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Unformatted text preview: Solution Methods for Microeconomic Dynamic Stochastic Optimization Problems November 20, 2011 Christopher D. Carroll 1 Abstract These notes describe some tools for solving microeconomic dynamic stochastic optimization problems, and show how to use those tools for estimating a standard life cycle consumption/saving model using microeconomic data. No attempt is made at a systematic overview of the many possible technical choices; instead, I present a specific set of methods that have proven useful in my own work (and explain why other popular methods, such as value function iteration, are a bad idea). Paired with these notes is Mathematica and Matlab software that solves the problems described in the text. Keywords Dynamic Stochastic Optimization, Method of Simulated Moments, Structural Estimation JEL codes E21, F41 PDF: http://econ.jhu.edu/people/ccarroll/SolvingMicroDSOPs.pdf Web: http://econ.jhu.edu/people/ccarroll/SolvingMicroDSOPs/ Archive: http://econ.jhu.edu/people/ccarroll/SolvingMicroDSOPs.zip (Contains LaTeX code for this document and software producing figures and results) 1 Carroll: Department of Economics, Johns Hopkins University, Baltimore, MD, http://econ.jhu.edu/people/ccarroll/ , email@example.com , Phone: (410) 516-7602 The notes were originally written for my Advanced Topics in Macroeconomic Theory class at Johns Hopkins University; instructors elsewhere are welcome to use them for teaching purposes. This draft incorporates several improvements related to new results in the paper Theoretical Foundations of Buffer Stock Saving (especially tools for approximating the consumption and value functions). Like the last major draft, it also builds on material in The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems published in Economics Letters , available at http://econ.jhu.edu/people/ccarroll/EndogenousArchive.zip , 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 first year macro, available at http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption . I am grateful to several generations of graduate students in helping me to refine 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, to Damiano Sandri for exceptionally insightful help in revising and updating the method of simulated moments estimation section, and to Weifeng Wu and Metin Uyanik for revising to be consistent with the method of moderation and other improvements. All errors are my own. Contents 1 Introduction 3 2 The Problem 4 3 Normalization 5 4 The Usual Theory and Some Notation 6 5 Solving the Next-to-Last Period 7 5.1 Discretizing the Distribution . . . . . . . . . . . . . . . . . . . . . . .....
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This note was uploaded on 11/27/2011 for the course ECON 101 taught by Professor Robert during the Fall '08 term at Montgomery College.
- Fall '08