Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach
Achdou, Yves; Han, Jiequn; Lasry, Jean-Michel; Lions, Pierre Louis; Moll, Benjamin (2022), Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach, The Review of Economic Studies, 89, 1, p. 45-86. 10.1093/restud/rdab002
TypeArticle accepté pour publication ou publié
Journal nameThe Review of Economic Studies
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Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Department of Mathematics - Princeton University
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lions, Pierre Louis
Collège de France - Chaire Équations aux dérivées partielles et applications
Department of Management - London School of Economics and Political Science [LSE]
Abstract (EN)We recast the Aiyagari–Bewley–Huggett model of income and wealth distribution in continuous time. This workhorse model—as well as heterogeneous agent models more generally—then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (1) an analytic characterization of the consumption and saving behaviour of the poor, particularly their marginal propensities to consume; (2) a closed-form solution for the wealth distribution in a special case with two income types; (3) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including—but not limited to—the Aiyagari–Bewley–Huggett model.
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