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Solving models with jump discontinuities in policy functions

Görtz, Christoph and Mirza, Afrasiab (2016) Solving models with jump discontinuities in policy functions. Discussion Paper. University of Birmingham, Birmingham UK.

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We show that the Value Function Iteration (VFI) algorithm has difficulties approximating models with jump discontinuities in policy functions. We find that VFI fails to accurately identify both the location and size of jump discontinuities while the Endogenous Grid Method (EGM) and the Finite Element Method (FEM) are much better at approximating this class of models. We further show that combining value function iteration with a local interpolation step (VFI-INT) is sufficient to obtain accurate approximations. Differences between policy functions generated by VFI and these alternative methods are economically significant. We highlight that these differences across methods cannot be identified using Euler equation errors as these are not a sufficient measure of accuracy for models with jump discontinuities in policy functions. As a result, speed comparisons across methods that rely on Euler equation errors as a measure for accuracy can be misleading. The combination of computational speed, relatively easy implementation and adaptability make VFI-INT especially suitable for approximating models with jump discontinuities in policy functions.

Type of Work:Monograph (Discussion Paper)
School/Faculty:Colleges (2008 onwards) > College of Social Sciences
Number of Pages:45
Department:Birmingham Business School
Date:09 May 2016
Series/Collection Name:Birmingham Business School Discussion Paper Series
Keywords:Dynamic Equilibrium Economics, Non-Convex Capital Adjustment Costs, Computational Methods, Nonlinear Solution Methods, Euler equation errors
Subjects:H Social Sciences > H Social Sciences (General)
H Social Sciences > HB Economic Theory
H Social Sciences > HG Finance
Copyright Status:This discussion paper is copyright of the University and the author. In addition, parts of the paper may feature content whose copyright is owned by a third party, but which has been used either by permission or under the Fair Dealing provisions. The intellectual property rights in respect of this work are as defined by the terms of any licence that is attached to the paper. Where no licence is associated with the work, any subsequent use is subject to the terms of The Copyright Designs and Patents Act 1988 (or as modified by any successor legislation). Any reproduction of the whole or part of this paper must be in accordance with the licence or the Act (whichever is applicable) and must be properly acknowledged. For non-commercial research and for private study purposes, copies of the paper may be made/distributed and quotations used with due attribution. Commercial distribution or reproduction in any format is prohibited without the permission of the copyright holders.
Copyright Holders:The Authors and the University of Birmingham
ID Code:2163

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