Capital, Predistribution and Redistribution

by Thomas Piketty on January 4, 2016

In my view, _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, we have been able to collect a relatively large historical database on the structure of national income and national wealth and the evolution of income and wealth distributions, covering three centuries and over 20 countries. In effect, we have been extending to a larger scale the pioneering historical data collection work of Simon Kuznets and Tony Atkinson (see Kuznets, 1953, and Atkinson and Harrison, 1978). My first objective in this book is to present this body of historical evidence in a consistent manner, and to try to analyze the many economic, social and political processes that can account for the various evolutions that we observe in the different countries since the Industrial Revolution (see Piketty and Saez, 2014, for a brief summary of some of the main historical facts). Another important objective is to draw lessons for the future and for the optimal regulation and taxation of capital and property relations. I stress from the beginning that we have too little historical data at our disposal to be able to draw definitive judgments. On the other hand, at least we have substantially more evidence than we used to. Imperfect as it is, I hope this work can contribute to put the study of distribution and of the long run back at the center of economic thinking.

In this essay, I seek to discuss a number of implications of my findings, in particular regarding the optimal regulation of capital and the complementarity between the “predistribution” and the “redistribution” approach. I will also attempt to address some of the very valuable comments made by the participants to the Crooked Timber symposium. First, I will clarify the role played by r>g in my analysis of wealth inequality. Next, I will present some of the implications for optimal taxation, starting with inheritance taxation and then moving with annual taxation of wealth, capital income and consumption. Finally, I will emphasize the need to develop a multi-sector approach to capital accumulation. This will lead me to stress the limits of capital taxation and the complementarity with other public policies aimed at regulating the accumulation and distribution of capital (such as land use, housing policies, intellectual property rights, co-determination and participatory governance).

_What r>g can and cannot explain_

In my analysis, the size of the gap between r and g, where r is the rate of return on capital and g the economy’s growth rate, is one of the important forces that can account for the historical magnitude and variations in wealth inequality. In particular, it can contribute to explain why wealth inequality was so extreme and persistent in pretty much every society up until World War I (see _Capital…_, Chapter 10).

That said, the way in which I perceive the relationship between r>g and inequality is often not well captured in the discussion that has surrounded my book. For example, I do not view r>g as the only or even the primary tool for considering changes in income and wealth in the 20th century, or for forecasting the path of inequality in the 21st century. Institutional changes and political shocks – which to a large extent can be viewed as endogenous to the inequality and development process itself – played a major role in the past, and it will probably be the same in the future. In addition, I certainly do not believe that r>g is a useful tool for the discussion of rising inequality of labor income: other mechanisms and policies are much more relevant here, e.g. supply and demand of skills and education. For instance, I point out in my book (particularly Ch. 8-9) that the rise of top income shares in the US over the 1980-2010 period is due for the most part to rising inequality of labor earnings, which can itself be explained by a mixture of three groups of factors: rising inequality in access to skills and to higher education over this time period in the United States, an evolution which might have been exacerbated by rising tuition fees and insufficient public investment; exploding top managerial compensation, itself probably stimulated by changing incentives and norms, and by large cuts in top tax rates (see also Ch. 14;  Piketty, Saez and Stantcheva, 2014); changing labor market rules and bargaining power, in particular due to declining unions and a falling minimum wage in the United States (see Ch.9, fig.9.1). In any case, whatever the relative weight one chooses to attribute to each factor, it is obvious that this rise in labor income inequality in recent decades has little to do with r-g.

I should also make clear that there are many important issues regarding the determinants of labor income inequality which are not adequately addressed in my book. As rightly argued by Margaret Levi (this symposium), the changing nature of the workplace and the evolution of organized interests – particularly unions – do not play a sufficiently important role in my analysis (see however the discussion on salary scales and unions in Chap.9). As Danielle Allen (this symposium) rightly points out, education does not matter solely – and arguably not primarily – for reducing inequality in skills and labor market outcomes: it also plays a key role in fostering participation to the democratic process, which in turn largely determines inequality dynamics. The role played by gender and racial inequality and discrimination is also insufficiently analyzed, as pointed out by Anne Cudd (this symposium). I do stress the importance of foreign ownership, colonial coercion and slavery in the historical evolution of private wealth since the Industrial revolution, particularly in Britain, France and the United States (see Chap.3-5). But the issue of labor market discrimination is largely neglected. More generally, although I do try to show the importance of beliefs systems and perceptions about inequality and its legitimacy, Chris Bertram (this symposium) is perfectly right to point out that this could and should be addressed in a much more systematic manner in the future.

_r>g and the amplification of wealth inequality_

I now clarify the role played by r>g in my analysis of the long-run level of wealth inequality. Specifically, a higher r-g gap will tend to greatly amplify the steady-state inequality of a wealth distribution that arises out of a given mixture of shocks (including labor income shocks).

Let me first say very clearly that r>g is certainly not a problem in itself. Indeed, 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. For instance, in the standard dynastic model where each individual behaves as an infinitely lived family, the steady-state rate of return is well known to be given by the modified “golden rule” r = θ + γ g  (where θ is the rate of time preference and γ is the curvature of the utility function). E.g. if θ=3 percent, γ=2, and g=1 percent, then r=5 percent. In this framework, the inequality r>g always holds true, and does not entail any implication about wealth inequality.

In a representative-agent framework, what r>g means is simply that in steady-state each family only needs to reinvest a fraction g/r of its capital income in order to ensure that its capital stock will grow at the same rate g as the size of the economy, and the family can then consume a fraction 1-g/r. For example, if r=5 percent and g=1 percent, then each family will reinvest 20 percent of its capital income and can consume 80 percent. This tells us nothing at all about inequality: this is simply saying that capital ownership allows to reach higher consumption levels – which is really the very least one can ask from capital ownership.[^fn1]

So what is the relationship between r-g and wealth inequality? To answer this question, one needs to introduce extra ingredients into the basic model, so that inequality arises in the first place.[^fn2]  In the real world, many shocks to the wealth trajectories of families can contribute to making the wealth distribution highly unequal (indeed, in every country and time period for which we have data, wealth distribution within each age group is substantially more unequal than income distribution, which is difficult to explain with standard life-cycle models of wealth accumulation). There are demographic shocks: some families have many children and have to split inheritances in many pieces, some have few; some parents die late, some die soon, and so on. There are also shocks to rates of return: some families make good investments, others go bankrupt. There are shocks to labor market outcomes: some earn high wages, others do not. There are differences in taste parameters that affect the level of saving: some families consume more than a fraction 1-g/r of their capital income, and might even consume the full capital value; others might reinvest more than a fraction g/r and have a strong taste for leaving bequests and perpetuating large fortunes.

A central property of this large class of models is that for a given structure of shocks, the long-run magnitude of wealth inequality will tend to be magnified if the gap r – g is higher. In other words, wealth inequality will converge towards a finite level. The 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. But this finite inequality level will be a steeply rising function of the gap r-g. Intuitively, a higher gap between r and g works as an amplifier mechanism for wealth inequality, for a given variance of other shocks. To put it differently: a higher gap between r and g allows to sustain a level of wealth inequality that is higher and more persistent over time (i.e. a higher gap r-g leads both to higher inequality ad lower mobility). Technically, one can indeed show that if shocks take a multiplicative form, then the inequality of wealth converges toward a distribution that has a Pareto shape for top wealth holders (which is approximately the form that we observe in real world distributions, and which corresponds to relatively fat upper tails and large concentration of wealth at the very top), and that the inverted Pareto coefficient (an indicator of top end inequality) is a steeply rising function of the gap r – g. The logic behind this well-known theoretical result (which was established by many authors using various structure of demographic and economic shocks; see in particular Stiglitz, 1969) and this “inequality amplification” impact of r – g is presented in Chapter 10 of my book.[^fn3]

The important point is that in this class of models, relatively small changes in r – g can generate large changes in steady-state wealth inequality. E.g. simple simulations of the model with binomial taste shocks show that going from r-g=2% to r-g=3% is sufficient to move the inverted Pareto coefficient from b=2.28 to b=3.25. Taken literally, this corresponds to a shift from an economy with moderate wealth inequality – say, with a top 1 percent wealth share around 20-30 percent, such as present-day Europe or the United States – to an economy with very high wealth inequality with a top 1 percent wealth share around 50-60 percent, such as pre-World War 1 Europe.[^fn4]

Available micro-level evidence on wealth dynamics confirm that the high gap between r and g is one of the central reasons why wealth concentration was so high during the 18th-19th centuries and up until World War 1 (see Ch. 10; Piketty, Postel-Vinay, Rosenthal (2006, 2014)). During the 20th century, it is a very unusual combination events which transformed the relation between r and g (large capital shocks during 1914-1945 period, including destruction, nationalization, inflation; high growth during reconstruction period and demographic transition; higher bargaining power for organized labor). In the future, several forces might push toward a higher r-g gap (particularly the slowdown of population growth, and rising global competition to attract capital) and higher wealth inequality. But ultimately which forces prevail is relatively uncertain. In particular, this depends on the institutions and policies that will be adopted in many different areas.

