Società italiana di economia pubblica

WORKING PAPERNo 706

marzo 2016

 

CAPITAL, GROWTH AND INEQUALITY IN PIKETTY'S APPROACH. IS IT ABLE TO EXPLAIN LEVEL AND CHANGES OF INEQUALITY IN THE

PERSONAL INCOME DISTRIBUTION?

Renata Targetti Lenti, Università di Pavia

JEL Classification: P16, P48, D31

Keywords: Capitalism, Inequality, Income Distribution

società italiana di economia pubblica

c/o dipartimento di scienze politiche e sociali – Università di Pavia

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Capital, growth and inequality in Piketty's approach. Is it able to explain level and changes of inequality in the

personal income distribution?

Renata Targetti Lenti1

Abstract The paper is a critical review of Piketty’s book “Capital in the XXI Century”. The book provides a general theory of the functioning of a capitalist economy. Piketty’s intent is to link the functional and personal income distribution to the economic growth. The setting can be called "classic". However Piketty is not interested in explaining the role of capital accumulation on economic growth, but instead the inverse relation, that is the role of economic growth on the increase of the returns to capital, on the concentration of wealth and of income’s inequality in capitalist economies. In this review Piketty’s framework is discussed arguing that it can explain only partially level and changes of the personal income distribution. The factors which explain the dynamic of wealth (accumulation of capital) are different from those which explain the dynamics of labor income (demand and supply of skills and education, technology). It is very difficult, therefore, to reach a consensus on a shared theory of personal income distribution. Piketty links in a very innovative way the returns from capital r to the rate of growth of national income g comparing them in a macroeconomic framework. He claims that when returns on capital rise more quickly than the overall economy and taxes on capital remain low, a vicious circle of ever-growing dynastic wealth, and growing inequality, takes place. However the fact that r exceeds g explains nothing about the rise in inequality. An analysis of the generation of personal incomes, and consequently of inequality, requires a suitable framework that links personal endowments to incomes. At the end I will indicate some steps that could be required by framework suitable to analyze the personal income generation process. JEL Classification: P16, P48, D31 Keywords: Capitalism, Inequality, Income Distribution

                                                            1 Università degli Studi di Pavia, e-mail: targetti@unipv.it

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1.Introduction Capital in the XXI Century is an economic, social and political history of the evolution of income and wealth. Thomas Piketty has summarized the main features of its extensive and well-documented analysis in a series of interviews and conferences. He claimed that Capital in the 21st century is primarily a book about the history of the distribution of income and wealth. Thanks to the cumulative efforts of several dozen scholars a relatively large historical database on the structure of national income and national wealth and the evolution of income and of wealth distribution, covering three centuries and over 20 countries has been collected. The economic, social and political processes that can account for the many evolutions that we observe in the various countries since the Industrial Revolution have been analyzed (Piketty, 2015a, p.1). The result has been a revolution in the understanding of long-term trends in inequality. Previously the analysis of the inequality in income distribution rarely had been carried out in the long run. Even when it was taken into account, the estimates of inequality concerned only income, and almost never wealth. Piketty’s book has been translated into Italian and published by Bompiani in 2014 (Il capitale nel XXI secolo). It was published in French in 2013 (Le Capital au XXI siècle) and, almost immediately, it was translated and published in English in April 2014 (Capital in the Twenty-First Century). Numerous newspapers and magazines, especially Americans, have hosted reviews, almost always very positive. For well-known economists such as Krugman (2014), Stiglitz (2014a, 2014b), Milanovic (2014), Solow (2014). Capital in the XXI Century is an important contribution to economic thought, and in particular the interpretation of the relationship between growth and inequality in the long run. Some critical reviews were also published more recently. The reliability of the data has been challenged by a speech by Chris Giles (2014), responsible for the economic part of the Financial Times. These remarks fail to significantly weaken the volume content and were followed by equally numerous articles in defense of Piketty. According to Andrea Brandolini (2014, p. 2), empirical data are the volume’s core knob “a distinctive feature that gives it originality and strenght". Piketty’s book has already allowed, and will allow in the future, to promote a very rich and innovative debate. It has placed at the center of the economic and political debate the issue of inequality and its perpetuation through the generations along the hereditary transmission of different forms of physical (productive, land and estate) and financial capital. The functional distribution of income between capital and labor become again a central theme of economic analysis as it used to be for the economists of the nineteenth century. The debate on growing inequality was been raised, firstly, by Stiglitz (2012) with The Price of Inequality. It was been enriched by two other works: Inequality (Atkinson, 2015) and The Great Divide (Stiglitz, 2015). Factors that have contributed to the increase in inequality in the last years are numerous. Some are specific and endogenous to the different national contexts, others are exogenous. In industrialized countries, factors as the decay of labor unions and of collective bargaining, the erosion of minimum wages, the increase in the relative weight of capital in comparison to labor, the increasing weight of top incomes from labor, the unequal access to education, the regional dualism, in addition to demographic factors and fiscal, redistributive and monetary policy, are considered sources of inequality. These factors, however, cannot, by themselves, explain the rise in inequality in recent decades. The opening and the liberalization of national and international markets, the intensification of globalization and of the Information and Communication Technology (ICT) are certainly among the most important external factors that contributed to the increasing inequality.

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The main thesis of Piketty’s book is that poverty and growing inequality in wealth’s and income’s distribution are the critical issues facing the world today. These inequalities are deeply rooted “within modern industrial capitalism”. The main forces that shape the concentration of incomes are not only economical, but also institutional and political. They are path of growth of the economy, wars, rules of transmission of heritage, taxation and inflation. These factors are estimated and discussed in an overall economic framework. In some 950 pages of the French original, and in 696 pages of the English translation, are packed so many topics, insights, comments and observations that affect almost any sphere of economics, than no single survey can summarize them. In this review I will focus mainly on the factors which can explain the trends of the concentration of wealth and of personal income distribution. I shall also present some features of the theoretical framework discussing some of the aspects which can be considered weak from the analytical and methodological point of view. In particular I will discuss Piketty’s framework as a schema which can be considered suitable, or not, to explain level and changes of the personal income distribution. 2. “Bringing Income Distribution in from the Cold”. Economic inequality has long been one of the major themes of socio-political debate and conflict, but interest in this topic from the point of view of economic research has waned over time. GDP per capita was widely considered to be a satisfactory indicator of economic prosperity. Having been rather neglected during the period of sustained economic growth in Western Europe and North America that followed the Second World War, the 1960s and 1970s saw a resurgence in interest that has been further accentuated by recent trends. A very substantial body of research on inequality has been accumulated, building on the potential of improved data and focused on clarifying concepts and measures, capturing trends, and understanding the causal processes at work back and forth to the economy. The interest toward inequality in income distribution raised with the deterioration of social and economic conditions following globalization, financial crisis and unemployment. Inequality has become the focus of remarkably wide-ranging attention, from Davos “World Economic Forum” and the State of the Union Presidential address to Oxfam Reports and to, finally, also academic journals across a variety of disciplines. Globalization has increasingly influenced economic and political conditions in the developed and developing countries. It has raised new concerns about the gap between developed and developing countries. The share of profits in national income has risen in rich nations and the mobility of capital has led to financial crisis. The increase in the size of the labour force engaged in the global economy with the opening up of China and India to greater levels of trade in goods and services over the past decade has potentially dramatic implications for workers in OECD countries, not least for labour’s bargaining power vis-à-vis mobile capital. The question is ‘why should economists “care’ about inequality’? Equity is a fundamental value in democracies. It is connected to the functioning of the economic system (Atkinson, 1997). Economic inequalities can be conceived of as inequalities which produce some other economic effect or as being an outcome of the underlying economic process. Individual differences provide behavioural incentives to work, save, or take an entrepreneurial risk. Inequalities tend to be self-enforcing and self-sustaining. Inequality in one respect or for one group may hang together with

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equality in another respect or for other groups. Linkages and effects amongst and between inequalities are not necessarily obvious and their unrevealing requires analytical effort. The issue of inequality was been released from the agenda of economic research, also as a result of the growing influence of neo-classical thought. The belief that there may be a trade-off between equality and efficiency has played an important part in the way economists (certainly from a standard neoclassical perspective) have approached the topic. If seeking to redistribute income and other economic resources reduces efficiency and economic growth and thus the size of the ‘pie how do we evaluate the costs and benefits? Robert Lucas (2004, p.15) claimed “Of the tendencies that are harmful to sound economics, the most seductive, and in my opinion the most poisonous, is to focus on questions of distribution”. The progress in economic theory has led to reconsider in recent time the relation between efficiency and equity so that their separability is no longer accepted. In particular, no longer the two concepts can be separated, especially when we take into account the existence of information asymmetries and market imperfections (Kanbur, Lustig, 1999). The first consequence of such non-separability is that income inequality become an integral part of the analysis of economic performance, not a simple “additional” factor to be considered when efficiency has been achieved. More recently, considerable attention has also been paid to the ways in which higher inequality could act as an obstacle to growth. Social protection and the Welfare State more broadly (e.g. via education and health care) can potentially serve to provide an environment that stimulate rather than undermines economic growth. Even more important is the realization that policies might improve both equity and efficiency simultaneously and avoid the trade-off altogether. Special attention must has been paid both to the role of Institutions. Differences in institutions and policies are likely to play an important role in explaining the different levels and trends of wage and income inequality across countries. For instance it has been shown that a substantial portion of wage polarization can be explained by differences in union density across countries. A growing concern has been addressed “to bring the study of income distribution in from the cold” as Atkinson has written, reintegrating it with the core concerns of that discipline. The well-known Kuznets’ inverted U shaped curve between income inequality and the level of income was accepted as true for many years. According to this interpretation inequality increases at low income levels, peaks at some middling income, and diminishes as country becomes richer (Kuznets, 1955). Kuznets, in his monumental study of income distribution in the US (Kuznets, 1953) had observed a big fall in the income share of the richest for the period between 1929 and 1946. But this result was true only for this first period. The following empirical evidence did not confirm this hypothesis. However First Kuznets can be criticized for not using sufficient empirical evidence or reading too much in the very few data points. Inequality in income distribution high income countries is very high and increasing with the rise of income. The share of total income going to the top 1% is rising. A rise of top income inequality in the English speaking countries “and the more modest rise in continental Europe and Japan” occurred from about 1980, in sharp contrast to the decline seen over the previous 40 years. A very recent Oxfam Reports (2016) show that we are living in an Economy for the 1%. The wealth of the world is divided in two: almost half going to the richest one percent; the other half to the remaining 99 percent. Since the turn of the century, the poorest half of the world’s population has received just 1% of the total increase in global wealth, while half of that increase has gone to the top 1%. A global network of tax havens further enables the richest individuals to

