THE PROPAGATION OF UNCERTAINTY SHOCKS: ROTEMBERG VERSUS CALVO

• DOI: http://doi.org/10.1111/iere.12450
• Published date: 01 August 2020
• Date: 01 August 2020
• Author: Joonseok Oh

INTERNATIONAL ECONOMIC REVIEW

Vol. 61, No. 3, August 2020 DOI: 10.1111/iere.12450

THE PROPAGATION OF UNCERTAINTY SHOCKS: ROTEMBERG VERSUS

CALVO∗

BYJOONSEOK OH1

Freie Universit¨

at Berlin, Germany

This article studies the effects of uncertainty shocks on economic activity, focusing on inflation. Using a

vector autoregression, I show that increased uncertainty has negative demand effects, reducing GDP and prices.

I then consider standard New Keynesian models with Rotemberg-type and Calvo-type price rigidities. Despite

the belief that the two schemes are equivalent, I show that they generate different dynamics in response to

uncertainty shocks. In the Rotemberg model, uncertainty shocks decrease output and inflation, in line with the

empirical results. By contrast, in the Calvo model, uncertainty shocks decrease output but raise inflation because

of firms’ precautionary pricing motive.

1. INTRODUCTION

Recently, uncertainty has received substantial attention in the wake of the Great Recession

and the subsequent slow recovery. Many researchers have argued that uncertainty is an impor-

tant factor in determining business cycle fluctuations. In a New Keynesian framework, increased

uncertainty leads to a decrease in aggregate demand because of precautionary saving motives

and time-varying markups. Although the impact of uncertainty on aggregate demand is well

understood, the effects on inflation have not been yet explored in the literature.

In this article, I study how increased uncertainty affects economic activity, concentrating in

particular on inflation. First, I conduct a structural vector autoregression (VAR) analysis on

quarterly U.S. macroeconomic data. I consider eight widely cited U.S. uncertainty measures

from the literature. These eight measures can be categorized into four groups: (i) macroe-

conomic uncertainty, (ii) financial uncertainty, (iii) survey-based uncertainty, and (iv) policy

uncertainty. The VAR analysis shows that an exogenous increase in any of these uncertainty

indices results in significant falls in output and prices. In other words, uncertainty shocks act in

the same way as aggregate demand shocks.

To explain these empirical findings, I compare two standard New Keynesian models with the

most common sticky price assumptions: the Rotemberg (1982)-type quadratic price adjustment

cost and the Calvo (1983)-type constant price adjustment probability. In the Rotemberg model,

a firm can adjust its price whenever it wants after paying a quadratic adjustment cost. On the

∗Manuscript received October 2017; revised December 2019.

1I cannot find enough words to thank my advisors Evi Pappa and Axelle Ferriere for their continuous guidance and

support. I particularly benefit from the detailed comments of the editor Jes´

us Fern´

andez-Villaverde and two anonymous

referees. I am also indebted to ´

Arp´

ad ´

Abrah´

am, Pablo Anaya, Guido Ascari, Christian Bayer, Dario Bonciani, Christine

Braun, Flora Budianto, Jes´

us Bueren, Yongsung Chang, Daeha Cho, Sunghun Cho, Jaedo Choi, Charles Dennery, Juan

Dolado, Denis Gorea, Michael Haliassos, Yujung Hwang, Byeong-hyeon Jeong, ShinHyuck Kang, Kwang Hwan Kim,

Minki Kim, Mira Kim, Sun-Bin Kim, Changsu Ko, Luisa Lambertini, Francesca Loria, Karol Mazur, Johannes Pfeifer,

Christian Pr¨

obsting, Anna Rogantini Picco, Matthias Schmidtblaicher, Yongseok Shin, Chima Simpson-Bell, Hyuk

Son, Mathias Trabandt, and Yu Wu for many insightful discussions. I thank numerous seminar participants for useful

comments. All errors are my own. Please address correspondence to: Joonseok Oh, Chair of Macroeconomics, School

of Business and Economics, Freie Universit¨

at Berlin, Boltzmannstrasse 20, 14195 Berlin, Germany. Phone: +49 30 838

67525. E-mail: joonseok.oh@fu-berlin.de.

1097

C

2020 The Authors. International Economic Review published by Wiley Periodicals LLC on behalf of the Economics

Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research

Association

This is an open access article under the terms of the Creative Commons Attribution License, which permits use,

distribution and reproduction in any medium, provided the original work is properly cited.

