Making sense of Piketty's ‘fundamental laws’ in a Post-Keynesian framework: the transitional dynamics of wealth inequality
Stefan Ederer and Miriam Rehm
Keywords: Post-Keynesian; model; wealth; saving; inequality; Piketty; simulation
Published in print:Apr 2020
Category:Research
Article DOI:https://doi.org/10.4337/roke.2020.02.04Pages:195–219
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https://www.elgaronline.com/view/journals/roke/8-2/roke.2020.02.04.xml
If Piketty's main theoretical prediction (r > g leads to rising wealth inequality) is taken to its radical conclusion, then a small elite will own all wealth if capitalism is left to its own devices. We formulate and calibrate a Post-Keynesian model with an endogenous distribution of wealth between workers and capitalists which permits such a corner solution of all wealth held by capitalists. However, it also shows interior solutions with a stable, non-zero wealth share of workers, a stable wealth-to-income ratio, and a stable and positive gap between the profit and the growth rate determined by the Cambridge equation. More importantly, simulations show that the model conforms to Piketty's empirical findings during a transitional phase of increasing wealth inequality, which characterizes the current state of high-income countries: the wealth share of capitalists rises to over 60 per cent, the wealth-to-income ratio increases, and income inequality rises. Finally, we show that the introduction of a wealth tax as suggested by Piketty could neutralize this rise in wealth concentration predicted by our model.
1 INTRODUCTION
Thomas Piketty's best-selling book, Capital in the Twenty-First Century (Piketty 2014), triggered a renewed interest in empirical research regarding the accumulation and distribution of wealth, and a lively debate about their causes and consequences. Wealth determines income, power and opportunities, and lies at the very heart of economic inequalities. Understanding the dynamics of wealth accumulation and distribution is thus crucial to tackle these inequalities.
In a nutshell, Piketty's (2014) theoretical argument is that, since the profit rate is usually higher than the growth rate in an economy (an empirical regularity which he finds for most countries and time periods for which his detailed archival work provides data), over time wealth increases faster than income. This entails a more unequal distribution of income, because the share of profits increases and wealth ownership and capital income are more concentrated than labour income. A rising income inequality finally feeds back into a more unequal distribution of wealth, so that wealth will be ever-increasingly concentrated in the hands of a small elite. Piketty (2014) nevertheless carefully balances such a radical interpretation of his analysis with theoretical counter-tendencies, historical analysis and empirical work.
Empirically, Piketty (2014) provides extensive data on the historical evolution of wealth-to-income ratios, wealth, and personal income distribution. He shows that the wealth-to-income ratio has risen, and that wealth and income have become more unequally distributed in high-income countries since about the 1980s. Regarding the profit rate and the growth rate, he argues that they have been largely stable over the long run, but that the former is empirically higher than the latter.
The reception of the book in Post-Keynesian economics has been mixed. On the one hand, Post-Keynesian economists recognize the empirical contributions of the book: the collection of historical data and the carving out of observable patterns therein (Rowthorn 2014; Rehm and Schnetzer 2015; King 2017). On the other hand, Piketty's Neoclassical theoretical framework by which he explains the dynamics of wealth and income inequality has attracted the criticism of Post-Keynesian economists, in whose theoretical frameworks distribution has long played a major role (for example, Galbraith 2014; Palley 2014; López-Bernardo et al. 2016a). Based on the Cambridge equation (Pasinetti 1962), they point out that the wealth distribution in the long run can be stable, a statement that is clearly in contradiction to a reading of Piketty that takes his Neoclassical theory to its radical logical conclusions. Ederer and Rehm (2020) show that the empirical distribution of wealth is still less unequal than the one implied by a parameterized Post-Keynesian model.