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hide their wealth. A forty-year trend of increasing inequality, common to many advanced economies, deserves the search of forces which are deeply rooted “within modern industrial capitalism” (Solow, 2014, p.2). Piketty attempts to answer to some very important questions. Do the dynamics of private capital accumulation inevitably lead to the concentration of wealth in ever fewer hands? Or do the balancing forces of growth, competition, and technological progress lead in later stages of development to reduced inequality and greater harmony among the classes? (Piketty, 2014a, p. 11). Piketty finds the answers to its questions in the endogenous factors which determine the accumulation of capital and the changes in the capital’s and labor’s share in national income. The process “by which wealth is accumulated and distributed contains powerful forces pushing toward divergence, or at any rate, toward an extremely high level of inequality” (Piketty 2014a, p. 27). Growing inequality bring to discuss some issues as how inequality can be analyzed and what set of concrete proposals aimed at reducing it can be put forward. Many answers and proposals are in Piketty’s book. The relationships between variables as capital, saving and growth which are pushing toward divergence in income and wealth are well identified in a macro setting. But the personal income generating process, and its links with inequality, are not really analyzed. Piketty’s framework does not allow to build a theory of personal income distribution. As Pier Luigi Porta argues (2014) “Piketty’s analysis has been justly praised from most quarters. But he risks to focus too much on the symptoms rather than going direct to the heart of the matter and curing the illness”. 3. The model. The “first fundamental law of capitalism”. The book provides a general theory of the functioning of a capitalist economy. Issues on inequality are only one aspect of that general theory. Piketty’s intent is to link the functional and personal income distribution to the economic growth. The setting can be called "classic" in the wake of Smith, Ricardo and Marx. However Piketty is not interested in explaining the role of capital accumulation on economic growth, but instead the inverse relation, that is the role of economic growth on the increase of the returns to capital, on the concentration of wealth and of income’s inequality in capitalist economies. If the rate of return on private wealth (defined to include physical and financial capital, land and housing) exceeds the rate of growth of the economy, the share of capital income in the national product will increase. If most of that increase is reinvested, the capital to income ratio will rise. This will further increase the share of capital income in the net output. When returns on capital rise more quickly than the overall economy and taxes on capital remain low, a vicious circle of ever-growing dynastic wealth takes place. This is what happened in the 19th century, a cycle broken only by the wars and by the political revolutions of the first half of the 20th century. Piketty uses simple economic models to explain what is going on. He reverses the relationship between income distribution and growth as it has been interpreted in the traditional Keynesian models. Such models explain the rate of growth of the economy as a consequence of the ratio between the saving rate (resulting from the functional distribution of income between capital and labor) and the capital output ratio. Piketty, instead, investigates how the ratio between the saving rate and the rate of growth of the economy determines the capital output ratio, and consequently the share of capital in the national product. Piketty’s theory of income concentration can be called a “political theory” because the main forces that shape income concentration are political: wars, high taxation, and inflation (Milanovic, 2014, p. 529). Piketty claims that inequality in

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personal income distribution does not follow a deterministic process. In a sense both Marx and Kuznets were wrong. There are powerful forces pushing alternately in the direction of rising or shrinking inequality. Which one dominates depends on the institutions and on the policies that societies choose to adopt. Trends in capital and labor shares and their inequalities are both important. Income inequality combines forces arising from the inequality of capital ownership and capital income, and forces related to the inequality of labor income (Piketty, Saez, p. 842). The link is clear and very well documented by the empirical findings for the USA and other westerns countries. In a society where “patrimonial capitalism” prevail capital’s inequality mainly contributes to the rising of personal income inequality. When the percentage of people who do not need to work in order to earn their living (the rentiers) will go up the distribution of personal income will become even more unequal. Historical movements of income concentration are discussed by Piketty not only as important empirical finding, but, instead, they are set in an overall economic framework where we see why and how they emerged. The trends in the inequality of income’s distribution are placed in a larger framework of a similarly U-shaped movement in the capital-output ratio and of an inverted U-shaped movement in marginal tax rates. If the capital-income ratio is high and taxes low, the share of capital’s income in comparison with the labor share will increase, and consequently also income’s inequality will be rising. The analytical framework for the empirical analysis, and a tool for predicting rising inequality in the future, consists of two models: i) the first is a quite standard Harrod-Domar-Solow macro model aimed at determining the share of capital on national income and the capital-income ratio in the long run; ii) the second is a sub model “rather mathematical in nature” aimed at linking the concentration of wealth to the growth of the economy. It has been developed in detail in Piketty and Zucman (2015). Capital is a very heterogeneous concept. Capital is any endowment which generates a rent as the result of the functioning of a “pure and perfect” market for capital. It includes all forms of assets (housing, land, machinery, financial assets in the form of cash, bonds and shares, intellectual property) that generate a return/rent. In the Piketty’s concept of capital durable goods are not included. For that reason, according to Piketty’s estimates, 50% of the population does not have any kind of wealth. The “first fundamental law of capitalism” links α (the share of capital’s income on national product) to the capital output ratio β and to the average return to capital r where α = r x β. The capital output ratio (K/Y), that Piketty calls β, “measures the overall importance of wealth in a given society, as well as the capital intensity of production” (Piketty, Saez, 2014, p. 840). Assuming, as Piketty does in a first hypothesis, that r is equal to the marginal productivity of capital, it decreases when β increases. In the standard economic models with perfectly competitive markets, r is equal to the marginal product of capital. As the volume of capita rises, the marginal product tends to decline. In more complex models, instead, which are also more realistic, the rate of return on capital r may be higher or lower than the marginal productivity of capital. Firstly in a more complex economy, where many more diverse uses of capital exist, the marginal productivity of capital may be difficult to determine. Secondly, the owner of capital which is in a monopolistic position can impose a rate of return greater than the marginal productivity of the capital itself. “In any case, the rate of return on capital is determined by the following two forces: firstly by technology (what is capital used for?), and secondly by the abundance of the capital stock (too much capital kills the return on capital)” (Piketty, 2014a, p. 154).

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The central question becomes how much the return on capital r decreases when the capital/income ratio β increases (Piketty, 2014a, p.155). This depends on the elasticity of substitution (σ) between capital K and labor L in a CES production function where Y=F (K,L). The standard assumption is that the production function is a Cobb Douglas and the rate of substitution σ is equal to 1. In this case as the stock of capital rises, the return on capital r decreases exactly in the same proportion, so that α does’nt change (Piketty 2014a, p. 154). If the return on capital r falls more than proportionately when the capital income ratio β increases, then the share of capital’s income in national income decreases. In other words, the decrease in the return on capital more than compensates for the increase in the capital/income ratio. On the opposite, if the return r falls less than proportionately when β increases then the share of capital’s income increases with β. The effect of the decreased return on capital is simply to cushion and moderate the increase in α compared to the increase in the capital income ratio β. Piketty introduces the hypothesis that the rate of substitution is greater than one (σ>1) so that a rise of capital income ratio β also lead to a rise of the share of capital in national income. Intuitively, it makes sense to assume that σ tends “to rise over the development process, as there are more diverse uses and forms for capital and more possibilities to substitute capital for labor (e.g., replacing delivery workers by drones or self-driving trucks)” (Piketty, Saez, 2015, p. 841). The theoretical framework, the methodological approach and especially the concept of “capital” and of “saving rate” adopted by Piketty were challenged. French economists, especially, were critics of its approach (Aghion, 2014). Piketty answered to the numerous and different remarks on his book writing some new papers. He argued that the arguments of the book were been “simplified in the telling and retelling” so that the original message were misunderstood. Its message, however, is very clear. The factors that generate inequality, in income and wealth, are many: institutional, socio-economics and demographic. The factors which explain the dynamic of wealth (accumulation of capital) are different from those which explain the dynamics of labor income (demand and supply of skills and education, technology). It is very difficult, therefore, to reach a consensus on a shared theory of personal income distribution. Piketty’s definition of capital “interchangeable” with the concept of wealth has been criticized as too ambiguous. Capital in the Piketty approach is considered mainly as an asset that gives a rent to its owners. Rent must be considered not the result of any imperfection in the market, but as the consequence of a “pure and perfect” market for capital. It has absolutely nothing to do with the problem of imperfect competition or monopoly. Piketty argues that he is interested in a concept of capital which could be linked to the personal income distribution. Therefore the inclusion in personal wealth of any kind of asset is justified. This is a perspective different from the traditional one in which capital is a factor of production. In that case it will be linked to the output and not to the income of the owner. If capital is not the traditional neo-classical factor of production it is difficult to justify the use of a CES function as a tool for estimating the share of income from capital, depending on the value of the elasticity of substitution between capital and labor. Wealth is a very heterogeneous concept including assets that have value but does not produce anything (precious metals, works of art). Wealth’s owners can obtain rent, which becomes personal income, from many sources: financial gains, rent of an apartment. These rents are not the result of a relation between capital, labor and output. It is, then, necessary to build a new kind of models suitable to estimate the sources of returns to different kind of capital, and not only the returns based on the concept of a production function. It is not a simple task, of course, but a more clear distinction between the two concepts of capital as factor of production and capital as wealth need also new models.

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Some doubts have been advanced on the hypothesis that the elasticity of substitution between capital and labor is likely to remain higher than one, and that an increase in capital will not drive r down. This argument “is running against one of the fundamentals of economic theory: decreasing returns to an abundant factor of production. Piketty is indeed critical of a blind belief that marginal returns always set the price for labor and capital, but these arguments are not developed and come in the form of obiter dicta… (Milanovic 2014, p.527). Stiglitz (2014b) proposes an alternative hypothesis of the drivers of inequality in today’s US that can explain the “Piketty puzzle” of a rising wealth/income ratio together with a rise in r and stable wages. The answer must be found in the role of Institutions and policies as banking and finance. The banking system made credits easily available which in turn led to over-investment in housing and to the increase in the wealth/income ratio discussed by Piketty. This increase, however, did not led to greater productivity. The value of land and of real estate increased, not the physical quantity of productive capital. Banks, instead of lending to companies to invest in new capital, lent to people which spent money on housing and unproductive assets. Stiglitz (2014b) argues also that recently, the decline in interest rates, which followed expansionary policies, has exacerbated inequalities by increasing the value of stock options and other financial instruments available to those (entrepreneurs, managers) who belong to the richest classes of population. In this case growth, stimulated by policies especially when it is accompanied by lower interest rates, is a source of inequality, not the stagnation of economies. It is exactly the opposite of what is stated by Piketty.  

