Making sense of Piketty's ‘fundamental laws’ in a Post-Keynesian framework: the transitional dynamics of wealth inequality

Abstract

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.

Wealth inequality and aggregate demand

“…Lavoie (1998) is an early example, which focuses on firm saving and capital gains. Furthermore, contributions by A. K. Dutt (1990a), Palley (2012, 2017b), Taylor et al (2015, 2019) and Ederer and Rehm (2020a, 2020b) endogenously model the wealth distribution, and discuss the existence and stability of a long‐run equilibrium wealth share. In contrast to the standard Bhaduri and Marglin model and more in the spirit of Pasinetti (1962), these models explicitly distinguish between classes instead of functional income groups.…”

“…They, therefore, typically include a comprehensive personal income distribution. Ederer and Rehm (2020a, 2020b) furthermore differentiate the wealth compositions of workers and capitalists, which implies differential rates of return on their assets (Ederer et al, 2020).…”

“…It makes the usual assumptions that growth is driven by aggregate demand, and that the profit share is determined by the mark‐up of firms over unit labor costs. Drawing on Dutt (1990a), Palley (2012, 2017b) and Taylor et al (2015), and closely following Ederer and Rehm (2020a, 2020b), we introduce four novel aspects with respect to the original Bhaduri‐Marglin model: (a) Workers save a certain part of their income, (b) they accumulate wealth and are, thus, entitled to profit income, (c) wage income is split between workers and capitalists, and (d) workers and capitalists have different wealth compositions, and thus different rates of return on their assets. We discuss the implications of the first two extensions in this section and turn to the last two in Section 5.…”

“…The equilibrium is unique and stable at positive values for u and z , as long as the differential in saving rates is large enough (i.e., ). For a detailed stability analysis of the dynamics of the wealth share (albeit without an investigation of its impact on the demand regime), we refer the reader to Ederer and Rehm (2020a, 2020b).…”

“…At the same time, the wealth distribution itself is influenced by the personal--and thus also the functional--income distribution, since wealth (abstracting from inheritances) is accumulated over time. Building on Pasinetti (1962), a small but growing literature extends Post-Keynesian (Dutt, 1990b;Ederer & Rehm, 2020a, 2020bLavoie, 1998;Palley, 2012Palley, , 2017bTaylor et al, 2015Taylor et al, , 2019 and Classical-Marxian models (Petach & Tavani, 2020) to include this cumulative dynamic.…”