A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity

CAEPR Working Paper 2017-006

71 Pages Posted: 5 Jul 2017 Last revised: 25 Jul 2017

See all articles by Grey Gordon

Grey Gordon

Federal Reserve Banks - Federal Reserve Bank of Richmond

Shi Qiu

Indiana University Bloomington, Department of Economics, Students

Multiple version iconThere are 2 versions of this paper

Date Written: April 10, 2017

Abstract

A divide and conquer algorithm for exploiting policy function monotonicity is proposed and analyzed. To solve a discrete problem with n states and n choices, the algorithm requires at most n log2(n) 5n objective function evaluations. In contrast, existing methods for non-concave problems require n^2 evaluations in the worst case. For concave problems, the solution technique can be combined with a method exploiting concavity to reduce evaluations to 14n 2 log2(n). A version of the algorithm exploiting monotonicity in two state variables allows for even more efficient solutions. The algorithm can also be efficiently employed in a common class of problems that do not have monotone policies, including problems with many state and choice variables. In the sovereign default model of Arellano (2008) and the real business cycle model, the algorithm reduces run times by an order of magnitude for moderate grid sizes and orders of magnitude for larger ones. Sufficient conditions for monotonicity are provided.

Keywords: Computation, Monotonicity, Grid Search, Sovereign Default

JEL Classification: C61, C63, E32, F34

Suggested Citation

Gordon, Grey and Qiu, Shi, A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity (April 10, 2017). CAEPR Working Paper 2017-006, Available at SSRN: https://ssrn.com/abstract=2995636 or http://dx.doi.org/10.2139/ssrn.2995636

Grey Gordon (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of Richmond ( email )

P.O. Box 27622
Richmond, VA 23261
United States

Shi Qiu

Indiana University Bloomington, Department of Economics, Students ( email )

Bloomington, IN
United States

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