The Krusell–Smith Method

Lecture 5 · 2026-04-14

An incomplete-markets heterogeneous-agent model with both idiosyncratic and aggregate risk, in which the wealth distribution is itself an endogenous, infinite-dimensional state variable. The Krusell–Smith method confronts this challenge through approximate aggregation: it replaces the full law of motion of the distribution with a forecasting rule for aggregate capital (a log-linear regression of \(\log K'\) on \(\log K\), estimated separately in good and bad aggregate states), and iterates an outer fixed point until that rule is self-consistent. The lecture covers the algorithm, accuracy checks, and the limits of its applicability, and provides a complete JAX implementation based on policy function iteration.

Materials

Readings

  • Krusell & Smith (1998), “Income and Wealth Heterogeneity in the Macroeconomy,” JPE 106(5), 867–896.