EXTREME EVENTS AND OPTIMAL MONETARY POLICY

• Author: Francisco Ruge‐Murcia,Jinill Kim
• DOI: http://doi.org/10.1111/iere.12372
• Date: 01 May 2019
• Published date: 01 May 2019

INTERNATIONAL ECONOMIC REVIEW

Vol. 60, No. 2, May 2019 DOI: 10.1111/iere.12372

EXTREME EVENTS AND OPTIMAL MONETARY POLICY∗

BYJINILL KIM AND FRANCISCO RUGE-MURCIA1

Korea University, Korea; McGill University, Canada

This article studies the implication of extreme shocks for monetary policy. The analysis is based on a small-

scale New Keynesian model with sticky prices and wages where shocks are drawn from asymmetric generalized

extreme value distributions. A nonlinear perturbation solution of the model is estimated by the simulated method

of moments. Under the Ramsey policy, the central bank responds nonlinearly and asymmetrically to shocks.

The trade-off between targeting a gross inflation rate above 1 as insurance against extreme shocks and targeting

an average gross inflation at unity to avoid adjustment costs is unambiguously decided in favor of strict price

stability.

1. INTRODUCTION

Economies are occasionally subjected to extreme shocks that can have profound and long-

lasting effects—think, for example, of the oil shocks in the 1970s or the financial shocks associ-

ated with the Great Recession. Thus, it is important to design policy by taking into account the

fact that extreme events can happen sometimes. This article studies the positive and normative

implications of extreme shocks for monetary policy using a small-scale New Keynesian model

with sticky prices and sticky—and more downwardly rigid—wages (see Kim and Ruge-Murcia,

2009). Crucially, the model relaxes the usual assumption that shocks are normally distributed

and assumes instead that they are drawn from asymmetric distributions with an arbitrarily long

tail. Methodologically, we use tools from extreme value theory, which is a branch of statistics

concerned with extreme deviations from the median of probability distributions. This theory

was developed primarily in meteorology and engineering, where designers are interested in

protecting structures against infrequent—but potentially damaging—events like earthquakes

and hurricanes.2

Previous research on the positive analysis of monetary policy typically works under the dual

assumptions that the propagation mechanism is linear and that shocks are symmetric, usually

normal. In some normative analysis, it is necessary to go beyond a linear approximation of

the model dynamics to avoid spurious welfare implications, and a second-order approximation

is consistent with any two-parameter distribution. Since the normal distribution satisfies this

two-degrees-of-freedom specification, the normal distribution is also widely used in normative

analysis. This strategy leads to tractable models, but, as we argue below, it is unsatisfactory for

understanding policy responses to extreme events.

Instead, the shock innovations in our model are assumed to be drawn from generalized

extreme value (GEV) distributions. This distribution is widely used in extreme value theory to

∗Manuscript received June 2018; revised August 2018.

1This article was previously circulated under the title “Extreme Events and the Fed.” The authors benefitted from

comments by Luigi Boccola, Marcelle Chauvet, the editor (J. Fern´

andez-Villaverde), and two anonymous referees.

Ruge-Murcia acknowledges the support from the Social Sciences and Humanities Research Council (SSHRC), and

from the Bank of Canada through its Fellowship Program. Kim’s work was supported by a grant from Korea Uni-

versity (K1808651). Please address correspondence to: Francisco Ruge-Murcia, Department of Economics, McGill

University, 855 Sherbrooke Street West, Montreal, Quebec H3A 2T7, Canada (CA). Phone: +1 (514) 398 6063. E-mail:

francisco.ruge-murcia@mcgill.ca.

2Key contributions in extreme value theory are Fisher and Tippett (1928), Gnedenko (1943), and Jenkinson (1955).

For a review of applications in engineering, meteorology, and insurance, see Coles (2001) and Embrechts et al. (2011).