I should also stress that the dynamics of wealth inequality always involve country-specific factors. Each country has its own unique relation to inequality and the concentration of wealth. In my book, I particularly stress the contrast between European and North American patterns. But this is true for other parts of the world, as exemplified for instance by John Quiggin (this symposium) about Australia’s egalitarian tradition and specific trajectory with respect to inequality.

It should also be noted that the impact of growth slowdown on the gap r-g is fundamentally ambiguous. In the benchmark dynastic model outlined above (which might not be particularly plausible), it all depends on the value of curvature of the utility function (smaller or larger than one). More generally, this will depend on the structure of intertemporal preferences and saving motives, as well as on the parameters of the production technology (in particular the elasticity of substitution between capital labor). In multi-sector models of capital accumulation, which as I argue below are far more realistic, almost anything can happen, depending in particular on the specific rules, relative prices, institutions and changing bargaining power of the various social groups in the relevant sectors.

In my book I also emphasize the fact that the measurement of capital income is biased in different ways in high-growth and low-growth societies. That is, high growth periods arguably require more entrepreneurial labor in order to constantly reallocate capital and benefit from higher returns (in other words, measured rates of return must be corrected downwards in order to take into account mismeasured labor input in high-growth societies, particularly in reconstruction periods). Conversely, measured rates of returns might be closer to pure returns in low-growth societies (where it is relatively easier to be a rentier, since capital reallocation requires less attention). In my view, this is one of the main reasons with low-growth societies are likely to be characterized by a higher gap between r and g (where r is the pure rate of return to capital, i.e. after deduction for formal and information portfolio management costs and related entrepreneurial labor).[^fn5] This is certainly an issue that would deserve additional research in the future.

_On the optimal progressive taxation of income, wealth and consumption_

I now move to the issue of optimal taxation and redistribution. The theory of capital taxation that I present in _Capital in the 21st Century_ is largely based upon joint work with Emmanuel Saez (see in particular Piketty and Saez 2013a). In this paper, we develop a model where inequality is fundamentally two-dimensional: individuals differ both in their labor earning potential and in their inherited wealth. Because of the underlying structure of demographic, productivity and taste shocks, these two dimensions are never perfectly correlated. As a consequence, the optimal tax policy is also 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. The optimal tax rate on inheritance is always positive, except of course in the extreme case with an infinite elasticity of capital accumulation with respect to the net-of-tax rate of return (as posited implicitly in the benchmark dynastic model with infinite horizon and no shock). 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.[^fn6]

In effect,  what we do in this work is to extend the « sufficient statistics » approach to the study of capital taxation. The general idea behind this approach is to express that optimal tax formulas in terms of estimable “sufficient statistics” including behavioral elasticities, distributional parameters, and social preferences for redistribution. Those formulas are aimed to be robust to the underlying primitives of the model and capture the key equity-efficiency trade-off in a transparent way. This approach has been fruitfully used in the analysis of optimal labor income taxation (for a recent survey, see Piketty and Saez 2013b). We follow a similar route and show that the equity-efficiency trade-off logic also applies to the taxation of inheritance. This approach successfully brings together many of the existing scattered results from the literature.

Next, if we introduce capital market imperfections into our basic inheritance tax model, then we find that one needs to supplement inheritance taxes with annual taxation of wealth and capital income. Intuitively, in presence of idiosyncratic shocks to future rates of return, it is impossible to know the lifetime capitalized value of an asset at the time of inheritance, and it is optimal to split the tax burden between these different tax instruments. For instance, assume I received from my family an apartment in Paris worth 100 000€ back in 1975. In order to compute the optimal inheritance tax rate, one would need to know the lifetime capitalized value of this asset. But of course, back in 1975, nobody could have guessed that this asset would be worth millions of euros in 2015, or the annual income flows generated by this asset between 1975 and 2015. In such a model, one can show that it is optimal to use a combination of inheritance taxation and annual taxation of property values and capital income flows (Piketty and Saez, 2013a).

One difficulty is that optimal tax formulas soon become relatively complicated and difficult to calibrate, however. In particular, the optimal split between annual taxes on wealth stock and annual taxes on capital income flows depends on the elasticity of rates of return with respect to taxation (i.e. the extent to which observed rates of return are sensitive to individual effort and portfolio decisions, as opposed to idiosyncratic, uninsurable shocks). Naturally, intertemporal substitution elasticities also play a role. Substantial additional research is necessary before we can provide a realistic, complete calibration of the optimal capital tax system (which involves a mixture of progressive taxes on inheritance, annual wealth holdings and annual capital income flows).

In my book, I propose a simple rule-of-thumb to think about optimal annual tax rates on wealth and property. Namely, one should adapt the tax rates to the observed speed at which the different wealth groups are rising over time. For instance, if top wealth holders are rising at 6-7% per year in real terms (as compared to 1-2% per year for average wealth), as suggested by Forbes-type wealth rankings (as well as by recent research by Saez and Zucman (2014) suggesting that US wealth concentration has increased even more in recent decades than what I argue in the book, as pointed out by Olivier Godechot in this symposium), and if one aims to stabilize the level of wealth concentration, then one might need to apply top wealth tax rates as large as 5% per year, and possibly higher (see Ch. 15; see also Ch. 12, Tables 12.1-12.2). Needless to say, the implications would be very different if top wealth holders were rising at the same speed as average wealth. One of the main conclusions of my research is indeed that there is substantial uncertainty about how far income and wealth inequality might rise in the 21st century, and that we need more financial transparency and better information about income and wealth dynamics, so that we can adapt our policies and institutions to a changing environment, and experiment different levels of wealth tax progressivity. This might require better international fiscal coordination, which is difficult but by no means impossible (Zucman, 2014).

An alternative to progressive taxation of inheritance and wealth is the progressive consumption tax (see e.g. Gates 2014, and the essay by Ken Arrow in this symposium). This is in my view a highly imperfect substitute, however. First, meritocratic values imply that one might want to tax inherited wealth more than self-made wealth, which is impossible to do with a consumption tax alone. Next, and most importantly, the very notion of consumption is not very well defined for top wealth holders: personal consumption in the form of food or clothes is bound to be a tiny fraction for large fortunes, who usually spend most of their resources in order to purchase influence, prestige and power. When the Koch brothers spend money on political campaigns, should this be counted as part of their consumption? When billionaires use their corporate jets, should this be included in consumption? A progressive tax on net wealth seems in my view more desirable than a progressive consumption tax, first because net wealth is easier to define, measure and monitor than consumption, and next because it is better indicator of the ability of wealthy taxpayers to pay taxes and to contribute to the common good (see Ch.15).