Both Piketty and Post-Keynesians, however, consider the transition phase – the world in which this and the next generation lives – as the relevant reference point for economic analysis. The development of income and wealth inequality over the next decades matters. The goal of this paper is to develop a Post-Keynesian model that explains this short-run dynamic of wealth accumulation and distribution, for which Piketty (2014) presents abundant empirical evidence. We therefore do not focus on the long-run equilibrium steady state. In the ‘transitional phase’, that is, when the wealth share of capitalists is below its long-run equilibrium value, a rising wealth-to-income ratio and increasingly unequal distributions of wealth and income can be described well by our Post-Keynesian model. Due to its focus on the long run, these short-run dynamics have not been investigated by Piketty's Post-Keynesian critics so far. This paper intends to close this gap.
To do so, we build a Post-Keynesian model in the tradition of Bhaduri and Marglin (1990) which incorporates an endogenous wealth distribution. We extend the model by blended incomes of workers and capitalists, differential rates of return, and capital gains. We show that a stable wealth share is a likely outcome in the long run, and both the euthanasia and the triumph of the rentier are special cases, and thus we reiterate the critique of Piketty's hypothesis of an ever-increasing wealth concentration. Furthermore, we use the model to explain a ‘transitional dynamic’ that resembles the empirical evidence presented by Piketty and his projections to the future. A rising wealth-to-income ratio, rising wealth and income inequality and a profit rate that is higher than the growth rate of the capital stock (and thus income) are all consistent with our extended Post-Keynesian model.
Piketty, like many Post-Keynesians, is concerned with the factors that might disturb this long-run capitalist path towards an equilibrium. He worries that the world of increasing inequality, which his data describes, might be prone to upheavals, social unrest and war. This is why Piketty focuses on finding democratic, political solutions – such as a wealth tax – to the ever-rising importance of inherited wealth over wealth acquired through work. We follow his suggestion and implement a wealth tax in the model and show that this stabilizes both wealth and income inequality.
The structure of the paper is as follows. The literature review in Section 2 discusses both Piketty and his Post-Keynesian critics, as well as the Post-Keynesian models of distribution. Section 3 describes the model and its short- and long-term equilibria in detail. Section 4 presents the transitional dynamics of the model. Section 5 discusses the model extensions. Section 6 presents a numerical simulation of both short-run dynamics and the long-run equilibrium. Section 7 discusses the effects of a wealth tax. Section 8 concludes
If Piketty's main theoretical prediction (r > g leads to rising wealth inequality) is taken to its radical conclusion, then a small elite will own all wealth if capitalism is left to its own devices. We formulate and calibrate a Post-Keynesian model with an endogenous distribution of wealth between workers and capitalists which permits such a corner solution of all wealth held by capitalists. However, it also shows interior solutions with a stable, non-zero wealth share of workers, a stable wealth-to-income ratio, and a stable and positive gap between the profit and the growth rate determined by the Cambridge equation. More importantly, simulations show that the model conforms to Piketty's empirical findings during a transitional phase of increasing wealth inequality, which characterizes the current state of high-income countries: the wealth share of capitalists rises to over 60 per cent, the wealth-to-income ratio increases, and income inequality rises. Finally, we show that the introduction of a wealth tax as suggested by Piketty could neutralize this rise in wealth concentration predicted by our model.
1 INTRODUCTION
Thomas Piketty's best-selling book, Capital in the Twenty-First Century (Piketty 2014), triggered a renewed interest in empirical research regarding the accumulation and distribution of wealth, and a lively debate about their causes and consequences. Wealth determines income, power and opportunities, and lies at the very heart of economic inequalities. Understanding the dynamics of wealth accumulation and distribution is thus crucial to tackle these inequalities.
In a nutshell, Piketty's (2014) theoretical argument is that, since the profit rate is usually higher than the growth rate in an economy (an empirical regularity which he finds for most countries and time periods for which his detailed archival work provides data), over time wealth increases faster than income. This entails a more unequal distribution of income, because the share of profits increases and wealth ownership and capital income are more concentrated than labour income. A rising income inequality finally feeds back into a more unequal distribution of wealth, so that wealth will be ever-increasingly concentrated in the hands of a small elite. Piketty (2014) nevertheless carefully balances such a radical interpretation of his analysis with theoretical counter-tendencies, historical analysis and empirical work.
