Journal Article

Distributional Comparative Statics

Martin Kaae Jensen

in The Review of Economic Studies

Volume 85, issue 1, pages 581-610
Published in print January 2018 | ISSN: 0034-6527
Published online May 2017 | e-ISSN: 1467-937X | DOI: https://dx.doi.org/10.1093/restud/rdx021
Distributional Comparative Statics

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  • Mathematical Methods; Programming Methods; Mathematical and Simulation Modelling
  • Information, Knowledge, and Uncertainy
  • Intertemporal Choice and Growth
  • Macroeconomics: Consumption, Saving, Production, Employment, and Investment
  • Welfare and Poverty

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Abstract

Distributional comparative statics is the study of how individual decisions and equilibrium outcomes vary with changes in the distribution of economic parameters (income, wealth, productivity, information, etc.). This article develops new tools to address such issues and illustrates their usefulness in applications. The central development is a condition called quasi-concave differences, which implies concavity of the policy function in optimization problems without imposing differentiability or quasi-concavity conditions. The general take-away is that many distributional questions in economics which cannot be solved by direct calculations or the implicit function theorem, can be addressed easily with this article’s methods. Several applications demonstrate this: the article shows how increased uncertainty affects the set of equilibria in Bayesian games; it shows how increased dispersion of productivities affects output in the model of Melitz (2003); and it generalizes Carroll and Kimball (1996)’s result on concave consumption functions to the Aiyagari (1994) setting with borrowing constraints.

Keywords: Distributional comparative statics; Concave policy functions; Income distribution; Inequality; uncertainty; Heterogenous firms; Bayesian games; Dynamic stochastic general equilibrium models; Arg max correspondence; C61; D80; D90; E20; I30

Journal Article.  17192 words.  Illustrated.

Subjects: Mathematical Methods; Programming Methods; Mathematical and Simulation Modelling ; Information, Knowledge, and Uncertainy ; Intertemporal Choice and Growth ; Macroeconomics: Consumption, Saving, Production, Employment, and Investment ; Welfare and Poverty

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