A divide and conquer algorithm for exploiting policy function monotonicity

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 nlog2(n)+5n objective function evaluations. In contrast, existing methods for nonconcave problems require n2 ev...

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Veröffentlicht in:Quantitative economics Jg. 9; H. 2; S. 521 - 540
Hauptverfasser: Gordon, Grey, Qiu, Shi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New Haven, CT The Econometric Society 01.07.2018
Blackwell Publishing Ltd
John Wiley & Sons, Inc
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ISSN:1759-7331, 1759-7323, 1759-7331
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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 nlog2(n)+5n objective function evaluations. In contrast, existing methods for nonconcave problems require n2 evaluations in the worst case. For concave problems, the solution technique can be combined with a method exploiting concavity to reduce evaluations to 14n+2log2(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 in 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 and code are provided.
AbstractList 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 nlog2(n)+5n objective function evaluations. In contrast, existing methods for nonconcave problems require n2 evaluations in the worst case. For concave problems, the solution technique can be combined with a method exploiting concavity to reduce evaluations to 14n+2log2(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 in 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 and code are provided.
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 nlog[sub.2](n)+5n objective function evaluations. In contrast, existing methods for nonconcave problems require n[sup.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+2log[sub.2](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 in 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 and code are provided.
Audience Academic
Author Gordon, Grey
Qiu, Shi
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Snippet 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,...
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SubjectTerms Algorithms
Business cycles
C61
C63
Computation
discrete choice
Divide & conquer algorithms
E32
Econometrics
Economic models
F34
Function
grid search
monotonicity
Risk assessment
sovereign default
State
Variables
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Title A divide and conquer algorithm for exploiting policy function monotonicity
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