Continuous-Time Heterogeneous Agent Models

Lecture 8 · 2026-05-12

Continuous-time heterogeneous agent models (HACT / Huggett type): the income process is modeled as a continuous-time Markov chain, and we derive the HJB equation for the value function together with the Kolmogorov Forward (KF) equation for the distribution, which form a coupled system of partial differential equations. Numerically, we discretize via finite differences (using an upwind scheme and boundary handling for the state constraint), and compare explicit iteration with an implicit (sparse linear system) solver; we then solve the KFE for the stationary distribution and back out the equilibrium interest rate. Everything is implemented in Python/JAX.

Materials

• Slides: HTML · PDF

Readings

• Achdou, Han, Lasry, Lions & Moll (2022), “Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach,” Review of Economic Studies 89(1), 45–86.
• Huggett (1993), “The Risk-Free Rate in Heterogeneous-Agent Incomplete-Insurance Economies,” Journal of Economic Dynamics and Control 17(5–6), 953–969.
• Candler (1999), “Finite-Difference Methods for Dynamic Programming Problems,” in Computational Methods for the Study of Dynamic Economies, Cambridge University Press.
• Ahn, Kaplan, Moll, Winberry & Wolf (2018), “When Inequality Matters for Macro and Macro Matters for Inequality,” NBER Macroeconomics Annual 32(1), 1–75.