Long-run Distribution Of Wealth Research Articles

On the long-run wealth distribution in a simple Ramsey model with heterogeneous households

This paper analyzes the long-run wealth distribution in a Ramsey model where individuals have a common rate of time preference but different intertemporal elasticities of substitution. As a result, it is shown that heterogeneity among households in intertemporal substitution is sufficient for the existence of a non-degenerate long-run wealth distribution. We also investigate the properties of the long-run wealth distribution and the transition of capital and consumption using the phase diagram.

Capital Income Risk and the Dynamics of the Wealth Distribution

In this paper, we develop and numerically solve a model of idiosyncratic labour income and idiosyncratic interest rates to predict the evolution of a wealth distribution over time. Stochastic labour income follows a deterministic growth trend and it fluctuates between a wage and unemployment benefits. Stochastic interest rates are drawn initially (ex-ante heterogeneity), fluctuate between two values (ex-post heterogeneity) and can differ in their arrival rates (financial types). A low interest rate implies a stationary long-run wealth distribution, a high interest rate implies non-stationary wealth distributions. Our baseline model matches the evolution of the wealth distribution of the NLSY 79 cohort from 1986 to 2008 very well. When we start in 1986 and target 2008, we obtain a fit of 96.1%: The fit for non-targeted years is 77.0% on average. When targeting the evolution of wealth, the fit is 88.9%. With a more flexible interest rate distribution, the fit can even be increased to 96.7%. Comparing calibrated mean returns with data shows that the flexible interest rate distribution has empirically not convincing superstar states. In the baseline model, mean returns are empirically convincing. Surprisingly, the standard deviation of model returns is an order of magnitude lower than the empirical standard deviation.

Income Shares, Secular Stagnation, and the Long-Run Distribution of Wealth

Four alarming stylized facts have recently emerged in the United States: (i) a decline in the labor share of income; (ii) a decline in labor productivity; (iii) an increase in the top 1% wealth share, and (iv) an increase in the capital-income ratio. In Capital in the XXI Century, Thomas Piketty’s argument is that the r > g inequality determines an increase in the capital-income ratio; if the elasticity of substitution in production is above one, the profit share rises. We provide a contrasting explanation that draws from the Post Keynesian approach to differential saving propensities between classes and the Classical-Marxian theory of induced technical change. In a simple model of ‘capitalists’ and ‘workers,’ we show that institutional changes that lower the labor share—declining unionization, increasing monopsony power in the labor market, the global ‘race to the bottom’ in unit labor costs, or the exhaustion of path-breaking scientific discoveries—can reduce labor productivity growth because of the lessened incentives to innovate to save on labor costs. A falling labor share reduces workers’ total savings, and wealth concentrates in the capitalists’ hands. A higher profit share and wealth share both put pressure on accumulation: but the long-run growth rate, which is anchored to labor productivity growth, has fallen. To restore balanced growth, the capital-income ratio must rise, independent of the elasticity of substitution. These tendencies are not inevitable: taxation can be used to implement any wealth distribution targeted by policymakers; while worker-crushing institutional arrangements can also in principle be reversed through policy. Neither change appears likely given the current institutional and global policy climate.

Capital Income Risk and the Dynamics of the Wealth Distribution

In this paper, we develop and numerically solve a model of idiosyncratic labour income and idiosyncratic interest rates to predict the evolution of a wealth distribution over time. Stochastic labour income follows a deterministic growth trend and it fluctuates between a wage and unemployment benefits. Stochastic interest rates are drawn initially (ex-ante heterogeneity), fluctuate between two values (ex-post heterogeneity) and can differ in their arrival rates (financial types). A low interest rate implies a stationary long-run wealth distribution, a high interest rate implies non-stationary wealth distributions.Our baseline model matches the evolution of the wealth distribution of the NLSY 79 cohort from 1986 to 2008 very well. When we start in 1986 and target 2008, we obtain a fit of 96.1%: The fit for non-targeted years is 77.0% on average. When targeting the evolution of wealth, the fit is 88.9%. With a more flexible interest rate distribution, the fit can even be increased to 96.7%. Comparing calibrated mean returns with data shows that the flexible interest rate distribution has empirically not convincing superstar states. In the baseline model, mean returns are empirically convincing. Surprisingly, the standard deviation of model returns is an order of magnitude lower than the empirical standard deviation.

