Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

Yves Achdou, Jiequn Han, Jean Michel Lasry, Pierre Louis Lions, Benjamin Moll

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)45-86
Number of pages42
JournalReview of Economic Studies
Issue number1
StatePublished - Jan 1 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Consumption
  • Continuous time
  • Heterogeneous a
  • Inequality
  • Wealth distribution


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