Jean-Paul Fitoussi

How to Safeguard General Support and Legitimacy of Monetary Policy during Times of Economic Distress in a Monetary Union?

The two recent macroeconomic shocks that hit the world economy -the surge of oil and food prices and the subprime crisis -have revived the attention of policy makers and economists on the consequences of shocks, symmetric and asymmetric, and on the appropriateness of the EMU institutional framework to respond to these shocks. The briefing paper outlines the doctrine that underlies the ECB response to the shock, i.e. an exclusive focus on inflation, and argues that this policy is likely to be ineffective, while it will certainly have deep distributional consequences, having the same analytical effect as of a regressive tax on low income wage earners. The paper then discusses in more general terms how the European institutions face difficulties in the classical instrument/objective assignment problem, which stems from an excess of confidence in market adjustment mechanisms. This contrasts with the case of the US, where market forces and policy interventions complement each other in a virtuous way. The paper then concludes with a number of proposed changes in the economic governance of Europe, which would make the policy reaction to shocks easier and more effective.

In the past months two major sources of uncertainty loomed on the world economy. First, the recent turbulences on the financial markets, triggered by the subprime crisis, whose effects seem not to be over, and are beginning to spill to the real sector through increased credit constraints and deteriorating private agents' confidence. The second element of uncertainty, even more dramatic, is the steep increase of food and raw materials prices1 that depends on both structural and contingent factors, and whose social consequences are causing increasing concern.

The combined macroeconomic effect of these two crises is quite visible. Growth forecasts for the years 2008-2009 are being revised downwards for most countries and economic zones, and the debate is still heated as of how lasting the effects of this twin crisis will be.

An important effect of this period of turbulence is the revived attention on the consequences of shocks on the economy, and on the appropriate policy responses. This is particularly important in the European Monetary Union, where the treaties have left a good deal of ambiguity in the objectives/instruments assignment. How to safeguard the general support in macroeconomic policies in general and in particular monetary policy during times of economic distress in a monetary union is hence a very relevant question. Monetary policy being the main federal policy of the EU, general support in it is crucial for its legitimacy. This moment of crisis becomes then an occasion to assess whether the current institutional framework of the EMU is appropriate to respond to the different types of shocks that hit the European economies, and to assess its effectiveness and credibility. This paper will at first outline the doctrine that lies behind the current European institutional framework, and then argue that while coherent, such framework may be inappropriate to respond to a number of shocks; in particular, in the current situation the policies followed by the European governments and by the ECB are likely to exacerbate the problems faced by the European economies, and by low income wage earners in particular. I will conclude that a more pragmatic approach is desirable, and that the example of the United States may prove helpful.

The Design of the Institutions for European Economic Governance

In my briefing paper of March 20072 I described at length the theoretical framework that influenced the creation of the Maastricht institutions. That discussion may be briefly summarized as follows:

1) Once public intervention has coped with externalities, clearing and complete markets that are populated by rational agents usually yield the best possible outcome in terms of resource allocation and growth.

2) When that is not the case, the responsibilities lie with frictions and market failures.

3) The role of e conomic policy is then simply to remove or minimize these frictions on the supply side ( through structural reforms and a reduction of government's size).

4) Any active intervention on the demand side is useless, if not harmful. Once conditions on the supply side are established, the economy will attain the most efficient position unless distorted by public intervention.

5) This has important consequences in terms of policy: if tradeoffs do not exist, the policy maker is not confronted by choices, and there is no role for activist macroeconomic policies. Fixed rules are the preferred tool for conducting policy because they prevent biases in policy makers' actions and constitute an anchor for private expectations. Hence the search for price stability and the obedience to a fiscal rule (the SGP) is more than enough to take care of demand.

Coherently with this conclusion, the European institutional setup, de facto, gives up discretionary economic policy. Monetary p olicy is delegated to an independent monetary a uthority, the European Central B ank, which is not accountable to any political body. Fiscal policy is strongly constrained by the Stability and Growth Pact, which barely leaves space for automatic stabilizers to work. Within this framework, whenever a shock hits the economy the bulk of t he adjustment relies on market forces (wage and price flexibility, factor mobility, etc etc), while fiscal and especially monetary policy have a limited role. In particular, barring very particular cases monetary policy has to focus on its primary objective, inflation.

The almost exclusive focus on inflation explains the choice to focus on a headline inflation objective, that is to react to price increases even when they do not directly depend on domestic conditions. In the June 2008 ECB Monthly Bulletin, the ECB explains its strategy as follows:

"The Governing Council emphasises that maintaining price stability in the medium term is the ECB's primary objective in accordance with its mandate. The Governing Council is monitoring very closely all developments. It is in a state of heightened alertness. By acting in a firm and timely manner, the Governing Council will prevent second-round effects and ensure that risks to price stability over the medium term do not materialise. It is its strong determination to secure a firm anchoring of medium and long-term inflation expectations in line with price stability. […] Against this background [of increased oil and non energy commodity prices hikes,], it is imperative to secure that medium to longer-term inflation expectations remain firmly anchored in line with price stability. All parties concerned, in both the private and the public sector, must meet their responsibilities. Wage-setting needs to take into account productivity developments, the still high level of unemployment in many economies, and price competitiveness positions. Moderate labour cost increases are particularly necessary in countries which have lost price competitiveness in recent years. Broadly based second-round effects stemming from the impact of higher energy and food prices on price and wage-setting behaviour must be avoided. In this context, the Governing Council is concerned about the existence of schemes in which nominal wages are indexed to consumer prices. Such schemes involve the risk of upward shocks in inflation leading to a wage-price spiral, which would be detrimental to employment and competitiveness in the countries concerned. The Governing Council therefore calls for such schemes to be avoided." 3To summarize, the ECB argues that it has to tighten its stance (or not to ease it, which during times of economic distress amounts to the same) in reaction to domestic and imported inflation pressures alike, because the latter risks triggering wage-price spirals (second-round effects). The possible deflationary effects of such a stance are not a major concern of the ECB, whose primary objective is price stability. This is in stark contrast with the US Fed, which has to balance the objective of price stability with the support to economic activity, and thus focuses on core inflation (excluding oil and food prices). The result of these two different views in the past months has been a significant drop of US interest rates (from 5.25% to 2%), while the ECB rate remained rock-steady at 4%.

The Dilemmas of Economic Policy in the Eurozone

The ECB theoretical framework, and the strategy that it follows coherently with this framework, are today running into two related dilemmas. The first is the one I already mentioned above, and that has been the subject of other briefing papers, between the inflation and growth objective. Only three months ago 4 , writing about the subprime crisis, I challenged the ECB explicit assumption, that inflation is always a monetary phenomenon, and that the interest rate instrument should be devoted exclusively to dealing with inflation pressures.

The second dilemma, that is much less debated but at least as important as the first, is related to the redistributive effects of shocks and monetary policy's reaction. The impact of the current shocks on prices is more important for low and fixed income categories, who spend a much larger share of their income in the goods that have seen their price explode (oil, primary goods, etc), and who are unable to transfer these increases on other categories.

As a consequence, the burden of these price increases falls disproportionately on the shoulders of low income categories, and these shocks are analytically equivalent to regressive tax increases. This explains why according to many surveys purchasing power is the main concern of households in many countries across Europe.