939

C

(2018) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

940 KIM AND RUGE-MURCIA

model the maxima (or minima) of a sequence of random variables.3The distribution has three

independent parameters that determine its first, second, and third moments. To be consistent

with considering three moments of the distribution, we approximate the model dynamics using a

third-order perturbation, and so our approximate solution is nonlinear. The nonlinear model is

estimated by the simulated method of moments (SMM). To disentangle the relative contribution

of asymmetric shocks and nonlinearity to our results, we also estimate a nonlinear version of

the model with normal innovations. Results show that the data prefer a specification where

monetary policy innovations are drawn from a positively skewed distribution, and productivity

and preference innovations are drawn from negatively skewed distributions. This conclusion is

based on structural estimates from the model and also supported by reduced-form estimates

from the raw data.

Using the estimated parameters, we examine the normative implications of the model under

the Ramsey policy. We find that the benevolent monetary authority responds asymmetrically

to shocks, and the change in the nominal interest rate is generally larger than that under

the Taylor policy. In addition to investigating the optimal monetary policy response to large

shocks, this article derives specific policy prescriptions concerning optimal inflation targets.

This issue is important because, in light of the recent Global Financial Crisis, Williams (2009,

2014), Blanchard et al. (2010), and Ball (2014) propose increasing inflation targets in order to

provide a larger buffer zone from the zero lower bound (ZLB) on interest rates. In one of the

few contributions to the literature on optimal policy in an environment with extreme shocks,

Svensson (2003) notes the tension between (i) acting prudently and incorporating systematically

the possibility of extreme shocks into policy (e.g., by raising the inflation target) and (ii) taking

a wait-and-see approach. Under the wait-and-see approach, the monetary authority acts only if

and when an extreme shock occurs and adjusts the policy variables appropriately to counteract

its effects. Our model incorporates such a trade-off and uses quantitative analysis to compare

these two strategies using a well-defined welfare metric. We show that the solution to the trade-

off is solved unambiguously in favor of the wait-and-see approach. The reason is simply that,

although prudence calls for an optimal gross inflation target above 1 as an insurance against

extreme shocks that would require costly nominal wage cuts, such a target involves price-and-

wage adjustment costs that must paid in every period. Thus, under the Ramsey policy the

optimal gross inflation rate is virtually indifferent from 1 (i.e., strict price stability).

The New Keynesian model used to study extreme shocks is based on our previous work (Kim

and Ruge-Murcia, 2009). We use this model for two reasons. First, this model is highly nonlinear

because of the asymmetry in wage adjustment costs. Nonlinearity is a key ingredient in evalu-

ating the economic implications of extreme shocks because it can give rise to prudent behavior.

Second, this model has a well-defined cost of deflation in the form of very costly nominal wage

cuts.4However, this project makes a distinct contribution from Kim and Ruge-Murcia (2009).

Our previous contribution attempts to evaluate Tobin’s argument that inflation “greases the

wheels” of the labor market. That is, that inflation eases the adjustment of the labor market

after an adverse shock by speeding the decline of real wages. Instead, this article examines the

recent argument that in anticipation of extreme shocks, the monetary authority should increase

inflation targets (see the literature cited above). By relaxing the usual assumption that shocks

are normally distributed and using a third-order perturbation method to solve the model, we

3In the context of financial markets, this distribution could be motivated, for example, by Stein (2014), who argues that

the most optimistic investors drive asset prices, and by Adrian and Duarte (2017), who model financial intermediaries

subject to occasionally binding value-at-risk constraints. More generally, since many economic shocks—strikes, weather,

political uncertainty, changes in commodity prices, etc.—feature long tails, the most constructive interpretation is to

think of the GEV distribution as a way to capture a wide array of potentially large disturbances that are summarized

here using a parsimonious number of structural shocks.

4As an alternative, one could consider the costs associated with the ZLB on nominal interest rates. We do not pursue

this strategy here, but refer the reader to the extensive literature on this topic (see, e.g., Coibion et al., 2012, and the

references therein).