accruing to the bottom deciles, particular the second to the fifth deciles. These findings are robust to initial conditions which could drive trends in income inequality and broadband diffusion.

We use these estimates to conduct some counterfactual analyses. First, we find that between 2009 and 2013 in France, broadband adoption alone contributes to 34% of income growth and 80% of inequality reduction, while quality improvement accounts for 6% and 20% respectively.

Second, a percentage point increase in broadband penetration raises income per capita by 0.06%, not far from the estimates by [START_REF] Czernich | Broadband Infrastructure and Economic Growth[END_REF], while 1 Mbps increase in download speed raises income per capita by 0.02%. Third, the effects of broadband penetration is non-linear with maximal impact at early stage of diffusion, when the penetration rate is below 50%. Finally, we also find that the positive effects of broadband Internet on income distribution depends on education, measured by the number of years of schooling. Higher level of education, as well as lower inequality in education, increase the magnitude of the effects of broadband Internet.

The findings of this paper are closely related to literature on the economic effects of Information and Communication Technologies (ICT). [START_REF] Roller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF] and [START_REF] Czernich | Broadband Infrastructure and Economic Growth[END_REF] study the effects of telecoms infrastructure on income per capita but did not investigate the effects on income inequality. Recent studies on inequality include [START_REF] Forman | The Internet and Local Wages: A Puzzle[END_REF] who investigate the effects of ICT investment on the wage gap between US counties. However, they did not focus on household broadband usage. [START_REF] Akerman | The Skill Complementarity of Broadband Internet *[END_REF] use detailed micro data for Norway and find that skilled workers' wages are improved when firms start to use broadband.

The remaining of the paper is organized as follows. Section 2 summarizes the related literature, emphasizing the lack of studies on the effects of broadband Internet on income inequality.

Section 3 presents some background information about the diffusion of broadband Internet in France. Section 4 introduces the data along with some descriptive statistics. Section 5 presents the econometric model and discusses the estimation strategy. Section 6 presents the results and section 7 concludes.

Related literature

As reviewed by [START_REF] Bertschek | The economic impacts of telecommunications networks and broadband internet: A survey[END_REF], the economic effects of ICT have been the topic of a vast literature, starting from the early 90s. Most studies have investigated the effects of ICT on several economic outcomes such as gross domestic product (GDP), employment and productivity, but few have evaluated its effects on income inequality.

Early empirical studies such as [START_REF] Cronin | Telecommunications Infrastructure and Economic Growth[END_REF], [START_REF] Madden | CEE Telecommunications Investment and Economic Growth[END_REF] and [START_REF] Roller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF] were conducted at the country level and find positive effects of telecommunications infrastructure on economic growth. For instance, [START_REF] Roller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF] use country-level data from the OECD member countries and find that 10 percentage points increase in the penetration rate of fixed telephony raises GDP per capita by 0.45%. These effects become substantially larger when the penetration rate of fixed telephony is higher than the critical mass of 40%, due to network externalities. As suggested by [START_REF] Lam | Economic Growth, Telecommunications Development and Productivity Growth of the Telecommunications Sector: Evidence around the World[END_REF] and [START_REF] Chakraborty | Mainline' Telecommunications Infrastructure, Levels of Development and Economic Growth: Evidence from a Panel of Developing Countries[END_REF], the positive effects of telecommunications infrastructure on income are also found in developing countries. More specifically, [START_REF] Gruber | Mobile telecommunications and the impact on economic development[END_REF] also find positive effects for mobile telephony. [START_REF] Czernich | Broadband Infrastructure and Economic Growth[END_REF] is the closest to our paper as they investigate the effects of fixed broadband Internet. Using country level data from the OECD, they find that 10 percentage point increase in fixed broadband penetration raises gross national income per capita by 0.9-1.5 percentage point. As in [START_REF] Roller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF], they also investigate and find a critical mass of 20% above which the effects of broadband on income becomes larger. However, their study was conducted at the country level and they did not estimate the impact on income distribution.

Country-level studies may suffer from differences in unobserved institutional features such as competition and regulatory policies, even though they use country fixed-effects or rely on a set of countries with similar level of development. Some recent studies investigate the effects of telecommunications infrastructure at the infra-country level, thus controlling for institutional differences. For instance, [START_REF] Yilmaz | Geographic and Network Neighbors: Spillover Effects of Telecommunications Infrastructure[END_REF] use state-level data from the US to study the effects of telecommunications infrastructure investment on output growth. [START_REF] Shiu | Causal Relationship between Telecommunications and Economic Growth in China and its Regions[END_REF] and [START_REF] Ward | Mobile telecommunications service and economic growth: Evidence from China[END_REF] investigate similar effects in China. These studies suggest that the positive effects of telecoms investment typically apply to high-income areas.

To investigate the underlying mechanisms of the relationship between telecoms investment and economic growth, some recent papers have analyzed the effects on employment and productivity. Basically, broadband Internet tends to promote employment and raise wages, but with mixed effects on productivity. More specifically, [START_REF] Kolko | Broadband and local growth[END_REF] use county-level data from the US and find positive effects of the number of broadband providers on employment. Likewise, [START_REF] Forman | The Internet and Local Wages: A Puzzle[END_REF] find that investment in Internet has raised wages and employment, but only in very few counties, the overall effect being not significant. Using town-level data from Germany, [START_REF] Czernich | Does broadband internet reduce the unemployment rate? Evidence for Germany[END_REF] find no effects of broadband availability on unemployment rate. [START_REF] Ivus | The employment and wage impact of broadband deployment in Canada[END_REF] find that in Canada the effects of broadband on employment is positive only in the services sector.

Regarding productivity, [START_REF] Bertschek | More bits-more bucks? Measuring the impact of broadband internet on firm performance[END_REF] in Germany find positive and significant effects of broadband usage on firms' innovation activities, but no effect on labor productivity.

In the same vein, [START_REF] Colombo | ICT services and small businesses' productivity gains: An analysis of the adoption of broadband Internet technology[END_REF] in Italy find that the adoption of basic broadband application does not increase firms' productivity, however higher speed broadband can increase productivity if combined with strategic and organizational changes. Likewise, [START_REF] Bertschek | The economic impacts of telecommunications networks and broadband internet: A survey[END_REF] in Germany find that labor productivity increases with the share of employees with mobile Internet access. However, the effects on productivity may depend on sectors. For instance, [START_REF] Greenstein | Modern Telecommunications Infrastructure and Economic Activity: An Empirical Investigation[END_REF] show that telecommunications investment has positive impact on firms' revenue in technology-intensive sectors such as finance, insurance and real estate. On the contrary, they find no effect in the manufacturing sector.

This paper takes a closer look at the distribution of income, thus going beyond average income.

To the best of our knowledge, the literature has not yet dealt with the effects of broadband on income inequality. One exception is [START_REF] Forestier | Can information and communication technologies be pro-poor?[END_REF] who rely on country-level data and find a positive correlation between the penetration rate of fixed telephony and inequality.

Background on broadband Internet in France

Broadband Internet has been deployed in France since 2000. Until 2013, the majority of the broadband coverage of the territory is provided by digital subscriber line (DSL) technologies via the incumbent operator's copper network. This network consists of about 33 million lines, deployed during several decades to provide fixed telephony. It covers the entire territory and spreads over more than 15,800 local exchanges. It was, therefore, not designed to convey DSL signals and provide DSL access. Indeed, the propagation of DSL signals is weaken over long distances. This signal attenuation is measured in decibels (dB) and depends on the distance traveled and the diameter of the copper lines. The eligibility threshold for a DSL line corresponds to a maximum signal attenuation of 78 dB, allowing a nominal speed up to 512 Kilobits per second (Kbps), or slightly more than 5 km for a copper pair with a diameter of 0.4 mm.

The length of the copper line, between the local exchange and the household, has no major impact on fixed telephony. However, it introduces a wide disparity in access to broadband Internet. Thus, while households located near the local exchange can enjoy a speed of more than 20 Megabits per second (Mbps), those over 5 km away cannot benefit from broadband access. The longest lines are mostly located in rural areas, but also in areas which have been recently urbanized. At the end of 2013, less than 1% of the lines were not eligible for broadband services via DSL technology.

In order to improve DSL quality in terms of speed, the incumbent operator has progressively upgraded the copper local loop which consists of bringing optical fiber to the sub-distributor and keeping the copper network for the last miles, that is between the sub-distributor and the households. Such an operation is therefore faster and less costly than fiber-to-the-home (FTTH) deployment and can be an alternative and temporary solution before future FTTH deployment. After the operation, the majority of the inhabitants concerned will benefit from speed higher than 5 Mbps. With ADSL2+ or VDSL technology the theoretical speed could increase to respectively 25 Mbps or 50 Mbps, provided that the distance does not exceed 2.5 km or 1 km.

Figure 1 presents the evolution of broadband Internet penetration rate in France. ADSL is the main technology among all broadband connections. It still represents 90% of fixed broadband connections, compared to 6% for cable and 3% for FTTH. The total broadband subscribers have increased from 19.1 Million in 2009to 24.3 Million in 2013. More than 5 Million households have adopted broadband access during this period.

The rapid growth in broadband Internet usage is having a dramatic effect both on private and public sectors. The online environment has become a more efficient alternative to traditional offline setting. Broadband Internet access provides consumers with an abundance of products and services in a short amount of time. The Internet offers a centralized solution and increase the efficiency in many usages. According to a national survey conducted in France (CREDOC, 2014), 48% of interviewees use Internet for social networking, 47% to download music, 25% for job search, 51% for administrative procedures and 51% for online shopping.

