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.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
