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 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Grey surname: Gordon fullname: Gordon, Grey – sequence: 2 givenname: Shi surname: Qiu fullname: Qiu, Shi |
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| Cites_doi | 10.1016/0022-0531(87)90117-7 10.1016/j.econlet.2013.04.031 10.2307/2527416 10.1007/BF01227624 10.1287/moor.1070.0290 10.1287/opre.50.5.796.365 10.1016/0165-1765(86)90168-0 10.1016/j.jedc.2010.09.010 10.3982/ECTA7583 10.1016/S1094-2025(02)00005-4 10.1162/003355302753399481 10.1016/S0377-2217(01)00297-1 10.1016/j.red.2013.07.001 10.1287/opre.2015.1425 10.1016/j.jedc.2016.05.016 10.1080/07350015.1990.10509768 10.1515/9781400822539 10.1007/s00199-009-0450-4 10.2139/ssrn.2995636 10.2307/j.ctvjnrt76 10.2307/2951479 10.1002/9780470316887 10.1287/opre.26.2.305 10.1016/j.econlet.2005.09.013 10.2307/2951526 10.1016/j.jedc.2005.07.008 10.1111/j.1468-0262.2006.00752.x 10.3982/QE643 10.1257/aer.98.3.690 |
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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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