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Ination and Exchange Rate Pass-Through: a

Quantitative Assessment of Theoretical and

Empirical Models1

Giancarlo Corsettia

European University Institute, University of Rome III and CEPR

Luca Dedolab

European Central Bank

Sylvain Leducc

Federal Reserve Board

April 2005

PRELIMINARY AND INCOMPLETE

1We thank Jon Faust, Linda Goldberg, and seminar participants at the Bank of Portugal, the 2004

Society for Economic Dynamics meetings and the workshop \The Importance of the External Dimension

for the Euro Area: Trade, Capital Flows, and International Macroeconomic Linkages," hosted by the

European Central Bank. Giancarlo Corsetti work on this paper is part of the Pierre Werner Chair in

Monetary Union at the Robert Schuman Center for Advanced Studies of the EUI. The views expressed

here are those of the authors and do not necessarily reect the positions of the ECB, the Board of Gov-

f th F d l R S t th i tit ti ith hi h th th li t d


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Abstract

This paper develops a quantitative open-economy model to investigate the contributions of price

discrimination and nominal rigidities to the observed low degree of exchange-rate pass-through

and local currency price stability. In our framework, price discrimination results from the

presence of distribution services which makes the elasticity of demand dier across markets. As

a result, our model predicts a long-run exchange-rate pass-through coecient of 85% and 43%

on import prices at the border and at the retail level, respectively. Over short horizons, a small

amount of nominal rigidities lower these values to 14% and 7%. After documenting the business

cycle properties of exchange rates and prices in the theoretical economies, we compare the

performance of two pass-through regression models alternatively used in the empirical literature

with the structural features of the dierent articial economies. Using simulated time series,

we show that these empirical models, despite suering from measurement errors and omitted

variables bias, perform surprisingly well, especially in economies characterized by a high nominal

exchange rate volatility.


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1 Introduction

The slow and incomplete pass-through of exchange rate movements into import prices anddomestic ination is a dening feature of the international economy. Between 2002 and 2004,

for instance, the dollar depreciated 15% on a trade-weighted basis, both in real and in nominal

terms, and 26% against the major currencies. Yet, over the same period, the import price of

non-petroleum goods has risen only by 5%; core consumer prices rose by 4.7%.

The literature has identied several stylized facts on prices and exchange rates. First, the

elasticity of consumer prices to exchange-rate movements is quite low, even in the case of very

large nominal devaluations. For instance, Burstein, Eichenbaum and Rebelo [2005] document

that in the aftermath of currency crises in East Asia and Latin America the increase in the CPI

has generally been 10 times smaller than that in the nominal exchange rate. Second, exchange

rate pass-through into import prices is higher than the consumer price elasticity, but clearly far

from complete. Based on a sample of 76 developing and industrialized countries, Frankel, Parsley

and Wei [2004] nd that, over a one year horizon, import prices in the local currency reect on

average around 60% of exchange rate uctuations | three times as much as the consumer price

index, which only reects 20% of exchange rate movements. Third, the degree of pass-through

varies over dierent time horizons: it is typically quite low in the short run, but rises with time

|without necessarily becoming complete in the long run. For instance, using dierent methods,

Campa and Goldberg [2002] conclude that across OECD countries the average exchange rate

pass-through into import prices is 46% in the short run, and 64% over the long run. Finally, the

degree of pass-through (to both the CPI and import prices) seems to have fallen since the early

1990s, a point discussed by Taylor [2000] and Frankel, Parsley and Wei [2004] among others.

Against the wealth of empirical evidence documenting these facts, the economic mechanismsunderlying incomplete pass-though are subject to a far-reaching debate (see the survey in Gold-

berg and Knetter [1997]). Traditional explanations stress the role of nominal price rigidities.

Recently, however, this view has been challenged on both theoretical and empirical ground. In

the words of Charles Engel (2005 p 3) \nding that prices do not respond much to exchange


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adjustment by rms.

Understanding the relative importance of dierent factors causing a low pass-through is

crucial both for model building and policy analysis. A core implication of low pass-through is

that high exchange-rate volatility will systematically drive apart cross-borders prices of otherwise

identical goods | i.e. there will be deviations from the law of one price. In the absence of

nominal rigidities, such deviations would correspond to optimal pricing strategies by rms. In

the presence of nominal rigidities, instead, they would correspond to suboptimal uctuations of

rms' prots. Hence, nominal exchange rates may not play the stabilizing role attributed to

them by the received wisdom, either as a substitute for relative price adjustment in the presence

of nominal rigidities, or as automatic mechanisms of risk insurance when markets are incomplete.