In terms of usage evolution, an increasing number of individuals used the Internet to search for job. In 2006 only 16% interviewees used Internet for job search. This number has risen to 19% in 2009 and 25% in 2013. One person in two (55%) in 2013 (instead of 40% in 2008) used the Internet for administrative procedure and income tax return (for people aged 18year-old population and more). For income tax return, only 7.4 Million households in 2009 used Internet for the declaration compared to 14.7 Million in 2014. Other usage growth is also observed in e-commerce. In addition, more than one person in two used Internet for shopping.

If the number of people concerned did not change between 2011 and 2012, the volumes of transaction, 45 Billion Euros in e-commerce in 2012, compared with 38 Billion Euros in 2011, were steadily increasing due to the increase in the average number of transactions per buyer.

Depending on the income level, the usage of Internet may vary. In general, high-income people use more Internet than low-income people whether for e-administration, e-commerce, or for entertainment. However, job search and social networking are two exceptions. According to CREDOC (2014), 31% of low-income individuals used the Internet to search for job, compared to 18% of high-income individuals.

The European Commission cares about the quality of broadband Internet access in terms of download speed. In September 2016, it announced that by 2025 all European households should have access to connections with speed of at least 100 Mbps. The Commission proposed "a new European Electronic Communications Code including forward-looking and simplified rules that make it more attractive for all companies to invest in new top-quality infrastructures, everywhere in the EU, both locally and across national borders". According to the Commission, these investments could "boost the GDP of the EU by an additional 910 billion Euros and create 1.3 million new jobs by 2025".

2009-2013

Source: National telecoms regulator statistics (ARCEP).

Data and descriptive statistics

Data

We build a panel of 5,021 French towns over 5 years, from 2009 to 2013.2 This set of towns represents 75% of the French population. The panel is slightly unbalanced with 4.8 observations per town on average. For each town, we obtain information on broadband adoption and quality, income distribution, as well as socio-demographic characteristics.

The broadband data comes from the French incumbent operator, but covers all households, including the customers of its rivals. It includes the number of residential connections under the major technologies, that is cooper (xDSL), cable and fiber (FTTH) technologies, and the distribution of maximal download speeds. 3We calculate broadband penetration per town as the ratio of the number of residential connections to the number of households. We use the distribution of maximal download speeds to construct the median download speed per town as our measure of the quality of broadband Internet access. This way of measuring quality is consistent with the framing of broadband policies. Typically, they aim at increasing the speed available to a certain proportion of the population. For instance, the European Commission aims at providing at least 100 Megabits per second to half European households by 2020.

Interestingly, the broadband data also provides a measure of signal attenuation. This measure the intensity of data transmission signal, expressed in decibels, and is highly correlated with the distance between users' premises and local exchanges. In general, the longer the distance, the greater the noise. It is time-invariant and strongly determines the quality of broadband Internet. The greater the noise, the lower is the quality of broadband Internet access. It is exogenous because predetermined by the traditional telephony network. It will be useful for our identification strategy. This variable mimics the distance between users' premises and local exchanges as used in [START_REF] Czernich | Does broadband internet reduce the unemployment rate? Evidence for Germany[END_REF]. We obtain measures of signal attenuation conducted by the incumbent operator in 2009.

The income distribution data comes from the national statistical office (INSEE). It includes the deciles of income, the mean income, and the Gini coefficient of inequality, available for towns with at least 2000 inhabitants to protect tax payers' privacy. Income is measured at the household level as total earnings per unit of consumption, before taxation and social benefits.

As such, the observed income distribution is not affected by ex-post redistribution policies.

We do not observe income generated from some online sharing platforms such as Airbnb that households were not requested to report to the tax administration. We use both the Gini index as well as inter-deciles ratios as measures of inequality.

Town-level socio-demographic characteristics also come from INSEE and include the distribution of age and education. We use both the average and standard deviation of age and education as controls for socio-demographic characteristics of the population.

Table A-1 in the Appendix presents the data along with their summary statistics.

among 8.6 million available connections in France, corresponding to a take-up rate of 16%. For fiber technology, we estimated the total number of lines by multiplying the incumbent's number by a surcharge coefficient given that we know the number of incumbent's FTTH consumers per town and that its market share is around 70% on FTTH.

Descriptive statistics

In Table 1 we present the characteristics of the 5021 towns in 2013 and compare with national statistics. It turns out that our sampled towns are richer, more educated, more densely populated and more unequal. The average income is 26758 euros compared to 23,634 euros at the country level. On average, 42% of adults graduated from college compared to 37% at the country level. The average population density is 8 times larger and the Gini coefficient is 0.31 on average, compared to 0.29 at the country level. These features are characteristics of urban areas. Table 2 presents the initial level and the evolution of broadband internet and income inequality in these areas.

Broadband adoption was already significant in 2009. The average penetration rate stood at 54%, meaning that more than half of the households had access to broadband Internet in 2009.

It spanned from 16% to 146% in 2009.4 By 2013, average broadband adoption increased by 11 percentage points up to 65%, corresponding to a yearly increase of 2.2 percentage points.

The lowest and largest penetration rates rose respectively to 21 and 181%. This rising trend reduces heterogeneity in broadband adoption across towns, suggesting a convergence. The standard deviation drops from 9.4 in 2009 to 9.2 in 2013.

In the meantime, the quality of broadband Internet access, measured by the median download speed, has improved. The average download speed doubled between 2009 and 2013, from 6.5 Mbps to 13 Mbps. This improvement in quality stems from the deployment of faster broadband technologies such as cable, VDSL and fiber.5 More importantly, quality improvement also reflect DSL network upgrade which basically consists in reducing the distance between users' premises and local exchanges. Contrary to the convergence in broadband adoption, we observe rising heterogeneity in the quality of broadband Internet across towns. The standard deviation of the median download speed more than doubled between 2009 and 2013, from 2.8 to 6.7.

Variation in broadband penetration is positively correlated to variation in broadband quality.

As can be observed from Figure A-1 in the Appendix, larger increase in broadband penetration is observed in towns with higher increase in the median download speed. This positive correlation is driven by the effect of quality on the valuation of Internet access. In addition, and as emphasized in the background section, variation in broadband quality is strongly determined by the signal attenuation. Towns with smaller signal attenuation experience bigger increase in the quality of broadband Internet access. As a consequence, the penetration rate of broadband Internet increases more in towns with smaller signal attenuation. This negative correlation is depicted in Figure 2 by the downward sloping linear fit.

Mean income grew at 2.3% per year between 2009 and 2013. Given a yearly average inflation rate of 1.4%, the yearly growth rate of real income is 0.9%. Cross-town income heterogeneity, as measured by the coefficient of variation, the ratio of standard deviation to the average income, does not change significantly. The coefficient of variation remains flat at 0.28. Therefore, there is not enough variations to study cross-town inequality.

On average, within-town income inequality, measured by the Gini index at the town level, rises slightly between 2009 and 2011 before falling afterwards. The average Gini index rises from 0.319 in 2009 to 0.320 in 2011, and falls to its initial level in 2013. This break in the trend of income inequality is primarily due to a change in economic policies as the political power switched from the right to the left-wing in 2012. We introduce year fixed effects into the econometric model to account for this break.

Overall, income inequality tends to falls between 2009 and 2013. As shown in Figure 2, the magnitude of this falls tends to be smaller in towns with higher signal attenuation. It turns out that there is a negative relationship between the diffusion of broadband Internet and income inequality, driven by the magnitude of signal attenuation. We exploit this relationship in order to estimate the causal impact of broadband Internet on income inequality.

Econometric model and estimation

This section presents the econometric model and the estimation strategy.

Econometric model

The effects of Internet diffusion on income inequality stem from several sources. In this paper, we focus on the short-term effects of broadband internet usage by households. By doing so, we discard wage effects stemming from factors productivity, as well as long-term effects stemming from health and education.

Households' Internet usage can affect their income mainly due to employment. It eases access to job information and improve the quality of job matching. In addition, wider Internet adoption by other households generates demand for electronic equipment that could boost labor demand, and creates the virtual network necessary for the deployment of online platforms dealing with new economic activities such as e-commerce, search and social-networking.

The impact of Internet adoption on households' income may differ according to their profiles due to differences in terms of usage and skill biases. While some households mainly use Internet access for leisure, others use it for job purposes. As emphasized in the background section, poor households are more likely to search for job on the Internet. Likewise, the labor demand generated by the wider diffusion of the Internet can be biased in favor of lowskilled workers. While the creation and maintenance of Internet platforms require high-skilled workers, the delivery of goods to end-users heavily relies on low-skilled workers.

In order to test the effect of broadband Internet on income distribution, we specify the following reduced-form econometric model:

Y = α + βP + γX + (1)
Where Y is a measure of income inequality in the population, typically the Gini index. We take advantage of the availability of income deciles by using inter-decile ratios as alternatives measures of income inequality. These latter enable us to identify, when relevant, losers and winners from broadband Internet. We also use average income as a dependent variable in order to estimate the overall effect of broadband Internet on income.

P denotes the measure of broadband adoption. In the context of significant penetration rate in advanced countries, the impact of quality upgrading, using cable or fiber technology, has become a more important policy question. We estimate the impact of quality q by replacing penetration in equations (1). We expect the impact of quality on income distribution to be qualitatively similar to the impact of adoption because the two are positively correlated.