4. The “second fundamental law of capitalism”. The value of β in the long run is determined through the so-called Harrod-Domar-Solow formula. The hypothesis is that capital-to-income ratio converges toward β=s/g, where s is the long-run annual saving rate and g is the long-run annual total growth rate. The growth rate g is the sum of the population growth rate (including immigration) and the productivity growth rate (real income growth rate per person). “This formula holds whether savings are invested in domestic or foreign assets (it also holds at the global level)” (Piketty, Saez, p. 840). This is the “second fundamental law of capitalism”. The higher the savings rate and the lower the growth rate, the higher the capital/income ratio β will be (Piketty, 2014a, p. 44). In a stagnant economy, where the amount of capital is high, the rate of saving exceeds the rate of growth, (s>g) so that β will be high and increasing. If both α and β are increasing, also the concentration of wealth will be high and increasing. At least it is what we observe in historical series. The tendency for capital to grow faster than the economy is also more likely when the growth of the economy is relatively slow because of both demographic or technical tendencies are weak. This tendency for low growth societies to reconstitute very large stocks of capital is expressed by β = s/g. In recent decades, the rise in the capital/income ratio β came together with a rise in the net-of-depreciation capital share α, which in a one-good model with perfect competition implies an elasticity of substitution higher than one. In a one-good model with perfect competition and high substitutability between capital and labor (which might happen because of the rise of new capital intensive technologies such as robots of various sorts), the rate of return will decline relatively little as β rises. Also the net-of-depreciation capital share α will be rising. However Piketty claims that the one-good, perfect competition model is not a very satisfactory model, to say the least. In practice, the right model to think about rising capital income ratios and capital shares is

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a multisector model (with a large role played by capital-intensive sectors such as real estate and energy, and substantial movements in relative prices) with important variations in bargaining power over time. In particular, intersectoral elasticities of substitution combining supply and demand forces can arguably be much higher than within sectors capital/labor elasticities. Piketty, Saez (2014) illustrate the use of the second law in doing comparative statics. In the long run they claim one can show that the wealth-to-income (or capital-to-income) ratio converges toward β=s/g where s (the net saving rate) is the long-run annual saving rate and g is the long-run annual total growth rate of the net income. “The growth rate g is the sum of the population growth rate . . . and the productivity growth rate. . . .That is, with a saving rate s =10% and a growth rate g =3%, then β ≈ 300%. But if the growth rate drops to g=1.5%, then β ≈ 600%. In short: Capital is back because low growth is back. . . .In the extreme case of a society with zero population and productivity growth, income Y is fixed. As long as there is a positive net saving rate s > 0, the quantity of accumulated capital K will go to infinity… With positive but small growth, the process is not as extreme: The rise of β stops at some finite level. But this finite level can be very high” (Piketty, Saez, 2014, p.840). A critic of the Piketty’s “second fundamental law of capitalism” has been advanced by Krusell and Smith (2014). They claim “Though Piketty calls [the second law] an ‘accounting equation’, it really is a theory, because it builds in a certain form of savings behavior”. Piketty’s assumption that the net saving rate is constant is actually the same assumption made in the very earliest formulations of the neoclassical growth model, including that by Solow in his original paper. But this hypothesis has been changed in the more recent versions. In the textbooks the capital-to-income ratio is not s/g but rather s/(g+d) where d is the rate at which capital depreciates. The gross savings rate, i.e. gross investment (including depreciation), and not the net saving rate s is considered constant. With the textbook formula, growth approaching zero would increase the capital-output ratio much more modestly in a sharp contrast with Piketty’s theory. In both the textbook Solow model and the optimizing model “the net saving rate goes to zero as growth goes to zero, rendering the second law… difficult to interpret” (Krusell and Smith, 2014, p.744). On the opposite in Piketty’s model the net saving rate is kept constant at a positive value when growth falls. The real problem are the assumptions that Piketty points out on the value of the net saving rate compared to the growth rate. He asserts that the net saving rate and the growth rate are “influenced by any number of social, economic, cultural, psychological, and demographic factors” and are “largely independent of each other”(Piketty, 2014a, p.199). “Piketty here treats the net saving rate as a free parameter, analogously to how the textbook Solow model treats the gross saving rate” (Krusell and Smith, 2014, p.742). In the standard theories of saving based on optimizing behavior and widely used in macroeconomics, instead, gross saving comove positively with g. A central issue, largely absent in Piketty’s book, is the role of depreciation that destroys capital and forces capitalists to devote resources not to its accumulation. “Piketty’s predictions for the twenty first century depend critically on the saving theory that one employs and that the theory he uses…..The textbook Solow model, which maintains a constant gross saving rate, does a better job of matching past data, but models based on standard intertemporal utility maximization provide an even better match, since these predict falling net and gross saving rates as g falls, as it has been observed in long-run data. These models are also firmly grounded on empirical work documenting how households save” (Krusell and Smith, 2014, p.747).

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The conclusion perhaps, can be that a theory which could not only interpret past movements in wealth inequality, but also should help to foresee future trends in inequality is still lacking. The second fundamental law is quite weak because historical data on US are in contrast with the Piketty’s hypothesis of a stable value of saving rate and independent from the rate of growth. However without Piketty’s impressive data work, these movements would have been neither emphasized nor quantified. “In postwar U.S. data with declines in growth, the net savings rate has fallen historically, and is currently actually already close to zero. Decadal averages of savings rates and growth rates, show a clear positive relationship. That s will remain constant and positive in the twenty-first century does not appear like a good assumption at all. Projecting into the future based on Piketty’s second fundamental law, with g going to zero, appears unwise” (Krusell and Smith, 2014, p.739). The validity of Piketty’s model thus depends crucially on two key propositions: i) the relative stability of the rate of return on capital in the face of capital deepening; ii) a constant or rising saving ratio when the growth is slowing down. Both hypothesis have been rejected mostly on a theoretical ground. According to Piketty the answers to that questions cannot be given in abstract but only looking to the empirical evidence. This is the methodological approach that Piketty both pioneered and clearly prefers. But the results can differ because the data samples are different. Criticisms were followed by several articles in defense of Piketty. The author himself answered by pointing out that the results obtained, showing an increasing inequality, and the consequent negative effects in terms of growth, based on empirical evidence, can only be the result of an imperfect inference, as it always happens in social sciences. As Amartya Sen (2014) claimed, “in any study of this kind you have to use diverse sources of data, and it is inescapable that you have to establish certain linkages on which it is possible to have debates”. 5. The “fundamental contradiction of capitalism”. The inequality r > g in the long run. Piketty claims that capitalists save a sufficiently large share of their returns to ensure that their capital will grow at least as fast as the economy. This is especially likely to be true for the seriously wealthy, who are also likely to enjoy the highest returns. People with inherited wealth need save only a portion of their income from capital to see that capital grow more quickly than the economy as a whole. “Under such conditions, it is almost inevitable that inherited wealth will dominate wealth amassed from a lifetime’s labor by a wide margin, and the concentration of capital will attain extremely high levels” (Piketty, 2014a, p. 25). These levels are incompatible with the meritocratic values and the principles of social justice prevailing in modern democratic societies. The way by which wealth is accumulated and distributed contains forces pushing toward divergence, toward an extremely high level of inequality. Capital produces earnings and returns and thus it accumulates and self-develops. The inequality r>g is the fundamental contradiction of the patrimonial capitalism and cannot be eliminated by a degree of additional competition. The divergence r > g “has nothing to do with market imperfections” (Piketty 2014a, p. 298). This process of capital accumulation generates a changing functional distribution of income in favor of capital and because incomes from capital are more concentrated than incomes from labor, also the personal income distribution will get more unequal. The distributional effects of the r>g inequality are deleterious for the society as a whole: they favor property-owners over labor, not working over working, make mockery of equal opportunity and meritocracy, and undermine democracy as the rich use their money to buy policies they like. A vicious circle of ever-growing dynastic wealth starts, which cannot be reduced by an additional level of competition. Also personal income distribution will become

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more unequal. In Piketty’s own words: "When the rate of return on capital is higher than the growth rate of the economy, logic dictates that inherited wealth is growing faster than GDP and personal income" (page 25). Answering to Mankiw (2015) Piketty claims that “the inequality r>g holds true in the steady-state equilibrium of the most common economic models, including representative-agent models where each individual owns an equal share of the capital stock….and does not entail any implication about wealth inequality” (Piketty, 2015a, p. 49). Sala-I-Martin (2014) and Debraj Ray (2014) argue that The inequality r > g is a condition of economic efficiency. An economy where r <g is inefficient in the sense that it has been saved too much. Therefore the r>g relationship does not tell us anything about increasing inequalities. Only a detailed study of inheritance can enlighten us as to whether inheritances are key factors in explaining inequalities. Piketty does not trust that r > g is the only or even the primary tool for considering changes in income and wealth inequality. Institutional changes and political shocks, which can be considered endogenous to the inequality and to the development process itself, are also very important (Piketty, 2015a, p. 48). He also do not believe that r > g is a useful tool for the discussion of rising inequality of labor income. Supply and demand of skills and education are more important factors in this case. No doubt that the rise in labor income inequality in recent decades in the USA has something to do with r-g. This is, however, a very important historical evidence. In the real world, many shocks to the wealth trajectories of families can contribute to make the wealth distribution highly unequal. These shocks are related to financial or estates rate of return, demographic factors, differences in saving behavior, differences in propensity to invest, differences in taste parameters, in labor market features, in the institutional and political setting. Differences in earnings to be saved and cumulated are also important shocks. Wealthier people can obtain higher average returns than less wealthy people. Unequal returns on capital, then, are a divergence force for that significantly amplifies and aggravates the effects of the inequality depending on r > g. (Piketty, 2015a, p. 50). These shocks will ensure that there is always some degree of downward and upward wealth mobility, so that wealth inequality remains bounded in the long run. For a given structure of shocks, the long-run magnitude of wealth inequality will tend to be magnified by a higher gap r- g, for a given variance of other shocks. To put it differently: a higher gap between r and g leads to a steady-state level of wealth inequality that is higher and more persistent over time. A higher gap r-g leads both to higher inequality and lower mobility. It implies that past wealth is capitalized at a faster pace, and that it is less likely to be overtaken by the general growth of the economy. Under fairly general conditions, if shocks take a multiplicative form, one can show that the top tail of the distribution of wealth converges toward a Pareto distribution for top wealth holders. This is approximately the form that we observe in real world distributions, and which corresponds to relatively fat upper tails and a large concentration of wealth at the very top. The inverted Pareto coefficient (measuring the thickness of the upper tail and hence the inequality of the distribution) increases with r- g. It is a steeply rising function of the gap r- g. “The effect of r-g on inequality follows from its dynamic cumulative effects in wealth accumulation models with random shocks, and the quantitative magnitude of this impact seems to be sufficiently large to account for very important variations in wealth inequality… Most importantly, it is really the interaction between the r-g effect and the institutional and public policy responses—including progressive taxation of income, wealth, and inheritance; inflation; nationalizations, physical destruction, and expropriations; estate division rules; and so on—which in my view, determines the dynamics and the magnitude of wealth inequality.” (Piketty, 2015b, p. 75-76). The gap

