Working Paper: NBER ID: w23732
Authors: Yves Achdou; Jiequn Han; Jean-Michel Lasry; Pierre-Louis Lions; Benjamin Moll
Abstract: 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: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one; (iv) characterization of “soft” borrowing constraints. 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.
Keywords: Income Distribution; Wealth Distribution; Macroeconomics; Heterogeneous Agents
JEL Codes: D31; E00; E21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| low income shocks (I32) | individuals reaching the borrowing constraint (D10) |
| interest rate low relative to the rate of time preference (E43) | higher marginal propensity to consume (MPC) (E21) |
| intertemporal elasticity of substitution weakly greater than one (D15) | unique stationary equilibrium (D50) |
| soft borrowing constraints (F34) | spikes in wealth distributions at zero net worth (D31) |