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Lecture Notes On Solution Methods for Microeconomic

Dynamic Stochastic Optimization Problems
Christopher D. Carroll
March 3, 2009


These notes sketch a set of techniques that are useful in solving microeconomic dynamic
stochastic optimization problems. I make no attempt at a systematic overview of the
many possible technical choices; instead, the notes present a speci c set of methods and
techniques that I have found useful in my own work. Associated with these notes is
Mathematica and Matlab software that solves the problems described in the text. These
notes were originally written for my Advanced Topics in Macroeconomic Theory class at
Johns Hopkins University; instructors at other institutions are welcome to use them for
teaching purposes.
These notes improve on earlier versions in several respects, especially by revising
the notation and software to be consistent with those in my paper \The Method
of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems"
published in Economics Letters, available at, and by including sample code for a method of simulated
moments estimation of the life cycle model a la Gourinchas and Parker (2002) and
Cagetti (2003). Background derivations, notation, and related subjects are treated in my
class notes for rst year macro, available at
I am grateful to several generations of graduate students in helping me to re ne these
notes, to Marc Chan for help in updating the text and software to be consistent with
Carroll (2006), to Kiichi Tokuoka for drafting the section on structural estimation, and to
Damiano Sandri for exceptionally insightful help in revising and updating the method of
simulated moments estimation section. All errors are my own.
Department of Economics, Johns Hopkins University, Baltimore, MD 21218-2685, 410-516-
7602 (office),   Tell A Friend