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between the net rate of capital’s return and the rate of growth of the economy is certainly not the only determinant of a steady-state wealth inequality. It is one important determinant, however. It is possible to show that over a wide range of models, the long-run magnitude and concentration of wealth and inheritance are a decreasing function of g and an increasing function of r. “Both the wealth/income ratio and the concentration of wealth tend to take higher steady-state values when the long-run growth rate is lower and when the net-of-tax rate of return is higher” (Piketty, Zucman, 2015, p. 1343-1344). Piketty argues, also, that the size of the gap between r and g is one of the important forces that can account for the historical magnitude and variations in wealth inequality. A higher r-g tends to magnify steady-state wealth inequalities. From a theoretical perspective the effect of a decline in the growth rate g on the gap r-g is ambiguous: it could go either way, depending on how a change in g affects the long-run rate of return r. This depends on a mixture of forces, including saving behavior, multisector technological substitution, bargaining power and institutions. Generally speaking, a lower g, due either to a slowdown of population and/or to a productivity decrease, tends to lead to a higher steady-state capital/output ratio β = s/g and therefore to lower rates of return to capital r (for given technology). The key question is whether the fall in r is smaller or larger than the fall in g. If one instead assumes a fixed, exogenous saving rate s, then the steady-state capital output ratio β will rise even more strongly as g declines. There is no a general reason why r − g should increase as g declines: it could potentially go either way. Historical evidence and new technological developments suggest that it should increase. Low growth is inevitable once countries have reached a very high level of income. It is the “dead hand” of the past generations (high β ratio) and the high returns on capital that destroy the fabric of today’s advanced capitalist societies. Piketty argues that when growth is slow, it is almost inevitable that the return on capital is significantly higher than the growth rate, which automatically results in an outsized importance of accumulated in the past wealth inequalities. “The inequality r > g in one sense implies that the past tends to devour the future: wealth originating in the past automatically grows more rapidly, even without labor, than wealth stemming from work, which can be saved. Almost inevitably, this tends to give lasting, disproportionate importance to inequalities created in the past, and therefore to inheritance” (Piketty, 2014a, p. 267). 6. The empirical findings: trends in capital/output ratio β, in the capital share α and in the inequality r > g in the long run. Using the best available historical data, Piketty shows how the capital/output ratio β, the share of capital in income α, and the rate of return on capital r, evolved over time (Piketty, 2014b). Piketty discusses the changes observed and what are the main social and economic forces at work, why do these forces change over time, and what we can predict about how the rate of return on capital will evolve in the twenty-first century. Capital/ output ratio β has been measured by dividing wealth measured in local currency of the time by national income, also measured in local currency of the time. The wealth/income ratio then has “years” as a dimension. This ratio has been rising in the advanced countries from around 1700 until the First World War. It has been moderately rising or stable around a value equal to 6 to 7 “years of national income” since the end of the nineteenth century until the First World War (fig. 1). Piketty explains the rise as the outcome of a continuous high return on capital acting upon a steadily accumulating capital in an environment that was institutionally favorable to capitalists rather than to workers. In some European countries (Germany, France, United Kingdom) β has

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followed a pronounced U-shaped pattern over the past century. After the period of the “Belle Époque” β declines precipitously in continental Europe, UK and Japan (less so in the US). It then fell to about 2 to 3 “years” of national income in the 1950s. It has risen regularly since then, and it is now back to about 5 to 6 “years” of national income scarcely less than the level observed in the eighteenth and nineteenth centuries and up to the eve of World War I. With reduced taxes on profits and income (a point which Piketty extensively documents), and quasi elimination of taxes on inheritance, the rebuilding of capital accelerated and β began its steady climb, reaching in the early 21st century values very similar to that prevailing a century ago.

Figure 1, The capital/income ratio in Europe, 1870-2010

The capital/output ratio β increased in all advanced countries. In Italy β increased more rapidly due to the rise of prices of real estates, to the transfer of public capital into private hands and, finally, to the public debt placement (Figure 2). A comparison between the trends in private and public capital one shows, in Italy, a decrease of the public capital, in the period 1970-2010. Only in Canada a similar trend is observed. Figure 2, Private and public capital in rich countries, 1970-2010

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The US shows also a slightly U-shaped curve, with a capital/output ratio standing at a relatively lower level in the mid-20th century than at both ends of the century. Anyway this trend is much less marked than in Europe. As a matter of fact the pattern is flatter (Piketty, Saez, 2014, p. 840). At least three factors can explain this difference (Figure 3). Figure 3, Wealth-Income ratios: Europe and the United States,

The United States is an outlier because it was a “wealth-young country” where the weight of the “dead hand of the past generations”, that is of those who had accumulated capital in the past and transmitted it to the current generation, was relatively low (Milanovic, 2015, p. 522). Secondly, in the early years land, a component of capital, in the wide open spaces of North America was cheap. Thirdly, the lower capital/income ratio in the United States probably reflects the higher level of productivity. In this country a given amount of capital could support a larger production of output than in Europe. The two world wars caused much less destruction and dissipation of capital in the United States than in Britain and France. In all three countries, and elsewhere as well, the wealth/income ratio has been increasing since 1950, and is almost back to nineteenth-century levels (Solow, 2014, p. 5). The fall of European wealth/income ratios following the 1914–1945 capital shocks can be well accounted for by three main factors: direct war-related physical destruction of domestic capital assets and lack of investment. A large fraction of 1914–1945 private-saving flows was absorbed by the enormous public deficits induced by war financing. There was also massive dissaving in some cases, e.g., foreign assets were sold to purchase government bonds and the resulting public debt was eventually wiped away by inflation. Finally a fall in relative asset prices occurred. Real estate and stock market prices were both historically very low in the immediate postwar period, partly due to rent control, nationalization, capital controls, and various forms of financial repression policies. “In France and Germany, each of these three factors seems to account for about one-third of the total decrease in wealth-income ratios. In the United Kingdom, where domestic capital destruction was of limited importance (less than 10% of the total), the other two factors each account for about half of the decline in the aggregate wealth-income ratio” (Piketty, Saez, p.840). After the World War II European economies, US and Japan expanded the fastest in their histories. The European economies and Japan almost fully caught up with the United States in terms of worker’s per-hour productivity, the capital/output ratio and net return on capital were low, taxation high, the functional distribution shifted in favor of labor, and the personal income

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distribution became more equal. This was the so called “Golden Age”. But with the Thatcher-Reagan revolutions in the late 1970s capitalism reverted to the form it had in the late 19th century. The choice to include houses in total capital has been questioned. “Housing is a very particular component of capital and its interpretation has always been subject to complex discussions, even within the neo-classical world. In particular, housing capital does not provide a good measure of actual return on capital” (Bonnet et. al, 2014, p. 2). The value of housing capital estimated at the price of houses is not necessarily correlated with the share of income it generates in national income. In fact, if this value has rapidly progressed in several countries over the last decades, the corresponding share of income, on the opposite, has only progressed slowly in the most extreme cases, or remained stable as in France, or even decreased as in Japan. ((Bonnet et. al, 2014, p. 6) Returns on housing capital (the key ingredient in the Piketty’s model) should be measured by the “monetary rent” on housing that owners/landlords receive or by the “implicit” rent that owner-occupiers have. These are precisely the source of the dynamics of the accumulation of capital, rather than the prices which have been over their long run value for more than a decade (Trannoy and Wasmer, 2013). Housing capital based on housing prices can be overvalued or undervalued and it is generally disconnected from the value of rents that is from the inequality generating process that the author wants to establish. The prices of real estate follow trajectories not linked to the growth of the economy and that can fluctuate more than national income. It has been shown by Bonnet and its coauthors (Bonnet et. al, 2014) that the real estate capital that does not reflect long-term trends, particularly because it incorporates the phenomena of real estate bubbles. The value of real estate, if based on current prices, incorporates a speculative component which influences the monetary value of capital. This is why the value of capital increased in the last decades without a parallel rise in the productivity level. “For the value of housing capital to be consistent with the underlying theoretical analysis, the value must correspond to an actualized value of rent and not rely on housing prices…. Rising housing prices do not necessarily lead to a rise in the income of homeowners or landlords and accordingly why housing inflation does not trigger a divergent accumulation of wealth by the richest people.” (Bonnet et. al, 2014, p. 3). Bonnet and its coauthors recalculated the value of housing capital based on rent indices considering it the right measure. They found that “the rise in the capital/income ratio has been modest over the recent period” (Bonnet et. al, 2014, p. 3). When one corrects the measure of real estate capital, the ratio between capital and income either stagnated or increased slightly instead of increasing steadily. In the longer run, however, a decline in the capital/income ratio rather than a U curve has been observed, contradicting Piketty’s thesis. The value of the real estate β remains constant between 1950 and 2010 drops slightly between 1950 and 1970, remains constant between 1970 and 2000 and increases only between 2000 and 2010. The rise in the prices of household had, however, consequences on the wealth trajectories of individuals and dynasties: in particular, it is increasingly difficult for an individual without initial wealth to become a homeowner in France. The available data indicate that capital’s share of income α increased in most rich countries between 1975 and 2010 to the extent that the capital/income ratio increased (figure 4). Based on historical evolutions observed in Britain and France, the capital share of income α, follows the same U-shaped curve as the capital income ratio β with a high level in the eighteenth and nineteenth centuries, a drop in the middle of the twentieth century, and a rebound in the late twentieth and early twenty-first centuries. However the evolution of the rate of return on capital r