X is a vector of households' socio-demographic characteristics including the distribution of age and education. is a vector of unobservables including wage productivity stemming from firms, household's labor supply and income shocks.

Estimation strategy

We introduce town and year fixed effects into equation (1) in order to account for time invariant wage effects as well as common income shocks. The estimated equation can be expressed as:

Y it = α + βP it + γX it + µ i + ν t + ε it (2)
Ordinary Least Squares estimate of parameter β in equation ( 2) would be biased due to unobserved labor supply and the correlation between the unobserved determinants of income inequality and households' preferences for broadband Internet. In order to identify the causal impact of broadband Internet on income inequality, we implement a Wald-differencein-difference (Wald-DiD) estimation strategy which basically corresponds to the ratio of the DiD in income distribution to the DiD in broadband Internet. We use a Wald-type estimator because towns differ only in the intensity of treatment and, as a result, do not allow implementing a sharp DiD, but rather a fuzzy DiD. As suggested by Figure 2, difference in treatment intensity is mainly driven by the time-invariant and exogenous signal attenuation. This latter does not directly affect the distribution of income, because it is predetermined by the initial structure of the fixed telephony network. Therefore, it can be used a group variable.

Causal identification relies on the assumption that variation in income inequality is identical across towns with the same level of signal attenuation. As emphasized by de Chaisemartin & D'Haultfoeuille (2017), the wald-DiD can be biased when treatment effect is unstable or heterogeneous. We assume stability and homogeneity of the treatment effect.

The Wald-DiD estimator writes:

β = (Y it -Y it ) -(Y jt -Y jt ) (P it -P it ) -(P jt -P jt )
Where i and j index two groups of towns, with different level of signal attenuation, and t and t index time.

Implementing the Wald-DiD with a continuous group variable amounts to using the interaction of signal attenuation and time as an instrument for broadband Internet in equation ( 2).

This estimator is similar to the one used by [START_REF] Duflo | Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment[END_REF] in the evaluation of the impact of school construction on education and wage in Indonesia.6

We employ an alternative identification strategy that relies on cross-sectional variations in broadband Internet and inequality and controls for initial conditions.

Results

This section presents the main results, some robustness checks and policy implications.

Main results

Table 3 presents a synthesis of the main results. Detailed results are presented in Tables A-2

to A-7 in the appendix.

We start by estimating the impact of broadband Internet on mean income and present the main results in the first column of Table 3. Overall, mean income increases with broadband adoption and quality. A percentage point increase in broadband penetration raises mean income by 0.20%, according to the OLS estimate, and 0.14%, according to the Wald-DiD estimate. Likewise, 10 Mbps increase in broadband download speed raises mean income by respectively 0.1% and 0.4%.

The Wald-DiD estimate of the impact of broadband adoption is smaller than the OLS estimate, contrary to the estimate of the impact of broadband quality. This is because variation in income is positively correlated with variation in broadband adoption but negatively correlated with variation in quality. Indeed, larger variation in income is observed in poorer towns where variation in broadband adoption is stronger while variation in quality is weaker. However, Wald-DiD estimates are less precise than OLS'. The confidence interval of the Wald-DiD overlaps that of the OLS estimates.

As discussed in section 4.2, broadband penetration increases by 2.2 percentage point per year.

The Wald-DiD estimate implies that mean income should rise by 0.31%, compared to 0.9% overall increase in mean income. Therefore, broadband adoption contributes to the third of the increase in mean real income between 2009 and 2013. Similarly, average download speed increase by 1.3 Mbps per year, implying 0.05% yearly rise in mean income. Therefore, broadband quality accounts for 6% of the increase in mean income between 2009 and 2013.

The second column of Table 3 presents The remaining columns of Table 3 report the estimates when income inequality is measured by inter-decile ratios, that is the ratio of bottom deciles to the ninth decile. Using this dependent variable enable us to identify winners and losers from the diffusion of broadband Internet. It turns out that the inequality reducing effect of broadband Internet is mainly driven by a relative improvement in the income of the bottom deciles. Figure 3 depicts the OLS and Wald-DiD point estimates of the effect of broadband Internet on inter-deciles ratios. While, the first decile seems not to be affected by broadband Internet, we observe that the second to the fifth deciles benefit relatively more from broadband Internet than the top income deciles.

Regarding the controls, Tables A-2 to A-7 in the appendix show that there is no relationship between income and age probably because income is per consumption unit. Income inequality is lower in towns where the population is more aged or more educated. In addition, income inequality is higher in towns where the population is more heterogeneous in terms of demographics and education. Finally, the year fixed effects exhibits the break in the trend of income inequality, rising from 2009 to 2011 and falling afterwards.

The instrumental variable estimation strategy underlying the Wald-DiD estimates passes all standard statistical tests. In particular, the first-stage F-statistic is greater than 300 in the case of broadband penetration and 1000 in the case of broadband download speed. These statistics are largely above the critical threshold of under-identification, meaning that signal attenuation is a strong predictor of broadband adoption and quality. In addition, Stock and Yogo's weak identification test statistic is also above its critical threshold, rejecting the hypothesis that the interaction between time and signal attenuation is a weak instrument.

Ȳit G it R i1t R i2t R i3t R i4t R i5t R i6t R i7t R i8t
Panel

Robustness checks

We test the robustness of the Wald-DiD estimates with respect to initial conditions. Indeed, the negative relationship between broadband Internet and income inequality may be driven by difference across towns in terms of initial conditions. We specify the following model, in accordance with [START_REF] Forman | The Internet and Local Wages: A Puzzle[END_REF]:

Y iT -Y i0 = α + β(P iT -P i0 ) + γ(X iT -X i0 ) + λX i0 + ε i (3)
This equation regresses variations of the dependent variable Y over variations of broadband Internet P , controlling for variation in characteristics X and initial characteristics X 0 . The initial date, denoted by 0, is set to 1999, before the deployment of broadband Internet:

P i1999 =0.
T , the final date, is set to the year 2013. The outcomes of the estimation are qualitatively similar when we use other years as the final date.

Equation ( 3) is estimated using instrumental variable strategy. As discussed in section 5.2, signal attenuation is a strong determinant of the diffusion of broadband Internet but does not directly affect income distribution. It is, therefore, used as an instrument for both broadband penetration and download speed. The outcomes of the estimation are reported in Tables A-6

and A-7 in the Appendix.

The initial characteristics are statistically significant. In particular, mean income increase less in towns with initially higher level of education, and more in towns with initially more aged population. Likewise, the Gini coefficient falls less in towns with initially higher level of education or more aged population. In spite of these effects, the estimates of the effects of broadband Internet remain qualitatively the same. Broadband adoption and quality significant increase income and reduces income inequality. In addition, broadband Internet benefits to the bottom deciles relatively more than the top deciles. However, the magnitude of the estimates is larger probably because we include earlier periods of broadband deployment into the estimation.

Policy implications

We use the estimates of the Wald-DiD estimator in order to investigate the monetary benefit of broadband adoption and quality, the existence of a critical mass and heterogeneous effects with respect to town characteristics.

Monetary benefit of broadband Internet

We calculate the marginal effect of broadband Internet on the income of the average town in 2013. As presented in Table 2, its mean income is 26758 euros. The monetary benefit of 1 additional percentage of broadband penetration is 37.5 euros per year, per consumption unit.

Given that the gross national income in 2013 is roughly 40,000 euros, the marginal effect of broadband Internet on income per capita is 0.06%.7 Interestingly, this figure is not far from the one found by [START_REF] Czernich | Broadband Infrastructure and Economic Growth[END_REF], that is 0.09-0.15% for OECD countries, lending additional support to our main results.

The same evaluation made with the marginal effects of quality yields an estimated effects of 10.7 euros per 1 Mbps of additional download speed provided to half of the population. This marginal effect corresponds to an increase by 0.02% of income per capita. Given that the average median download speed is 13 Mbps in 2013, raising the median speed up to 30 Mbps in 2020 as targeted by the European Commission would generate on average 121.3 euros per capita. We do not evaluate the European digital agenda of reaching a median speed of 100

Mpbs because it involves a technological change, that is investment in fiber and cable, that is not covered by our econometric model.

Non-linear effects

As emphasized by [START_REF] Roller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF], the adoption of telecommunications technology entails network effects and, as result, the effect of adoption becomes positive only after a critical mass of early users. This critical mass is typically low, between 20 and 40% as suggested by [START_REF] Roller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF] and [START_REF] Czernich | Broadband Infrastructure and Economic Growth[END_REF]. However, our data set covers a period during which broadband penetration was already significant. For instance, the fifth percentile of broadband penetration was already 40% in 2009, our first year of observation of broadband data. Therefore, our data set does not allow the identification of a critical mass.

Yet, we explore the existence of non-linear effects in order to determine the level at which the effect of broadband adoption is maximal.

We test non-linearity of the impact of broadband adoption on income distribution by specifying the following equation:

Y it = δ + j β j ∆ j P it + γX it + µ i + ν t + ε it (4)
Where ∆ j is a dummy for a certain range of broadband penetration. We experiment several cut-off points of broadband penetration and retain the following three: up to 50%, between 50 and 70%, above 70%. The coefficient β j represents the impact of broadband adoption on income inequality, measured by the Gini index G it , when broadband penetration is within the range j.

Equation ( 4) is estimated using OLS estimator as well as the Wald-DiD estimator which relies on the interactions between the dummy variables, year and signal attenuation as instruments.