If we keep in mind this fact, the ECB argument that restrictive monetary policy should also be used against imported inflation in order to fight second round effects, acquires a new meaning. Acting as the watchdog of wages (the very last sentence of the citation above is revealing in this respect) the ECB controls inflation, but in doing so it exacerbates the redistributive effects of i mported inflation that disproportionately affects low income categories. In other words, to avoid a price inflation spiral, the "external tax" due to the increase in oil prices in particular should be paid only by the wage earners. Then the decrease in purchasing power of the median worker would calm inflationary pressure helping the ECB to reach its inflation target. To that mechanism will cooperate also the decrease in purchasing power due to the increase in food prices. Thus, inflation controls come at the price of an increasing income inequality, and depressed domestic aggregate demand, thus linking the two dilemmas in a vicious circle. Furthermore, even abstracting from considerations about inequality and growth, we can raise doubts on the effectiveness of this strategy. Both the subprime crisis and the oil and food price increases are shocks that hit the entire Euro zone, but whose effects are different in the different countries depending on a number of f actors like the productive structure, the energy mix, the response of the labour market, the distribution of income, etc. While purely asymmetric shocks (e.g. a natural disaster, a social conflict) are much easier to identify and tackle, the real difficulty lies in the diagnosis of asymmetric effects of common shocks. Once again we can rely on simple textbook analysis to show that using the common monetary i nstrument to address country specific inflation problems is useless, so that it risks hampering the credibility of the institution.

The standard argument that the ECB opposes to these criticisms is that market forces would be able to take care of these asymmetric shocks through relative price and wage changes, migration etc. The International Policy Group that I coordinated at OFCE 5 had already warned in the early 1990s, that even in the US, where cultural and economic obstacles are much lower than in the Euro zone, persistent differences across states would show that market mechanisms alone were not able to absorb shocks. Thus, we suggested that asymmetric shocks would result, in absence of policy reactions, in increased unemployment and labour market tensions, an argument that was further validated by the works of [START_REF] Blanchard | Regional Evolutions[END_REF], and [START_REF] Decressin | Regional Labor Market Dynamics in Europe[END_REF].

We can add a few further considerations on the inadequacy of market flexibility and structural reforms as the sole answers to asymmetric shocks. First they may result in competition among member states (for example tax competition), triggering a race to the bottom that risks hampering the solidarity among countries that was the basis of the European construction. Second, reforms are not implemented in one day. Measures aimed at increasing flexibility, especially in the labour markets, will most likely result in long transitions during which reforms may have countercyclical effect, exacerbating the effects of shocks.

Our Policy Group also suggested that, following a standard textbook analysis, the loss of monetary sovereignty linked to the EMU should be compensated by a reinforced fiscal autonomy, and that the European institutions in the making (that later resulted in the Stability and Growth Pact) were actually going in the opposite direction and did not adequately respond to the standard objective/instrument assignment. Thus, I could only observe with preoccupation the slow but inexorable drift of the European institutions toward a restrictive interpretation of the SGP that we observed in the past few months, with increased focus on the medium term objective of a balanced budget rather than on the ceiling of 3%. What is puzzling is the autonomous dynamic of the stability pact which despite reforms to allegedly increase its flexibility seems to become more and more rigid. The focus of the Commission is by now much less on the level of the deficit than on its medium term evolution towards zero! Many European economists are now advocating the introduction in national constitutions of a fiscal rule whose effect will be to constrain countries to obey the stability pact. Notice that outside Europe almost no economists, or politicians are pleading for such a move, and that inside Europe but mezzo voce many politicians are criticizing the stability pact.

It is nevertheless reassuring that today, after a decade of policy inertia that was among the causes of disappointing macroeconomic performances for the Euro zone, we are asked to reconsider the issue of appropriate responses to macroeconomic shocks. I see this as an implicit acknowledgement that policy should be given a more active role.

What Institutions for a More Effective Economic Policy?

I see the main problem of the current institutional framework in its global coherence with a theoretical approach that confines macroeconomic policy t o a marginal role in the management of the economy. In this respect, the US may serve as a model in that their institutions rely o n the complementarities between market based adjustments and discretionary fiscal and monetary policy. Thus I would strongly argue in favour of a global reappraisal of policy intervention.

For what concerns monetary policy, the present times of economic distress shed light on an essential problem, which is more or less hidden in normal circumstances: the political nature of monetary policy decision. We have seen that monetary policy affects four variables which usually are considered as primary objectives of any government: inflation, growth (and thus employment), the degree of i nequalities, and through exchange rate variations the external balances. (And I skip wealth which is obviously affected by the rate of interest). A robust result in economics is that when an instrument is used to reach several objectives, the policy maker has to make trade-offs. In a democratic regime, trade-offs have to be made by the elected representatives of the population: they imply political choices and thus political responsibility. They can't be left to a technocratic body. It may well be that a government proceeds exactly to the same choices than those of the ECB, but it will then bear full responsibility for this choice.

In saying that, I am not criticizing the ECB. It has indeed no other choice than fulfilling its mandate which has been politically designed. But one has not to be an expert to understand that in making it such a way that a "technocratic body" has to bear responsibility for a political choice, it may loose its legitimacy. These remarks belabour the obvious which is that full responsibility can only be born by the political structure, and that "independent body" have to be accountable.

As for fiscal policy, while maintaining some form of peer pressure to avoid free riding and spillovers within the EMU, I strongly argue for a renewed role of discretion for governments that already lost the monetary instrument with the Euro. Scrapping the objective of a balanced budget over the cycle, introducing some form of golden rule of the type implemented in the UK, increasing the number of exceptions to the 3% ceiling, or raising the ceiling altogether, are all measures that would allow European governments to recover some room for policy in their action.

To better deal with asymmetric shocks a solidarity fund could be envisioned, to which countries would contribute in good times.

The ECB forecasts international food prices to increase by 44% in

See ECB Monthly Bulletin, June 12 th 2008, p 81.

Jean-Paul Fitoussi, Wage Setting and Price Stability, Briefing paper prepared for the Committee For Economic and Monetary Affairs, no 2007-1, March 2007. The interested reader may also look at Fitoussi and Saraceno (forthcoming).

ECB Monthly Bulletin, 12 June 2008, pp.

4-5. 4 Jean-Paul Fitoussi, ECB Objectives and Tasks: Price Stability vs. Lender of Last Resort, Briefing paper prepared for the Committee For Economic and Monetary Affairs, no 2008-1, March 2008.

[START_REF] Fitoussi | Competitive Disinflation : The Mark and Budgetary Politics in Europe[END_REF].


Jean-Paul Fitoussi

Are We Experiencing a New (and Lasting) Upward Shift in Inflation?

The long wave of globalization will most probably lose part of its strength in the next few years. As a consequence inflation will not remain as low as it has been for the past three decades, where the growth strategy of emerging countries, especially China, has mainly relied on exports to the global market. The very success of this strategy implies that the western world would not still for long be able to pursue a growth strategy based on (excessively) cheap imports. A look at price indexes shows that inflation has been in the recent past on an upward trend and that it varies considerably across sectors. At the very least, the rate of inflation may become much more volatile in the decades to come. Besides the obvious consequence of actualizing its inflation target, the ECB should also rethink its policy (and its relationship with the other actors of economic policy in Europe) to put in place strategies aimed at accompanying the structural adjustment of the economy (that may be a cause of a slightly higher inflation). The increasing income inequality may also prove to be a problem for monetary policy, because it tends to generate stagflationary outcomes if it is not being taken care of. If the short term prospect is for the rate of inflation to decrease, the longer term prospect is that it may well decrease towards a new equilibrium rate higher that the preceding one which is reflected in the present objective of the ECB.