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significantly reduces the amplitude of this U-curve for the capital share α. “The return on capital was particularly high after World War II, when capital was scarce, in keeping with the principle of decreasing marginal productivity. But this effect was not strong enough to invert the U-curve of the capital/income ratio, β, and transform it into an inverted U-curve for the capital share α” (Piketty, 2014a, p.156). The increase in the capital/income ratio β followed by a slight increase in α, and vice versa corresponds to a situation in which there are many different uses for capital in the long run so that the elasticity of substitution between capital and labor is greater than one. The observed historical evolutions suggest that it is always possible, at least up to a certain point, to find new and useful things to do with capital (Piketty, 2014a, p.157-159). Moreover “productivity growth has been running ahead of real wage growth in the American economy for the last few decades so the capital share has risen and the labor share fallen (Solow, 2014, p.7). Historical reality is more complex than the idea of a completely stable capital/labor split suggests. The Cobb-Douglas hypothesis could be a good approximation for certain sub periods or sectors and, in any case, is a useful starting point for further reflection. But this hypothesis does not satisfactorily explain the diversity of the historical patterns that we observe over the long, short, or medium run, as the data collected by Piketty show. Figure 4, The capital share α in rich countries, 1975-2010 13

The upward trend of capital’s share is consistent not only with an elasticity of substitution between capital and labor greater than one but also with an increase in capital’s bargaining power vis-à-vis labor over the past few decades, which have seen increased mobility of capital and heightened competition between states to attract investments. It is likely that the two effects have reinforced each other in recent years, and it is also possible that this will continue to be the case in the future. N no self-corrective mechanism exists to prevent a steady increase of the capital/income ratio, β, together with a steady rise in capital’s share of national income, α. Whether the capital share α will keep rising in future decades is an open question. It depends both on technological forces, on the bargaining power of capital and labor and on the collective institutions regulating the capital/labor relationship (the simple economic model with perfectly

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competitive markets seems excessively naïve). “But from a logical standpoint, this is a plausible possibility, especially if the population and productivity growth slowdown pushes the global capital income ratio β toward higher levels.” (Piketty, Saez, 2014, p.841). Figure 5 compares the net rate of return r (after taxes) with the rate of growth g for the period 1000-2100. In particular capital losses due to destruction of property in the period 1913–1950 are estimated. A huge positive gap between r and g (g>r) from Antiquity to the early 20th century, its inversion (g>r) for the most of the 20th century, and then, recently, again a positive gap appear. Piketty shows that r has generally been stable during the last two centuries despite massive changes in the β ratio. He also argues that, even if we go further back into the past to the Roman times, r has been steady at around 5-6%. The gap r − g appears to be smaller when the growth rate is higher. This would tend to support the view that lower growth rates in the 21st century (in particular due to the projected decline of population growth) are likely to contribute to a rise of r − g. A concatenation of circumstances (wartime destruction, progressive tax policies made possible by the shocks of 1914–1945 and exceptional growth during the three decades following the end of World War II) created a historically unprecedented situation. This period called “the Golden Age” was a very special and unrepeatable phenomenon in the history of capitalism. Due to the process of convergence, Europe’s capitalist economies and Japan grew faster than they would have if they were at the technological frontier. Increasing population growth rate also drove g ever higher (note that g is the sum of population growth and the growth of per capita income). On the other hand, institutional factors, including high taxation and the threat of Communism (which Piketty does not mention) kept r low, and thus uniquely in the history of capitalism reversed the inequality r>g. All signs are, however, that the gap r-g will become again positive. During the 20th century, growth rates were exceptionally high (in particular due to very high population growth, which even today represents about half of global gross domestic product growth), and rates of return were severely reduced by capital shocks (destructions) and the rise of taxation. Simple simulations show that this effect is sufficiently important to explain why wealth concentration did not return to pre-WWI levels in the postwar period. Rising inequality rests primarily on the ability of the economy to absorb increasing amounts of capital without a substantial fall in the rate of return. Figure 5, After tax rate of return vs. growth rate at the world level from Antiquity until 2100.

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The inequality r > g has clearly been true throughout most of the human history, right up to the eve of World War I, and it will probably be true again in the twenty-first century. Its truth depends, however, on the shocks to which capital is subject, as well as on what public policies and institutions are put in place to regulate the relationship between capital and labor (Piketty 2014a, p. 254). Ultimately, which forces prevail is relatively uncertain. Piketty sees, interestingly, today’s processes of growing financial sophistication and international competition for capital as helping to keep r high. While many people question financial intermediation and blame it for the onset of the Great Recession, Piketty thinks that it helps to uncover new and more productive uses for financial capital and to maintain the rate of return high. But far from making this high an r a good thing for the economy, he regards it as undesirable unless checked by higher taxation (Milanovic 2014, p.525). The inescapable fact is that the rate of return on capital was always at least 10 to 20 times greater than the rate of growth of output (and income). Indeed, this fact is to a large extent the foundation of a capitalist society. It is what allowed to a class of owners to devote themselves to something other than their own subsistence. In the future, several forces might push again toward a higher r − g gap (particularly the slowdown of population growth, and an increasing global competition to attract capital) and higher wealth inequality. First, economic policies, in particular the taxation of profits, have changed. Then, demographic transition (low rate of population growth) now affects all European countries, and to a lesser extent the United States, which of course reduces g further. “The end of convergence implies that all advanced countries will grow at the rate of technological progress which, Piketty believes, is around 1-1.5% per year. Add to it 1% population growth and g cannot exceed 2.5% per year. If r remains, as Piketty thinks, at its historical rate of 4-5% p.a., all the negative developments from the 19th century will be repeated” (Milanovic 2014, p. 525). The fact that the rate of return to capital r is permanently higher than the economy’s growth rate g does not in itself imply anything about wealth inequality. Many other forces might have led to greater inequality of wealth in the 21st century, including a rise in the variance of shocks to demographic factors, rates of return, labor earnings, tastes for saving and bequests, and so on. “Conversely, a reduction of the variance of these shocks could lead to a decline in wealth inequality. The gap between (1 − t) r and g is certainly not the only determinant of steady-state wealth inequality. It is one important determinant, however, and there are reasons which might

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push toward a persistently high gap between the net-of-tax rate of return (1 − t) r and the growth rate g in the 21st century—which might in turn lead to higher steady-state wealth inequality (other things equal)” (Piketty, 2015b, p.79). Other factors might also have played a role. For instance, the rise of a wealthy middle class might partly come from the fact that the growth of incomes and living standards eventually induced the raise of middle class saving. However, this process does not seem to have taken place in pre-WWI Europe, because of the powerful unequalizing impact of the r – g factor. To the extent that population growth (and possibly productivity growth) will slow down in the 21st century, and that after-tax rates of return to capital will rise (due to rising international tax competition to attract capital, and maybe also to changing technology), it is likely that r – g will increase again in the 21st century, which could lead to a structural rise in wealth concentration. Finally, the last reason (and arguably the most important one) why r − g might be high in the 21st century is due to the unequal access to high financial returns. That is, even though the gap between the average rate of return r and the growth rate g is not particularly high, it could be that large potential financial portfolios have access to substantially higher returns than smaller ones. Financial deregulation might have contributed to such an evolution. For example, according to Forbes rankings, the wealth of top global billionaires seem to be rising much faster than the average wealth. This evolution cannot continue for too long, unless one is ready to accept an enormous increase in the share of world wealth belonging to billionaires (and a corresponding decline in the share going to the middle class). Moreover, larger university endowments tend to obtain substantially higher returns. Given that even small changes in r − g can have large amplifying effects on changes in wealth inequality, this effect is potentially important. Overall, substantial uncertainty remains about how far wealth inequality might rise in the 21st century; more transparency and better information about wealth dynamics are needed. Some results offered by the empirical research on trends in capital/output ratio, rent on capital, share of capital in national income, rate of growth of the economy can be summarized. Piketty documents how for the past three decades, from the post-war reconstruction to the seventies (the so-called "golden age"), the rapid industrialization process, along with progressive fiscal policies and public spending, has sustained the growth of the middle class, the consolidation of democracy and an high rate growth in all the western countries. This phase has been reversed since the end of the last century. In parallel to the increase in inequality a slowdown in growth, if not an actual decline has been observed, at least in some countries. An increase in inequality ends with the slow growth rather than stimulating it. First of all there is no general tendency towards greater economic equality. Secondly, the relatively high degree of equality observed after the World War two partly a result of policy, especially progressive taxation, but even more of the destruction of inherited wealth because of the war, particularly within Europe between 1914 and 1945. A further lesson is that the “patrimonial capitalism” of the late 19th century could be recreated, if fiscal and redistributive policies will not be introduced. An important finding is that the ratio of capital to income in Europe has been rising above US levels: another important finding is the big recent rise in the income shares of the top 1 per cent in English speaking countries (above all the US) since 1980. 7. The empirical findings. Wealth and income inequalities. Piketty has revolutionized the field of researches on income distribution by the use of fiscal sources and by his focus on top income shares. In collaboration with Facundo Alvaredo, Anthony Atkinson and Emmanuel Saez (2014) he uses very detailed fiscal data to trace the