The outcome of the estimation is reported in Table 4 below. It turns out that the impact of broadband adoption is positive and concave on income, and negative and convex on income inequality. Therefore, the effect of broadband adoption is the highest at lower level of penetration. In particular, the effect is higher when the penetration rate is below 50%. The t-test shows significant difference only between the first and second dummies. This result is consistent with the finding that the second to the fifth deciles benefit relatively more from broadband adoption.

Heterogeneous effects

We also investigate the heterogeneity of the effects of broadband adoption with respect to education. This investigation follows from the underlying mechanisms of the effects of broadband Internet on income distribution. As discussed in section 5.1, these effects work through the use of Internet for job purposes. However, this mechanism requires that broadband users possess basic skills to search for job using the Internet. We specify the following econometric model in order to determine whether the effect of broadband adoption on income distribution hinges upon education.

Y it = α + βP it + λP it * X 1it + γX 2it + µ i + ν t + ε it (5)
X 1it is a vector of education-related variables, namely the share of high-school graduates and the standard deviation of the number of years of schooling. The parameter λ captures the heterogeneity of the effect of broadband adoption. X 2it is a vector of mean and standard deviation of age. Equation ( 5) is estimated using Wald-DiD estimator, with the interactions between education, time and signal attenuation as instruments. The outcome of the estimation is reported in Table 4. It turns out that all the effect of broadband adoption on the distribution of income works through education. The effect of broadband alone on mean income is positive, but not statistically significant. On the contrary, the interaction is positive and highly significant. The effect of broadband adoption on income inequality increases with the number of years of schooling, but decreases with the dispersion of schooling. ). Ȳit and G it stand respectively for mean income and the Gini coefficient. P it ≡ penetration rate. ∆ j are dummies for penetration. ∆ 0 ≡ 0 < P ≤ 50, ∆ 1 ≡ 50 < P ≤ 70 and ∆ 2 ≡ 70 < P ≤ 1. X 11it ≡ mean education, X 12it ≡ std. education, X 21it ≡ mean age, X 22it ≡ std. age. Wald-DiD estimates.

21

This paper investigates the impact of broadband Internet on the distribution of income. It finds that both broadband adoption and quality raises mean income and reduces income inequality. More specifically, a percentage increase in broadband penetration raises income per capita by 0.06%, not far from cross-country estimates by [START_REF] Roller | Telecommunications Infrastructure and Economic Development: A Simultaneous Approach[END_REF] and [START_REF] Czernich | Broadband Infrastructure and Economic Growth[END_REF] in the OECD area. Likewise, 1 Mbps additional download speed raises income per capita by 0.02%. These effects are economically significant. Between 2009 and 2013 in France, broadband adoption contributes to 34% of the rise in average income and 80% of the fall in the Gini index of income inequality, whereas quality improvement accounts for 6% of income growth and 20% of inequality reduction. The positive effect of broadband on income inequality stems from a relative greater monetary benefit accruing to the bottom deciles, particularly form the 2nd to the 5th deciles.

However, the effects of broadband adoption is slightly non-linear: positive and concave on mean income and negative and convex on income inequality. As a result, the effects of broadband Internet is maximal when the penetration rate is still low, below 50%. Early broadband data are necessary to access the existence of a critical mass. In addition, the effects of broadband adoption is highly dependent on the level and inequality in education.

The positive effects of broadband Internet on the distribution of income is stronger when the level of education is higher or when there is less inequality in education. These findings are robust to initial conditions which may drive trends in income inequality and the diffusion of broadband Internet.

They imply that public subsidy of broadband adoption targeted at the poor may be welfare enhancing because they have higher return but lower rate of adoption. The effect of raising broadband speed is economically significant. The estimated benefit can be compared to the cost of fiber deployment in public policy assessment. The heterogeneous effects with respect to education suggest that broadband diffusion policies should be complemented with access to education.

The analysis in this paper entails some limitations that could be addressed in future works.

First, by focusing on income deciles, we overlook the issue of social mobility, whereby individuals move across deciles. Second, we assume in the analysis that the effects of broadband on inequality work through employment, but have not investigate the effects of broadband diffusion on the labor market. Finally, education is assumed exogenous in our short-term analysis. However, broadband diffusion may affect schooling in the longer run. Future works should address these issues. Note: The penetration rate can be greater than 1 due to multiple subscriptions per household.

Figure 1 :

 1 Figure 1: Evolution of fixed broadband access by technology

Figure 2 :

 2 Figure 2: Broadband adoption, inequality and signal attenuation

  the estimates of the impact of broadband Internet on income inequality, measured by the Gini index. It turns out that income inequality falls with the diffusion of broadband Internet. Ten percentage points increase in broadband penetration lowers the Gini coefficient by 0.002 and 0.005 under OLS and Wald-DiD respectively. Similarly, 10 Mbps increase in broadband download speed lowers the Gini coefficient by respectively 0.001 and 0.002. OLS tend to underestimate the magnitude of the effect of broadband Internet on inequality due to reverse causality. Indeed, an increase in income inequality is expected to reduce broadband penetration or quality improvement because of smaller income accruing to the poor. Using the same figures of the yearly change in broadband penetration and download speed, we expect the Gini index to fall yearly by 0.001 due to broadband adoption and by 0.0003 point due to the improvement in broadband quality. As a result, broadband adoption and quality account for respectively 80% and 20% of the fall in income inequality between 2009 and 2013.

  000)Robust standard errors in parentheses. Significant at 1%(***), 5%(**) and 10%(*). Panels A, and B are estimated on a panel of 5021 towns from 2009 to 2013, controlling for mean and standard deviation of age and share of high school graduates. Town and years fixed effects are included. Ȳit , G it and R ijt stand respectively for mean income, Gini index and the ratio of decile j to decile 9. The first-stage F-statistics is greater than 300, that is higher than the critical threshold. The Wald-DiD estimates pass the weak identification test of Stock and Yogo.

Figure 3 :

 3 Figure 3: Marginal effects of broadband Internet on inter-decile ratios

Figure A- 1 :

 1 Figure A-1: Relationship between broadband penetration and download speed

Table 1 :

 1 Sample description in 2013

	sampled towns country

Table 2 :

 2 Descriptive statistics of the main variables

		Year Mean St. Dev.	Min	Max
	Penetration (%)	2009	53.6	9.4	16.1	146.3
		2013	65.2	9.2	20.8	181.0
	Quality (Mbps)	2009 2013	6.5 13.0	2.8 6.7	0.5 0.5	12.0 20.0
	Mean income (euros)	2009 23883 2013 26758	6739 7511	11737 12332 100872 89243
		2009 0.319	0.043	0.222	0.573
	Gini	2011 0.320	0.046	0.218	0.596
		2013 0.312	0.045	0.214	0.567

Table 3 :

 3 Estimates of the effects of broadband Internet on income inequality

Table 4 :

 4 Non-linear and heterogeneous effects of broadband adoption

		Non-linear effects	Heterogeneity
		Ȳit	G it	Ȳit	G it
	P it * ∆ 0	0.159 * *	-0.055 * *
		(0.076)	(0.022)
	P it * ∆ 1	0.152 * *	-0.054 * * *
		(0.073)	(0.021)
	P it * ∆ 2	0.156 * *	-0.052 * *
		(0.071)	(0.021)
	P it			0.092	-0.097 * * *
				(0.063)	(0.027)
	X 11it	0.103 * * *	-0.018 * * *
		(0.013)	(0.005)
	P it * X 11it			0.182 * * *	-0.025 * * *
				(0.025)	(0.009)
	X 12it		0.008 * * *
			(0.002)
	P it * X 12it				0.013 * * *
					(0.003)
	X 21it	-0.001 *	-0.001 * * *	-0.001 *	-0.001 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	X 22it		0.003 * * *		0.003 * * *
			(0.001)		(0.001)
	y2010	0.015 * * *	0.003 * * *	0.014 * * *	0.003 * * *
		(0.002)	(0.001)	(0.002)	(0.001)
	y2011	0.060 * * *	0.006 * * *	0.059 * * *	0.007 * * *
		(0.005)	(0.002)	(0.005)	(0.001)
	y2012	0.073 * * *	0.005 * *	0.072 * * *	0.005 * * *
		(0.007)	(0.002)	(0.007)	(0.002)
	y2013	0.088 * * *	0.001	0.087 * * *	0.001
		(0.008)	(0.002)	(0.008)	(0.002)
	N	24309	24309	24309	24309
	N_g	5021.00	5021.00	5021.00	5021.00
	g_avg	4.84	4.84	4.84	4.84
	F	5685.29	242.74	7133.00	291.27
	Robust standard errors in parentheses. Significant at 1%(***),
	5%(**) and 10%(*

Table A -

 A 1: Summary statistics

	Variable description	Obs	Mean	Std. Dev. Min	Max
	ȳit	average income	24309	25493	7411 11701 105969
	yi1t	1st decile	24309	8739	2938	1	19899
	yi2t	2nd decile	24309	12457	3090	2653	26799
	yi3t	3rd decile	24309	15220	3313	4851	33926
	yi4t	4th decile	24309	17671	3623	7106	39752
	yi5t	5th decile	24309	20075	4056	9306	47316
	yi6t	6th decile	24309	22653	4645 11379	57640
	yi7t	7th decile	24309	25705	5467 13660	72656
	yi8t	8th decile	24309	29836	6768 16576	98884
	yi9t	9th decile	24309	37211	9548 20845 161574
	Git	Gini coefficient	24309	0.318	0.045	0.215	0.596
	Pit	penetration	24309	0.604	0.103	0	1.815
	qit	speeds (Mbps)	24309	9.972	6.040	0.5	20
	di2009	signal attenuation (db) 24309	29.23	11.96	7.803	76.85
	X11it	mean education	24309	0.399	0.108	0.142	0.848
	X12it	std education	24309	0.399	0.108	0.142	0.848
	X21it	mean age	24309	0.366	0.072	0.092	0.717
	X22it	std age	24309	0.366	0.072	0.092	0.717
	X3it	density	24309	531	1532	5	32859
	t	year	24309 2011.03	1.413	2009	2013