_Capital-income ratios vs capital shares: towards a multi-sector approach_

One of the important findings from my research is that capital-income ratios β=K/Y and capital shares α tend to move together in the long run, particularly in recent decades, where both have been rising. In the standard one-good model of capital accumulation with perfect competition, the only way to explain why β and α move together is to assume that the capital-labor elasticity of substitution σ that is somewhat larger than one (which could be interpreted as the rise of robots and other capital-intensive technologies).[^fn7]

Let me make clear however this is not my favored interpretation of the evidence. Maybe robots and high capital-labor substitution will be important in the future. But at this stage, the important capital-intensive sectors are more traditional sectors like real estate and energy. I believe that the right model to think about rising capital-income ratios and capital shares in recent decades is a multi-sector model of capital accumulation, with substantial movements in _relative_ prices, and with important variations in bargaining power over time (see _Capital…_, Ch. 3-6). Indeed, large upward or downward movements of real estate prices play an important role in the evolution of aggregate capital values during recent decades, as they did during the first half of the 20th centuries. As rightly argued by J.W. Mason (his symposium), movements in relative asset prices play an absolutely central role in the dynamics of wealth-income ratios. Changes in relative asset prices – particularly real estate prices –  can in turn be accounted for by a complex mixture of institutional and technological forces, including rent control policies and other rules regulating relations between owners and tenants, the transformation of economic geography, and the changing speed of technical progress in the transportation and construction industries relative to other sectors (see Ch. 3-6; Piketty and Zucman (2014)). In practice, intersectoral elasticities of substitution combining supply and demand forces can often be much higher than within-sector elasticities (see e.g. Karababounis and Neiman (2014) about the role played by the declining relative price of equipment).

More generally, one central reason why my book is relatively long is because I try to offer a detailed, multidimensional history of capital and its metamorphosis. Capital ownership takes many different historical forms, and each of them involves different forms of property relations and social conflict, which must be analyzed as such (see e.g. my analysis of slave capital in 19th century U.S. in Ch.4; see also Ch.5 on the stakeholder German capitalism model, with large gaps between the social and market values of corporations). This multidimensional nature of capital creates substantial additional uncertainties regarding the future evolution of inequality, as illustrated by the examples of housing and oil prices. In my view, this reinforces the need for increased democratic transparency about income and wealth dynamics.

_Property, predistribution and redistribution_

Finally, let me conclude by making clear that the historical and political approach to inequality, property relations and institutions that I develop in my book should be viewed as exploratory and incomplete. In particular, I suspect that new social movements and political mobilizations will give rise to institutional change in the future, but I do not pursue this analysis much further. As I look back at my discussion of future policy proposals in the book, I may have devoted too much attention to progressive capital taxation and too little attention to a number of institutional evolutions that could prove equally important. Because capital is multidimensional and markets are imperfect, capital taxation needs to be supplemented with other asset-specific policies and regulations, including for instance land use and housing policies and intellectual property right laws. In particular, as rightly argued by Elizabeth Anderson in this symposium, monopoly power and the regulation of intellectual property rights play an important role in the dynamics of private wealth accumulation. Given the central role played by changing real estate values and rent levels in the aggregate evolution of capital-income ratios and capital shares in recent decades, it is clear that land use and housing policies have potentially a critical role to play, in particular to regulate and expend access to property. On the other hand, it is equally clear that such policies are sometime difficult to implement (e.g. public construction policies or housing subsidies have not always been very successful in the past), so they should certainly be viewed as complementary rather than substitute to progressive taxation.

Also, in my book I do not pay sufficient attention to the development of other alternative forms of property arrangements and participatory governance. One central reason why progressive capital taxation is important is because it can also bring increased transparency about company 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. In other words, “social-democratic” institutions such as progressive taxation (see Miriam Ronzoni in this symposium) can foster institutions that question in a more radical manner the very functioning of private property (note that progressive capital taxation transforms large private property as a temporary attribute rather than a permanent one – already a significant change). However these other institutions – whose aim should be to redefine and regulate property rights and power relations – must also be analyzed as such – a step that I do not fully follow in this book.

In his essay, Martin O’Neill (this symposium) stresses the proximity between my views and those of James Meade’s ideas about the “property-owning democracy”. I could not agree more. In particular, I think that the opposition between “predistribution” and “redistribution” – which became relatively common in policy debates since the 1990s, particularly in the context of New Labour Britain – is largely misguided. Both approaches are complementary, not substitutes. Like Meade, I believe that progressive taxation of income, inheritance and wealth is important both for redistribution and predistribution: of course it is an indispensable tool in order to limit market-induced inequality ex post; but it also reduces asset inequality ex ante, and most importantly it helps foster financial transparency, without which economic democracy and alternative forms of property cannot flourish. The logic of redistribution and the logic of opportunities, rights and participation must be pursued together. Atkinson’s recent book on “Inequality – What can be done” beautifully illustrates how Meade’s line of thought can be pursued in order to develop a new progressive agenda for the 21st century, with capital endowments financed by progressive inheritance taxation, new forms of public property funds, and more genuine economic and social democracy.

The last chapter of my 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” (p. 570). I do not push this line of investigation much further, which is certainly one of the major shortcomings of my work. Together with the fact that we still have too little data on historical and current patterns of income and wealth, these are some of the key reasons why my book is at best an introduction to the study of capital in the 21st century.


Atkinson, Anthony and Alan Harrison, Distribution of Personal Wealth in Britain, 1923-1972, Cambridge University Press, 1978

Atkinson, Anthony, Thomas Piketty and Emmanuel Saez, « Top Incomes in the Long Run of History », _Journal of Economic Literature_, 2011, vol.49(1), pp.3-71.

Gates, W., “Why Inequality Matters”, Gates Notes, October 2014

Karabarbounis, Loukas and Brent Neiman, “Capital depreciation and Labor shares around the World: Measurement and Implications,” _NBER Working paper_, 2014

Kuznets, S., Shares of Upper Income Groups in Income and Savings, 1913-1948, National Bureau of Economic Research, 1953

Piketty, Thomas, Capital in the 21st Century, Harvard University Press, 2014

Piketty, Thomas, Gilles Postel-Vinay and Jean-Laurent Rosenthal, “Wealth Concentration in a Developing Economy: Paris and France, 1807-1994,” _American Economic Review_, 2006, 96(1), pp.236-256

Piketty, Thomas, Gilles Postel-Vinay and Jean-Laurent Rosenthal, “Inherited vs. Self-Made Wealth: Theory and Evidence from a Rentier Society (1872-1927),” _Explorations in Economic History_, 2014.

Piketty, Thomas and Emmanuel Saez, “A Theory of Optimal Inheritance Taxation,” _Econometrica_, 2013a, vol.81(5), pp.1851-1886

Piketty, Thomas and Emmanuel Saez, “Optimal Taxation of Labor Income,” _Handbook of public economics_, North-Holland, 2013b, vol.5, chap.7, p.391-474.

Piketty, Thomas and Emmanuel Saez, “Inequality in the long run,” Science, 2014

Piketty, Thomas, Emmanuel Saez, and Stefanie Stantcheva, “Optimal Taxation of Top Labor Incomes : A Tale of Three Elasticities”, _American Economic Journal : Economic Policy_, 2014

Piketty, Thomas and Gabriel Zucman, “Capital is Back: Wealth-Income Ratios in Rich Countries 1700-2010,” _Quarterly Journal of Economics_, 2014.

Piketty, Thomas and Gabriel Zucman, “Wealth and Inheritance in the Long Run,” in _Handbook of Income Distribution_, A. Atkinson and F. Bourguignon, eds., volume 2, Elsevier, 2015

Saez, Emmanuel and Gabriel Zucman, “The Distribution of Wealth, Capital Income, and Rates of Returns in the U.S. Since 1913,” NBER Working paper, 2014

Stiglitz, J.E., “Distribution of Income and Wealth Among Individuals,” _Econometrica_, 1969, vol.37(3), pp. 382-397

Zucman, Gabriel, “Taxing Across Borders: Tracking Personal Wealth and Corporate Profits,” _Journal of Economic Perspectives,_ 2014.

[^fn1]: The inequality r<g would correspond to a situation which economists often refer to as “dynamic inefficiency”: in effect, one would need to invest more than the return to capital in order to ensure that one’s capital stock keeps rising as fast as the size of the economy. This corresponds to a situation of excessive capital accumulation.