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evolution of income and wealth distribution in different countries. This choice is in line with the previous researches of Simon Kuznets who first used tax data, instead of household’ surveys, to study the links between economic growth and personal income distribution in the 1950s. The revolution that Piketty and his coauthors have brought to the field has certainly made everybody much more sensitive to the need to combine (nobody yet knows how) household surveys, that provide reasonably reliable income estimates for the bulk of the population, with fiscal data that are undoubtedly better suited for the very top of the income distribution. However the use of fiscal data can be questioned as the sole (or even the best) approach to the analysis of income distribution. Its advantages can be easily mentioned: long-term series (centuries or more in developed countries), ability to focus on top incomes and to capture them much better than household surveys. Some “caveats” relating to any use of fiscal data must be stressed. Historically, income tax returns have been filed by a small percentage of the population even in today’s rich countries, so the long-term series can be of dubious quality. The same is true in developing countries now. At best we might know the top of an income distribution (the richest tax-filers) but we don’t any information about the bulk of the population. Whether the highest tax-filers are really the richest people is also questionable. Not only because of the obvious incentive to underreport income or because in the past some particularly rich classes were exempt from taxation. There is also an important, even if technical, detail. Taxes are paid by fiscal units, not by individuals: so the richest fiscal units may change with the tax rules (e.g., whether it is more advantageous to file jointly or separately). Moreover, the income that is reported to tax authorities is the fiscal income, not the concept of disposable income. For example, until 1987 interest on government bonds does not appear in US tax returns because it was not subject to taxation; however every economist would include it in income. Even if we disregard these problems, Piketty’s calculations refer mostly to market income, that is income before government transfers and taxes. The concentration of market income among fiscal units may, or may not, tell us much about the inequality of disposable income among individuals, which is ultimately the concept we are interested in. It is quite possible that an increased concentration of market income, such as Piketty and Saez (2014) report for the United States, is not accompanied by an increased concentration of disposable income if taxes and transfers have become more redistributive. It could even happen that disposable income inequality declines. It did not happen in the case of the United States, as we will see. But such a divergent movement cannot be excluded in principle. Piketty mentions some of these caveats (Piketty, 2014a, p. 440; p. 520ff) but essentially ignores them. It is striking, although not altogether surprising, to read a book which in a significant part deals with inter-personal income distribution, but does not contain a single reference to household surveys or to the Gini coefficient. In effect the latter is dismissed as an “aseptic” measure of inequality because of its lack of intuitive meaning (what does a Gini of 0.45 mean to an average person?). It conveys, Piketty argues, very little information about income distribution. Piketty thinks that such very “aseptic” feature has contributed to Gini’s popularity with statistical offices and politicians. On the contrary, income shares are intuitive and meaningful. Piketty’s preference is to split the distribution into four parts: bottom 50 percent, the next 40 percent, top decile and, as a part of it, top 1 percent. Piketty focus on what he calls “concentration” of wealth and incomes rather than inequality. Trends of concentration in the distribution are measured by the value of the share owned (wealth) or earned (income) by the last decile of the population. Figure 6, Wealth Inequality: Europe and the United States, 1870-2010

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Available micro-level evidence on wealth dynamics for Europe and United Nations, reported in figure 6, shows that wealth inequality is currently much less extreme than a century ago. It decreased steadily from 1910 to 1930 in USA and from 1910 to 1970 in Europe. Then it increased steadily from 1970 to 2010 showing higher values in USA in comparison to Europe. In the last period wealth it is very unequally distributed. In the United States, the top 10 percent owns about 70 percent of the whole capital, half of that belonging to the top 1 percent;” the next 40 percent— who compose the “middle class”—owns about a quarter of the total (much of that in the form of housing), and the remaining half of the population owns next to nothing, about 5 percent of total wealth. Even that amount of middle-class property ownership is a new phenomenon in history” (Solow, 2014, p.10). The typical European country is a little more egalitarian: the top 10 percent owns about 63 percent of the whole capital. The top 1 percent owns 25 percent of the total capital, and the middle class 35 percent (a century ago the European middle class owned essentially no wealth at all). The high gap between r and g presented in previous figure 5 is one of the main reasons why wealth concentration was so high during the eighteenth–nineteenth centuries and up until World War I (see Piketty 2014a) in pretty much every society. In this period the rate of return r was decreasing, but higher than g. After 1910 the inequality became g>r bringing to a decrease in wealth concentration. After 1950 the fundamental inequality r>g started again to increase, and consequently also wealth concentration rose. “There was very little taxation or inflation up until 1914, so the gap was particularly high in pre–World War I societies, which in dynamic models of wealth accumulation with random shocks leads to very large wealth concentration. In contrast, following the large capital shocks of the 1914–1945 period the rate of return r precipitously fell below the growth rate. ….In 1932, despite the economic crisis, income from capital still represented the main source of income for the top 0.5 percent of the distribution. But when we look at the composition of the top income group today, we find that a profound change has occurred. To be sure, today as in the past, income from labor gradually disappears as one moves higher in the income hierarchy, and income from capital becomes more and more predominant in the top centiles and thousandths of the distribution: this structural feature has not changed. There is one crucial difference, however: today one has to climb much higher in the social hierarchy before income from capital outweighs

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income from labor. Currently, income from capital exceeds income from labor only in the top 0.1 percent of the income distribution”.(Piketty, 2015b, p.77). Figure 7, Income Inequality in the United States, 1910-2010

The empirical evidence of income inequality in the United States shows an inverted U-curve in a first period, between 1910 and 1940 (figure 7). After a long period of stability during the Golden Age (1942-1970) inequality has started to grow systematically since the early ‘70. Subsequently, since 1970, the share of the last decile has again grown to a rather high level, around 50%, in 2010 (Piketty, 2014, p.48). The turnaround is due not only to the Reagan and Thatcher policies that lowered taxes on the rich, but also to the entrance of Asians in the labor markets of rich Countries, depressing the wages of unskilled workers, and also to the baby boom. The findings for this second period contradict the well-known Kuznets’ inverted U shape curve of income inequality according to which inequality increases at low income levels, peaks at some middling income, and diminishes as country becomes rich (Kuznets, 1955). Kuznets, in his monumental study of income distribution in the United States (Kuznets, 1953), had observed a big fall in the income share of the richest for the period between 1929 and 1946, but this result was true only for the first period. Piketty criticizes the Kuznets curve on several grounds. i) firstly Kuznets is criticized for not using sufficient empirical evidence or reading too much in very few data; ii) secondly Piketty does not see any spontaneous forces in capitalism that would drive inequality of incomes down; rather, the only spontaneous forces will push concentration of incomes up. Kuznets posited that income inequality first rises with economic development when new, higher productivity sectors emerge (e.g., manufacturing industry during the industrial revolution) but then decreases as more and more workers join the high-paying sectors of the economy. Our data show that this is not the reason why income inequality declined in developed countries during the first half of the 20th century. iii) thirdly Piketty thinks that Kuznets misinterpreted a temporary slackening in inequality after World War II as a sign of a more benign nature of capitalism, while it was, Piketty argues, due to the unique and unrepeatable circumstances. There was no “structural transformation” of capitalism. iv) fourthly, he thinks that Kuznets’ theory owes its success in part to the optimistic message that it conveyed during the Cold War, namely that poorer capitalist

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economies were not condemned to high inequality. There was the light at the end of the tunnel: if you followed the Washington prescriptions long enough, not only mean income will grow but inequality will become lower; v) finally Kuznets’ overly optimistic theory of a natural decline in income inequality in market economies largely owed its popularity to the Cold War context of the 1950s as a weapon in the ideological fight between the market economy and socialism (Piketty, Saez, p.842). Figure 8, Income inequality: Europe and the United States, 1870-2010

Inequality in total income is now substantially higher in the US than in Europe, while the opposite was true until World War I (see Figure 8). At that time, high inequality was mostly due to the extreme concentration of capital ownership and capital income. Over the 1980–2010 period, instead, the rise of top income shares in the United States in comparison with Europe is mostly due for to rising inequality of labor earnings. This rise of top labor’s income it is clearly a very important historical development which can itself be explained by a mixture of two groups of factors: the rising inequality in access to skills and higher education during this period in the United States and the exploding top managerial incomes. Could the large increase in US labor income inequality in recent decades be explained by insufficient educational investment for large segments of the US labor force, an evolution which might have been exacerbated by rising tuition fees and insufficient public investment? In such case, massive investment in higher education would be the right policy to curb rising income inequality. The most widely used economic model to explain changes in labor’s income is based on the idea of a “race” between education and technology. The expansion of education leads to a rise in the supply of skills, while technological change leads to a rise in the demand for skills. Depending on which process occurs faster, the inequality in labor incomes will either fall or rise. One proposed explanation for the increase of inequality in recent decades has been the rise in the global competition for skills, itself driven by globalization, skill-biased technological change and the rise in information technologies. Such skill-biased technological progress is not sufficient to explain important variations among countries. The rise in labor income inequality was relatively limited in Europe (and Japan) compared to the United States, despite similar technological changes. In the very long run, European labor income inequality appears to be relatively stable

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(there is no major downward or upward trend in the wage shares received by the various deciles and percentiles of the wage distribution). This suggests that the supply and demand for skills have increased approximately at the same pace in Europe. Although the race between education and technology is very appealing, it cannot account for every fact. In particular, it fails to explain the unprecedented rise of top labor incomes that has occurred in the United States over the past few decades. A large part of the rise in the top 10% income share comes from the top 1% (or even the top 0.1%). This is largely due to the rise in top executive compensation in large US corporations (both financial and nonfinancial) itself probably stimulated by changing incentives and norms and by large cuts in top tax rates (see also Piketty 2014a, ch.14; Piketty et. al. 2014). To a large extent, according to the evidence presented by Piketty, in US a society of rentiers has been progressively substituted by a society of managers. Piketty doubts that labor incomes of bankers and financiers might be determined by marginal productivity. He cites evidence to show that such top earnings depend mostly on chance events which have nothing to do with the quality of the management. Their high wages are the product of a collusive agreement between themselves and the boards. The boundaries between the various subgroups that make up the top decile of the income hierarchy have changed over time: income from capital used to predominate in the top centile but today predominates only in the top thousandth. A society in which the top centile is dominated by rentiers (people who own enough capital to live on the annual income from their wealth) progressively becomes a society in which the top of the income hierarchy, including to upper centile, consists mainly of highly paid individuals who live on income from labor. One might also say, more correctly (but less positively), that we have gone from a society of super-rentiers to a less extreme form of rentier society, with a better balance between success through work and success through capital. It is important, however, to clarify that this major upheaval came about, in France at any rate, without any expansion of the wage hierarchy which has been globally stable for a long time. The universe of individuals who are paid for their labor has never been as homogeneous as many people think. Some facts about the composition of top incomes deserve attention. About 60 percent of the income of the top 1 percent in the US today is labor income. Only when you get to the top tenth of 1 percent does income from capital start to predominate. The income of the top hundredth of 1 percent is 70 percent from capital. This is a fairly recent development. In the 1960s, the top 1 percent of wage earners collected a little more than 5 percent of all wage incomes. This fraction has risen pretty steadily until nowadays, when the top 1 percent of wage earners receive 10-12 percent of all wages. The story for France is not very different, though the proportion of labor income is a bit higher at every level. Piketty attributes such a fact to the rise of what he calls “supermanagers”. The very highest income class consists, to a substantial extent, of top executives of large corporations, with very rich compensation packages (a disproportionate number of these, but by no means all of them, come from the financial services industry). With or without stock options, these large pay packages get converted into wealth and future income from wealth. But the fact remains that much of the increased income (and wealth) inequality in the US is driven by the rise of these supermanagers (Solow, 2014, p.10). How does the view of the “return of capital” or even of the “return of the rentier” square with the evidence of the rising importance of education and of the increasing importance of high labor incomes among the top 1%? Aren’t we far from the rentier capitalism of the 19th century Europe? According to Piketty high β does not mean today exactly the same thing as more than 100 years ago. We are indeed living in a “patrimonial capitalism” (a new term coined by Piketty