Table A -

 A 2: Broadband adoption and income inequality -OLS

		income	Gini	ratio_d9d1 ratio_d9d2 ratio_d9d3 ratio_d9d4 ratio_d9d5 ratio_d9d6 ratio_d9d7 ratio_d9d8
	pen_FBB	0.199*** -0.020***	0.058	-0.067***	-0.072***	-0.069***	-0.050***	-0.037***	-0.022***	-0.009
		(0.017)	(0.004)	(0.058)	(0.012)	(0.010)	(0.009)	(0.008)	(0.007)	(0.006)	(0.006)
	age_mean	-0.001*	-0.001***	-0.006***	-0.004***	-0.002***	-0.001**	-0.001**	-0.000	-0.000	0.000
		(0.000)	(0.000)	(0.002)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	share_bac	0.106*** -0.021***	-0.180***	-0.092***	-0.059***	-0.052***	-0.039***	-0.036***	-0.023***	-0.015**
		(0.013)	(0.004)	(0.053)	(0.016)	(0.012)	(0.010)	(0.010)	(0.009)	(0.008)	(0.008)
	edu_sd		0.006***	0.148***	0.032***	0.016***	0.008**	0.003	0.000	-0.000	0.000
			(0.002)	(0.036)	(0.006)	(0.004)	(0.004)	(0.004)	(0.003)	(0.003)	(0.003)
	age_sd		0.004***	0.028***	0.014***	0.008***	0.007***	0.005***	0.004***	0.003***	0.001*
			(0.000)	(0.004)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
	y2010	0.013***	0.002***	0.009***	0.004***	0.003***	0.003***	0.002***	0.001***	0.001	0.000
		(0.001)	(0.000)	(0.003)	(0.001)	(0.001)	(0.001)	(0.000)	(0.000)	(0.000)	(0.000)
	y2011	0.056***	0.004***	0.014***	0.009***	0.007***	0.006***	0.004***	0.003***	0.001**	0.000
		(0.002)	(0.000)	(0.005)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
	y2012	0.068***	0.001***	-0.001	0.005***	0.005***	0.004***	0.002**	0.002**	0.001	-0.000
		(0.002)	(0.000)	(0.007)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
	y2013	0.082*** -0.003***	0.016**	0.006***	0.001	-0.001	-0.003***	-0.003***	-0.003***	-0.003***
		(0.002)	(0.001)	(0.008)	(0.002)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
	Observations	24,309	24,309	24,309	24,309	24,309	24,309	24,309	24,309	24,309	24,309
	R-squared	0.729	0.125	0.014	0.025	0.044	0.056	0.054	0.044	0.030	0.016
	Number of commune	5,021	5,021	5,021	5,021	5,021	5,021	5,021	5,021	5,021	5,021

Table A -

 A 3: Broadband quality and income inequality -OLS

		income	Gini	ratio_d9d1 ratio_d9d2 ratio_d9d3 ratio_d9d4 ratio_d9d5 ratio_d9d6 ratio_d9d7 ratio_d9d8
	median_Speed	0.0001**	-0.0001***	-0.0004*	-0.0004***	-0.0003***	-0.0002***	-0.0002***	-0.0001***	-0.0001***	-0.0000
		(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	age_mean	-0.0006	-0.0009***	-0.0060***	-0.0037***	-0.0020***	-0.0010***	-0.0007**	-0.0004	-0.0004	0.0001
		(0.000)	(0.000)	(0.002)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	share_bac	0.1010*** -0.0223***	-0.1763***	-0.0966***	-0.0635***	-0.0559***	-0.0420***	-0.0383***	-0.0242***	-0.0159**
		(0.013)	(0.004)	(0.053)	(0.016)	(0.012)	(0.010)	(0.010)	(0.009)	(0.008)	(0.008)
	y2010	0.0201***	0.0013***	0.0120***	0.0019***	0.0007	0.0003	-0.0001	-0.0001	-0.0001	-0.0001
		(0.001)	(0.000)	(0.002)	(0.001)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	y2011	0.0711***	0.0028***	0.0198***	0.0055***	0.0030***	0.0016***	0.0008**	0.0004	0.0002	-0.0002
		(0.001)	(0.000)	(0.003)	(0.001)	(0.001)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	y2012	0.0877***	-0.0001	0.0077**	0.0003	-0.0013**	-0.0020***	-0.0020***	-0.0015***	-0.0012***	-0.0010***
		(0.001)	(0.000)	(0.003)	(0.001)	(0.001)	(0.001)	(0.000)	(0.000)	(0.000)	(0.000)
	y2013	0.1048*** -0.0045***	0.0256***	0.0007	-0.0053***	-0.0073***	-0.0076***	-0.0067***	-0.0052***	-0.0039***
		(0.001)	(0.000)	(0.003)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.000)	(0.000)
	edu_sd		0.0057***	0.1508***	0.0299***	0.0135***	0.0061	0.0014	-0.0010	-0.0010	-0.0001
			(0.002)	(0.037)	(0.006)	(0.004)	(0.004)	(0.004)	(0.003)	(0.003)	(0.003)
	age_sd		0.0040***	0.0266***	0.0145***	0.0087***	0.0074***	0.0058***	0.0045***	0.0030***	0.0014**
			(0.000)	(0.003)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
	Observations	24,309	24,309	24,309	24,309	24,309	24,309	24,309	24,309	24,309	24,309
	R-squared	0.725	0.125	0.014	0.025	0.042	0.053	0.053	0.043	0.030	0.016
	Number of commune	5,021	5,021	5,021	5,021	5,021	5,021	5,021	5,021	5,021	5,021

Table A -

 A 4: Broadband adoption and income inequality, Wald-DiD Table A-5: Broadband speed and income inequality, Wald-DiD Table A-6: Broadband adoption and income inequality -Forman Table A-7: Broadband quality and income inequality -Forman