Wealth Distribution, Elasticity of Substitution and Piketty: An ‘Anti‐Dual’ Pasinetti Economy

ABSTRACTThis paper studies the dynamics of wealth distribution between workers and capitalists in a neoclassical growth model with differential saving rates. It shows that if capitalists are thriftier than workers and the factors elasticity of substitution is high enough to ensure endogenous growth, capitalists’ share of total wealth asymptotically tends to one. It is also proved that a tax on capital income shifts the long run distribution of wealth in workers’ favor, and that the capitalists’ share of total wealth is a decreasing function of the tax rate. The results of the paper are compared to Piketty's ‘fundamental laws’ of capitalism.

Ergodic Inequality

Weak conditions are provided under which society’s long-run distribution of wealth is independent of initial asset holdings.

Optimal Taxation of Capital Income: A Mirrleesian Approach to Capital Accumulation

Many authors have argued that capital income risk is a major determinant of wealth inequality. Inspired by this, I develop a model of optimal taxation of capital income in which wealth and income inequality is a result of capital income shocks together with frictions in financial markets. I use the model to study optimal taxation of various types of capital income: capital income from controlled businesses, outside the business as well as bequests. In presence of risk-return trade-offs, i.e., when more productive investments are riskier, I show that it is typically optimal to have progressive saving taxes. Furthermore, in an intergenerational context, I show that bequest taxes should be negative. Finally, I study the implications of the model on long run efficient distribution of wealth. I show that the long-run distribution of wealth has a fat-tail distribution and compare the efficient tail of the wealth distribution to the one resulting from an incomplete market model.

Optimal progressive capital income taxes in the infinite horizon model

This paper analyzes optimal progressive capital income taxation in an infinite horizon model where individuals differ only through their initial wealth. We consider progressive capital income tax schedules taking a simple two-bracket form with an exemption bracket at the bottom and a single marginal tax rate above a time varying exemption threshold. Individuals are taxed until their wealth is reduced down to the exemption threshold. The fraction of individuals subject to capital income taxation vanishes to zero in the long-run in analogy to the zero long-run capital tax result of Chamley and Judd with optimal linear taxes. However, in contrast to linear taxation, optimal nonlinear capital taxation can have a drastic impact on the long-run wealth distribution. When the intertemporal elasticity of substitution is not too large and the top tail of the initial wealth distribution is infinite and thick enough, the optimal exemption threshold converges to a finite limit. As a result, the optimal tax system drives all the large fortunes down a finite level and produces a truncated long-run wealth distribution.

Constrained Efficiency in the Neoclassical Growth Model With Uninsurable Idiosyncratic Shocks

We investigate the welfare properties of the one-sector neoclassical growth model with uninsurable idiosyncratic shocks. We focus on the notion of constrained efficiency used in the general equilibrium literature. Our characterization of constrained efficiency uses the first-order condition of a constrained planner's problem. This condition highlights the margins of relevance for whether capital is too high or too low: the factor composition of income of the (consumption-)poor. Using three calibrations commonly considered in the literature, we illustrate that there can be either over- or underaccumulation of capital in steady state and that the constrained optimum may or may not be consistent with a nondegenerate long-run distribution of wealth. For the calibration that roughly matches the income and wealth distribution, the constrained inefficiency of the market outcome is rather striking: it has much too low a steady-state capital stock.

Strategic saving decisions in the infinite-horizon model

We study a mechanism that prevents the long-run distribution of wealth from becoming degenerate in the Ramsey–Cass–Koopmans model when households have different time-preference rates. This mechanism is based on the observation that price-taking behavior is no longer justified when all wealth is owned by a single household. Formalizing this observation, we obtain a model with a unique stationary equilibrium in which, depending on the parameter constellation, any number of households can own positive stocks of capital. We characterize this equilibrium and show for example that an increase in the dispersion of the time-preference rates across households unambiguously increases aggregate output. Whereas the main results are derived for a rather general class of production functions, we devote a separate section to the special case of the Cobb–Douglas technology for which the equilibrium conditions are particularly simple.

Trade, skill acquisition and distribution

The paper examines how international trade affects long-run distribution of wealth and income. Given a child's ability, the wage differential and the interest rate, a parent decides whether or not to educate the child and how much to borrow or lend. Trade, by affecting the wage differential, influences the interest rate, the proportion of population that acquires education and thereby income–wealth distribution. Two countries are distinguished by differences in educational infrastructure and loan market environments. The trade-pattern and the distributional implications of both sources of comparative advantage are similar. Free international mobility of loans may have different implications.