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to designate the heritance-based capitalism), but with (i) lower concentration of property at the top, (ii) property that has penetrated much more deeply into the middle classes, and with (iii) labor incomes received by top managers and bankers which place them, alongside the “rentiers”, into the top 1%. Among the members of the top 1% “cohabit” the “coupon-clipping rentiers” and the “working rich”. Essentially, the modern “patrimonial capitalism” has succeeded in spreading modest property across the entire top half of the income distribution (as opposed to top 5% in the early 1900s) and in creating high labor incomes. But the ownership of capital, often through inherited wealth, still remains crucially important. Piketty shows that the annual flow of inheritances as a share of national income in today’s France, UK and Germany is about the same as one century ago that is between 8 and 12 percent of national income. Moreover, the percentage of population born in the 1970-1980s that receives inheritance equal to the capitalized lifetime earnings of a worker in the bottom half of the wage distribution is about 12%, again the same as one century ago. Among the coming generations it will likely reach 15%. In conclusion, Piketty agrees: “today’s “patrimonial capitalism” is not exactly the same as a century ago: it has a broader base and the concentration of wealth at the top is less; high labor incomes are more frequent. But its key feature—ability to generate a satisfactory income without the pain of work—is still there. Societies where the ratio between capital and income β is high, and the rate of return on capital exceeds the rate of growth of the economy, will always tend to convert entrepreneurs into “rentiers”. In such societies “the idea that free competition will put an end to a heritage-dominated society and will lead to an ever more meritocratic world is a dangerous illusion” (Piketty, 2014a, p. 299). Moreover income from wealth is probably even more concentrated than wealth itself because, as Piketty notes, “large blocks of wealth tend to earn a higher return than small ones. Some of this advantage comes from economies of scale, but more may come from the fact that very big investors have access to a wider range of investment opportunities than smaller investors” (Solow, 2014, p.10). 8. Is Piketty’s approach able to explain the inequality in personal income distribution? Several daily and weekly newspapers have hosted reviews of "Capital in the Twenty-First Century”, generally very positive (Krugman, 2014; Stiglitz, 2014a; Solow, 2014). Few reviews have been critical. Firstly they limited themselves to criticize the reliability of the sources used and of the estimates presented (Giles, 2014). Criticism on the sources, however, does not appear to have significantly weakened the volume’s content. The aim of the research was mainly to collect a big amount of “historical evidence and to analyze the economic, social, and political processes that can account for the evolutions that we observe in the various countries since the Industrial Revolution” (Piketty, 2015a, p.48). Piketty succeeded in answering, from the empirical point of view, to all the questions raised in his Introduction estimating, in the long run, the trends of capital/output ratio, of the return to capital, of the share of capital on national income, of inequality in the wealth and income distribution. The above criticisms, any way, were followed by several articles in defense of Piketty. The author himself answered pointing out that the results obtained, showing an increase in the inequality, and its negative effects in terms of growth based on empirical evidence, can only be the result of an imperfect inference, as it always happens in social sciences. As Amartya Sen (2014) claimed, “in any study of this kind you have to use diverse sources of data, and it is inescapable that you have to establish certain linkages on which it is possible to have debates”.

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More recently, the theoretical framework, the methodological approach and especially the concept of “capital” and of “saving rate” adopted by Piketty have been challenged. French economists, in particular, especially, were critics of its approach (Aghion, 2014). Piketty replied to the numerous and different remarks on his book writing some new papers. He argued that the arguments of the book were been “simplified in the telling and retelling” so that the original message were misunderstood. Its message, however, is very clear. The factors that generate inequality, in income and wealth, are numerous institutional, socio-economic and demographic. The factors which explain the dynamics of wealth (accumulation of capital) are different from those which explain the dynamics of labor income (demand and supply of skills and education, technology). It is very difficult, therefore, to reach a consensus on a “shared theory” of personal income distribution. The above issue deserves a deeper discussion and some critical remarks. The question becomes: is the Piketty’s approach the right one not only to explain trends in inequality, but also to enlighten the factors which originate the inequality in personal income distribution? Piketty links in a very innovative way the returns from capital to the rate of growth of national income. Trends of capital’s rent r and of income’s rate of growth g are compared in a macroeconomic framework. From such relation Piketty derives the value of the concentration of wealth, of capital incomes and finally the inequality in the personal income distribution. Inequality’s measures as the shares of the richest decile in the wealth and income distribution are estimated in a separated way and not together. Debraj Ray (2014, p.9) claims that “the fact that r exceeds g explains nothing about the rise in inequality”. An analysis of the process which determines the generation of personal incomes must start from the individual endowments of capital and labor. Capital/wealth obtained through work or hereditary transmission must be linked to capital income in a circular loop. To capture these linkages is a difficult task, also owing to the lack of suitable data, but without such linkages, the generating process which leads to inequality cannot be understood. This kind of analysis requires a suitable framework. The factors that can be considered as sources of individual incomes, in the short run, are not only endowments (physical and human capital) but also the "ability" to transform these endowments into personal income. In the long run, however, the accumulation of capital (earned or inherited) plays a very important role in generating income and inequality. Piketty's analysis focuses on this circular process, and therefore into the perpetuation of inequality. Pier Luigi Porta, for example, argues that “Piketty’s analysis has been justly praised from most quarters. But he risks to focus too much on the symptoms rather than going direct to the heart of the matter and curing the illness”. The structure of the factors ownership of individuals grouped into family units of different composition and size determines the distribution of market income. The mechanisms that regulate the market distribution of income among the various units must be brought back to these variables that contribute to the “generation” of the added value, belonging to an economic system divided into sectors of production, business units and different professions. The ways in which the individual endowments translate into earnings depends on their prices as a result of structural and cyclical market equilibria. This process can be represented by a "generating function of income", that is by a function f which ensures the correspondence between the disposable income yi and the endowments owned given a rate of exchange (price). In a first very

simplified specification it can be assumed that endowments are human capital cu, physical

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capital cf as well as the capability to obtain transfers from the government or other subjects tr .

This function can be expressed as: yi = f (cu, cf , tr)

Two groups of variables, micro and macro, contribute in generating the income function. On one side the value of the endowments can be considered the result of the factors that determine the earning capacity of a subject such as personal abilities (innate or acquired), age, ownership of capital assets accumulated or inherited. All these factors are taken in consideration by the traditional theories of personal income distribution. On the other side the ways through which resources are exchanged in the market and translated into income depends on micro and macroeconomic variables. In particular the prices of the endowments synthesize the structural economic characteristics of the different markets: more precisely the different rate of unemployment and/or of prevailing inflation. The capability of earn a certain level of market income depends on the position of each unity in a given socio-economic setting, that is on the relation between the characteristics of each subject and the setting in which he operates: not only by market conditions, but also by the structure of the property, as well as by the legal rules and the social, cultural and religious features of a country. In a monetary economy these conditions can be expressed by a vector of prices and the final result can be represented by a monetary income. In a second step the distribution of the disposable income,, is obtained from the distribution of market income taking into account of the impact of the redistributive policies. This impact reflects the structure of the redistributive mechanisms that operate through the tax system (more or less progressive) and through the social security. Each economic unit (individual or household) according to its position within the economic system and to the interactions with the other units (enterprises, government) will contribute to the inequality in the distribution of both market and disposable income. The inequality will be higher as the ownership of capital/wealth is more concentrated, as the dispersion of wages and salaries is wider, as the exclusion from the market and the marginalization affect systematically some components of the labor force, specific industrial sectors or regions. Many factors generate a wide dispersion of personal incomes around the average values. Typical in this respect is the impact of innate ability and/or acquired through education. In a system where incomes are earned in the market, but the capabilities are enhanced by the social and economic organization, the unequal distribution of abilities tend to produce an unequal distribution of incomes, thus emphasizing the importance of factors such as the "fate" and the luck. It is often not by skill, but by luck that an entrepreneur anticipates a sudden turn in demand, or an employee invests in a specialization that tomorrow will be much in demand and very gainful. These elements of unpredictability and chance are strictly linked to the innovation process. The luck, however, has a very important role in the accumulation process of wealth and heritages, as Piketty has shown. Investment in both human capital (through education) and age are very important factors to explain the earning capacity of the subjects, and therefore the inequality in personal income distribution. They, on the other hand, depend in turn by factors linked to the characteristics of the family of origin (wealth and level of education of the parents), and those of the subject itself (learning ability, school) as well as to the structure of the school system. Occupational choice, and the consequent social position, in turn depend not only on the level of education, but also by the family background and the paternal prestige. The middle class would use education not only