Empirically, Piketty (2014) provides extensive data on the historical evolution of wealth-to-income ratios, wealth, and personal income distribution. He shows that the wealth-to-income ratio has risen, and that wealth and income have become more unequally distributed in high-income countries since about the 1980s. Regarding the profit rate and the growth rate, he argues that they have been largely stable over the long run, but that the former is empirically higher than the latter.
The reception of the book in Post-Keynesian economics has been mixed. On the one hand, Post-Keynesian economists recognize the empirical contributions of the book: the collection of historical data and the carving out of observable patterns therein (Rowthorn 2014; Rehm and Schnetzer 2015; King 2017). On the other hand, Piketty's Neoclassical theoretical framework by which he explains the dynamics of wealth and income inequality has attracted the criticism of Post-Keynesian economists, in whose theoretical frameworks distribution has long played a major role (for example, Galbraith 2014; Palley 2014; López-Bernardo et al. 2016a). Based on the Cambridge equation (Pasinetti 1962), they point out that the wealth distribution in the long run can be stable, a statement that is clearly in contradiction to a reading of Piketty that takes his Neoclassical theory to its radical logical conclusions. Ederer and Rehm (2020) show that the empirical distribution of wealth is still less unequal than the one implied by a parameterized Post-Keynesian model.
Both Piketty and Post-Keynesians, however, consider the transition phase – the world in which this and the next generation lives – as the relevant reference point for economic analysis. The development of income and wealth inequality over the next decades matters. The goal of this paper is to develop a Post-Keynesian model that explains this short-run dynamic of wealth accumulation and distribution, for which Piketty (2014) presents abundant empirical evidence. We therefore do not focus on the long-run equilibrium steady state. In the ‘transitional phase’, that is, when the wealth share of capitalists is below its long-run equilibrium value, a rising wealth-to-income ratio and increasingly unequal distributions of wealth and income can be described well by our Post-Keynesian model. Due to its focus on the long run, these short-run dynamics have not been investigated by Piketty's Post-Keynesian critics so far. This paper intends to close this gap.
To do so, we build a Post-Keynesian model in the tradition of Bhaduri and Marglin (1990) which incorporates an endogenous wealth distribution. We extend the model by blended incomes of workers and capitalists, differential rates of return, and capital gains. We show that a stable wealth share is a likely outcome in the long run, and both the euthanasia and the triumph of the rentier are special cases, and thus we reiterate the critique of Piketty's hypothesis of an ever-increasing wealth concentration. Furthermore, we use the model to explain a ‘transitional dynamic’ that resembles the empirical evidence presented by Piketty and his projections to the future. A rising wealth-to-income ratio, rising wealth and income inequality and a profit rate that is higher than the growth rate of the capital stock (and thus income) are all consistent with our extended Post-Keynesian model.
Piketty, like many Post-Keynesians, is concerned with the factors that might disturb this long-run capitalist path towards an equilibrium. He worries that the world of increasing inequality, which his data describes, might be prone to upheavals, social unrest and war. This is why Piketty focuses on finding democratic, political solutions – such as a wealth tax – to the ever-rising importance of inherited wealth over wealth acquired through work. We follow his suggestion and implement a wealth tax in the model and show that this stabilizes both wealth and income inequality.
The structure of the paper is as follows. The literature review in Section 2 discusses both Piketty and his Post-Keynesian critics, as well as the Post-Keynesian models of distribution. Section 3 describes the model and its short- and long-term equilibria in detail. Section 4 presents the transitional dynamics of the model. Section 5 discusses the model extensions. Section 6 presents a numerical simulation of both short-run dynamics and the long-run equilibrium. Section 7 discusses the effects of a wealth tax. Section 8 concludes
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