[^fn2]: In the dynastic model with no shock, there is no force generating inequality out of equality (or equality out of inequality), so any initial level of wealth inequality (including full equality) can be self-sustaining, as long as the modified Golden rule is satisfied. Note however that the magnitude of the gap r-g has an impact on the steady-state inequality of consumption and welfare: if r-g is small then high-wealth dynasties need to reinvest a large fraction of their capital income, so that they do not consume much more than low wealth dynasties.

[^fn3]: For detailed references to this literature on dynamic wealth accumulation models with random shocks, see the on-line appendix to chapter 10 available at See also Piketty and Zucman (2015, section 5.4).

[^fn4]: In the special case with binomial saving taste shocks with probability p, one can easily show that the inverted Pareto coefficient is given by b= log(1/p)/log(1/ω), with ω=s e(r-g)H (s is the average saving taste, r and g are the annual rate of return and growth rate, and H is generation length). See Piketty and Zucman (2015, section 5.4) for simple calibrations. Atkinson, Piketty and Saez (2011, figures 12-15) provide evidence on the long-run evolution of Pareto coefficients.

[^fn5]: Indeed the historical estimates on pure rates of return that I present in my book are largely built upon this assumption. See the discussion in Chapter 6.

[^fn6]: See Piketty and Saez, 2013a, fig.1-2 and table 1. Note that the optimal inheritance tax rate can also be expressed as an increasing function of the gap r-g.

[^fn7]: With Y=F(K,L)=[aK(σ-1)/σ +(1-a)L(σ-1)/σ ] σ/(σ-1), the marginal productivity of capital is given by r =FK = a (Y/K)1/σ = a β-1/σ , and the capital share is given by α=rβ=aβ(σ-1)/σ . See Piketty and Zucman (2014, 2015).



Lee A. Arnold 01.04.16 at 4:02 pm

Thanks for your book!


Bloix 01.04.16 at 4:23 pm

“some families have many children and have to split inheritances in many pieces … some families consume more than a fraction 1-g/r of their capital income … others … have a strong taste for leaving bequests and perpetuating large fortunes”

Prof Piketty – given your taste for literary references, I wonder if you’re familiar with the opening lines of chapter 1 of Meredith’s The Egoist (1879):

“There was an ominously anxious watch of eyes visible and invisible over the infancy of Willoughby, fifth in descent from Simon Patterne, of Patterne Hall, premier of this family, a lawyer, a man of solid acquirements and stout ambition, who well understood the foundation-work of a House, and was endowed with the power of saying No to those first agents of destruction, besieging relatives. He said it with the resonant emphasis of death to younger sons. For if the oak is to become a stately tree, we must provide against the crowding of timber. Also the tree beset with parasites prospers not. A great House in its beginning lives, we may truly say, by the knife. Soil is easily got, and so are bricks, and a wife, and children come of wishing for them, but the vigorous use of the knife is a natural gift and points to growth. Pauper Patternes were numerous when the fifth head of the race was the hope of his county.”


bob mcmanus 01.04.16 at 6:11 pm

Thanks for your book, your work, and your public availability.


Rakesh Bhandari 01.04.16 at 6:58 pm

Piketty: “It should also be noted that the impact of growth slowdown on the gap r-g is fundamentally ambiguous…In multi-sector models of capital accumulation, which as I argue below are far more realistic, almost anything can happen, depending in particular on the specific rules, relative prices, institutions and changing bargaining power of the various social groups in the relevant sectors.”

Almost anything can happen; theoretical speculation can yield many different scenarios, and models can formalize these many speculations.

But this is why Piketty’s work is primarily historical: “The new methods often lead to a neglect of history and the fact that historical experience remains our principal source of knowledge.” p. 575

The Belle Epoque yielded very high levels of wealth concentration though it was a time of robust technology-driven growth; it was however a time of low taxation and low population growth in France relative to the US. All these characteristics make that historical experience salient today. Needless to say, it took enormous shocks to deconcentrate wealth.

True enough, a combination of new land use policies, laxer intellectual property rights and greater organizing capacity for labor would likely today reduce the level of wealth and income inequality going forward, but historical experience gives us good reason to believe that wealth will become dangerously concentrated again unless something like the global wealth tax is also implemented. Even that in the absence of radical new forms of ownership may not be enough.

Those of us who have been following the international Piketty debate will note that almost all of this statement already appeared in replies in the Journal of Economic Literature, the British Journal of Sociology and HAU.

Interestingly what I thought was the deepest interpretation of what Piketty had actually written–Henry Farrell’s reply–is not remarked upon.


Rakesh Bhandari 01.04.16 at 10:19 pm

Piketty: “For detailed references to this literature on dynamic wealth accumulation models with random shocks, see the on-line appendix to chapter 10 available at”
Perhaps this is the real theoretical center of the book? Will have to study the appendix here.


Rakesh Bhandari 01.05.16 at 12:25 am

Piketty and Saez, Science 23 MAY 2014 • VOL 344 ISSUE 6186:
“How can we account for the very high level of
wealth concentration that we observe in historical
series, and what does this tell us about the
future? The most powerful model to analyze structural
changes in wealth inequality is a dynamic
model with multiplicative random shocks. That is,
assume that the individual-level wealth process
has the following general form: zit+1 = witzit + eit,
where zit is the position of individual i in the
wealth distribution prevailing at time t (i.e., zit =
kit/kt where kit is net wealth owned by individual
i at time t, and kt = average net wealth of
the entire population at time t), wit is a multiplicative
random shock, and eit is an additive
random shock.
The shocks wit and eit can be interpreted as
reflecting different types of events that often
occur in individual wealth histories, including
shocks to rates of return (some individuals may
get returns that are far above average returns;
investment strategies may fail and lead to family
bankruptcy); shocks to demographic parameters
(some families have many children; some
individuals die young); shocks to preferences
parameters (some individuals like to save, some
prefer to consume their wealth); shocks to productivity
parameters (capital income is sometimes
supplemented by high labor income); and so on.
Importantly, for a given structure of shocks,
the variance of the multiplicative term wit is an
increasing function of r – g, where r is the (net-oftax)
rate of return and g is the economy’s growth
rate. Intuitively, a higher r – g tends to amplify
initial wealth inequalities: 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,
one can show that the top tail of the distribution
of wealth converges toward a Pareto distribution,
and that the inverted Pareto coefficient (measuring
the thickness of the upper tail and hence the
inequality of the distribution) increases with r – g
(3, 14, 24–26).
The dynamic wealth accumulation model with
multiplicative shocks can explain the extreme
levels of wealth concentration that we observe in
the data much better than alternative models. In
particular, if wealth accumulation were predominantly
driven by lifecycle or precautionary motives,
then wealth inequality would not be as large
as what we observe (it would be comparable in
magnitude to income inequality, or even lower).
The dynamic multiplicative model can also
help to explain some of the important historical
variations that we observe in wealth concentration
In particular, it is critical to realize that r – g
was very large during most of human history
(Fig. 4). Growth was very low until the industrial
revolution (much less than 1% per year), whereas
average rates of return were typically on the order
of 4 to 5% per year (historically, in preindustrial
agrarian societies, annual rent on land,
the main capital asset, was about 4 to 5% of the
land value) and taxes were minimal. Growth
rates rose substantially during the 18th and
19th centuries, but they remained relatively
small (1 to 1.5%) compared to rates of return.
This large gap between r and g explains why
wealth concentration was so large until World
War I and why wealth concentration was smaller
in the United States, where population growth
was faster.’


Neville Morley 01.05.16 at 8:30 am

Just to echo Rakesh Bhandari’s closing comments at #4, it’s very much to be regretted that there’s no engagement with Henry’s contribution, precisely because it opened up a different line of discussion of Piketty’s book. The other contributions were of consistently high quality – but, as this post shows, to some extent they run in parallel to critiques offered elsewhere, at least in terms of the points they focus on, hence can simply be incorporated into a largely pre-existing response.


reason 01.05.16 at 2:17 pm

Small correction to an excellent contribution:
“… in particular to regulate and expAnd access to property …”


Jacob Hartog 01.05.16 at 8:59 pm

Given that r>g only leads to an increase in inequality of the marginal propensity to consume out of wealth is lower for the rich, isn’t it more plausible to convince the rich to spend their money than to find (probably doomed) ways of taking it from them? You don’t have to go back very far to find persistent downward mobility among the rich precisely because they had large families, hired personal servants, and generally had a social mandate to “act rich.”