		income income d_income Gini Gini d_Gini ratio_d9d1 ratio_d9d2 ratio_d9d3 ratio_d9d4 ratio_d9d5 ratio_d9d6 ratio_d9d7 ratio_d9d8 ratio_d9d1 ratio_d9d2 ratio_d9d3 ratio_d9d4 ratio_d9d5 ratio_d9d6 ratio_d9d7 ratio_d9d8 d_decile1 d_decile2 d_decile3 d_decile4 d_decile5 d_decile6 d_decile7 d_decile8 d_income d_Gini d_decile1 d_decile2 d_decile3 d_decile4 d_decile5 d_decile6 d_decile7 d_decile8
	pen_FBB median_Speed pen_FBB median_Speed	0.138** 0.0004** 0.700*** -0.051*** -0.0002*** -0.177*** -0.157 -0.0005 -1.876*** -0.215*** -0.0006*** -1.175*** 0.002*** -0.0005*** -0.0055*** -0.0035*** -0.0033*** -0.0019*** -0.0019*** -0.0019*** -0.0013*** -0.164*** -0.144*** -0.084** -0.054 -0.025 -0.0005*** -0.0004*** -0.0002** -0.0002 -0.0001 -1.103*** -0.630*** -0.649*** -0.642*** -0.426*** -0.155 0.019 0.0001 -0.0005
		(0.064) (0.000) (0.139) (0.018) (0.000) (0.044) (0.000) (0.000)	(0.168) (0.000) (0.654) (0.002)	(0.067) (0.000) (0.304) (0.001)	(0.052) (0.000) (0.305) (0.001)	(0.045) (0.000) (0.214) (0.001)	(0.041) (0.000) (0.164) (0.000)	(0.039) (0.000) (0.155) (0.141) (0.036) (0.000) (0.151) (0.032) (0.000) (0.000) (0.000) (0.000)
	age_mean age_mean d_share_bac d_share_bac	-0.001 -0.0006 -0.906*** -0.001*** -0.0009*** -0.279*** -0.006*** -0.0059*** -3.500*** -0.003*** -0.0036*** -0.570*** -0.600*** -0.3575*** -4.3354*** -1.0933***	-0.002*** -0.0019*** 0.776*** 0.2844**	-0.001* -0.0010*** 0.017 -0.2636*** -0.4080*** -0.001 -0.0007** -0.119 0.271*** -0.000 -0.0004 0.284*** -0.000 -0.0004 0.305*** 0.000 0.0001 -0.0153 0.0944 0.2359***
		(0.000) (0.000) (0.086) (0.000) (0.000) (0.027) (0.049) (0.018)	(0.002) (0.002) (0.381) (0.267)	(0.001) (0.000) (0.183) (0.119)	(0.000) (0.000) (0.188) (0.121)	(0.000) (0.000) (0.144) (0.099)	(0.000) (0.000) (0.109) (0.073)	(0.000) (0.000) (0.097) (0.089) (0.000) (0.000) (0.099) (0.000) (0.000) (0.064) (0.062) (0.070)
	share_bac share_bac d_pop_65p d_pop_65p	0.104*** 0.1020*** -1.362*** -0.019*** -0.0223*** -0.291*** -0.166*** -0.1762*** -0.812** -1.181*** -0.3375*** -1.3008***	-0.083*** -0.0965*** 0.413** 0.1065	-0.053*** -0.0635*** 0.974*** 0.6865***	-0.047*** -0.0559*** 0.099 -0.0655	-0.037*** -0.0420*** -0.035*** -0.0383*** -0.023*** -0.0242*** 0.039 0.355*** 0.421*** 0.307*** -0.017** -0.0160** -0.1304 0.1873** 0.3095*** 0.2666***
		(0.013) (0.013) (0.089) (0.005) (0.004) (0.027) (0.066) (0.023)	(0.052) (0.053) (0.386) (0.353)	(0.016) (0.016) (0.169) (0.144)	(0.012) (0.012) (0.174) (0.143)	(0.011) (0.010) (0.130) (0.116)	(0.010) (0.010) (0.101) (0.085)	(0.009) (0.009) (0.091) (0.081) (0.009) (0.008) (0.091) (0.008) (0.008) (0.078) (0.073) (0.082)
	y2010 y2010 share_bac1999 share_bac1999	0.015*** 0.0197*** -2.125*** 0.003*** 0.0014*** -0.023 -1.706*** -0.1315***	0.017*** 0.0121*** 2.108*** 0.9596***	0.009*** 0.0022*** 0.957*** 0.2382***	0.006*** 0.0009* 0.768*** 0.0928	0.005*** 0.0005 0.039 -0.3464*** -0.3874*** -0.2813*** -0.2123*** -0.2190*** 0.003* 0.002 0.001 -0.001 -0.0000 -0.0000 -0.0002 -0.0002 0.010 0.112 0.049 -0.124
		(0.002) (0.001) (0.081) (0.001) (0.000) (0.026) (0.029) (0.007)	(0.007) (0.002) (0.394) (0.111)	(0.003) (0.001) (0.190) (0.064)	(0.002) (0.000) (0.190) (0.061)	(0.002) (0.000) (0.133) (0.052)	(0.002) (0.000) (0.105) (0.049)	(0.001) (0.000) (0.100) (0.092) (0.001) (0.000) (0.102) (0.001) (0.000) (0.049) (0.043) (0.055)
	y2011 y2011 pop1999_65p pop1999_65p	0.061*** 0.0699*** 0.271*** 0.006*** 0.0030*** -0.120*** 0.030** 0.0201*** -1.895*** 0.286*** -0.1234*** -1.9365*** -1.5845*** -1.6355*** -0.6567*** -0.3885*** -0.3618*** -0.3065*** -0.1262*** 0.021*** 0.015*** 0.012*** 0.007** 0.004 0.002 -0.002 0.0065*** 0.0038*** 0.0024*** 0.0012* 0.0006 0.0000 -0.0006 -1.559*** -1.611*** -0.643*** -0.374*** -0.348*** -0.297*** -0.123***
		(0.005) (0.001) (0.046) (0.001) (0.000) (0.013) (0.037) (0.012)	(0.013) (0.003) (0.179) (0.172)	(0.005) (0.001) (0.088) (0.078)	(0.004) (0.001) (0.098) (0.085)	(0.004) (0.001) (0.077) (0.071)	(0.003) (0.001) (0.050) (0.046)	(0.003) (0.001) (0.048) (0.043) (0.003) (0.001) (0.045) (0.003) (0.000) (0.043) (0.041) (0.044)
	y2012 y2012 Constant Constant	0.074*** 0.0860*** -7.143*** 0.005** 0.0003 0.082*** -6.878*** 0.0159***	0.022 0.0081** -0.360 -1.0584*** -0.5576*** -0.4244*** -0.1536*** -0.0716*** -0.0973*** -0.0634*** 0.021*** 0.014*** 0.012** 0.006 0.003 0.001 0.0018 -0.0002 -0.0009 -0.0015* -0.0013* -0.0014* -0.120 -0.014 0.081 0.170** 0.142** 0.095 0.016 -0.003 -0.0016** -0.0421**
		(0.007) (0.001) (0.060) (0.002) (0.000) (0.019) (0.014) (0.005)	(0.018) (0.004) (0.277) (0.067)	(0.007) (0.001) (0.128) (0.030)	(0.005) (0.001) (0.129) (0.033)	(0.005) (0.001) (0.092) (0.027)	(0.004) (0.001) (0.069) (0.018)	(0.004) (0.001) (0.066) (0.060) (0.004) (0.001) (0.064) (0.003) (0.001) (0.017) (0.016) (0.017)
	y2013 edu_sd y2013 Observations Observations edu_sd R-squared R-squared First-Stage F-statistic 0.089*** (0.007) 0.1027*** (0.002) 4,917 0.007*** 0.001 (0.002) (0.002) -0.0040*** (0.000) 4,418 4,917 4,418 0.0057*** 0.666 0.110 0.738 0.212 (0.002) 184.6 163.1 First-Stage F-statistic 2868 2554	0.041** (0.020) 0.156*** (0.037) 0.0261*** (0.004) 4,416 4,416 0.1509*** 0.085 0.110 (0.037) 162.9 2553	0.023*** (0.008) 0.038*** (0.006) 0.0024 (0.002) 4,416 4,416 0.0301*** 0.053 0.159 (0.006) 162.9 2553	0.012** (0.006) 0.019*** (0.005) -0.0040*** (0.001) 4,416 4,416 0.0136*** 0.025 0.159 (0.004) 162.9 2553	0.008 (0.005) 0.011*** (0.004) -0.0059*** (0.001) 4,416 4,416 0.0062 -0.051 0.045 (0.004) 162.9 2553	0.001 (0.005) 0.004 (0.004) -0.0070*** (0.001) 4,416 4,416 -0.001 (0.005) 0.001 (0.004) -0.0064*** (0.001) 4,416 -0.003 (0.004) -0.000 (0.003) -0.0054*** (0.001) 4,416 -0.006* (0.004) -0.001 (0.003) -0.0046*** 4,416 4,416 4,416 4,416 (0.001) 0.0015 -0.0009 -0.0011 -0.036 -0.075 -0.028 0.015 0.075 0.046 0.035 0.021 -0.0002 (0.004) (0.003) (0.003) (0.003) 162.9 162.9 162.9 162.9 2553 2553 2553 2553
	age_sd age_sd		0.003*** 0.0039***	0.024*** 0.0265***	0.011*** 0.0144***	0.006*** 0.0086***	0.005*** 0.0073***	0.005*** 0.0058***	0.004*** 0.0045***	0.003*** 0.0030***	0.002** 0.0014**
			(0.000) (0.000)		(0.004) (0.003)	(0.002) (0.001)	(0.001) (0.001)	(0.001) (0.001)	(0.001) (0.001)		(0.001) (0.001)	(0.001) (0.001)	(0.001) (0.001)
	Observations Observations	24,309 24,309	24,309 24,309			24,309 24,309	24,309 24,309	24,309 24,309	24,309 24,309	24,309 24,309		24,309 24,309	24,309 24,309	24,309 24,309
	R-squared R-squared	0.729 0.724	0.121 0.124			0.013 0.014	0.016 0.024	0.038 0.041	0.051 0.052	0.053 0.052		0.044 0.043	0.030 0.030	0.015 0.016
	Number of commune Number of commune	5,021 5,021	5,021 5,021			5,021 5,021	5,021 5,021	5,021 5,021	5,021 5,021	5,021 5,021		5,021 5,021	5,021 5,021	5,021 5,021
	First-Stage F-statistic First-Stage F-statistic	413.8 1873	384.2 1853			323.9 1537	323.9 1537	323.9 1537	323.9 1537	323.9 1537		323.9 1537	323.9 1537	323.9 1537

The penetration rate of fixed broadband reached 30% in

in OECD countries, corresponding to 90% household penetration rate, under the assumption of 3 members per household.

In this paper we define a town as a municipality with more than 2000 inhabitants, the income data disclosure threshold used by the statistical office, INSEE.

Data on other technologies such as satellite and Wimax, was not available. These technologies represent 1-2% of total broadband connections. We approximate the number of active cable connections per town by multiplying the number of available connections by the national take-up rate, that is the share of active connections at the national level. We obtain the number of available cable connections from the national regulator. According the cable operator, 1.4 million households in 2013 have adopted cable-based broadband

The penetration rate can be above 100% due to multiple subscriptions per household.

VDSL stands for Very-high-bit-rate Digital Subscriber Line. It is a faster variant of the standard DSL technology.

[START_REF] Duflo | Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment[END_REF] uses Wald difference-in-difference to estimate the impact of school construction on schooling in Indonesia. Basically, she compares change in schooling between regions with different intensity of school construction.

We first convert the marginal effect per consumption unit (CU) of 37.5 euros into a marginal effect per individual using the ratio 44 millions CU for 66 millions individuals. This conversion yields 25 euros per capita.


