© 2017 The Department of Economics, University of Oxford and John Wiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 80, 2 (2018) 0305–9049
Solving Models with Jump Discontinuities in Policy
ortz and Afrasiab Mirza
Department of Economics, University of Birmingham, Edgbaston, Birmingham, UK
(e-mail: firstname.lastname@example.org), (e-mail: email@example.com)
We compare global methods for solving models with jump discontinuities in the policy
function. We ﬁnd that differences between value function iteration (VFI) and other methods
are economically signiﬁcant and Euler equation errors fail to be a sufﬁcient measure of
accuracy in such models. 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 VFI with a local interpolation step (VFI-INT) is sufﬁcient to obtain accurate
approximations. The combination of computational speed, relatively easy implementation
and adaptability make VFI-INT especially suitable for approximating models with jump
discontinuities in policy functions: while EGM is the fastest method, it is relatively complex
to implement; implementation of VFI-INT is relatively straightforward and it is much faster
We examine differences in the answers produced by global approximation methods for solv-
ing dynamic economies where agents face non-concave problems (i.e. non-convex choice
sets). Non-concave problems can result from the inclusion of ﬁxed adjustment costs that
are empirically relevant in many circumstances.
In such problems, agents make discrete
JEL Classiﬁcation numbers: C63, C68, E37.
*We thank Francesco Zanetti and two anonymous referees for their constructive comments, which signiﬁcantly
improved the paper. We further thank Christian Bayer, Andrew Clausen, Wouter den Haan, Giulio Fella, John Fender,
Jesus Fernandez-Villaverde,Tom Holden, Julia Iori, Kaushik Mitra, Christopher Otrok, Morten Ravn, Pontus Rendahl,
Peter Sinclair, Carlo Strub, Konstantinos Theodoridis, H˚akon Tretvoll, John Tsoukalas, Fabio Verona and participants
at the Society of Computational Economics 2013 Conference and the Royal Economic Society Annual Meeting 2014
for useful comments and suggestions. All remaining errors are our own. G¨ortz acknowledges support from a British
Academy Small Grant.
The relevance of ﬁxed adjustment cost is highlighted for example in studies of investment (e.g. Caballero et al.,
1995; Doms and Dunne, 1998; Power, 1998; Cooper, Haltiwanger and Power, 1999; Nilsen and Schiantarelli, 2003;
Cooper and Haltiwanger, 2006; Whited, 2006; Bayer, 2006; Khan and Thomas, 2008; Bloom, 2009; Wang and Wen,
2012), consumer-durables choice (e.g. Jose Luengo-Prado, 2006; Bajari et al., 2013), portfolio choice models with
transaction costs and asset prices (e.g. Vayanos, 1998), costly technology adoption (e.g. Khan and Ravikumar, 2002)
and optimal dynamic capital structure choice (e.g. Hennessy and Whited, 2005).