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...

Full description

Saved in:
Bibliographic Details
Published in:Quantitative economics Vol. 9; no. 2; pp. 521 - 540
Main Authors: Gordon, Grey, Qiu, Shi
Format: Journal Article
Language:English
Published: New Haven, CT The Econometric Society 01.07.2018
Blackwell Publishing Ltd
John Wiley & Sons, Inc
Subjects:
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
ISSN:1759-7331, 1759-7323, 1759-7331
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1759-7331
1759-7323
1759-7331
DOI:10.3982/QE640