Vivien Georges

Pascal Houngbonon

Da Costa

Georges V Houngbonon
email: georges-vivien.houngbonon@ecp.fr

Pascal Da-Costa
email: pascal.da-costa@ecp.fr

Declining Labor Share and Innovation *

Keywords: Innovation, Labor share. JEL Classification: D63, D33, E25, O31

come

Introduction

Declining labor share, that is the share of value added accruing to labor, is well documented in the economic literature. [START_REF] Karabarbounis | The Global Decline of the Labor Share[END_REF] document 5% drop in the global corporate labor share since the 80s and show that this trend stems from within industry rather than between industries. More recently, Autor et al. (2017b) highlight the role of large firms in driving the downward trend in the labor share. As suggested by [START_REF] Alvaredo | Global inequality dynamics: New findings from wid[END_REF], declining labor share tends to raise income inequality, because wealth distribution is typically more concentrated than labor endowment. More importantly, declining labor share hinders growth because it reduces household consumption. One countervailing factor to these adverse effects is innovation, as declining labor share makes more profit available to finance investment. However, there is still a lack of evidence on the relationship between labor share and innovation.

In this paper, we use firm-level panel data on Research and Development (R&D), capital and labor expenditures, to investigate the relationship between the labor share and innovation.

Our data come from FactSet, an online database similar to Thomson Reuters and Bloomberg, and cover 4760 international companies from developed economies over 20 years, from 1994 to 2013. The labor share is measured by the ratio of labor expenditures to value added, and innovation is measured by R&D intensity, the ratio of R&D expenditures to sales.

We first document a 15 percentage points fall in the labor share between 1994 and 2013, consistently with a divergence between labor productivity and average wage of our sampled firms. A similar downward trend is observed for R&D expenditures which fall by 0.2 percentage point during the same period. Secondly, we investigate the correlation between these two variables by estimating a fixed effects regression, controlling for the intensity of competition, cash flow and debt stock. We find a robust, positive and statistically significant correlation between R&D intensity and labor share. A counterfactual analysis of the effects on output suggests that a percentage point decline in the labor share reduces output growth by 0.01 percentage point in the short run, and up to 0.02 in the long run, due to declining R&D expenditures.

The findings of this paper are related to the literature on the causes and consequences of the evolution of the labor share. [START_REF] Karabarbounis | The Global Decline of the Labor Share[END_REF] document a declining labor share but did not relate its to innovation within the firm. Autor et al. (2017a,b) emphasize the role of large firms in driving the declining labor share, but they also did not relate its to innovation. This paper complements the literature by showing that the declining labor share can reduces output through lower innovation.

The remainder of the paper is organized as follows. Section 2 briefly summarizes the related

Related literature

Declining labor share is well documented in the macroeconomic literature. At the global scale, [START_REF] Karabarbounis | The Global Decline of the Labor Share[END_REF] find a 5% decline in corporate labor share since the 1980s.

In the OECD, the share of national income accruing to labor drops from 66% in 199066% in to 62% in 200966% in , according to OECD (2012)). This downward trend is steeper in high-productivity industries.

In general, the labor share falls when average wage increases less than labor productivity (OECD, 2015). Several factors have been put forward to explain this divergence between labor productivity and average wage. OECD (2012) and ILO (2010) examine the sectoral shift hypothesis, according to which falling labor share stems from a shift of employment from labor-intensive to capital-intensive sectors where the labor share is lower. They find that the overall downward trend in the labor share is largely due to variation within industries, rejecting the sectoral shift hypothesis. [START_REF] Bentolila | Explaining movements in the labor share[END_REF] highlight the role of several factors such as globalization, capital-augmenting technological change, product and labor market institutions, and the bargaining power of labor. [START_REF] Hutchinson | Globalisation, concentration and footloose ILO[END_REF] reassessed these factors and find that the effects of globalization is smaller than the effects of skill-biased technological change and the cyclical price change of intermediary goods. [START_REF] Epstein | Threat effects and the internationalization of production[END_REF] pinpoint the effect of unemployment induced by the threat to internationalize production. [START_REF] Weil | The fissured workplace: Why work become so bad for so many and what can be done to improve it[END_REF] stresses the role of finance through its influence on business to increase shareholder value and to focus on core activities while subcontracting labor-intensive activities.

More recently, Autor et al. (2017a,b) examine the microeconomic causes of the falling aggregate labor share and find that industry concentration, as reflected by the rise of "superstars" firms, is the main driver. Using data from the US, they observed that the labor share of the average firm is rather flat, suggesting that falling aggregate labor share might be driven by rising heterogeneity between firms as competition develops into a "winner take most" feature.

A straightforward impact of the falling labor share is rising inequality because capital is more concentrated than labor endowment [START_REF] Alvaredo | Global inequality dynamics: New findings from wid[END_REF]. However, the relationship can be complex as the labor share typically increases for top wage earners [START_REF] Atkinson | Factor shares: The principal problem of political economy[END_REF]. Another effect is on household consumption due to higher propensity to consume from labor income than from capital income. As a result, falling labor share can hinder economic growth. To counter this effect, one might expect that falling labor share means more profit available for investment. However, recent statistics from the G20 countries show no positive effects of the falling labor share on investment (OECD, 2015). Rather, aggregate investment remains stable while the labor share is falling.1

According to OECD (2015), the disconnection between labor share and investment can be explained by two factors. First, much of increase in profit occurred in the financial sector, and second, in advanced countries, profits of non-financial firms have increasingly been used to pay dividends and to invest in financial assets rather than to make productive investments.

However, the correlation between labor share and investment can be jointly driven by factors such as the intensity of competition and financial constraints. As shown by [START_REF] Aghion | Competition and Innovation: An Inverted-U Relationship[END_REF] and [START_REF] Hashmi | Competition and Innovation: The Inverted-U Relationship Revisited[END_REF], investment, and more specifically innovation, tends to fall with competition, particularly at higher initial level of competition. Moreover, [START_REF] Carpenter | Is the Growth of Small Firms Constrained by Internal Finance[END_REF] and [START_REF] Savignac | Impact of financial constraints on innovation: What wan we learn from a direct measure[END_REF] show that financial constraints could affect investment. In the following sections, we revisit the relationship between labor share and innovation, focusing at the firm level and controlling for confounding factors such as the intensity of competition and financial constraints.

Empirical framework

Data and descriptive statistics

Our data come from FactSet, an online financial database similar to Thomson Reuters and Bloomberg databases. 2 We use these data to build a panel of 4760 international companies over 20 years, from 1994 to 2013. The panel is strongly unbalanced due to missing values on key variables such as R&D expenditures, labor expenditures, capital expenditures and debt services. The average number of observations per company is 2.74, making a total of 13063 observations. Up to 10% of these companies have their headquarters in the United States of America (US) or Canada, 35% in Europe or Africa and 55% in the Asia-Pacific region, mainly Australia, China, Japan and Hong Kong. These companies operate in all sectors of the economy. However, 84% generate positive international sales. We exclude companies that did not innovate during the period of the study. More specifically we remove companies with zero total research and development (R&D) expenditures over the 20 years of observation.

For these companies, we obtain yearly data about firms' size, expenditures and financial status.

Size variables include sales and the number of employees, both full-time and part-time workers.

Expenditures data include total operational expenditures, as well as expenditures in R&D, capital, and labor. Capital expenditures are typically investments in equipment and physical infrastructures. Labor expenditures encompasses wages. Financial status data include free cash flow and debt.

Table 1 below describes the main variables. The summary statistics suggest that our sample is made of large firms. The average firm employs 14,000 workers and generates 6 billions of US dollars yearly sales.3 Our sample also comprises smaller firms as suggested by a median size which is smaller than the average. Firms with zero sale and workers are typically new entrants.

On average, R&D expenditures represent 1% of sales, whereas capital expenditures represent 8% of sales. R&D and capital expenditures are lumpy as firms do not invest every year (zero expenditures). Labor expenditures account for 9-10% of sales. Free cash flow is calculated as the difference between cash flow (depreciation and amortization) and capital expenditures. It can be negative if internal funds are not sufficient to cover capital expenditures. Debt stock represents 32% of sales. We follow the literature by measuring innovation as R&D expenditures [START_REF] Aghion | Competition and Innovation: An Inverted-U Relationship[END_REF][START_REF] Aghion | Innovation, Firms and Wage Inequality[END_REF]. Alternative measures such as citations-weighted patents and factor productivity are not available in our dataset. By using R&D expenditures, we focus on the input of innovation, instead of the output. We neutralize the firm size effects by taking the ratio of R&D expenditures to sales. Let rd it denote innovation in firm i in year t. It can be expressed as:

rd it = RD it Y it
Where RD it and Y it stand respectively for R&D expenditures and sales. The distribution of rd it is highly skewed toward zero. More than 90% of firms spend less than 5% of their revenues in R&D. The largest R&D expenditures represents 22% of sales.

Labor share is measured at the firm level as the ratio of wages to value added. This latter corresponds to the sum of wages and profit. Formally, the labor share can be expressed as:

lshare it = w it N it w it N it + π it
w denotes average wage and N the number of workers. Profit π it is calculated as:

π it = Π it -(A it + I it )
Where A it denotes depreciation and amortization, and and I it denotes debt interest.

Labor share is also highly skewed, but towards 1. The average labor share stands at 70%, while the median is close to 77%. These joint downward sloping trends suggest a positive correlation between labor share and innovation. However, they might be driven by firm specific effects such as entry and exit. For instance, to the extent that new entrants have lower R&D intensity and lower labor share, a rise in entry could drive the joint downward trends. In addition, the intensity of competition as well as financial constraints could jointly drive labor share and innovation. We specify an

Econometric model

To test the relationship between labor share and innovation, we specify the following econometric model:

rd it = α + βlshare it + γX it + µ t + µ i + ε it (1)
X is a vector of controls and µ t , µ i and ε it are respectively time fixed effects, firm fixed effects and residuals.

