Consumer Search, Incomplete Exchange Rate Pass‐Through, and Optimal Interest Rate Policy

• Published date: 01 March 2019
• Author: DUDLEY COOKE
• Date: 01 March 2019
• DOI: http://doi.org/10.1111/jmcb.12518

DOI: 10.1111/jmcb.12518

DUDLEY COOKE

Consumer Search, Incomplete Exchange Rate

Pass-Through, and Optimal Interest Rate Policy

This paper studies utility-maximizing monetary policy in a two-country

economy with consumer search frictions. Search frictions provide a mi-

crofoundation for incomplete exchange rate pass-through and international

deviations from the law of one price (LOP). I show that optimal interest

rate policy targets deviations from the LOP and acts to mitigate the effect

of search frictions. In a quantitative setting, with internationally correlated

technology and preference shocks, optimal policy generates positive cross-

country correlation of nominal interest rates.

JEL codes: E31, E52, F41

Keywords: consumer search, exchange rate pass-through, interest rate

policy.

EXCHANGE RATE PASS-THROUGH TO IMPORT prices is a key factor

in the design of monetary policy in open economies. Research concerned with the

policy implications of incomplete exchange rate pass-through has focused primarily

on frictions associated with infrequent price adjustment.1This paper studies utility-

maximizing monetary policy in an open economy, where prices are flexible, but

exchange rate pass-through is incomplete due to consumer search frictions.2Search

frictions provide a microfoundation for incomplete exchange rate pass-through and

I thank two anonymous referees and the Editor (Kenneth West) for comments and suggestions that

helped improve the paper. I also thank Tatiana Damjanovic, Engin Kara, and Christian Siegel for discus-

sions. A previous version of this paper was presented at the University of Nottingham.

DUDLEY COOKE is Senior Lecturer at Department of Economics, University of Exeter (E-mail:

d.cooke@exeter.ac.uk).

Received October 7, 2016; and accepted in revised form April 4, 2018.

1. Monacelli (2005) shows that incomplete exchange rate pass-through can introduce a trade-off

between stabilizing producer price inflation and either the output gap or deviations from the LOP.Engel

(2011) shows that incomplete pass-through generates a trade-offamong inflation, output gap, and currency

misalignment objectives, the latter of which is a weighted average of deviations from the LOP across

countries. A further discussion of these points is contained in Section 3.6.

2. I focus on Ramsey-optimal monetary policy. A Ramsey-optimal policy is one which maximizes

the lifetime utility of the representative agent, subject to the equilibrium conditions of the economy. An

extensivediscussion of Ramsey-optimal monetary policy is contained in Schmitt-Grohe and Uribe (2010).

Journal of Money, Credit and Banking, Vol.51, Nos. 2–3 (March–April 2019)

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2018 The Ohio State University

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international deviations from the law of one price (LOP). The main result of the paper

is that monetary policy should target deviations from the LOP and mitigate the effect

of search frictions.

Tounderstand the role of consumer search frictions for monetary policy, consider a

standard, two-country (home and foreign), two-good economy, with country-specific

real shocks to technology or preferences, and a cash-in-advance restriction on house-

hold transactions.3Suppose the home country receives a positive shock that causes

its terms of trade—the relative price of home’s output—to deteriorate. As home con-

sumption and labor supply rise, the optimal policy response is to raise the nominal

interest rate. This policy lowers (raises) labor supply in the home (foreign) country,

while allowing both countries to benefit from an increase in consumption. In this

example, interest rate policy is driven by international risk sharing and the efficient

use of resources (specifically, labor) across countries.

When there are consumer search frictions, movements in the real wage affect the

opportunity cost of search, and this leads to an endogenous price markup. Because

the opportunity cost of search may differ across countries, so can markups. Consumer

search frictions therefore result in international deviations from the LOP. Deviations

from the LOP mean that country-specific real shocks generate smaller movements in

the terms of trade than when product markets are frictionless. There is also a reduced

incentive to share risk internationally because consumption implicitly accounts for

local-market (nontraded) search activity.

I start by providing analytical solutions for optimal interest rate policy when

international deviations from the LOP and the price markup for the domestic good

are the only relevant policy targets. I showthat, for a given markup, the home interest

rate should fall when the export price of the home good rises relative to the domestic

price; that is, the optimal interest rate depends negatively on the deviation from the

LOP. Interest rates do not account directly for search activities over imported goods.

Thus, while monetary policy acts to stabilize deviations from the LOP by raising the

opportunity cost of search in the domestic market, the policymaker is forced to trade

off one inefficiency—the deviation from the LOP—for another—the domestic price

markup.

I also find that the optimal response of the interest rate is stronger—that is, monetary

policy is more aggressive—when exchange rate pass-through is low. This is reflected

in the finding that, for a given policy in each country, the lower is the degree of

exchange rate pass-through, the greater is the movement in the deviation from the

LOP, and the greater (smaller) is the change in relative home consumption (output).

Optimal policy acts to bring movements in the terms of trade closer to that which

would occur with full pass-through. However, due to the trade-off generated by

deviations from the LOP and the domestic price markup, optimal policy does not

replicate the outcome with frictionless product markets.

3. I consider economies with complete international asset markets and no physical capital. See Heath-

cote and Perri (2002) on the transmission of real shocks with physical capital and the role of international

financial markets.