The recent evolution of commodity prices has raised a number of questions that are relevant for policy making in general, and for monetary policy in particular. The public debate has focused on the decreasing purchasing power of householdespecially the poorest ones -and on the action economic policy makers should take in order to contrast this trend. This briefing paper will try to give elements to answer two questions. The first is whether we are heading towards the end of the era of (abnormally) low inflation that we experienced since the middle of the 1980s. The answer to this first question will be yes, as the structural factors that kept inflation lower in the past are fading, and hence it is realistic to expect an increase of say one point in the equilibrium inflation rate. The second and related question is whether this should imply a different attitude of central banks, notably the ECB. I will argue that, besides the obvious implication that the target inflation rate should be raised for credibility reasons, the structural factors behind the increase of inflation, and the consequences in terms of aggregate welfare and income distribution should be addressed by monetary policy and fiscal policy alike. The surge in oil prices, accompanied by a surge in food prices, has had the expected effect of increasing headline inflation all over the world. But since already some decades, the message of the analysis of Michael Bruno and Jeffrey Sachs has well been understood: an oil shock would lead to an episode of stagflation in a context where wage indexation is pervasive. So almost everywhere in advanced countries wage indexation has disappeared from the economic scene, as both the stability of core inflation and the stagnation of real wages seems to indicate. 0 4 -0 0 0 7 -0 0 1 0 -0 0 0 1 -0 1 0 4 -0 1 0 7 -0 1 1 0 -0 1 0 1 -0 2 0 4 -0 2 0 7 -0 2 1 0 -0 2 0 1 -0 3 0 4 -0 3 0 7 -0 3 1 0 -0 3 0 1 -0 4 0 4 -0 4 0 7 -0 4 1 0 -0 4 0 1 -0 5 0 4 -0 5 0 7 -0 5 1 0 -0 5 0 1 -0 6 0 4 -0 6 0 7 -0 6 1 0 -0 6 0 1 -0 7 0 4 -0 7 0 7 -0 7 1 0 -0 7 0 1 -0 8 0 4 -0 8 0 7 -0 8

EU CORE US CORE EU HEADLINE US HEADLINE

1 -0 0 0 4 -0 0 0 7 -0 0 1 0 -0 0 0 1 -0 1 0 4 -0 1 0 7 -0 1 1 0 -0 1 0 1 -0 2 0 4 -0 2 0 7 -0 2 1 0 -0 2 0 1 -0 3 0 4 -0 3 0 7 -0 3 1 0 -0 3 0 1 -0 4 0 4 -0 4 0 7 -0 4 1 0 -0 4 0 1 -0 5 0 4 -0 5 0 7 -0 5 1 0 -0 5 0 1 -0 6 0 4 -0 6 0 7 -0 6 1 0 -0 6 0 1 -0 7 0 4 -0 7 0 7 -0 7 1 0 -0 7 0 1 -0 8 0 4 -0 8 0 7 -0 8 Hence this time the oil tax has mainly fallen on the shoulders of the wage earners. In the language of the ECB it seems, at least until now, not to have had second rank effects. But this type of adaptation to a supply shock has necessarily a growth effect: the slowing down of consumption and its subsequent effect on investment is reducing the rate of growth almost everywhere. This is a first "disinflation" factor characterizing the present situation. A second factor has to be found in the reversal of oil prices (at least their levelling off) and the reversal of food prices whose surge was in part due to specific factors not likely to replicate in the future.

According to this appraisal, the causes behind inflation have had their maximum effect in 2008. It has to be recalled that from July 2007 and July 2008, oil prices have more than doubled and since the July peak, they are decreasing (with some fluctuations). The same is true for the bulk of commodity prices. Inflation is thus expected to recede in the year to come in advanced economies. Some economists are also arguing that there is another factor behind the increase in commodity prices, namely the financial crisis: when financial assets prices would have decreased enough, the expectation of their return to normal will add a further deflationary effect on commodity prices.

For all these reasons the fear of stagflation -the synchronous increase of the rates of inflation and unemployment -seems to be grossly exaggerated.

But this does not amount to saying that monetary policy is not confronted with a problem. It is certainly in emerging and developing economies where oil, food and other commodities account for a much larger fraction of the Consumer price index. But it is also in advanced economies because the global context is exhibiting a noticeable and foreseeable change. Globalization has had and continues to have the expected beneficial effect in favouring growth in the developing countries which have chosen a growth strategy based on openness to trade. As a consequence, the world is becoming more balanced, and the period of abnormally cheap exports which has helped to lower the equilibrium rate of inflation in the western world is progressively coming to an end .That process will take still some more decades to be accomplished, but already the discrepancy between the terms of trade of the advanced economies and the emerging countries is slowly reducing. Moreover, the process is already sufficiently advanced, that absent radical technological progress, the pressure on the price of exhaustible resources will continue to increase.

Are We Experiencing an Increase in the Equilibrium Inflation Rate?

Figures 1 and 2 report the evolution of global commodity indexes from the Dow Jones and the Economist respectively, together with selected subcategories.

Figure 1 shows an impressive increase of energy prices since the beginning of 2008 to the peak of July (more than 70%), but also an equally impressive decrease (almost 30%) during the month of August. These fluctuations drove the average index as well. 0 / 0 7 0 2 / 0 7 0 3 / 0 7 0 4 / 0 7 0 5 / 0 7 0 6 / 0 7 0 7 / 0 7 0 8 / 0 7 0 9 / 0 7 1 0 / 0 7 1 1 / 0 7 1 2 / 0 7 0 1 / 0 8 0 2 / 0 8 0 3 / 0 8 0 4 / 0 8 0 5 / 0 8 0 6 / 0 8 0 7 / 0 8 0 8 / 0 8

DJ AIG-Spot CommodityIndex -PRICE INDEX DJ AIG-Energy Spot Index -PRICE INDEX DJ AIG-Exc Energy Spot Index -PRICE INDEX Source: Dt t
Similarly, figure 2 shows that without food, the price index increase was not dramatic, while food prices almost doubled from January 2007 to the peak of last July.

Thus, we can observe three major stylized facts. The first is an upward trend of the price level. The second is an increasing variability, with fluctuations easily above 10% from one month to the other. And the third is a very unequal distribution across commodities and sectors, with commonly used commodities (food, energy) increasing significantly more than the average.

In Fitoussi and Gergescu-Roegen (1980), we linked the equilibrium level of inflation to the structure of the economy. That paper noticed how asymmetric price behaviour may be a natural consequence of uncertainty, that pushes prudent entrepreneurs to prefer price adjustments to quantity adjustments (i.e., new capacity building) when observing increases in demand. The degree of asymmetry increase with uncertainty, and there is little doubt that in a period of financial crisis uncertainty becomes pervasive. In sectors experiencing excess supply, price adjustments are much more difficult to achieve as they are constrained by institutions in general, and social ones in particular. This asymmetry on the price dimension is mirrored by a converse asymmetry in the quantity dimension, i.e., quantity adjustments are stronger in sectors characterized by excess supplies. Price behaviour asymmetry determines a positive inflation rate in equilibrium (i.e. when aggregate demand and supply are equal) because prices increase in sectors with excess demands more than they decrease in sectors with excess supply. An important consequence of this definition of equilibrium inflation is that for a given average excess demand (say zero), increased variance at the sector level implies an increase in the equilibrium inflation rate. The data below show clearly than something of this kind (increased dispersion) is a characteristic of the present period. Another mechanism by which sector heterogeneity brings about a positive equilibrium inflation rate is the tendency for wages to move together, while productivity growth is very different between sectors (lower for example in the services sector).

Whatever its origin, this link between average inflation and the structural differences across sectors becomes important in light of the stylized facts analyzed above.

For reasons already developed, we should not observe further increases in the rate of inflation, quite the contrary. The consensus for the Euro area is for example of an inflation rate that should stabilize around 3% by the end of 2008.

Nevertheless, a detailed analysis of the factors that determined the path of inflation in the past pushes to believe that the abnormally low inflation levels of the past will not be easily found again. At minimum the rate of inflation could exhibit in the future much more volatility.

