THE TRANSMISSION MECHANISM IN GOOD AND BAD TIMES

• Date: 01 November 2015
• DOI: http://doi.org/10.1111/iere.12136
• Author: Haroon Mumtaz,Paolo Surico
• Published date: 01 November 2015

INTERNATIONAL ECONOMIC REVIEW

Vol. 56, No. 4, November 2015

THE TRANSMISSION MECHANISM IN GOOD AND BAD TIMES∗

BYHAROON MUMTAZ AND PAOLO SURICO1

Queen’s Mary University, U.K.; London Business School and CEPR, U.K.

Does the transmission of economic policies and structural shocks vary with the state of the economy? We answer this

question using a strategy based on quantile regressions, which account for endogenous regressors and state-dependent

parameters. An application to U.S. real activity and interest rate reveals pervasive asymmetries in the propagation

mechanism across good and bad times. During periods when real activity is above its conditional average, the estimates

of the degree of forward-lookingness and interest rate semi-elasticity are significantly larger (in absolute value) than the

estimates associated with below-average periods. Results are robust to alternative strategies to model state-dependent

parameters.

1. INTRODUCTION

The great recession of 2007–09 has sparked renewed interest in the extent to which monetary

and fiscal policies can stimulate the economy during good and bad times. On one hand, a number

of empirical contributions have used vector autoregressions (VAR) or augmented distributed

lag (ADL) models to show that stabilization policies may have asymmetric effects over the

business cycle (see, for instance, Auerbach and Gorodnichenko, 2011, for fiscal policy and

Tenreyro and Thwaites, 2013, for monetary policy). On the other hand, dynamic stochastic

general equilibrium (DSGE) models typically assume that the effects of the short-term interest

rate and government spending on real activity during expansions are as large as the effects

during contractions.2

In this article, we assess the evidence for asymmetries in the consumption–interest rate re-

lationship, which we argue can be interpreted as an Investment-Saving (IS) curve. Relative to

the more reduced-form evidence from VAR and ADL models, our strategy accounts for en-

dogenous regressors by using an instrumental variables method. Relative to the more structural

evidence from DSGE models, our single equation approach allows us to model explicitly the

link between parameters evolution and the state of the economy in a way that is both flexible

and computationally feasible.

We propose an empirical model where the coefficients are allowed, but not required, to vary

with the (unobserved) state of the economy, which is endogenously determined within the esti-

mation method. Our method is based on Instrumental Variable Quantile Regressions (IVQR),

which are designed to handle simultaneously endogenous regressors and state-dependent pa-

rameters. To illustrate the potential of using quantile regressions (QRs) on time-series data, we

also present a time-varying coefficient interpretation of our estimates, which complements re-

cent evidence of parameter instability in DSGE models. Furthermore, we show that the evidence

against a linear IS curve specification is robust to using instrumental variable Markov-switching

and threshold models, though these estimates are less accurate than the IVQR estimates.

∗Manuscript received December 2011; revised July 2014.

1We are grateful to the editor, Jes´

us Fern´

andez-Villaverde, and three anonymous referees for very useful comments

and suggestions. Financial support from the European Research Council Starting Independent Grant—Agreement

263429—is gratefully acknowledged. Please address correspondence to: Paolo Surico. E-mail: psurico@london.edu.

2Although recent advances have made it possible to solve structural models that feature a zero bound for the nominal

interest rate (see Fern´

andez-Villaverde et al., 2012), we are not aware of contributions that have estimated this type of

nonlinearity in the context of a DSGE model.

1237

C

(2015) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1238 MUMTAZ AND SURICO

Our findings on post-WWII U.S. data can be summarized as follows. First, there is strong

evidence for state dependence in the weight of the forward-looking component of the IS

curve: Periods in the bottom (top) 10% of the conditional distribution of real activity are

characterized by fully backward- (forward-) lookingness. Second, there is also a significant

extent of asymmetry in the estimates of the interest rate semi-elasticity with values around

−0.005 below the 70th percentile and values between −0.02 and −0.08 above that. This suggests

that monetary policy is more effective during periods of expansions. Third, a constant parameter

specification of the IS curve relationship significantly overestimates (underestimates) the degree

of forward-lookingness and the interest rate semi-elasticity during periods of low (high) real

activity conditional on covariates. Fourth, mapping the state-dependent estimates into time-

varying coefficients reveals that periods of conditionally low (high) real activity coincide with

periods of unconditionally below-trend (above-trend) consumption/output. The implication is

that our findings can be equivalently cast in terms of phases of the business cycle. Fifth, our

results are robust to employing alternative (i) filters to isolate cyclical components, (ii) measures

of real activity, (iii) instrument sets, (iv) specifications of the lag structure in the transmission

mechanism, and (v) strategy to identify the unanticipated component of movements in the

interest rate.

Finally, our findings may help reconcile conflicting evidence from earlier contributions. Esti-

mates of the degree of forward-lookingness in IS curve specifications range from values not sta-

tistically different from 1 (Ireland, 2004) to values not significantly different from 0 (Fuhrer and

Rudebusch, 2004). The semi-elasticity of interest rate is often statistically insignificant (Lind ´

e,

2005), and when it is not, the point estimates are so small as to imply only modest effects through

the transmission of structural shocks or economic policies (Dennis, 2009). The evidence on state-

dependent parameters presented in this article may thus offer a way to rationalize the seemingly

contrasting estimates that are based on linear models and different U.S. post-WWII samples.

The article is organized as follows: The empirical model is presented in Section 2. In Section

3, we lay out the estimation method to explore state dependence and account for endogeneity.

Section 4 introduces the data and the instrument sets. In Section 5, we present the main results of

the article, the robustness to alternative methods to model state-dependent parameters, as well

as a time-varying coefficient interpretation of the QR estimates. A sensitivity analysis is offered

in Section 6. Section 7 compares the forecasting performance of the IVQR model relative to

alternative strategies to deal with parameter instability. The Appendix reports a Monte Carlo

analysis to assess the small sample bias associated with the QR method presented in Section 3

as well as convergence results for our Markov chain Monte Carlo (MCMC) algorithm.

2. A STATE-DEPENDENT PARAMETER TRANSMISSION MECHANISM

In this section, we lay out a flexible empirical model that will be used in Section 3 to investigate

asymmetries in the transmission mechanism. In Section 4, we confirm the robustness of the

empirical findings using two popular methods to estimate state-dependent parameters, namely,

Markov-switching and threshold models.

Our approach builds on Koenker and Xiao (2006), who develop asymptotic theory and

inference tools for quantile autoregressive (QAR) models. More specifically, suppose that a

cyclical measure of real activity ctevolves according to the following rule F(·):

ct=F(ct−1,ct+1,it..it−h,π

t+1..πt−h+1,ut)=F(it,dt)=F(Dt),(1)

where idenotes the nominal interest rate, πis inflation, and drefers to leads and lags of con-

sumption and inflation. The unobserved state of the economy, ut, is the source of heterogeneity.

Our aim is to estimate the shape of (1) using QR. Above all, this will not assume that the

relationship between consumption, its leads and lags, and the interest rate is linear. Furthermore,

we will consider the possibility that both the ex ante real rate and future consumption are

endogenous variables. The QR approach treats the measure of real activity as a potential latent