Our current cultural environment- including your book- encourages the rich to hide their wealth rather than spend it, and to direct their spending to status goods like housing,art, and education where it is likely to stay with other rich people. This directly contributes to the problem.

(For a theoretical explanation of why propensity to consume is an omitted variable, see


MisterMr 01.05.16 at 10:11 pm

@Jacob Hartog

But this works only if the rich spend enough to lose wealth (proportionally to growth).
If the rich consume more but not enough to lose wealth, we just get to a neo-feudal economy.


Peter T 01.06.16 at 2:44 am

“Persistent downward mobility” is a myth. Until the late C19, most rich were the directors of ongoing concerns called “family estates”. Entail, primogeniture and political power ensured the continuity of the core businesses (although there were, of course, the inevitable percentage of bankruptcies). These businesses continually spun off younger sons and daughters, who were variously placed through marriage or in the church, army, colonies and professions. Given the numbers, downward mobility was inevitable for this group, but they are not the “rich”, whose possession of most of the wealth stayed remarkably undisturbed.

What DID happen was that a large proportion of rich in Europe were invested in land, and were caught out buy the fall in agricultural incomes after 1870 (steamships, refrigeration, American wheat, Argentine beef, New Zealand lamb, Australian wool). Fixed costs met falling incomes, which is part of the story that ends in 1914.


Frank Shannon 01.06.16 at 6:51 am

I’d like to add my gratitude to Bob’s. Thank you.


bad Jim 01.06.16 at 8:01 am

Another alien once offered us “Truth, Justice, and the American Way.” That was Superman, in a more innocent time that featured higher taxes and a thriving working class. We haven’t lost the recipe for prosperity; it’s gathering dust on the shelf next to all the others we don’t use any more.


reason 01.06.16 at 2:46 pm

me @8
reading it again – maybe “exTend” is the correct way to read this?


Bruce Wilder 01.06.16 at 4:39 pm

J H: . . . isn’t it more plausible to convince the rich to spend their money than to find (probably doomed) ways of taking it from them?

As great as the difficulty of preventing the rich from “investing” in schemes to take money from the poor and merely middle-class as the means of keeping r out-running g?


notsneaky 01.06.16 at 7:41 pm

I actually liked the book, but if it had just come out and said right away that “r vs. g has nothing to do with capital’s share, or labor income inequality, but only with wealth inequality”, as Piketty pretty much does above, and then focused on that aspect rather than spending several chapters misleading the leader into thinking that r vs. g does actually have something to do with capital’s share or labor income inequality, … .whew … it would’ve been a much better book.


Rakesh Bhandari 01.06.16 at 9:52 pm

Piketty is explicit that r>g does not explain widening labor income inequality…in the book. He is also clear that marginal productivity theory does not do good job accounting for skyrocketing super-manager pay, which he accounts for in terms of factors such as the tax incentive for supermanagers to effectively pay themselves more and the breakdown of corporate governance.

Now there are two questions that need to be disentangled: the greater (personal) concentration of wealth concentration (how much of the wealth stock does the top centile own, what percentage of total capital income does the top one percent receive, or even what percentage of the income of the top centile comes from capital ownership and what percentage from labor and what percentage of the top centile in wealth holdings can be attributed to inheritance) and the change in the functional distribution of income against labor income.

A relation between r and g figures in the way he analyzes both; and in both cases r>g is only part of the explanation, a necessary but never sufficient condition.

For example, even if it is difficult to make new great fortunes due to g falling and thereby income not rising greatly out of which savings could be made to build wealth approaching the compounding fortunes that are being being bequeathed and gifted,

r>g may not still possibly not really amplify wealth inequality if there is something about being a rentier that raises the marginal propensity to consume sharply with each generation of inherited wealth.

Piketty is also clear that if too much capital kills the return on capital, then r>g will not change the functional distribution of income against labor.


notsneaky 01.07.16 at 12:31 am

Rakesh, that may be true (your 1st paragraph) but the part on labor income inequality is one chapter out of 16. And it’s explicitly labeled as the “Anglo-Saxon phenomenon” – i.e. stuff that’s different than what the rest of the book is talking about. And the rest of the book is about how r vs g is what it’s all about. In fact most of the rest is about insinuating that r vs g determines the share of capital vs labor income and overall inequality. Which it doesn’t.


Rakesh Bhandari 01.07.16 at 2:32 am

Don’t have the book with me, and I am going to interrupt my viewing of a compelling TV show that I have just discovered–“Maury” which is staging all the evidence that the evolutionary psychologists need, though I am really uncertain as to how draw this distinction between genitor and pater after watching this show.

Well, now to get back to this work on kinship as something which determines and is constituted by inheritance…I don’t think the inheritance of patrimonial wealth is at stake in these rather unpleasant disputes on “Maury”… *

Of course if capital share of income rises and it is already more unequally distributed than labor income and may well become even more concentrated, then of course that would be a powerful tendency for overall inequality to rise (or to return to Belle Époque levels), though of course that could be counteracted by a compression in the dispersion of labor incomes, e.g. through the end of apartheid labor market and liquidation of white wage premia, a la Acemoglu and Robinson.

Here is the point made well again by Milanovic.

*Sylvia Yanagisako: “Piketty’s analysis of the structure of inequality bears powerful implications for theories of capitalism, kinship, and class. Above all it provides overwhelming evidence of the crucial role inheritance has played and is once again increasingly playing in “advanced” industrial-capitalist societies. These findings should drive a gigantic nail in the coffin of theories positing the decline of the significance of kinship in “modern” (read capitalist) society. I say a gigantic nail rather than the last nail, because like so many ideological models dressed in empirical clothing, this myth of modernity appears to have zombie-like powers of regeneration.

As Susan Mckinnon and Fenella Cannell (2013: 3–4) note, for over 150 years theories of modernity have argued resolutely that kinship has lost the economic and political functions it once had in “traditional,” premodern societies and instead has become restricted to the “domestic domain” of childrearing and homemaking. From the nineteenth-century social evolutionary theories of Maine and Morgan, to Durkheim’s theory of the differentiation of domains in modern society, dominant theories of modernity have posited the formation of a secularized, rational public domain governed by economic and political institutions, in contrast to an affectively ordered domain of family. By the 1950s, Talcott Parsons took this even further by claiming that in modern society occupation depends on individual merit rather than on family membership, thus separating kinship from class and reducing the family’s function to the nurturance of children and the production of adult personalities.

Mckinnon and Cannell (2013) do not deny that significant transformations have occurred in marriage, family, and kinship since the nineteenth century. But they reject the assumption that kinship has declined in importance. Piketty’s findings about the structure of wealth inequality provide not only overwhelming evidence of the continuing importance of kinship but they also offer a valuable clue to help us understand why so little attention is paid to inheritance in theories of modernity and kinship.”


Henry Farrell 01.07.16 at 4:20 am

I should note that Thomas’s not mentioning my piece in his reply is completely down to me rather than to Thomas – he wrote the piece under very substantial time constraints (given the circumstances we’re grateful that he was able to do it) and I explicitly invited him not to respond to my post, so as to ease the burden slightly. In addition, I think it would have been trickier for him to respond to some parts of my argument (how can you respond to an analysis of your work as major sociological phenomenon without coming across either as arrogant or Uriah-Heepish) while other bits were more or less redundant with the rest of the seminar (there is a lot of overlap between what I said, and what Miriam Ronzoni said).


Rakesh Bhandari 01.07.16 at 4:56 am

@20 Very gracious but Piketty did not really reply to Ronzoni either. I did not remember you emphasizing that Piketty implies what Ronzoni was calling social democratic optimism at odds with his own historical findings and analysis.