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as an investment in children but also as a factor that raises the access barriers to different kind of professions. The framework above sketched can acquires an even greater explanatory power if we take into account the issues discussed by Piketty, although its approach is different from that outlined. Piketty, namely, links the inequality in personal income distribution mainly to wealth concentration, and to the patrimonial capitalism as a factor which explains the perpetuation of inequality in the long run. An increase in the share of capital income is considered the origin of the growing inequality in personal income distribution. In this perspective, the link between functional and personal income distribution is very clear and it is, according to Atkinson (2009), one of the most important issues of political economy. But also the capability to obtain income from the endowments is an important piece in the “puzzle” of the personal income generation. The distribution of income (or earnings) can be seen as at the core of economic inequality. However, the flow of income is only part of the story. The accumulated stock of wealth also constitutes a key economic resource, be it for its major role in economic ‘power’ towards the top of the distribution on the one hand or its provision of coverage for financial risks, for example, in old age, on the other hand. Inequality in the access to economic resources, in endowments, and in opportunities, and the way these affect economic outcomes for individuals and families are crucial. These inequalities are inextricably tied up with institutional structures, including the market and concomitant private and social property rights, and they may both affect, and be affected by, aggregate economic performance. Understanding these relationships is the primary aim of research on economic inequality. 9. Economic policy recommendations. The last chapters of "Capital in the Twenty-First Century” are dedicated to discuss some policy proposals. According not only to Piketty, but also to other authors like Stiglitz (2014b), the sources of inequality in the today US are so profound that measures as the increase in minimum wage and better education will not go to the root of the problem. Social mobility can be increased by improving the quality of the school. US are the country of the OECD where school performance depends greatly on the social origin of the pupils. Social mobility stimulates growth through innovation while it reduces income inequality: taxation must be considered one tool among many others to increase social mobility while stimulating growth through innovation. However more radical policies are needed for curbing inequality as the introduction of capital taxes on highest incomes. “A well designed tax system can do more than just raise money—it can be used to improve economic efficiency and reduce inequality. Our current system does just the opposite” (Stiglitz, 2014c). Piketty claims that it is necessary to prevent that only the richest group are able to gain prominent positions in the society. Therefore it is necessary to introduce alternative policies because the composition of wealth is heterogeneous. It is necessary to reform the tax system by adopting progressive taxation not only on income but also on the different types of wealth: it would be especially necessary to introduce a progressive tax on estates and inheritances and to standardize the taxation of capital worldwide or at least Europe-wide. In order to limit the high concentration of top incomes Piketty imagines a role for high (“confiscatory”) taxation. High taxes on the super-rich will have minimal revenue effect. But they will dissuade bankers and managers from asking for such exorbitant remunerations. As Piketty points out, when, as in the

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1960s and the 1970s, US marginal tax rate on highest incomes was in the neighborhood of 90%, it did not make sense for managers to insist one more million if 90% of it would end in taxman’s coffers. But with a marginal tax rate of 25%, the story is entirely different. So the role of “confiscatory” (marginal) taxation is not to garner revenue but to limit “socially unproductive” high incomes which are a waste in the sense that they are not needed to produce greater output. Taxation is also needed to curb political power of the rich. The policy recommendation that has attracted higher attention is Piketty’s call for a global taxation of capital. The only way to reverse the r>g inequality, if g is exogenously given, is to reduce r. A progressive wealth tax on a global scale, based on the automatic exchange of bank information, is suggested by Piketty not only as "useful utopia", but as a proposal to think about and discuss. Could be the tool to reverse the weight of inherited capital? Despite its perhaps unrealistic nature (Piketty calls it a “useful utopia”) one would be wrong to dismiss the proposal out of hand. Nobody believes that such recommendation could be implemented hic et nunc, and neither does Piketty: however it is based on several strong points. The analysis sketched so far (if one accepts it fully) shows the dangers of an inheritance based system which favors those who do not need to work for their sustenance. This situation can be modified precisely through a tax on capital, whether in form of tax on land or on inheritance. They have a long history precisely because some forms of capital were difficult to hide, but to extend them to include all forms of capital seems logically consistent. Technical requirements for such a tax (which in a rudimentary form exists in most advanced economies) are not overwhelming. Housing is already taxed; the market value of different financial instruments is easily ascertainable and the identities of owners are known. The problems are, of course political. The application of such a tax by individual countries, even the most important, like the US, can easily lead to an outflow of capital. Thus, international collaboration is indispensable: but such collaboration is unlikely to be supported by the countries that currently benefit the most from the opacity of financial transactions and offer tax havens to the rich. Moreover, some emerging market economies may be unwilling to subscribe to it too. But a more modest proposal built by the OECD members (or EU and US) is, Piketty argues, feasible. He takes the US legislation (Foreign Account Tax Compliance Act) as one of the first steps that could lead to regional taxation of capital. The recent (2010) legislation contained in the Foreign Account Tax Compliance Act (FATCA) can be seen as a first step that could lead, in the United States, the regional capital taxation. FATCA is a federal law that requires US citizens, including those living abroad, to report their financial accounts held outside of the United States also requires foreign financial institutions to report all 'Internal Revenue Service (IRS) the names of US clients. Congress passed FATCA to make it harder for US taxpayers hiding assets held in offshore accounts and shell companies, in order to recover federal tax revenues. FATCA is one of the measures introduced in the United States as an incentive to stimulate the recruitment of new workers by companies. More complicated is the estimation of an optimal annual tax on capital and on capital income. It is impossible to predict what the future rate of return of assets will be, and then the present value of the same (Piketty, 2015, p.8). .The theory of optimal taxation of capital was developed by Piketty in a paper published by Emmanuel Saez (Piketty, Saez, 2013). Depending on the model developed in this work, and taking into account the fact that the inequality in income distribution depends, simultaneously, from capital and labour income Piketty makes a proposal that is a simple rule-of-thumb “One should adapt the tax rates to the observed speed at which different

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wealth groups are rising over time ... the optimal tax policy also is two-dimensional: it involves a progressive tax on labor income and a progressive tax on inherited wealth. Specifically, we show that the long-run optimal tax rates on labor income and inheritance depend on the distributional parameters, the social welfare function, and the elasticities of labor earnings and capital bequests with respect to tax rates .... For realistic empirical values, we find that the optimal inheritance tax rate might be as high as 50-60%, or even higher for top bequests, in line with historical experience"(Piketty, 2015a, p.51). Piketty admits to have, probably, devoted too much attention to progressive capital taxation and too little attention to a number of institutional changes that could prove equally important, as the development of alternative forms of property arrangements and participatory governance. Capital taxation is important because it can also bring increased transparency in company’s assets and accounts. In turn, increased financial transparency can help to develop new forms of governance; for instance, it can facilitate more worker involvement in company boards. But such further institutions also need to be analyzed on their own terms. Piketty in the last chapter of the book concludes: “Without real accounting and financial transparency and sharing of information, there can be no economic democracy. Conversely, without a real right to intervene in corporate decision-making (including seats for workers on the company’s board of directors), transparency is of little use. Information must support democratic institutions; it is not an end in itself. If democracy is someday to regain control of capitalism, it must start by recognizing that the concrete institutions in which democracy and capitalism are embodied need to be reinvented again and again” (Piketty, 2014a). References - Aghion P. (2014), La théorie de Piketty est contestable ainsi que l’analyse empirique qu’il utilise, L’Opinion, mai 13, at http://www.scoop.it/t/pjse-umr8545/p/4022351794/2014/06/02/philippe-aghion-la-theorie-de-piketty-est-contestable-ainsi-que-l-analyse-empirique-qu-il-utilise 8. - Alvaredo F., Atkinson A., Piketty T. and Emmanuel Saez E. (2014), The Top World Incomes Database, at http://topincomes.parisschoolofeconomics.eu/ - Atkinson A.B. (1997), Bringing Income Distribution in from the Cold, The Economic Journal, vol. 107 (441), pp. 297-321. March. - Atkinson A.B. (2015), Inequality. What Can Be Done? Cambridge MA: Harvard University Press. - Bonnet O., Bono P. H., Chapelle G. and Etienne Wasmer (2014), Does Housing capital contribute to inequality? A comment on Thomas Piketty’s Capital in the 21st Century, Discussion Paper 2014-07, Department of Economics, Sciences Po, Paris http://www.insee.fr/en/insee-statistique-publique/connaitre/colloques/acn/pdf15/ACN2014-Session5-4-texte-3.pdf - Brandolini A. (2014), Piketty e i dati, Menabò di Etica ed Economia, 20 settembre, http://www.eticaeconomia -Giles, Chris (2014), Piketty findings undercut by errors, “Financial Times”, may 2014. http://www.ft.com/intl/cms/s/2/e1f343ca-e281-11e3-89fd-00144feabdc0.html#axzz3P0S4pQBY -Giles C. (2014), Piketty findings undercut by errors, Financial Times, may 2014, at http://www.ft.com/intl/cms/s/2/e1f343ca-e281-11e3-89fd-00144feabdc0.html#axzz3P0S4pQBY

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- Piketty T. and Gabriel Zucman G. (2015), Wealth and Inheritance in the Long Run, in: Atkinson A. and François Bourguignon (eds.), vol 2, Handbook of Income Distribution, Elsevier, at http://piketty.pse.ens.fr/files/PikettyZucman2014HID.pdf - Porta P.L. (2014), Distributive Justice versus Commutative Justice, International Review of Economics, 61(2):197-201. -Ray D. (2015), Nit-Piketty. A comment on Thomas Piketty’s Capital in the Twenty First Century, CESifo Forum, 1/2015, march, at http://www.econ.nyu.edu/user/debraj/Papers/Piketty.pdf - Sala-I-Martin X. (2014), Piketty y “Capital en el Siglo XXI”, mimeo, at http://salaimartin.com/randomthoughts/item/720. - Sen A. (2014), Inequality: Why Thomas Piketty is Mostly Right, Social Europe, june 13. -Solow R. M. (2014), Thomas Piketty is right, Capital in the Twenty-First Century' by Thomas Piketty, reviewed, New Republic, April 22, at http://www.newrepublic.com/article/117429/ - Stiglitz J.E. (2012), The Price of Inequality: How Today's Divided Society Endangers Our Future, New York: W. W. Norton & Company. -Stiglitz J.E. (2014a), Democracy in the twenty-first century, Project Syndicate, December, at http://www.project-syndicate.org/commentary/joseph-e--stiglitz-blames-rising-inequality-on-an-ersatz-form-of-capitalism-that-benefits-only-the-rich -Stiglitz J.E. (2014b), Inequality in America: A Policy Agenda for a Stronger Future, 2014 Moynihan Prize Lecture. - Stiglitz J.E. (2014c), In defense of capitalism, Bill Moyers.com, August 2014, at http://billmoyers.com/2014/08/22/joseph-stiglitz-in-defense-of-capitalism/ - Stiglitz J.E. (2015), The Great Divide: Unequal Societies and What We Can Do About Them,  New York: W. W. Norton & Company.