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Wealth Inequality and the Financial Accumulation Process

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Abstract

Previous theoretical and computational analyses demonstrate that uncorrelated variations in individual asset returns promote extreme inequality in financial wealth. This paper describes a standard individual-based computational model of this financial accumulation process and then extends it in order to expose other key influences on wealth inequality. We find large effects of individual behavior, cultural practices, tax policy, and technological change. Specifically, we present simulation experiments with heterogeneous saving rates, a stylized marriage institution, a wealth tax structured to mirror contemporary policy proposals, and variations in wage growth. These experiments demonstrate that modest concessions to realism have large effects on long-run wealth inequality in models of the financial accumulation process.

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Fig. 1

Data Source: Davies et al. (2009)

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Notes

  1. In this literature, it is common to impose a zero-wealth boundary, which effectively truncates R at 0. Whether zero wealth is then likely to be an absorbing boundary for wealth accumulation depends on the model parameterization. For example, it is in Yunker (1999) but it is not in Biondi and Righi (2019).

  2. Biondi and Righi (2019) draw on (Theorem 2 Fernholz and Fernholz 2014) to provide a heuristic proof that this convergence is almost certain, and they provide simulation evidence that the speed of convergence depends on the standard deviation of the individual returns.

  3. Python code for this model is available upon request.

  4. This paper does not engage the debate over the boundaries between agent-based models, individual-based models, and econophysics models. Readers should adopt their preferred classification.

  5. Empirically, households appear to experience persistent differences in asset returns (Cao and Luo 2017). Levy and Levy (2003) suggest that individual investment talent may influence investment income, and they therefore extend their baseline model of the financial accumulation process so that \(R_{i,t}\) has an agent-specific mean. In this context, however, they end up arguing that chance (i.e., the stochastic component of \(R_{i,t}\)) must be more important than skill in producing observed wealth inequality. Our baseline implementation of the financial accumulation process therefore focuses on the role of chance. (However, see the "Labor Income and Wealth Inequal" section.)

  6. For this experiment, each agent’s saving rate is time invariant. Individual saving rates are distributed uniformly in an interval. The three intervals producing the illustrated results, as implied by the standard deviations reported in the figure legend, are roughly [0.45, 0.55], [0.40, 0.60], and [0.35, 0.65]. In terms of the algebra of the "Algebra for a Financial Accumulation Process" section, period T wealth becomes \(k_{i,T} = k_{i,0} \prod _{t=0}^{T-1} (1 + s_{W,i} r_{t})\), where \(s_{W,i}\) is the saving rate out of investment income for individual i and \(r_t\) is the shared net return on investments in period t.

  7. Not evident when comparing Fig. 5 with Fig. 4 is the difference in wealth mobility across time. When inequality is induced by the baseline financial accumulation process, there is always some individual mobility in the economy’s wealth distribution. In contrast, relative wealth rankings induced by idiosyncratic saving rates persist. As an aside, note that in contrast to Benhabib et al. (2019), these idiosyncratic saving rates are not responses to changes in wealth.

  8. Accordingly, estate taxes with a mean household lifespan of 100 years can have a similar dampening effect on inequality. (Results not shown.)

  9. Discussion of these effects by economists frequently have turned to the language of ethics. For example, Mill (1861) urged that it was “fair and reasonable that the general policy of the State should favour the diffusion rather than the concentration of wealth.” This section eschews the ethical, pragmatic, and legal questions in favor of a descriptive approach.

  10. Germany eliminated its wealth tax amid arguments that it would have to be confiscatory in order to raise substantial revenues. However, recent policy discussion has shifted towards restoring the wealth tax.

  11. Not only are these proposals controversial, but their constitutionality remains debatable: as a direct tax, a wealth tax may be subject to an apportionment rule (Johnsen and Dellinger 2018).

  12. This accords with the citizenship model of Isaac (2008) and public-service redistribution model of Biondi and Righi (2019). In terms of the algebra in the "Algebra for a Financial Accumulation Process" section and footnote 6, at time t an individual i not subject to the wealth tax now saves \(s_W r_{i,t-1} k_{i,t-1} + s_Y a_{t}\) where \(a_{t}\) is the period t national dividend per capita. Contrast with the insurance model of Isaac (2008) or the welfare model of Biondi and Righi (2019), wherein redistribution targets the poorest agents. Since (as shown below) even a national dividend proves very effective at reducing inequality, this paper does not additionally report results for means-tested redistribution.

  13. Reducing the efficiency of redistribution has the same effect on individual wealth accumulation as reducing the saving rate from the national dividend.

  14. For the reported experiment, the labor-income growth rates are deterministic. Allowing transient shocks produces similar results.

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  1. Department of Economics, American University, Washington, DC, 20016, USA

    Alan G. Isaac

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Isaac, A.G. Wealth Inequality and the Financial Accumulation Process. Eastern Econ J 47, 430–448 (2021). https://doi.org/10.1057/s41302-021-00191-x

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