At the basis of the era of low (and relatively stable) inflation that we experienced since at least two decades is the globalization process that had its more visible aspects in the fast integration of emerging economies (notably China and India) in the world economy. This led to what Freeman (2005) called the "great doubling" of the global labour force, that had strong deflationary effects. In the Briefing paper that I prepared for the EP in December 2007, I mentioned a number of factors that at different levels explained the tendency of global inflation to decrease. I report them here for the reader's convenience: 1. The more straightforward is the direct effect of cheap imports, which reduces the overall price level. This effect is larger for countries that have a higher share of imports in domestic consumption. 2. Related to the former, there is the substitution effect of cheaper imports for domestic goods. According to the ECB monthly bulletin, of August 2006, China and new member states have seen their exports to old member countries of the EU double from 1995 to 2004. 3. Trade openness has also an effect on domestic prices, through the downward pressure that it exerts on wages of sectors more exposed to foreign competition. The threat of delocalization and of outsourcing has been used to moderate wage growth and to keep labour costs low. 4. A global economy also tends to reduce bottlenecks and capacity constraints, thus reducing the sensitivity of inflation to domestic supply problems. Supply and demand are increasingly determined at a global scale. 5. Increased competition implies a process of selection in the domestic market, with less efficient firms that will be driven out of business. This implies an increase in overall productivity and a decrease of prices. 6. Finally, even when the share of imports is low, and hence the direct effect plays a limited role in affecting inflation, the simple threat coming from potential competitors will force domestic producers to keep prices low. The notion of market contestability, introduced by Will Baumol in oligopoly theory, fully applies to international trade, and explains why the reduction of inflation also appeared in relatively closed economies (like the US for example).

The briefing paper of December 2007 considered also the two apparently opposed views of Lawrence Ball (2006) andKenneth Rogoff (2004). The first argues that most of the effects of globalization on inflation are temporary, in the sense that they are linked to the current transition towards a more integrated world, which pushes prices downwards. Once the transition accomplished, concludes Ball, inflation will go back to more reasonable levels. Rogoff argues that Globalization has modified so deeply the economic environment that inflationary pressures are today permanently lower than in the past (notably through the increased competition that makes prices and wages more flexible). Both opinions seem to be correct but they are referring to two distinct mechanisms. Ball refers mainly to the effect of globalization on income -and the end of the terms of "trade's rent" -Rogoff to the effect of the dismantling of the barriers to trade on competition.

It is my opinion that we have already seen most of the second effect, and that the first (the Ball effect) will dominate in the future. The consequences of the huge structural shock represented by the big doubling are inevitably beginning to fade, as the generalized wage increases in China's urban areas witness. The balance between satisfying external and internal demand will certainly progressively change in china.

In the next few years the deflationary effects of emerging economies' participation to the global trade system will be reduced. Furthermore, the delocalization of production to low wage countries in the past has created an excess capacity, that on one side helped to keep prices low, and on the other induced firms to close production units in rich countries. Now that emerging economies are growing richer and increase their demand, we are heading towards less excess capacity.

A second important factor is that the increasing wealth of emerging economies increases demand (both for consumption and for production) of scarce and exhaustible resources like energy and food. This effect is for the moment weak and there is some debate among economists about its responsibility in the increase in the prices of commodities. Some for example would argue that the increase in the Chinese demand for oil between 2005 and 2008 represents 1% of total oil demand (and less than half of this amount for India) and can't thus explain the huge increase of oil prices. But in an oligopoly market where supply is controlled by producers, a marginal increase of demand may have huge effect on prices. And whatever the past this effect will certainly gain momentum in the future, and will contribute to a large increase of the rent of the owners of these goods.

A distinct argument is that the attempts of advanced countries to weaken their dependency on exhaustible resources and to respond to the increased demand of clean environment by their population may contribute to increase inflation pressures: climate change policies may in effect impose higher prices in energy and energyintensive goods and services. So what? Should we in order to avoid transitory increase in the equilibrium inflation rate, or in its volatility, renounce to invest in the future and especially in new technologies of environment and energy? If these investments prove profitable their effects on energy productivity will in the medium to long run decrease the pressure on prices. Moreover, there may be here a measurement problem: the increase in headline inflation consecutive to these policies may well reflect a quality effect because it affects positively the welfare of the people.

Finally, a sometimes ignored feature of globalization is the restructuring of the economy, which implies the reallocation across sectors of demand and productive capacity. During this process the variance of excess demands and supplies increases and the equilibrium inflation rate with it. This effect will of course become less important as the restructuring comes to an end, but it is likely to play an important role in the next years.

Thus, pressure for inflation to increase so as to reach a new equilibrium level (albeit still low) will come from rents, from price adjustment asymmetries, from climate change policies and from the reduction of excess capacity and excess supply of labour. This effect will be mitigated by a probable reduction in profit margins -which are at a very high level today as a consequence of the "great doubling"-as it is normal when the labour market is exhibiting a tendency towards a vanishing excess supply of labour. It has to be reminded as shown in the following graph that the share of wages in value added has decreased since the middle of the eighties, and has still decreased in the more recent period. That means it exists some room of manoeuvre for this share to rise in the future without creating inflationary pressures. 60% 65% 70% 75% 80% 85% 1 9 7 0 1 9 7 1 1 9 7 2 1 9 7 3 1 9 7 4 1 9 7 5 1 9 7 6 1 9 7 7 1 9 7 8 1 9 7 9 1 9 8 0 1 9 8 1 1 9 8 2 1 9 8 3 1 9 8 4 1 9 8 5 1 9 8 6 1 9 8 7 1 9 8 8 1 9 8 9 1 9 9 0 1 9 9 1 1 9 9 2 1 9 9 3 1 9 9 4 1 9 9 5 1 9 9 6 1 9 9 7 1 9 9 8 1 9 9 9 2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 2 0 0 5 2 0 0 6 2 0 0 7

What Implications for Monetary Policy?

If the analysis above were correct, the most immediate and obvious consequence would be the necessity of an upwards revision of the ECB target. I already argued in the past (Fitoussi ( 2002)) that the 2% objective had been chosen in a period of abnormally low inflation, and that we risked experiencing excessively restrictive monetary policy because of that. This argument is even stronger today: last July the ECB raised its rates of a quarter of a point, while the Euro zone was experiencing the first period of negative (quarter to quarter) growth. A too low inflation target may lead to a backward looking monetary policy! More generally, in a situation in which some goods exhibit important price increases due to structural factors, the only hope to avoid an increase in the general price level lies in the capacity for policy to be able to reduce the price level in other sectors, in order to compensate. I see two different ways to obtain this objective.

The first is a policy mix (low interest rates and targeted fiscal measures) able to facilitate investment and productivity growth in some sectors, thus lowering unit labour costs and prices.

The second is a policy mix aimed at reducing inflationary pressures through brakes on aggregate demand. The current policies carried out today in Europe are leading to a contractionary policy mix. The fear of second round effects, that I discussed at length in my briefing paper of December 2007, pushes the ECB to keep interest rates high in order to avoid wage increases, even when most of today's inflation is imported. This has the consequence of compressing real wages, a phenomenon that all European countries experienced, albeit with different intensities.

This strategy has undesirable contractionary consequences, and makes the burden of adjustment fall disproportionately on the shoulders of low and middle income households, as I will highlight below. But more importantly, it is not necessarily effective. The asymmetric behaviour of prices implies that, the generalized decrease in demand will call for an adjustment on quantities rather than on prices, and hence will be unable to compensate fully the increase of prices in the energy sector. This mechanism is the core of the increasing risk of entering a stagflation phase. But as said below the likely reversal of commodity prices increases make this risk more remote.

Thus, a policy of high rates and exclusive focus on inflation targeting do not seem to be the appropriate response to the current transition towards a slightly higher equilibrium rate of inflation, because they are likely to depress the economy while being ineffective to fight inflation.

If the above diagnosis is correct, what we need is a policy aimed at facilitating the restructuring of the economy, and at addressing the increasing variance of sector disequilibria. Monetary policy alone could not accomplish this task, and coordination with other policy tools (fiscal policy, competition policy, industrial policy) becomes necessary.