1098 OH

other hand, in the Calvo model, each firm may reset its price only with a constant probability

each period, independent of the time elapsed since the last adjustment. Although the two

assumptions have different economic intuitions, the predictions of the New Keynesian model are

robust against the pricing assumption up to a first-order approximation around a zero-inflation

steady state. For this reason, there is a widespread agreement in the literature that the pricing

assumption is innocuous for the dynamics of the standard New Keynesian model. However, by

employing a third-order perturbation, I show that the Rotemberg and Calvo models generate

very different results in response to uncertainty shocks. In particular, I separately consider five

different sources of uncertainty shocks in the models: (i) preference uncertainty, (ii) productivity

uncertainty, (iii) markup uncertainty, (iv) government spending uncertainty, and (v) interest rate

uncertainty. In all cases, increased uncertainty leads to a decrease in inflation in the Rotemberg

model, and to an increase in inflation in the Calvo model, while still resulting in a decrease

in output in both models. This result is important because inflation stabilization is one of the

main goals of monetary policy. For this reason, it is important to understand which propagation

mechanism holds in the data.

Uncertainty shocks have two effects on firms: an aggregate demand effect and a precaution-

ary pricing effect, as pointed out by Fern´

andez-Villaverde et al. (2015). Increased uncertainty

induces risk-averse households to consume less. The fall in aggregate demand lowers the de-

mand for labor and capital, which decreases firms’ marginal costs. In the Rotemberg model,

only the aggregate demand effect is at work for firms. To be specific, since their pricing decision

is symmetric, all firms behave as a single representative firm. Thus, the firms are risk-neutral

concerning their pricing decision: the firms’ marginal profit curve, a function of the reset price,

is constant. Therefore, the decrease in marginal costs induces firms to lower their prices. Con-

sequently, inflation decreases in the Rotemberg model. On the other hand, in the Calvo model,

both the precautionary pricing effect as well as the aggregate demand effect are operative when

an uncertainty shock hits. The Calvo pricing assumption generates heterogeneity in firms’ prices.

This implies that firms are risk-averse regarding their pricing decision: the firms’ marginal profit

curve is strictly convex. Thus, higher uncertainty induces firms that are resetting their prices

to increase them so as to self-insure against being stuck with low prices in the future. If firms

lower their prices, they may sell more but at negative markups, thereby incurring losses. As

a result, inflation increases in the Calvo model. Using a prior predictive analysis, I show that

the predictions of the two models are robust against the exact model parameterization and the

different sources of uncertainty. Therefore, the Rotemberg model is more consistent with the

empirical evidence than the Calvo model.

1.1. Related Literature. This article is related to three main strands of literature. First of

all, this article contributes to the literature that studies the propagation of uncertainty shocks

in New Keynesian models. This is the first article that highlights the different responses to

uncertainty shocks in the Rotemberg and Calvo models. The following papers that assume

the Rotemberg pricing argue that uncertainty shocks reduce output and inflation in the same

way as negative demand shocks: Bonciani and van Roye (2016), Leduc and Liu (2016), Basu

and Bundick (2017), Cesa-Bianchi and Fernandez-Corugedo (2018), and Katayama and Kim

(2018). On the contrary, Born and Pfeifer (2014) and Mumtaz and Theodoridis (2015), which

adopt Calvo pricing, argue that uncertainty shocks result in a decrease in output but an increase

in inflation, that is, negative supply shocks. Exceptionally, Fern´

andez-Villaverde et al. (2015)

study an inflationary effect of uncertainty shocks in a Rotemberg-type New Keynesian model.

However, this result is obtained because, in contrast to the above-mentioned literature, their

price adjustment cost directly affects firms’ marginal costs. Basu and Bundick (2017) attribute

this discrepancy to different sources of shocks and calibrations. However, I show that the

primary reason for the different results found in the literature is the adopted assumption of

price stickiness.

Second, this article organizes the literature that looks at the empirical impact of uncertainty

shocks on inflation. Caggiano et al. (2014), Fern´

andez-Villaverde et al. (2015), Leduc and Liu