Our goal is to estimate β, the correlation between labor share on innovation, controlling for the intensity of competition, financial constraints as well as time and firm-specific effects. Equation ( 1) is estimated on the basis of Ordinary Least estimator (OLS). Following [START_REF] Karabarbounis | The Global Decline of the Labor Share[END_REF], we expect β to be negative, meaning that declining labor share comes with rising innovation. This negative correlation would lend support to the hypothesis that capital-augmenting innovation tends to shift value added from labor to capital.

However, a positive β would mean a declining labor share and innovation.

We control for the intensity of competition and financial constraint. The intensity of competition is measured on the basis of the Lerner index of monopoly power. 4 Given that marginal cost is not observed, we assume that firms produce homogeneous products with constant marginal cost. Under this assumption, the Lerner index is equivalent to the ratio of profit to sales. This ratio is typically used as a measure of the intensity of competition as in [START_REF] Aghion | Competition and Innovation: An Inverted-U Relationship[END_REF]. We use two measures of financial constraint, namely the ratio of free cash flow to sales and the natural logarithm of debt stock.5

Results

Table 2 presents OLS estimates of equation ( 1). Consistently with Figure 1, the coefficient β is positive and statistically significant at 1% level. It implies that a percentage point decrease in labor share is associated with 0.005 percentage point fall in R&D intensity. In spite of its statistical significance, this correlation is economically small. It represents roughly 0.16% of the standard deviation of R&D intensity.

Controlling for the intensity of competition, cash flow and debt stock in specification (2) does not affect the sign, magnitude and precision of the estimate of the correlation between R&D intensity and labor share. This finding means that the positive correlation between labor share and innovation is not driven by the intensity of competition or by financial constraints.

Though, in accordance with the findings from the literature, R&D intensity significantly falls with the intensity of competition, and rises with cash flow and debt.

Specification (3) tests the validity of the econometric specifications (1) and (2) by using the logarithm of R&D expenditures as a dependent variable and the logarithm of sales as a control.

The coefficient of the logarithm of sales is not statistically different from 1, lending support to R&D intensity as a valid dependent variable in specifications ( 1) and ( 2). The Fisher's statistic of the test equals 0.

Specification (4) tests whether the declining R&D intensity is compensated by a rising capital expenditures. It turns out that capital expenditures also fall alike. A percentage point decline in the labor share is associated with 0.05 percentage point fall in capital expenditures. Hence, the rising profit share of firms in our sample has not been devoted to increasing investment within the firms.

Specification (5) presents the reduced-form estimate of the correlation between labor share and output. The estimation accounts for the adjustment cost in output by introducing the lagged of sales as an explanatory variable. We find a negative and significant correlation between labor share and output. This means that the declining labor is associated with rising sales, consistently with the large increase in productivity shown in Figure A-1. More specifically, a percentage point decline in the labor share corresponds to 0.10% rise in output. In addition, the coefficient of lagged sales is positive, significant and less than 1, lending support to an adjustment cost of output.

To test whether the declining R&D expenditures, induced by the falling labor share, reduces output growth we introduce R&D expenditures as a control in specification ( 6). The coefficient of labor share in this equation corresponds to the correlation with output holding R&D expenditures constant. OLS estimates presented in the last column of Table 2 show a stronger negative correlation between labor share and sales. If R&D expenditures were held constant, a percentage point decline in labor share would have been associated with 0.11% rise in sales. Therefore, the declining R&D expenditures, induced by a percentage point fall in labor share, costs 0.01 percentage to output growth. The adjustment cost is such that this cost is multiplied by a factor of 1.7 in the long run.

Conclusion

In this paper, we investigate the relationship between labor share and innovation. We find a robust, positive and significant correlation between labor share and innovation. This finding suggests that the internal funding capacity yielded by the declining labor share is not channeled into financing innovation within the firm. On the contrary, R&D expenditures decline along with the labor share. This downward trend in innovation lowers output growth by 0.01 percentage point for every percentage point decline in the labor share.

One potential explanation of the positive correlation between labor share and innovation is the rise of finance. The incremental profit generated by declining labor share is either used to invest in financial or in productive assets with higher returns that typically outweigh the cost to internal output growth. However, as emphasized by OECD (2015), aggregate investment in the G20 countries has remained rather flat so far. Therefore, an alternative explanation would be that rising profit is channeled into developing countries where the OECD (2015)

observe rising investment.

Of course, the relationship between labor share and innovation is not causal. As emphasized by [START_REF] Karabarbounis | The Global Decline of the Labor Share[END_REF], innovation, particularly in capital-augmenting technologies, is a strong determinant of the declining labor share. In addition, a confounding factor driving the correlation between labor share and innovation is the taxation policy. More favorable taxation of capital income, in the form of lower tax on investment return for instance, provide an incentive to redirect internal funds towards higher return investment outside the firm.

Future research should investigate these alternative mechanisms.

Figure 1

 1 Figure 1 presents the trends in labor share and innovation between 1994 and 2013. These trends have been obtained from the local polynomial smoothing of the yearly average labor share and R&D expenditures. The local polynomial smoother is useful to get rid of noises.

Figure 1

 1 Figure1highlights a dramatic fall in the labor share, by 15 percentage point in 20 years, from 80% in 1994 to 65% in 2013. This trend accords well with the findings from other studies on the evolution of the aggregate labor share such as OECD(2015). The magnitude of this fall is consistent with the findings byAutor et al. (2017b), whereby large firms are the main drivers of the declining labor share. This large decline in the labor share stems from a divergence between labor productivity and average wage. As shown in Figure A-1 in the appendix, labor productivity increases 8 folds between 1994 and 2013, whereas average wage merely doubles over the same period. A second force driving down the labor share is employment. Indeed, as shown in Figure A-1 in the appendix, the average number of workers per firm in our sample declines by 25%, from 16,000 in 1994 to 12,000 in 2013. Meanwhile, we also observe a slight fall in R&D intensity by 0.2 percentage point, from 1.55% in 1994 to 1.35% in 2013.

Figure 1 :

 1 Figure 1: Labor share and R&D intensity

Table 1 :

 1 Variables and descriptive statistics

	variable	definition	Obs.	min	med	mean	max	sd
	Y	Sales	13063	0.00 329.88	5940.39	2.87e+06 56738.08
	N	Number of workers	10569	0.00	2642 13555.75	595002 37162.22
	RD	R&D expenditures	13063	0.00	1.22	61.65	13460.69	443.08
	K	Capital expenditures 13063	0.00	12.54	518.23 708943.50	9081.49
	wN	Labor expenditures	13063	0.00	33.43	524.37 179638.03	4097.77
	Π	Ebitda	13063	-1572.30	48.65	1242.45 861836.81 14274.05
	cf	Free cash flow	13063 -2.12e+05	0.56	3.90 127710.15	3185.96
	x	debt stock	13057	0.00	63.47	1895.86	1.30e+06 22543.18

Sales and expenditures are expressed in millions of current US dollars. Ebitda stands for Earnings before interest, taxes, depreciation and amortization. Observations are at firm-year level.

Table 2 :

 2 Estimation results

		rd		lnRD	capex	lnsales
		(1)	(2)	(3)	(4)	(5)	(6)
	lshare	0.005 * * *	0.005 * * *	1.048 * * *	0.050 * * *	-0.101 * * *	-0.109 * * *
		(0.001)	(0.001)	(0.273)	(0.004)	(0.032)	(0.032)
	comp		-0.007 * * *	-0.103	0.017 * *	0.186	0.185
			(0.003)	(0.557)	(0.008)	(0.194)	(0.194)
	cashf low		0.011 * * *	0.616	-0.070 * * *	-0.085	-0.089
			(0.003)	(0.710)	(0.013)	(0.147)	(0.148)
	lndebt		0.0001 * *	0.046	0.0003	0.022 * * *	0.023 * * *
			(0.00007)	(0.033)	(0.0002)	(0.004)	(0.004)
	lnsales			1.006 * * *
				(0.142)
	lnsales t-1					0.415 * * *	0.412 * * *
						(0.084)	(0.084)
	lnrd						0.008 * * *
							(0.002)
	µ i , µt
	constant	0.010 * * *	0.015 * * *	-8.759 * * *	-0.001	10.888 * * *	10.866 * * *
		(0.001)	(0.003)	(2.792)	(0.009)	(1.606)	(1.595)
	N	13063	13052	13052	13052	12411	12411
	n	4760	4754	4754	4754	4580	4580
	T	2.74	2.75	2.75	2.75	2.70	2.70
	F	4.06	4.34	6.28	16.37	171.57	168.28
	Significant at 1%(

***), 5%(**) and 10%(*). Standard errors robust to heteroskedasticity and autocorrelation in parentheses. N =n T , where n is the number of firms.

Note that in the meantime investment has been rising in emerging countries.

FactSet is used in academic studies such as[START_REF] Ferreira | The colors of investors' money: The role of institutional investors around the world[END_REF].

For instance, the average large firm, as defined by the French statistical office in 2011, employs 18,000 workers and generates 6 billions euros.

The Lerner index can be expressed as p-c p , where p and c denote respectively price and marginal cost.

The sensitivity of free cash flow to investment has been criticized by[START_REF] Kaplan | Do Investment-Cash Flow Sensitivities Provide Useful Measures of Financing Constraints[END_REF] as a measure of financial constraint. However, as emphasized by[START_REF] Fazzari | Investment-Cash Flow Sensitivities are Useful: A Comment on Kaplan and Zingales[END_REF], it still provides a useful proxy for financial constraint.

Appendix