Fig 1 -

 1 Fig 1 -Dow Jones Price Index (2007=100)

Fig

  Fig 2 -Economist Price Index (2007=100)

Real wage per capita: Euro area

	EU CORE	US CORE	EU HEADLINE	US HEADLINE
	1,14
							deflated by value added prices
	1,12
	1,10										0.5%
	1,08
	1,06
	1,04				1.4%
	1,02
	1,00
	0,98
	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008

Real wage per capita: US

	1,18								consumption
										prices
	1,16
	1,14
	1,12
	1,10								0.5%	value added prices
	1,08
	1,06			2%
	1,04
	1,02
	1,00
	0,98
	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008

France Part des salaires dans la valeur ajoutée (en % )

	source OCDE, EO82, VA totale, coût facteurs, corrigée de la non salarisation
	RU
		RU :
		-1.8 points
	USA	USA : -2
		points
		Allemagne :
	Allemagne	-4 points

The situation is further complicated by the increasing income inequality that makes average inflation less and less significant. The dispute on perceived inflation may be partly explained along these lines. The unequal price increase impacts the different income brackets differently. More specifically, energy and food enter in a disproportionately large share in the consumption basket of lower income brackets, which as a consequence experience a larger loss of purchasing power. Nobody recognizes himself in an average figure in a context of growing inequalities. As a consequence the statistical apparatus that we currently use may become too abstract to correspond to perceptions.

Thus income inequality should also be targeted by policy, because for a given average rate of inflation, the negative effects are larger when income is more dispersed. Furthermore; an important consequence of increasing inequality is the accumulation of large liquidities in the hands of a few households. This inevitably has an impact on speculative movements, asset price inflation etc., which may be a major cause of concern for monetary policy. Hence the argument according to which the excessively high growth of monetary aggregates may be finally translating into consumer prices may be misleading. As argued in a former briefing paper excess liquidity may well be the symptom of excess saving due to a set of reasons: increasing inequalities, increased rents (high commodities prices), huge current account surplus in emerging countries etc… Thus "excess liquidity" is likely to affect much more asset prices than consumer prices. Ball, L. M. (2006). "Has Globalization Changed Inflation?" NBER Working Paper, 12687, Fitoussi, J.-P. (2002). La Règle Et Le Choix. Paris, La république des idées, Seuil. Fitoussi, J.-P. and N. Gergescu-Roegen (1980)


Keywords:

Ce texte est une réflexion sur les conditions sous lesquelles les méthodes d'appariement optimal (Optimal Matching Analysis, OMA) peuvent être utilisées en sociologie. Le succès de ces méthodes en biologie ne tient pas à une compatibilité particulière avec des processus biologiques mais plutôt à la manière dont des hypothèses théoriques en biologie sont mobilisées pour déterminer les coûts relatifs à ces méthodes d'appariement. Étant donné que les séquences en sociologie sont le plus souvent composées d'événements et de temps, la détermination des coûts dans les OMA appliqués en sociologie devrait être guidée par des éléments théoriques en sociologie du temps. Après une discussion de la signification et des conséquences des coûts en OMA, ce texte revient sur des éléments théoriques émanant de la sociologie du temps (Durkheim, Elias et Bourdieu) et montre comment on peut les intégrer dans une variante des méthodes d'appariement optimal appelée Dynamic Hamming. À ce titre, ce texte illustre comment la théorie sociologique peut aider à la détermination des coûts lorsque les méthodes d'appariement optimal sont utilisées en sociologie.

Optimal Matching Analysis and Biology

As with any new statistical method in the social sciences [START_REF] Desrosières | La politique des grands nombres[END_REF]) the use of Optimal Matching Analysis (OMA) was much debated at the end of the 1990s, especially with regard to the sociological interpretation of transformations and the role of costs in the findings [START_REF] Levine | But what have you done for us lately?: Commentary on Abbot and Tsay[END_REF][START_REF] Wu | Some comments on "Sequences analysis and optimal matching methods in sociology: Review and prospects[END_REF]. OMA was widely used in biology, where the three operations (insertion, deletion and substitution) supposedly are reflected in biochemical processes. Yet OMA was not created by biologists, but rather originated from research in computer science that Richard Hamming and Vladimir Levenshtein conducted in the 1950s and '60s [START_REF] Hamming | Error-detecting and error-correcting codes[END_REF][START_REF] Levenshtein | Binary codes capable of correcting deletions, insertions, and reversals[END_REF]. In OMA terms, Hamming's distance only uses substitution operations whereas the first distance put forward by Levenshtein uses all three operations, each with a unit cost (see Table 1). Thus the operations used in OMA have nothing to do with biochemical transformations; many of the latter, such as the transposition of sub-sequences, would be missing (Abbott 2000). While it is tempting to attribute the method's success in biology to these similarities, it is in fact through the interpretation and determination of costs that biologists were able to adapt OMA to their data. Yes (cost = 1) Levenshtein II No Yes (cost = 1)

The applications of OMA in biology are quite different from its use in the social sciences since in the former case the goal is not to create typologies, but more often to match a group of sequences with unknown properties to other sequences with known properties [START_REF] Durbin | Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids[END_REF]. Substitution costs are determined on the basis of phylogenetic hypotheses and statistical results, while insertion and deletion costs are set more arbitrarily. Indeed, substitution costs must reflect the probability of change and are empirically estimated from sample sequences with established or probable phylogenetic links. For example, the PAM (Point Accepted Mutation) matrixes are estimated on the basis of proteins that are experimentally or hypothetically related phylogenetically [START_REF] Dayhoff | A model of evolutionary change in proteins[END_REF].

The importance of costs

The main lesson that can be drawn from the use of OMA in biology is the importance of focusing on the interpretation and determination of costs rather than seeking an interpretation in the operations themselves.

The interpretation of substitution costs is key in this respect since they need to reflect the proximity between the different states in which the sequences unfold. In biology this proximity between states is interpreted in phylogenetic terms and the costs are therefore derived from samples based on phylogenetic knowledge and hypotheses. In the social sciences this probability must express the degree of sociological proximity between states. But what is meant by sociological proximity?

It is precisely this issue that other critiques have targeted. In fact, the first researchers to use OMA in sociology often expressed doubts as to their choice of costs and the sensitivity of their results to these choices. As Katherine Stovel and her colleagues stated, "The assignment of transformation costs haunts all optimal matching analyses" (Stovel et al. 1996, p. 394). If the results are too sensitive to costs it means that the costs, and not the data, are producing the results [START_REF] Wu | Some comments on "Sequences analysis and optimal matching methods in sociology: Review and prospects[END_REF]. Conversely, if the results are not sensitive to costs, how could OMA be valid [START_REF] Levine | But what have you done for us lately?: Commentary on Abbot and Tsay[END_REF]?

The empirical consequences of costs

Before delving into the interpretation and determination of costs, it is worth noting that in instances where the analysed data shows temporal regularities, costs can only have minor effects on the results. This is hardly surprising. In terms of classification analysis these are instances of strong clusters or stable groups, that is, groups of very similar individuals that will end up being grouped together no matter what distances and classification methods are used. (Lebart et al. 2006, p. 254). Classification specialists generally seek to identify these strong clusters. By definition, a group of virtually identical sequences needs very few transformations to make them identical, and any assigned cost will have very little influence on this group.

The greater the differences between the compared sequences the greater the importance of costs.

When the data include several strong clusters, costs are important at two levels. First, costs play a role in cases that do not fit into stable groups as easily as others do. Depending on their nature, costs assigned these atypical sequences to one or another of the strong clusters, and, if need be, to a more heterogeneous group including rare sequences. Second, costs also have an impact on the distance between the strong clusters and, in the case of an ascending hierarchical classification, affect the way in which they might be aggregated. Costs therefore play a role, albeit not always a clear one since it often involves variations in the number of sequences assigned to each stable group by the classification or partitioning algorithm.