Unless you think that Piketty’s argument made in technocratic terms is meant to warn a putatively existing or possibly existing Hegelian universal class of technocrats they must get rentiers to accede to a global wealth tax if social implosion is to be avoided. Ronzoni seemed to be trying to get Piketty to cop to this being the real political import of his work.


LFC 01.07.16 at 2:44 pm

What I took away as the key points of Henry Farrell’s contribution to the symposium, having looked at it again the other day: (1) the emphasis on the need for ‘transparency’ and more knowledge about exactly who the very rich are and what they have, though knowledge alone isn’t enough to bring change, and (2) if Piketty is right about the inherent tendency of capitalism (of whatever variety) to inequality *and* if certain others are right about the “seamlessness” of the translation of economic power into political power, things look pretty hopeless. Those who, unlike myself, have followed the whole Piketty debate closely might be able to guess — or maybe not — what P. would say in reply to these points.

P.s. I haven’t read Piketty’s reply (the OP) here beyond the opening. I also haven’t read Capital in the Twenty-first Century, nor do I have any immediate plans to do so.


Rakesh Bhandari 01.07.16 at 4:23 pm

@18 Piketty does not try to explain widening inequality as a whole by r>g; he does not explain the rise of super-manager income in the US that way. But this is not all he says. He returns to the problem in other chapters as well.

Piketty also explicitly connects rising inequality in US labor income to rising inequality in access to higher education and skills and to changing labor market rules and bargaining power and a falling minimum wage. And Piketty is explicit that all these three factors of supermanager power, inequality in access to skills and reduced bargaining power have played important roles in the US particularly in widening labor income inequality, which in turn accounts for most of the rise in total inequality in the US…given that capital has not come back “here” (an indexical by the way that makes methodological nationalism common sense) as much it has elsewhere.


engels 01.08.16 at 2:35 am

So nobody managed to troll Piketty into a blog spat. Disappointing…


Rakesh Bhandari 01.08.16 at 6:04 am

Sneaky Not had asserted that you can only get a relation between r>g and rising inequality by “massaging the data” as I think s/he put it. I am assuming that s/he was relying Acemoglu and Robinson’s regressions which showed that the relation cannot be seen in the data.

Piketty responded in the Journal of Economic Literature as well as in this from CESifo Forum March 2015:

“From that viewpoint, the cross-country regressions presented in their paper by Fuest, Peichl and Waldenström (who find that a higher r – g gap seems to lead to higher wealth inequality) strike me as more sophisticated and potentially more convincing that the cross-country regressions that were recently presented by Acemoglu and Robinson. There are several reasons for this: Fuest-Peichl-Waldentrom explicitely use wealth inequality measures, they control for income inequality and other factors, and they introduce substantial time lags.

In particular, one central factor which makes the Acemoglu-Robinson regressions particularly uncon- vincing is that they regress income inequality (rather than wealth inequality) on r – g. This is most problem- atic, since income inequality is primarily determined by the inequality of labour income (which typically represents between two thirds and three quarters of total income), which as I noted above has nothing to do with r – g, and is determined by completely different factors (supply and demand for skills, educational institutions, labour market rules, corporate governance, etc.). It makes more sense to run such a regres- sion with wealth inequality (controlling for labour in- come inequality), which is what Fuest-Peichl-Waldenström attempt to do. In addition, the process of inter- generational accumulation and the distribution of wealth is a very long-run process, so looking at cross- sectional regressions between income inequality and r – g (which is what Acemoglu and Robinson do, i.e. they regress income inequality at a given time t on the r – g gap at this same time t) is not very meaningful. Using 15-year time lags – the method used by Fuest- Peichl-Waldenström – looks potentially more promis- ing. The fact that they find statistically significant effects going in the right direction (according to the the- oretical model) also seems promising.

I should stress, however, that I am not sure whether there is a lot to learn at this stage from running explicit cross-country regressions between wealth inequality and r – g. In particular, it may well be necessary to in- troduce time lags over much longer time periods: the processes of wealth accumulation and transmission typically spans several generations, so it would per- haps be better to use the average r – g observed during the 30 or 50 years. The broad correlations between r – g and wealth inequality certainly seem to run in the right direction, both from a long run (18th–19th vs 20th centuries) and international (Europe vs United States) perspective. One problem with going beyond this observation is that there are relatively few countries with homogenous long-run series on wealth ine- quality, which makes it very difficult to run regressions. We are in the process of extending the ‘World Top Incomes Database’ (WTID) to a more ambitious ‘World Wealth and Income Database’ (W2ID) includ- ing a wealth distribution series for more countries, so this difficulty may be overcome in the future.6 But given the data limitations and the time lag specification problems that we currently face, I feel somewhat sceptical about running cross-country regressions.

In my view, a more promising approach – to this issue as well as many others – is a mixture of careful case studies and structural calibrations of theoretical mod- els. Although we do not have many historical series on wealth inequality, they show a consistent pattern. Namely, we observe extremely high concentration of wealth in almost every European society in the 18th and 19th centuries, up until World War I. In particular, in France, Britain and Sweden, the top 10 percent wealth share accounted for about 90 percent of total wealth (including the top 1 percent wealth share around 60–70 percent) in the 19th century and at the very beginning of the 20th century. If anything, wealth inequality seems to have risen somewhat during the 19th century and up until World War I – or perhaps to have stabilised at very high levels in around 1890– 1910. Thus, despite major changes in the nature of wealth during the 19th century – agricultural land as a form of wealth is largely replaced by real estate, busi- ness assets and foreign investment – wealth inequality was as extreme in the modern industrial society of 1914 as it had been under France’s ancien regime in 1789. The most convincing explanation for the very high wealth concentration in these pre-World War I European societies seems to be the very large r – g gap – that is, the gap between rates of return and growth rates during the 18th and 19th centuries. There was very little taxation or inflation up until 1914, so the gap (1-t)r – g was particularly high in pre-World War 1 societies, which in dynamic models of wealth accumu- lation with random shocks leads to very large wealth concentration. In contrast, following the large capital shocks of the 1914–1945 period – a time of physical destruction, periods of high inflation and taxation, and nationalizations – the after-tax, after-capital-losses rate of return fell precipitously below growth rates after World War I (see Chapter 10; Figure 10.9 compares the pre-tax pure rate of return with growth rate g, while Figures 10.10-10.11 show a post-tax, post- capital-losses rate of return).”


reason 01.08.16 at 2:44 pm

J H: @9
. . . isn’t it more plausible to convince the rich to spend their money than to find (probably doomed) ways of taking it from them?

Can you think of a better way to do that than inheritance taxes?


JW Mason 01.10.16 at 6:35 pm

This is a very substantial reply. I’m grateful to Professor Piketty for responding so thoroughly, and to CT for hosting this seminar.

I was hoping to write a more substantive reply to his reply, and maybe I will eventually on my blog. But in meantime, I just wanted to call attention to this section:

In the standard one-good model of capital accumulation with perfect competition, the only way to explain why β and α move together is to assume that the capital-labor elasticity of substitution σ that is somewhat larger than one (which could be interpreted as the rise of robots and other capital-intensive technologies).

Let me make clear however this is not my favored interpretation of the evidence. Maybe robots and high capital-labor substitution will be important in the future. But at this stage … I believe that the right model to think about rising capital-income ratios and capital shares in recent decades is a multi-sector model of capital accumulation, with substantial movements in relative prices, and with important variations in bargaining power over time . Indeed, large upward or downward movements of real estate prices play an important role in the evolution of aggregate capital values during recent decades, as they did during the first half of the 20th centuries. As rightly argued by J.W. Mason (his symposium), movements in relative asset prices play an absolutely central role in the dynamics of wealth-income ratios Changes in relative asset prices – particularly real estate prices – can in turn be accounted for by a complex mixture of institutional and technological forces, including rent control policies and other rules

Capital ownership takes many different historical forms, and each of them involves different forms of property relations and social conflict, which must be analyzed as such (see e.g. my analysis of slave capital in 19th century U.S. in Ch.4; see also Ch.5 on the stakeholder German capitalism model, with large gaps between the social and market values of corporations). This multidimensional nature of capital creates substantial additional uncertainties regarding the future evolution of inequality.

