Misspecification and Expectations Correction in New Keynesian DSGE Models

Published date01 October 2016
Date01 October 2016
©2016 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
doi: 10.1111/obes.12126
Misspecification and Expectations Correction in New
Keynesian DSGE Models*
Giovanni Angelini† and Luca Fanelli†
Department of Statistical Sciences, School of Economics, Management and Statistics,
University of Bologna, Bologna, Italy (e-mail: giovanni.angelini3@unibo.it;
This paper focuses on the dynamic misspecification that characterizes the class of small-
scale New Keynesian models currently used in monetary and business cycle analysis,
and provides a remedy for the typical difficulties these models have in accounting for the
rich contemporaneous and dynamic correlation structure of the data. We suggest using a
statistical model for the data as a device through which it is possible to adapt the econo-
metric specification of the New Keynesian model such that the risk of omitting important
propagation mechanisms is kept under control. A pseudo-structural form is built from the
baseline system of Euler equations by forcing the state vector of the system to havethe same
dimension as the state vector characterizing the statistical model. The pseudo-structural
form gives rise to a set of cross-equation restrictions that do not penalize the autocorrelation
structure and persistence of the data. Standard estimation and evaluation methods can be
used. We provide an empirical illustration based on USA quarterly data and a small-scale
monetary New Keynesian model.
I. Introduction
Small-scale dynamic stochastic general equilibrium models developed within the New
Keynesian tradition (henceforth NK-DSGE models) have been treated as the benchmark
JEL Classification numbers: C22; C51; C52; E32; E52.
*This paper is inspired by Chapter 3 of the first author’s PhD Thesis. The authors thank twoanonymous referees,
Francesco Zanetti and the following people for useful comments on previous versions of this article: Piergior-
gio Alessandri, Martin M. Andreasen, Emanuele Bacchiocchi, Gunnar B˚ardsen, Fabio Busetti, Efrem Castelnuovo,
Giuseppe Cavaliere, Michele Costa, Marco Del Negro, Davide Delle Monache, Massimo Franchi,Attilio Gardini,
Søren Johansen, Riccardo ‘Jack’ Lucchetti, Helmut L¨utkepohl, Ragnar Nymoen, Alessandro Notarpietro, Alessia
Paccagnini, Paolo Paruolo, Massimiliano Pisani, Majid Al Sadoom and Carlo Trivisano. We also thank the confer-
ence participants at the ‘Ninth International Conference on Computational and Financial Econometrics’, London
(December 2015), ‘Second Annual Conference of the International Association forApplied Econometrics’, Thessa-
loniki (June 2015), the ‘Sixth Italian Congress of Econometrics and Empirical Economics’, Salerno (January 2015),
and workshop participants at the ‘Padova MacroTalks’, Padova (July2015), ‘Second CIdE Workshop for PhD stu-
dents in Econometrics and Empirical Economics’,Perugia (August 2014). Both authors gratefully acknowledge partial
financial support from the Italian MIUR Grant PRIN-2010/2011, prot. 2010RHAHPL 003. The second author also
acknowledges RFO grants from the University of Bologna.
624 Bulletin
of much of the monetary policy literature, given their ability to explain the impact of
monetary policy on output and inflation. A recent generation of NK-DSGE models that
feature financial frictions and the fiscal/monetary policy mix are currently used to evaluate
macroeconomic scenarios and to predict economic activity.It is well recognized, however,
that these models capture only stylized features of the business cycle and the monetary
policy stance and display a limited time series performance (Henry and Pagan, 2004; An
and Schorfheide, 2007). Assessing the correspondence between what these models imply
and what the data tell us is a crucial step in the process of analyzing policy options and
their effects.
One important source of misspecification can be ascribed to the difficulties NK-DSGE
models display in generating sufficient endogenous persistence and propagation mecha-
nisms to match the persistence and propagation mechanisms observed in quarterly data.
An NK-DSGE models are built upon the rational expectations (RE) paradigm. Under RE,
agents are assumed to know the data generating process and form their expectations consis-
tently.Two types of restrictions arise on the model’s reduced for m solution: (i) parametric
nonlinear cross-equation restrictions (CER) that map the structural to the reduced form
parameters; (ii) constraints on the lag order and correlation structure of the variables. The
restrictions in (i) are the Hansen and Sargent’s (1980, 1981) traditional ‘metric’for the eval-
uation of models based on forward-looking behaviour and RE (see also Hansen, 2014).
Instead, the restrictions in (ii) are ‘implicit’, and very often, practitioners are not aware of
their role and importance in the empirical performance of NK-DSGE models.
The unique stable solution associated with NK-DSGE models can be represented as a
state space model, possibly expressed in minimal form (Komunjer and Ng, 2011), or as
finite-order vector autoregressive(VAR) systems in special cases.These solutions generally
involveone (two) lag(s) of the endogenous variables, giving rise to what wecall throughout
the paper an ‘omitted dynamics’ issue. By this term, we denote the situation that occurs
when the constraints in (ii) conflict with the propagation mechanisms one detects from the
data using a statistical model that does not embody all parametric constraints implied by the
theory.Testing the validity of the NK-DSGE model through the CER when the restrictions
in (ii) conflict with the actual autocorrelation structure of the data might distort the overall
evaluation process.
What should investigators do?The natural and obvious fix in these cases would require
the estimation of a theoretically micro-founded model with less restrictive dynamics than
the original New Keynesian model. An excellent example is provided in, e.g. Lubik and
Schorfheide (2004, section 5.D). These authors estimate a dynamically less restrictive ver-
sion of their NK-DSGE model as a robustness check, introducing a consumption Euler
equation which features habit formation that generalizes the previously specified purely
forward-looking consumption equation, and a ‘hybrid’ Phillips curve, as opposed to its
purely forward-looking version. Examples like this, nevertheless, are rare, because it is
not always practical to micro-found all propagation mechanisms that characterize quar-
terly (or monthly) time series. What do practitioners typically do? They generally follow
two approaches. Either they endow the shocks of the NK-DSGE model with more elabo-
rate and persistent time series models like, e.g. AR or ARMA-type processes (Smets and
Wouters, 2007; C´urdiaand Reis, 2010), without (apparently) changing the specification of
their structural equations, or they enrich the dynamics of the system by adding measure-
©2016 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

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