Determining costs first requires understanding and interpreting them with regard to the processed data and purpose of the analysis. In the social sciences the order of states is not tied to a biochemical combination as it is in biology, but rather to time. When a state is inserted in, or deleted from a sequence to make it identical to another, a time shift occurs between these two sequences. The more these two operations are used, the more the elements to be compared will be distant in the original sequences.

Insertion and deletion operations therefore warp the position of the elements of the sequence. On the other hand, substitution operations respect the position of sequence elements, the trade-off being that states are replaced. Once insertion and deletion operations have been used substitution operations do not introduce additional shifts; however, they only recognise the shifted positions of the states to be substituted. In sum, insertions and deletions shift the sequences in order to identify identically coded subsequences, while substitutions do not shift the sequences but replace states with others. In the first case the time structure of the sequences is altered, and in the second the states of which they are made undergo change (Lesnard 2010). When the substitution cost is double the insertion-deletion cost or more, substitution operations are no longer used since it is equivalent or less costly to insert the desired state and delete the other than it is to substitute them [START_REF] Kruskal | An overview of sequence comparison[END_REF]. Conversely, when substitution costs are very low compared to insertion-deletion costs, the latter operations are no longer used. As a result, any cost combination falls within the distances ranging between Levenshtein 2 and Hamming (see Figure 1). In the first case (Levenshtein 2) the algorithm seeks to shift the sequences in order to compare identically coded, but not necessarily contemporaneous sub-sequences. In the second, the algorithm only takes identical subsequences into account (that is, a series of identical states located in the same place in the sequences).

The Levenshtein 1 distance is a sort of compromise between these two poles. The choice of costs thus depends on the time scale and its importance for the analysis. The greater the importance of respecting the time scale, the more imperative it is for costs to approach or reach the Hamming distance.

Multiple substitution costs

By definition, in a state space the constituent states are considered to be different and to refer to situations that are not, from an analytical viewpoint, of the same nature. Several substitution costs are generally used and either empirically or theoretically defined to reflect the fact that some states are considered to be closer than others. Thus, in their study of intergenerational social mobility, Halpin and Chan define substitution costs according to a nomenclature of social classes and their theoretical distance [START_REF] Halpin | Class careers as sequences: An optimal matching analysis of work-life histories[END_REF].

Frequencies of transitions between states, calculated on the basis of all episodes, have also been used to define substitution costs. This solution is equivalent to assigning costs of substitution between states that decrease with higher levels of observed transitions between them. However, this practice has been challenged because substituting a state with another is theoretically not a transition and substitution costs must reflect the proximity of states [START_REF] Abbott | Measuring resemblance in sequence analysis: an optimal matching analysis of musicians careers[END_REF][START_REF] Halpin | Optimal matching analysis and life course data: The importance of duration[END_REF] The use of only one substitution cost therefore presumes that no state is a priori closer than another.

Using a matrix of substitution costs introduces information on the closeness of states into the analysis. To set lower substitution costs for certain states consists of positing that these states are close but different, allowing for the grouping of these sequences if they are sufficiently similar. In other words, if the differences between two sequences only concern certain states with low substitution costs, then the total minimum cost will be low and they will show close general proximity. In the context of sequence comparison in the social sciences, this close proximity between states can be interpreted to mean that even if a difference appears in two sequences at a given moment this difference is almost negligible, and that if the differences are of this nature then the algorithm should consider them to be unimportant. Indeed, a low substitution cost is only of interest if it is much lower than the combined cost of a deletion and an insertion. A low substitution cost will cause the algorithm not to shift the sequences to look for an identical sub-sequence, while a high cost will prompt a search for identical but shifted subsequences. Low substitution costs lead to the search for contemporaneous, identical sequences, thereby implying that the sequences are also close. In other words, to claim that certain states are close is equivalent to positing that the presence of these states in two sequences is the marker of their proximity as a whole, and that they might belong to very similar social rhythms. Conversely, if two sequences have two states with high substitution costs the implication is that the sequences are distant and that it is more useful to look for identical but shifted sequences. This also holds true in biology since substitution costs between two elements of a DNA sequence decrease the closer they are phylogenetically -a proximity that extends to all the sequences in which they appear.

In the time frame characterizing the use of OMA in the social sciences, substitution costs also relate to the whole sequence: does the presence of two different states point to two very different social rhythms? With a single substitution cost there is no reason to presume the answer to this question and the facts can speak for themselves: social rhythms appear in the typology. A matrix of substitution costs suggests the existence, be it theoretical or empirical, of certain social rhythms -combinations of states that signal closer proximity. Typologies created with a matrix of substitution costs present two types of groups. The first includes sequences where some parts are close but time-shifted while the second includes sequences where identical or very similar sub-sequences are contemporaneous.

More precisely, since the sequences that are not part of a strong cluster are most affected by costs, the sequences that are most difficult to classify will be assigned to the strong cluster to which they come closest. A matrix of substitution costs will then adjust this allocation by emphasizing either the closest contemporaneous sub-sequences (low substitution costs) or shifted identical sub-sequences (high substitution costs). Is it legitimate to assign the sequences to strong clusters in different ways, according to the proximity defined in the matrix of substitution costs? Rare sequences are, by definition, difficult to and given that the goal of taxonomy is to classify there are only two possible solutions: either assign them to strong clusters or relegate them all to an unclassifiable category.

There is a need here to distinguish between rare sequences with sub-sequences that approach strong clusters, and very rare sequences that are difficult to move toward a stable group. Empirically, what OSC -Notes & Documents N° 2014-01 Laurent Lesnard -Using Optimal Matching Analysis in Sociology: Cost Setting and Sociology of Time 5/12 most often appears is a catchall category that cannot be interpreted. So the question is whether it is desirable to assign rare sequences that share several characteristics with strong clusters. If the goal is to find the most homogeneous groups (outside of the one that brings together the unclassifiable sequences), then all of the costs must be high in order to increase the distance between them and the rare sequences. If less homogeneous classes are acceptable, then a matrix of substitution costs allows for more flexibility in managing allocations to stable groups.

From this perspective transitions provide partial information on social rhythms and it therefore seems reasonable to use this information; indeed, the use of a low substitution cost in the social sciences implies that the difference between the two states does not indicate that the sequences belong to two different groups of rhythms. Using transitions to determine substitution costs is equivalent to substituting diachronic proximity for synchronic proximity, which recognizes that certain states link together more often than others over time, pointing to a greater proximity of these states. However, using transitions between states to set substitution costs raises the issue of circularity because transitions are generally calculated from sequences that are then analysed with OMA. Insofar as this method is descriptive it is not really a problem, especially since transitions are aggregated while sequences are individual.

Optimal matching methods and social theory of time

A large portion of my research using OMA focuses on time use surveys [START_REF] Lesnard | Off-scheduling within dual-earner couples: An unequal and negative externality for family time[END_REF]Lesnard 2009;Lesnard 2010;[START_REF] Lesnard | Investigating scheduling of work: A two-stage optimal matching analysis of workdays and workweeks[END_REF]. These surveys feature a time diary in which respondents must describe activities over one or several days. The temporal dimension of the sequences derived from the time use surveys is therefore very strong. In this respect the analysis of time use through OMA aims to go beyond the so-called "time budget" approach, which reduces time uses to durations, by reintroducing chronology into the study of daily lives. It is therefore necessary to limit time distortions and curb the use of insertion and deletion operations that emphasize identical sub-sequences -that is, in terms of time use, the time-consuming identical activities that take place at different times of the day -and thereby focus on duration rather than timing. This is also true for other sequences that include a time dimension: when shifts are emphasized the similarities highlighted are series of identical states, meaning the duration of identical subsequences is emphasized to the detriment of timing. Sequences in the social sciences most often have a time dimension and the goal of OMA is precisely to underscore possible temporal regularities. The risk in intensively using insertions and deletions is to obtain results that are highly dependent on similarities in duration to the detriment of similarities in timing. It is perfectly legitimate to value duration over timing, but in this case solutions that are simpler and faster than OMA should be favoured, such as a cluster analysis directly and exclusively applied to duration.

