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A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity

Grey Gordon and Shi Qiu ()

No 2017-006, CAEPR Working Papers from Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington

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 (search for similar items in EconPapers)
JEL-codes: C61 C63 E32 F34 (search for similar items in EconPapers)
Pages: 71 pages
Date: 2017-04
New Economics Papers: this item is included in nep-cmp
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: A divide and conquer algorithm for exploiting policy function monotonicity (2018) Downloads
Working Paper: A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity (2015) Downloads
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