Estimating Nonlinear Business Cycle Mechanisms with Linear Vector Autoregressions: A Monte Carlo Study*
| Published date | 01 October 2022 |
| Author | Karsten Kohler,Robert Calvert Jump |
| Date | 01 October 2022 |
| DOI | http://doi.org/10.1111/obes.12498 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 84, 5 (2022) 0305-9049
doi: 10.1111/obes.12498
Estimating Nonlinear Business Cycle Mechanisms
with Linear Vector Autoregressions: A Monte Carlo
Study*
KARSTEN KOHLER† and ROBERT CALVERT JUMP‡
†Economics Department, Leeds University Business School, Maurice Keyworth Building,
Woodhouse, Leeds, LS2 9JT, United Kingdom (e-mail: k.kohler@leeds.ac.uk)
‡Institute for Political Economy, Governance, Finance and Accountability, University of
Greenwich, Old Royal Naval College, Park Row, Greenwich, London, SE10 9LS, United
Kingdom (e-mail: r.g.calvertjump@greenwich.ac.uk)
Abstract
The paper investigates how well linear vector autoregressions (VARs) identify endogenous
cycle mechanisms and cycle frequencies when the underlying process is a nonlinear limit
cycle. We conduct Monte Carlo simulations with five nonlinear models in which cycles
are driven by the interaction of two state variables. We find that while linear VARs
quantitatively underestimate the strength of the interaction mechanism, they successfully
identify the qualitative presence of a cycle mechanism in most cases (55%– 100%). Our
results further suggest that linear VARs are surprisingly successful at estimating cycle
frequencies of nonlinear processes.
I. Introduction
Since the rise to popularity of real business cycle theory in the 1980s, and then New
Keynesian DSGE models in the 1990s, macroeconomics has been dominated by the use
of linearized difference equations to model business cycles. Edward C. Prescott (1986,
p. 10) famously argued that,
‘some systems of low-order linear stochastic difference equations with a non-oscillatory deterministic
part, and therefore no cycle, display key business cycle features [...] I thus do not refer to business cycles,
but rather to business cycle phenomena, which are nothing more nor less than a certain set of statistical
properties of a certain set of important aggregate time series.’
Recently, however, the idea of endogenous cycles has re-emerged in macroeconomic
theory. Azariadis (2018)andGal
´
ı(2018), for example, call for new models with complex
eigenvalues and endogenous propagation mechanisms to account for periodic fluctuations
JEL Classification numbers: C15, C32, E32.
*We thank the editor Jonathan Temple, an anonymous referee, Roberto Dieci, Giorgos Galanis, Alexander
Guschanski, Achilleas Mantes, Christian Proa˜
no, Ron Smith, Engelbert Stockhammer, Frank Westerhoff, and
Rafael Wildauer for helpful comments. All errors are the authors’.
1077
©2022 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and
distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
1078 Bulletin
in output. An important stimulus has been empirical research on financial cycles that
finds dominant frequencies of 13– 16 years in aggregate financial variables such as private
credit and house prices (Borio, 2014; Aikman, Haldane and Nelson, 2015;R
¨
unstler
and Vlekke, 2017; Stockhammer et al., 2019; Strohsal, Proa˜
no and Wolters, 2019).
Borio (2014, p. 186) argues that these financial boom-bust episodes should be seen ‘as
the result of endogenous forces that perpetuate (irregular) cycles’, rather than the result of
random shocks propagated by linear mechanisms.
The re-emergence of endogenous cycles in macroeconomic theory is typified by the
recent contribution of Beaudry, Galizia and Portier (2020). They show that various US
macroeconomic indicators, such as hours worked per person and the unemployment rate,
exhibit a pronounced cycle of around 10 years in length. They build a stochastic
New Keynesian model with strategic complementarities in consumption, in which
nonlinearities generate a limit cycle that matches the periodicities found in the data.
Endogenous fluctuations are also a major theme in heterogeneous agents models of asset
price dynamics (e.g. Brock and Hommes, 1997; Chiarella, 1992; Dieci and He, 2018).
Similarly, the literature on behavioural New Keynesian models investigates endogenous
cycle mechanisms based on strategic interaction (Branch and McGough, 2010;Calvert
Jump and Levine, 2019).
Despite the re-emergence of endogenous cycles in macroeconomic theory and the
existence of various types of nonlinear time series models, linear vector autoregressive
(VAR) models still dominate macroeconometrics. Among other reasons, this is because
they provide flexible approximations to a variety of time series processes. In particular,
linear ARMA processes can be thought of as approximations to the Wold decomposition
of regular stationary processes (Francq and Zako¨
ıan, 1998), and ARMA models can be
found which approximate the spectra of any stationary process, nonlinear or otherwise
(Brockwell and Davis, 2006, pp. 130-133).
However, while VAR models can be thought of as approximations to a variety of
time series processes, their estimated coefficients will rarely correspond to the structural
parameters of a nonlinear data-generating process (DGP). This is a simple implication
of omitted variable (or omitted nonlinearity) bias. For example, Beaudry, Galizia and
Portier (2017) use a Monte Carlo simulation to show that univariate linear autoregressive
models fail to identify local instability when estimated on data generated by a nonlinear
limit cycle process, despite the linear model providing (in principle) a good approximation
to second moments. Specifically, Beaudry et al. (2017) find that the moduli of locally
unstable processes, as defined by their linearization, are underestimated by linear time
series models.
While we know that linear time series models underestimate the moduli of limit cycle
processes, the extent to which they accurately estimate the endogenous cycle mechanisms
and cycle lengths of nonlinear limit cycle processes is unknown. In this paper, we provide
an assessment of the quantitative relevance of this type of omitted nonlinearity bias in
an applied, small sample context. Using a series of Monte Carlo studies, we explore
what the linear projection of a vector process {Xt}on its own history – that is, a VAR
model – can tell us about the linear part – that is, the Jacobian matrix – of canonical
nonlinear business cycle models. Specifically, we study whether linear VAR models
are a reliable method of identifying the cyclical interaction mechanisms posited by a
©2022 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
Get this document and AI-powered insights with a free trial of vLex and Vincent AI
Get Started for FreeStart Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