I think it is fair to take this as a statement that Piketty agrees with the main points of my post here, and does NOT believe that the simple analytic models in the book and elsewhere in his work — based on aggregate variables like s, g, and r — can explain the bulk of historical changes in the capital share and the capital-income ratio. So my post should be understood as criticizing a common interpretation of K21, rather than the book itself. The — evidently mistaken — view that the r-s-g apparatus is intended to explain historical changes in distribution was expressed most insistently in this symposium by Rakesh Bhandari. It appears Piketty agrees more with us left critics than with his defenders like Rakesh.

But while this is said more clearly in the response here than I’ve seen it before, this is not a new position for Prof. Piketty. The point that r and g are only supposed to explain interpersonal distribution, and are irrelevant for the capital ratio, isn’t stated so explicitly in the book, as far as I can tell, but it’s definitely there. It was clearly understood in the first round of discussions about the book. (For instance, see this post by Matt Bruenig.) I should have acknowledged those earlier discussions here.


JW Mason 01.10.16 at 6:37 pm

Yikes, blockquote fail. The last two paragraphs are me, not a further nested quote.


Rakesh Bhandari 01.10.16 at 7:04 pm

What the right-wing critic Rakesh Bhandari said is that the analysis based on s/g was meant to account *only* for changes in the long-term beta, e.g. the rise of beta over the course of 19th century France, the cross sectional differences between Europe and the US over the last 100 plus years, and the movement of beta in Japan over the long-term through bubbles and their bursting. The right-wing critic also himself underlined that Piketty called attention to the huge role privatization and rising equity premia played in valuation of aggregate assets in the last forty years and that Piketty himself did not think s/g was doing even most of the work during medium-sized chunks of history in many places.
It’s a matter of getting the time horizon over which “the simple analytic models in the book and elsewhere in his work — based on aggregate variables like s, g, and r — can explain the bulk of historical changes in the capital share and the capital-income ratio.” (J.W. Mason)


Rakesh Bhandari 01.10.16 at 7:09 pm

At the same time, Piketty does not abandon s/g to explain the real estate bubble. From the Potemkin Review:

“Next, one of the big differences between the neoclassical model and the real world is that the real world is better described by a multidimensional capital model, where at the same time we have a real estate sector, energy sector, many different sectors with different capital intensities; and at this stage real estate and energy are much more important than robots in terms of capital intensity. Maybe at some point in the future robots will be important, but for now in order to understand the rising capital share in recent decades one has to look at real estate prices, the evolution of rental income, etc.

The huge rise in real estate prices is partly related to the logic of (s / g) that I describe in the book: when there is a slowdown of growth, and people keep saving, and they prefer to invest in real estate in Paris, Rome, or London instead of keeping all their savings in China for various reasons, then this contributes to the real estate bubble. So the two logics of capital accumulation, i.e. a growth slowdown coupled with higher capital accumulation, and a real estate bubble actually reinforce each other. Sometimes people seem to object, saying you can either have the (s / g) explanation or the real estate bubble explanation. But the real estate bubble has to come from somewhere, and I think it is very much related to the fact that in low growth countries like Italy, France, etc. people who have wealth need an outlet for their savings, and some of it goes to real estate.”

But at some point the return on such inflated assets should fall, no? So perhaps Piketty does have real trouble here.


JW Mason 01.11.16 at 3:43 am

It’s a matter of getting the time horizon over which “the simple analytic models in the book and elsewhere in his work — based on aggregate variables like s, g, and r — can explain the bulk of historical changes in the capital share and the capital-income ratio.”

I agree with this.

In general I’m a bit wary of the seductions of the long run. I think there are actually a quite limited number of problems where we can usefully partition the variables of interest into “fast” endogenous ones and “slow” exogenous ones. For example, in the case at hand, even abstracting away from valuation changes, I’m doubtful that the timeframe for the existing capital stock to adjust to a given savings rate is appreciably shorter than the timeframe over which the savings rate can be taken as fixed. I don’t believe Piketty gives us any reason to think otherwise.


JW Mason 01.11.16 at 3:48 am

And yes I saw that quote. I thought I even linked to that interview, but maybe not. I don’t think it’s very helpful for you. Aggregate savings are unrelated to private real estate transactions. It’s literally impossible for a higher s to be absorbed in real estate investment as he suggests here – saving by the buyer is just equal to dissaving by the seller. So in terms of the formal model, what he says here doesn’t really make sense. (To which I say, so much the worse for the model — this is one more example of how what Piketty says in words is more interesting than what he says in math.)


Rakesh Bhandari 01.11.16 at 4:45 am

. The chapter in question includes the phrase “in the long run”; it’s about the capital/income ratio ***in the long run***, so I humbly submit that much of your critique simply does not apply to what Piketty is hypothesizing.

Piketty himself grants that changes in K/Y and alpha cannot directly be accounted for in the short and medium term by a shift in an equilibrium s/g ratio–given the importance of bubbles, privatizations, changes in risk-taking appetites, changes in bargaining power in several specific sectors (which he evidently thinks accounts more for the recent rise in alpha than that part of the rise in K/Y accounted for a change in s/g).

I don’t have the book with me, and have not read the chapter in a month or so; but it is quite nuanced.
And we still have the question of the probative value of what he can explain in terms of his long-term model, which again includes the history of wealth in France from the Revolution to the Great War, the perduring higher K/Y ratio in Europe than in the US and the trajectory of Japan since the War. There is probably more, but this is what I remember from my reading. Why does his evidence have less probative value than the counter-examples you cite?

Now on the housing question.

First note that Piketty again underlines what he thinks is of major long-term significance–a significant reduction in g, which (if I remember his argument correctly) will only have global effect in some thirty years as catch-up growth ends and global population growth falls.

Piketty is not arguing that s/g is doing its work on real estate prices by raising s as you put it; s/g is rising because g is falling.

So if the savings out of income can’t profitably be invested to the same extent as in the past in new capital equipment which will be used by and needed for a quickly growing population–and here Piketty seems to share some in common with Hansen’s theory of secular stagnation– the savings may well go into the bidding up of the existing real estate stock; and whatever new housing and building are constructed, their values relative to the total capital stock may rise as well due to slower relative technological progress in real estate.

I may be missing what is an extremely clever point that you are making. If so, I apologize and ask for a further explanation.

What I think Piketty puts in jeopardy here is his prognosis of a relatively stable r. If income growth becomes anemic and housing values skyrocket due to their not being a significant downward adjustment in s, then the bubble is bound to burst as Michael Burry has taught us.

Sure (as James Galbraith has rightly noted) r may be stable in the long run since the returns (including imputed rents) will be calculated on the post-bubble and post-crisis value of the housing stock, but that would be cold comfort.


Bruce Wilder 01.11.16 at 7:19 pm

“the bubble is bound to burst”

Well, yes, greater financial volatility is likely to be the result of financial savings outrunning opportunities to invest in growth-enhancing capital stock.

Financial wealth has no other way of earning a return than as tax-farming or insurance. If the wealthy sell insurance, and those insurance contracts are structured properly, volatility just creates additional opportunities to shift the accumulation of capital (aka financial claims) upward. Oh, I’m sorry, middle-class person who sunk your life savings into a down-payment on a house, we have to have a recession now, and we must foreclose. Ooops, our bad, but we’re TBTF and you’re not. You lose everything; we lose nothing and next week when you have to rent a place to live, we will have your old place ready for you, at a modestly increased fraction of your income (from which you save nothing and we save a lot for the next cycle). Strapped for cash? Perhaps you should consider renting your furniture? Financing your kid’s college with loans? Financing your health care or dental work? Prices for those services are rising, driven by insurance-financing. And on and on.

