Program in Applied and Computational Mathematics
Princeton, NJ 08540
NBER Working Papers and Publications
|August 2017||Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach|
with Yves Achdou, Jean-Michel Lasry, Pierre-Louis Lions, Benjamin Moll: w23732
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...