Thus the analysis of time use surveys using OMA reveals more general problems with the use of this type of method on sequences in the social sciences; these are especially important in the case of time use where the point of using OMA is to identify different types of distributions of work hours, the warping that any insertion or deletion introduces into the subject of study itself is particularly problematic [START_REF] Lesnard | Off-scheduling within dual-earner couples: An unequal and negative externality for family time[END_REF].

Consequently, only substitution operations should be used. The state space is highly simplified: two for individual work hours (work and non-work), four for couples (nobody works, the two spouses work, one of the spouses works but the other does not and vice-versa). The issue I faced was whether to use one cost -Hamming's distance -or several. The Hamming distance effectively amounts to counting the number of discordant pairs in two sequences: any gap, even if it is minimal, increases the distance. Even though insertion-deletion operations are undesirable, I felt it was necessary to somewhat mitigate the radicalism of this parameterisation.

To this end I developed a variant of this distance: the dynamic Hamming distance (DHD) (Lesnard 2010). Like the Hamming distance, DHD only uses substitution operations in order to best preserve the timing of the sequences. Its specificity is in the use of costs, which depend on transitions between states and which change over time. The distance between states varies over time and decreases when the transitions before and after the considered date are strong between the state and the one for which it is to be substituted.

For example, in the 1998-99 time use survey the transition from no work to work accounted for 22% of the working population between 8:00 and 8:10 but only 3% between 10:40 and 10:50. With DHD the two states would be considered close at 8:00 and far at 10:40. For the vast majority of employed people the early morning is the beginning of the workday, so it would not be very costly to make identical two sequences that contain different states, given that differences at that time of day are not important. Midmorning, however, such differences indicate different working rhythms that will be reflected in the distances between their respective sequences. DHD thus takes limited gaps into account without resorting to insertions and deletions that would shift the sequences.

The transitions between the different possible states at any given moment illuminate certain aspects of social rhythms. However, the transition matrixes only provide macro-social information by date without links. With OMA these matrixes can be expressed in terms of distances between individual sequences, allowing for the creation of taxonomy. In other words, by integrating transitions between states in OMA, DHD individualizes them and connects them to one another in order to better identify the different social rhythms that underlie the aggregate figures of transition matrixes.

An arithmetically identical number of years (or minutes) may refer to substantial social differences. This is a classical result from the sociology of time pioneered by Hubert. Using his research on the links between time, magic and religion, Hubert showed that the calendar is underpinned not by a quantitative time, but rather a qualitative time made of discontinuous and heterogeneous episodes [START_REF] Hubert | Étude sommaire de la représentation du temps dans la religion et la magie[END_REF]. The linearity of calendars and clocks in no way implies that time is linear. By considering sequences in their entirety, OMA, and DHD in particular, help place the various elements into their context and thus restore this heterogeneity.

Sociology of time

The process of deriving substitution and transition costs and allowing them to vary over time also needs to be linked to the sociology of time program initiated by Hubert and Durkheim and further developed by Norbert Elias and Pierre Bourdieu. Building on Hubert's seminal work, Durkheim outlined an agenda to develop the sociology of knowledge. For Durkheim categories of understanding are not transcendental (that is to say innate, constitutive of human nature) but rather derive from the organization of life in society [START_REF] Durkheim | Les formes élémentaires de la vie religieuse[END_REF]. In an analysis of ethnographic writings and materials on the Aboriginal, Durkheim showed that time in these societies is a religious symbol that separates the sacred from the profane, forming two homogeneous, alternating periods of time that punctuate the Aboriginal calendar. This alternation also reflects the ebb and flow of community life: during sacred times the group gathers, whereas profane times are more isolating, focused on individual and family survival. The homogeneity of, and conceptual difference between the two times thus refer to distinct collective practices and temporalities, or relations to time: in other words the time category of understanding is interdependent with the Aboriginals' binary social rhythm.

One of the consequences of this first cornerstone of Durkheim's sociology of time is that a "calendar expresses the rhythm of collective activity while ensuring that regularity" (Durkheim 1912, p. 15). The history of calendars and other systems for determining time is also that of social rhythms and of temporality. Indeed, as Pierre Bourdieu put it, time is a symbolic system that is structured -by the collective rhythm, embodied by religion in less differentiated societies -and structuring -as a temporality or form of temporal knowledge (Bourdieu 2001, p. 201). Time, and more generally all symbolic systems, follows "logical conformism" (Bourdieu 2001, p. 204), meaning that it both accepts and validates the social order. A system for determining time, as a symbol, cannot be used if its use is not known and recognized by the whole group. In less differentiated societies that consist of small autonomous communities with a limited division of labour and somewhat interchangeable members, given that identity is not very individualised but rather dominated by the group, social order is based on respect for the group and its rhythm, through religion. In these societies, to follow the collective rhythm is to alternate between the sacred and the profane, and between collective time and more individual time.

Calendars and, in general, any system to determine time such as the clock, were not intended as time measuring instruments, but as a means to mark time: "the institution of calendars is not intended solely, and probably not even primarily, to measure time as a quantity. It does not derive from the idea of a purely quantitative time, but rather the idea of a qualitative time that is made of discontinuous and heterogeneous parts and that constantly turns on itself [START_REF] Hubert | Étude sommaire de la représentation du temps dans la religion et la magie[END_REF]. Calendars crystallize and stabilize collective rhythms and activities (Durkheim 1912, p. 15): "Units of time are not units of measurement but of a rhythm where oscillation between alternatives periodically leads back to the similar" [START_REF] Hubert | Étude sommaire de la représentation du temps dans la religion et la magie[END_REF].

It is therefore the tools developed in relation to the social symbol of time that bear the traces of shared transformations in the organization of society and time, that is, of collective rhythms and temporalities. To paraphrase Hubert, the history of calendars reflects the evolution in the "code of the qualities of time"1 , the direction and degree of diversification of collective life and also the "level of synthesis", as defined by Elias [START_REF] Elias | The Symbol Theory[END_REF], of the symbol of time.

In this respect, the appearance of bell clocks in European towns in the Middle Ages was a key step in the process of social and temporal differentiation. The different rhythms of urban collective life in the Middle Ages2 created synchrony issues throughout the day that were resolved by using multiple acoustic and optical signals: bands, flags, pennants, and especially bells. At first canonical hours -some marked by ringing church bells -were used as time references in several areas of collective life: for example, the market's opening coincided with the bell sounding the end of mass, while the end of the workday for day labourers was marked by the bell for the compline.

Beginning in the 14 th century the development of cities created the need for a wider variety of time signals that church bells alone could no longer handle. Cities decided to acquire bells to convene meetings, indicate payment due dates for interest and taxes, assemble each neighbourhood, set market hours, etc. This inflation of urban signals culminated with work bells that set working hours for salaried workers. The multiplication of urban signals also reflected the increasing division of labour since a number of them were no longer aimed at the community as a whole, but rather at particular groups (employees, members of various councils, travellers, merchants, etc.).