The conventional economic model of a flow of funds by which savings accumulates as a stock of capital used in a production function describing the distribution of income would not survive ten minutes of critical thought if most neoclassical economists actually knew anything about the economy or were not committed to reactionary political ideologies. If Piketty’s work has long-term value, it will be because it uses facts to erode confidence in such a priori conceptions. His is an indirect method of criticism. You cannot work thru what he’s saying without realizing that the neoclassical conceptions do not make a lot of sense. So, as JW Mason observed above,

It’s literally impossible for a higher s to be absorbed in real estate investment as he suggests here – saving by the buyer is just equal to dissaving by the seller. So in terms of the formal model, what he says here doesn’t really make sense.

An important part of the takeaway is that the formal model is crap, but that’s not Piketty’s fault and the facts are the facts.

If the short-run were a smooth path to the long-run, r > g would describe a prolonged and very slow process. But, that long-run of smooth short-runs doesn’t exist, and the dynamics can be rather more rapid and dramatic because of wealth transfers disguised in fluctuations in asset valuation and business activity.


MisterMr 01.11.16 at 10:56 pm

I find this discussion very interesting.
Some more or less random toughts:

1) I read Piketty’s book more than one year ago, so I can’t remember the details very well. However, IIRC, there are 4 distinct periods:
– Pre WW1: low wage share, low g, high wealth to income ratio, high concentration of wealth;
– interwar: hell breaks lose, lot of political turmoil plus the wars, hard to put this period in a model;
– WW2 to the 70s: high wage share, high g, low wealth to income ratio, wealth less concentrated;
– after the 70s: wage share falls, g falls, wealth to income ratio rises, wealth concentrates again.

As the periods were g is low are the same as the periods were the wage share is low, in this very long time frame it is difficult to tell if the cause of the increase and concentration of wealth is the falling g or the falling wage share; I think the falling wage share sounds more plausible because I think that increases in total income (g) more or less automatically show up as increased aggregate value of asset prices, so IMHO g cannot explain a fall of wealth to income ratio (at least not directly).

2) “movements in relative asset prices play an absolutely central role in the dynamics of wealth-income ratios Changes in relative asset prices – particularly real estate prices – can in turn be accounted for by a complex mixture of institutional and technological forces, including rent control policies and other rules… ” (Piketty cited by Mason).

However the problem is not the price of one asset price relative to another, but the price of all asset prices relative to income, so I’m not sure that the “multifaced” nature of capital is the problem, rather it seems to me that the aggregate savings are the cause, and these savings pump up the value of this or that type of asset depending on their peculiar carachteristic; in other words the nature of the assets influences were wealth is “stored”, not how much wealth is stored IMHO. Rentier assets like housing or land are more practical to store wealth because their supply is limited, so that they react with a relative increase in price instead that with more assets, so the increase in wealth shows up there IMHO.

3) “the bubble is bound to burst”

Unfortunately this isn’t true because, if the wage share is falling, and the share of income that goes into profit increasing, the amount of wealth relative to total income can increase even as the amount of wealth relative to total profits (r) stays the same, so this isn’t a bubble. It becomes a bubble only if/when the increase in wealth due to capital gains “pulls” the economy by increasing aggregate demand.
The real question is IMO why r stays the same as the wage share falls.

4) ” It’s literally impossible for a higher s to be absorbed in real estate investment as he suggests here – saving by the buyer is just equal to dissaving by the seller.” (J.W. Mason)

But, if I buy one house for 100, and my neighbour sells a similar house for 150, the savings of the seller and the buyer even out, but I (and all the other neighbours) just gained 50 of “net worth” (maybe this is Mason’s point?).


Peter T 01.11.16 at 11:52 pm

“saving by the buyer is just equal to dissaving by the seller”. This is equivalent to saying that some universal law requires that promise to pay equals ability to pay. It is true that much financial regulation is aimed (with indifferent success) at bringing the two into rough alignment, but this alignment is never total or constant. The gap and the fluctuations are a large part of what the macro-economy is about.


MisterMr 01.11.16 at 11:57 pm

A very pessimistic hypothesis, based on my understanding of Steve Keen’s model and on this blog post by J.W. Mason:
(Disclaimer: I’m not an economist)

1) The wage share of total income (W) fluctuates during the business cycle, depending on unemployment: when the economy is booming, business invest employing more people, so they “run out of workers” and are forced to pay higer wages. As the wage share increase, profits fall, triggering a crisis. The crisis causes profits to fall even further (so temporaneously W rises), until unemployment rises so much that wages fall, W falls and the cycle starts again. The system reaches “potential” output only when all workers are employed (unemployment of 0), so in reality the system only gets near to potential never reaches it.

2) The government influences the cycle basically by putting a floor under wages (by employng people directly, providing unemployment insurance etc).

3) When the cycle starts, business invest both in “real capital” and in rentier assets, pushing up the value of rentier assets relative to income.

4) The increase in value of asset prices causes an increase of the debt to income ratio, as people bet on the increase of asset prices.

5) When unemployment falls, the profit share falls, lowering the value of asset prices. This causes a balance sheet financial crisis, wich causes a recession. Thus the increase of debt puts a roof on the wage share (and a floor under asset prices if financial crises are averted).

6) Governments during the postwar period put an higher floor under wages, whereas in the “neoliberal” period they put a floor under asset prices (wich means that the “roof” on W becomes lower and lower). The fact that the wage share thus cycles at a lower level causes an higher wealth level through the high valuation of rentier assets, which gives a more or less constant r (because of the denominator effect of wealth).

7) High inflation and g might rise the roof over the wage share if they cause the debt to income ratio to fall, but only as long as both inflation and growth are not already calculated in the interest rate (otherwise the economy would need constant upward surprises in g or inflation to keep debt/income stable). In particular inflation and growth devalue preexisting debt, but cause nominal savings to be higher, so they cause the nominal value of assets to shoot up. The lower the wage share the less g and inflation are useful to lower the debt/income ratio. When the wage share becomes very low, and the wealth to income and debt to income ratio very high, only a wealth shock of huge proportions (like in the interwar period) can solve the problem.


JW Mason 01.12.16 at 2:25 am

“saving by the buyer is just equal to dissaving by the seller”. This is equivalent to saying that some universal law requires that promise to pay equals ability to pay.

What do you mean?


Peter T 01.12.16 at 5:04 am

Well to take a real estate transaction as an example, typically the seller gets a large credit at a bank, which is a promise guaranteed by the state and so is as solid as any such thing can be. The buyer pays part with a bank debit and more with a promise to make regular payments to the bank over some decades. As recent experience demonstrates, this is not nearly as solid.

More generally, money comprises various forms of debt (cash, credit cards, loans etc: M1, M2,… Mx). They key question on any debt is “how certain is it to be repaid?” The various forms range in certainty, both in themselves and over time (hard money vs soft). The amount of debt in circulation bears no fixed relation to the amount of actual goods and services available (much of it explicitly does not, as it relates to future goods and services).


reason 01.12.16 at 9:31 am

“typically the seller gets a large credit at a bank, which is a promise guaranteed by the state and so is as solid as any such thing can be”???

Which state guarantees mortgages? Are you saying the 2008 crash never happened?


Peter T 01.12.16 at 10:05 am


Perhaps I was not clear. The seller gets a large sum in the bank, state-guaranteed. The buyer pays with a mortgage – ie, a promise to pay the sum to the bank, plus interest, over a few decades. So the seller gets hard money, the buyer pays with soft money. The 2008 crash was in part due to banks thinking the money they were owed was firmer than it was (what’s the money equivalent to the Brinell Hardness scale?)


JW Mason 01.12.16 at 3:09 pm

if I buy one house for 100, and my neighbour sells a similar house for 150, the savings of the seller and the buyer even out, but I (and all the other neighbours) just gained 50 of “net worth” (maybe this is Mason’s point?)

Right. The point is that these valuation changes don’t show up as saving, and are explicitly excluded in Piketty’s “second law.”


JW Mason 01.12.16 at 3:12 pm

Peter T-

I don’t disagree with what you are saving, but it doesn’t seem to have anything to do with the Piketty quote I was responding to. He is talking about rich households wishing to hold an increasing portion of their wealth in the form of real estate. Not mortgage-financed purchases.

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