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An Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity

Author

Listed:
  • John Stachurski

    (Australian National University)

  • Alexis Akira Toda

    (University of California San Diego)

Abstract

It has been conjectured that canonical Bewley-Huggett-Aiyagari heterogeneous-agent models cannot explain the joint distribution of income and wealth. The results stated below verify this conjecture and clarify its implications under very general conditions. We show in particular that if (i) agents are infinitely-lived, (ii) saving is risk-free, and (iii) agents have constant discount factors, then the wealth distribution inherits the tail behavior of income shocks (e.g., light-tailedness or the Pareto exponent). Our restrictions on utility require only that relative risk aversion is bounded, and a large variety of income processes are admitted. Our results show conclusively that it is necessary to go beyond standard models to explain the empirical fact that wealth is heavier-tailed than income. We demonstrate through examples that relaxing any of the above three conditions can generate Pareto tails.

Suggested Citation

  • John Stachurski & Alexis Akira Toda, 2019. "An Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity," 2019 Meeting Papers 151, Society for Economic Dynamics.
    • Handle: RePEc:red:sed019:151
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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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