Dynamics of Wealth Inequality

We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We are mainly interested in interactions increasing wealth inequality that is in a local implementation of the accumulated advantage principle. Such interactions destabilise the system. They are confronted in the model with a global regulatory mechanism which reduces wealth inequality. There are different scenarios emerging as a net effect of these two competing mechanisms. When the effect of the global regulation (economic interventionism) is too weak the system is unstable and it never reaches equilibrium. When the effect is sufficiently strong the system evolves towards a limiting stationary distribution with a Pareto tail. In between there is a critical phase. In this phase the system may evolve towards a steady state with a multimodal wealth distribution. The corresponding cumulative density function has a characteristic stairway pattern which reflects the effect of economic stratification. The stairs represent wealth levels of economic classes separated by wealth gaps. As we show, the pattern is typical for macro-economic systems with a limited economic freedom. One can find such a multimodal pattern in empirical data, for instance, in the highest percentile of wealth distribution for the population in urban areas of China.Comment: 17 pages, 8 figures (references added, some material moved to appendix

Some problems in Piketty: An internal critique

Thomas Piketty’s evidence on wealth distribution trends in Capital in the Twenty- First Century shows that – contra his own interpretation – there has been little rise in wealth inequality in Europe and America since the 1970s. This article relates that finding to the other principal trends in Piketty’s analysis: the capital/national income ratio trend, the capital-labor split of total incomes and the income inequality trend. Given that wealth inequality is not rising markedly, what can we deduce about the putative causes that might be operating upstream? Only the capital-labor split looks like a plausible explanation of the wealth inequality trend

How Important is Discount Rate Heterogeneity for Wealth Inequality?

This paper investigates the role of discount rate heterogeneity for wealth inequality. The key idea is to infer the distribution of preference parameters from the observed age profile of wealth inequality. The contribution of preference heterogeneity to wealth inequality can then be measured using a quantitative life-cycle model.I find that discount rate heterogeneity increases the Gini coefficient of wealth by 0.06 to 0.11. The share of wealth held by the richest 1% of households rises by 0.03 to 0.13. The larger changes occur when altruistic bequests are large and when preferences are strongly persistent across generations. Discount rate heterogeneity also helps account for the large wealth inequality observed among households with similar lifetime earnings.wealth inequality, preference heterogeneity

Gamma-distribution and wealth inequality

We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown both through a variational approach based on the minimization of the Boltzmann entropy and a complementary microscopic analysis of the collision dynamics of molecules in a gas. In various relevant cases the equilibrium distribution is the same for all these models, namely a gamma-distribution with suitably defined temperature and number of dimensions. This in turn allows one to quantify the inequalities observed in the wealth distributions and suggests that their origin should be traced back to very general underlying mechanisms: for instance, it follows that the smaller the fraction of the relevant quantity (e.g. wealth or energy) that agents can exchange during an interaction, the closer the corresponding equilibrium distribution is to a fair distribution.Comment: Presented to the International Workshop and Conference on: Statistical Physics Approaches to Multi-disciplinary Problems, January 07-13, 2008, IIT Guwahati, Indi

How Important Is Discount Rate Heterogeneity for Wealth Inequality?

This paper investigates the role of discount rate heterogeneity for wealth inequality. The key idea is to infer the distribution of preference parameters from the observed age profile of wealth inequality. The contribution of preference heterogeneity to wealth inequality can then be measured using a quantitative life-cycle model. I find that discount rate heterogeneity increases the Gini coefficient of wealth by 0.06 to 0.11. The share of wealth held by the richest 1% of households rises by 0.03 to 0.13. The larger changes occur when altruistic bequests are large and when preferences are strongly persistent across generations. Discount rate heterogeneity also helps account for the large wealth inequality observed among households with similar lifetime earningsWealth inequality; preference heterogeneity

Equity culture and the distribution of wealth

Wider participation in stockholding is often presumed to reduce wealth inequality. We measure and decompose changes in US wealth inequality between 1989 and 2001, a period of considerable spread of equity culture. Inequality in equity wealth is found to be important for net wealth inequality, despite equity's limited share. Our findings show that reduced wealth inequality is not a necessary outcome of the spread of equity culture. We estimate contributions of stockholder characteristics to levels and inequality in equity holdings, and we distinguish changes in configuration of the stockholder pool from changes in the influence of given characteristics. Our estimates imply that both the 1989 and the 2001 stockholder pools would have produced higher equity holdings in 1998 than were actually observed for 1998 stockholders. This arises from differences both in optimal holdings and in financial attitudes and practices, suggesting a dilution effect of the boom followed by a cleansing effect of the downturn. Cumulative gains and losses in stockholding are shown to be significantly influenced by length of household investment horizon and portfolio breadth but, controlling for those, use of professional advice is either insignificant or counterproductive. JEL Classification: E21, G1

Wealth Inequality: Data and Models

In the United States wealth is highly concentrated and very unequally distributed: the richest 1% hold one third of the total wealth in the economy. Understanding the determinants of wealth inequality is a challenge for many economic models. We summarize some key facts about the wealth distribution and what economic models have been able to explain so far.

Older or Wealthier? The Impact of Age Adjustment on Cross-Sectional Inequality Measures.

Differences in individual wealth holdings are widely viewed as a driving force of economic inequality. However, as this finding relies on cross-section data, a concern is that one confuses older with wealthier. We propose a new method to adjust for age effects in cross-sections, which eliminates wealth inequality due to age, yet preserves inequality arising from other factors. Using a new cross-country comparable database, we examine the impact of age adjustments on wealth inequality across countries and over time. We find that the most widely used method yield a substantially different picture of age adjusted wealth inequality than our method.Wealth inequality; Life cycle; Age adjustments; Gini coefficient.

Wealth inequality and dynamic stability

In this paper we explore the link between wealth inequality and stability in a two-sector neoclassical growth model with heterogeneous agents. The stability of the steady state depends on the various parameters of the model and in particular on individual preferences. We show that when consumers have identical preferences and the inverse of absolute risk aversion (or risk tolerance) is a strictly convex function, inequality is a factor that favors instability. In the opposite case, inequality favors stability. Our characterization also shows that whenever absolute risk tolerance is linear, as when preferences exhibit hyperbolic absolute risk aversion (HARA), wealth heterogeneity is neutral. As there is not yet evidence on the concavity of absolute risk tolerance, our results unfortunately do not lead to a unique conclusion on the sign of the effect of wealth inequality on stability.Economic growth; Heterogeneity; Wealth and Income Inequality; Instability