Economic growth and status-seeking through personal wealth

I investigate the wealth distribution and endogenous fiscal policy in a two-class growth model in which individuals exhibit a desire for social status. The latter is increasing with individual wealth and decreasing with the average wealth of the society. First, I show that status-seeking is crucial in determining the long-run wealth distribution: agents with stronger status motive end up holding a higher level of wealth. Second, higher wealth inequality can be associated with a higher growth if the inequality is due to a stronger incentive of one class of agents to accumulate wealth. Third, the model implies that a higher growth rate may reduce welfare of one class of agents and increase welfare of the other one. Finally, when fiscal policy is determined through a voting mechanism, an increase in the strength of the status motive of the majoritarian class can reduce political-equilibrium growth.

EFFECTS OF DIFFERENCES IN RISK AVERSION ON THE DISTRIBUTION OF WEALTH

This paper studies the role played by differences in risk aversion in affecting the long-run distribution of wealth across agents in the context of an endowment economy. The economy is populated by two types of Epstein-Zin agents who differ only in their attitudes toward risk. By choosing riskier portfolio strategies, less-risk-averse agents enjoy returns on their investments characterized by a higher mean and a higher variance than the ones enjoyed by more-risk-averse agents. The former effect tends to make less-risk-averse agents wealthier over time, whereas the latter tends to make them poorer. The paper shows that, contrary to the results obtained using standard expected utility preferences, for some parameter values the long-run distribution of wealth is dominated by more-risk-averse agents.

Traders' Long-Run Wealth in an Artificial Financial Market

In this paper, we study the long-run wealth distribution of agents with different trading strategies in the framework of the Genoa Artificial Stock Market. The Genoa market is an agent-based simulated market able to reproduce the main stylised facts observed in financial markets, i.e., fat-tailed distribution of returns and volatility clustering. Various populations of traders have been introduced in a 'thermal bath' made by random traders who make random buy and sell decisions constrained by the available limited resources and depending on past price volatility. We study both trend following and trend contrarian behaviour; fundamentalist traders (i.e., traders believing that stocks have a fundamental price depending on factors external to the market) are also investigated. Results show that the strategy alone does not allow forecasting which population will prevail. Trading strategies yield different results in different market conditions. Generally, in a closed market (a market with no money creation process), we find that trend followers lose relevance and money to other populations of traders and eventually disappear, whereas in an open market (a market with money inflows), trend followers can survive, but their strategy is less profitable than the strategy of other populations.

On the Long-Run Distribution of Capital in the Ramsey Model

We study issues related to the long-run distribution of wealth in two variants of Ramsey's model of optimal capital accumulation. First we show that, in the case where a government levies a progressive income tax, there exist infinitely many stationary equilibria in which all households own positive capital stocks. Moreover, it is demonstrated that non-stationary equilibria can exhibit complicated dynamics. Then we discuss the case where households exercise market power on the capital market and we show that this may also lead to equilibria in which all households own positive amounts of capital. Journal of Economic Literature Classification Numbers: E62, O41.

Redistribution Policies under Capital Market Imperfection

We establish the existence and stability of the long-run wealth distribution in a credit constrained economy by applying the monotonicity condition developed by H. Hopenhayn and E. Prescott. There should emerge an egalitarian society in which all families experience upward and downward mobility, although a society of persistent inequality may occur in which rich entrepreneurs and poor lenders remain immobile between classes. The speed of transition from the latter to the former is shown to depend on the design of redistribution policies. Simulation results show that this occurs more rapidly when the government favours relatively rich lenders. JEL Classification Numbers: D31, G33, O12.

The Global Stability of Efficient Intertemporal Allocations

This paper describes a continuous time model of an economy with finitely many infinitely-lived consumers and a finite number of capital goods. Two objectives are achieved. First, recursive (nonadditive) utility functionals are formulated and analyzed. Second, these preference functionals are applied to analyze the nature of efficient allocations in a dynamic economy. Two classes of global turnpike propositions are proven which provide the basis for a model of the long-run distribution of wealth. These propositions also provide new perspective regarding existing stability literature based on additive utilities. Copyright 1987 by The Econometric Society.