The increasing need to synchronize certain groups fed into a complex system of acoustic and optical signals in big cities that probably reached its climax at the beginning of the 14 th century. Growth in the number of acoustic signals could in large part be attributed to the coordination needs of certain groups, as opposed to the urban communities as a whole. As long as collective life was punctuated by a series of events involving the entire community, a single signal could ensure coordination, as was the case in the sounding of canonical hours. The proliferation of bells testified to the division of labour, and therefore the pluralisation of time: in the towns of the Middle Ages, time was no longer alternating between the sacred and the profane, but differentiating with the development of functional interdependence. However, when the bells started sounding the temporal rhythms for certain segments of the population in addition to those for the community as a whole, they became less effective at finely synchronising sub-groups of the population.

Today, it is hard to imagine the background noise that the bell signals created on a daily basis: "Everyday life was temporally structured through and through by bell signals, with hardly a day resembling another.

Apart from signals for proclamations, prohibitions and ordinances, the inhabitants of the city also received a wealth of acoustic information about important public civic events" (Dohrn-van Rossum 1992, p. 217). Laurent Lesnard -Using Optimal Matching Analysis in Sociology: Cost Setting and Sociology of Time

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The introduction of bell clocks in the 14 th century unified and simplified the various acoustic signals.

The clock bells did not chime for anyone in particular. Rather, different groups or segments of the population could use the signal to synchronize. Because clocks can only ring for equal hours without introducing too many technical complications, the system of canonical hours, and attendant hold of religion over time, collapsed and liberated other collective times from their ties to religious time (Landes 2000, p. 81).

Bell clocks substituted a regular and neutral tempo for the profusion of specific and muddled signals.

However, hours did not mark any particular event; it was up to the local community's members to associate them to collective or private activities they wished, or were required to attend. Before bell clocks were introduced the relationship to time was theoretically still largely an external constraint that elicited poor anticipation. Everyone knew that it was time for a lunch break when they heard the work bell ring a second time. One only needed to recognize the sound of different bells to situate oneself in time. With bell clocks hours had to be linked to events: time constraints were no longer explicitly marked by a particular bell, but rather implicitly signalled. Each hour chime only evoked the constraints that one chose to associate with it.

Specific time constraints therefore had to be internalized by each individual. The introduction of the bell clock marked the beginning of the internalization of time constraints, or at least accelerated this process. With the clock striking hours, people had to get into the habit of adjusting their behaviour in response to the signal. The regularity of hours also allowed for a greater anticipation of the day's events, whereas the previous system was characterized by very low predictability. Thus the new system provided a greater opportunity to regulate one's behaviour, that is, to self-regulate. Paradoxically the homogeneity of the movement of the clock's hands was precisely the sign of the heterogeneity of time: autonomous social areas emerged along with their particular collective rhythms.

In the everyday life of individuals involved in a number of fields, time at the individual level alternated between the different times in various social fields (Halbwachs 1947, p. 167;Bourdieu 2003, p. 202). This meant that the rhythm of daily life was determined in large part by the rhythms associated with positions held in different social fields. Sequences of participation in social fields could come into conflict due to inconsistences in the rhythms associated with successively held positions.

Over the longer run, life courses can also be analysed as alternating participation in the principal social fields, which are the economic field and the family field (Bourdieu 1994, p. 135-45). In contemporary societies adult status is achieved through economic independence from one's original family and the formation of a so-called childbearing family. It therefore involves two forms of integration, in the productive and in the married and parental worlds, and is generally marked by events such as the end of studies, the first job, leaving the parental home, the first relationship and/or the first marriage and the birth of a first child [START_REF] Modell | Social change and transitions to adulthood in historical perspective[END_REF]). The study of early adulthood actually comes down to analysing access to the economic fields (directly or indirectly through marriage) and family field (with a new status, through the formation of a so-called childbearing family), as well as their interlinks.

A social field's time has two dimensions since it is both the rhythm of collective life for the group of agents involved, and a relationship to time and to the future in the field (temporality). Using all the OSC -Notes & Documents N° 2014-01 Laurent Lesnard -Using Optimal Matching Analysis in Sociology: Cost Setting and Sociology of Time 10/12 transitions as substitution costs is a way to break down the average rhythm they represent into homogeneous collective sub-rhythms, and thereby describe in detail the collective life of the field under consideration. With DHD the structure of the state space (distance between the states) is no longer static but bends to the rhythm of collective life. In theory this adaptation of Hamming's distance goes further since the temporality of one field flows from the field's repeated exposure to the collective rhythm. The use of transitions allows for collective rhythms to be described in ways that make sense in terms of a field's temporality. The differences between states, which are variable over time, have a meaning for the agents in the given field. To work or not at 9:00 AM is not socially very significant, while the opposite would be true for 11:00 PM. Similarly, to transition from unemployment to employment at age 20 or 25 does not have the same significance as a first entry into the labour market at age 30.

This is what makes OMA and DHD in particular a type of descriptive method that is especially well suited for sequences in the social sciences. The mean is also descriptive and could be used to describe these sequences, but it does not take into account the heterogeneity of time and therefore imposes the linear framework of the clock on time; as a result, the collective rhythms disappear. DHD is a method for describing sequences that incorporates the heterogeneity of time in its very design, drawing on the sociological theories of Durkheim, Elias and Bourdieu. It includes key elements from each of these authors. DHD centres on the Durkheim's dual concept of time as it was reworked in the research of Elias and Bourdieu on social differentiation and the concept of fields.

Strictly speaking, the use of DHD implies the adoption of this general theoretical framework. This means considering the state space -a cornerstone of OMA that is often little discussed -in this framework.

Discussion on the use of OMA in the social sciences has focused on transformation and cost issues and has relatively ignored the state space, which, unlike in biology and computer science, is not given but rather is a matter of choice. Field theory can help guide this choice: the state space must represent the simplified structure of a field. The different states should be able to capture the collective rhythm of the field or at least one of its aspects.

More generally, the inclusion of DHD in the theoretical basis of the sociology of time illustrates the links that can be made between theory and optimal matching methods. In the same way that regression models cast the functioning of society in terms of a "general linear reality" that is at odds with most sociological theories [START_REF] Abbott | Transcending general linear reality[END_REF], the choice of costs for OMA is never methodologically neutral. In particular, the use of insertions and deletions focuses the analysis on duration and therefore ignores similarities in timing but also more generally the heterogeneity of time. This may be perfectly legitimate, even if in this case it would be easier to use a simple cluster analysis on the durations, but it must be justified. Although the effect of costs on the results is often subtle, use of OMA in sociology must be made in a rigorous methodological framework so that it no longer appears as the black box disparaged by some of its critics.

Figure 1 -

 1 Figure 1 -Patterns corresponding to costs in Optimal Matching Analysis (Lesnard 2010)

  surveys. Indeed, in the even more specific case of research on the work hours of individuals and couples, OSC -Notes & Documents N° 2014-01 Laurent Lesnard -Using Optimal Matching Analysis in Sociology: Cost Setting and Sociology of Time 6/12

Table 1 -Hamming and Levenshtein Distances (Lesnard 2010)

 1

		Transformations used
	Distance	Substitution	Insertion and deletion
	Hamming	Yes (cost = 1)	No
	Levenshtein I Yes (cost = 1)

  ). OSC -Notes & Documents N° 2014-01 Laurent Lesnard -Using Optimal Matching Analysis in Sociology: Cost Setting and Sociology of Time

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"The calendar is the periodic order of rites. Its history also teaches us that it is the code of the qualities of time. The first calendars were almanacs that recorded, day by day, magico-religious forecasts and prescriptions"[START_REF] Hubert | Étude sommaire de la représentation du temps dans la religion et la magie[END_REF]).

Meetings of bourgeois councils or courts to deal with the affairs of the town, market gatherings, the beginning and end of work for day labourers, the opening and closing of city gates, and more unusual events such as gatherings to respond to threats of fire or of war(Landes 2000, p. 76; Dohrn-van Rossum 1992, p. 206).