Building on international business cycle models with traded and non traded goods (e.g.

Stockman and Tesar [1995]), this paper develops a framework to assess analytically and quan-

titatively the contribution of price discrimination and nominal rigidities to the low degree ofexchange-rate pass-through into consumer and producer prices observed in the data. First, as

in Corsetti and Dedola [2003], we specify a model in which distribution services intensive in

local inputs induce dierences in demand elasticities across countries. Thus, even in the absence

of nominal rigidities, the law of one price would not hold in general, as rms optimally charge

dierent prices in the domestic and foreign markets, and do not move prices one-to-one with ex-

change rate movements | the degree of pass-through depending on the type and persistence of

the shocks hitting the economy. Moreover, due to distribution, import prices at retail level will

not move in proportion import prices at the border. Second, we assume that foreign exporters

face frictions in adjusting prices in local currencies. Hence, we complement endogenous price

discrimination by rms with nominal rigidities.

We study four economies: one with exible prices, two with exible wages but dierent

price adjustment costs, and one with nominal wage rigidities. For these economies, we will

rst discuss their ability to capture the main features of exchange rates and relative prices

movements in the international business cycle. As shown in Corsetti, Dedola, and Leduc [2003],


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contribute signicantly to changes in real exchange rates; the nominal exchange rate is strongly

and positively correlated with the terms of trade, while the price of imports but only very weakly

with the consumer price level. Obstfeld and Rogo [2000] have argued that quantitative models

of the link between exchange rates and prices should be consistent with the above stylized facts.

To analyze dierent theories of incomplete pass-though in detail, we rst use our model to

derive an exact (linearized) equation for import prices in the exchange rate, marginal costs in

local currency, distribution costs and leads and lags in import prices driven by optimal forward-

looking price-setting. This equation allows us to account for the nominal and real determinants

of pass-through in the short and the long run | consistent with the results from the empirical

literature that, typically, pass-through is initially low and rises over time. In a structural sense,

our model predicts a long-run exchange rate pass-through coecient on import prices as high

as 0.85, corresponding to markup adjustments by rms that price-discriminate across national

borders. In the short run, assuming that prices are kept xed for 4.3 months, in line with theevidence in Bils and Klenow [2004], lowers this value to 0.14 | while nominal wage rigidities have

virtually no eect on it. At the consumer-price level of imported goods, our model generates

exchange-rate pass-though coecients that are half as large as those for import prices, and

even much lower for the aggregate CPI. Notice that, consistent with Giovannini [1988], Marston

[1990], and Campa and Goldberg [2002], we nd that imperfect exchange-rate pass-through lasts

longer than the period in which prices are sticky. Overall, we view these ndings as being in

line with the empirical evidence.

In light of our analytical dissection of the determinants of imperfect pass-through, our model

provides a unique tool assess the performance of regression models commonly used in the em-

pirical literature on pass-through. As is well known, because of data limitations, it is virtually

impossible to build empirical regression models that are free from omitted variable bias and/or

measurement errors. Using the time series simulated from our models, we run two typical re-

gressions | that we dub Pricing to Market (PTM) and Exchange Rate Pass-through (ERPT)

| and assess our results against the structural properties of our economies. Both regression


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ulated time series. Both specications are able to distinguish between short-run and long-run

pass-through when the two structural coecients are dierent and correctly set their estimates

equal when they are the same. While the PTM specication does very well in recovering the cor-

rect value of the long run structural coecient, regardless of the presence of nominal rigidities,

the ERPT specication displays a downward bias in its long-run estimates as large as 300 per-

cent, when the degree of price stickiness is large. Given that in this case the nominal exchange

rate predicted by our model is not as (relatively) volatile as in the data, our experiment suggests

that the measurement error in the proxies for unobservables included in this specication, i.e.

Foreign nominal wages for marginal costs, is too large to be oset by the variability in the other

regressors of interest, notably the exchange rate.

It is worth stressing that, for the benchmark economy with a limited degree of LCP, the

estimated coecient are quite close to those found in the empirical literature; for instance

Campa and Goldberg [2002] nd that on average across OECD countries, exchange rate pass-through into import prices is 46% in the short run and 64% over the long run. To the extent

that empirical estimates are reliable, our results suggest that only a limited amount of nominal

rigidities (consistent with the evidence in Bils and Klenow [2004]) is required for the theoretical

economy to be consistent with this dimension of the data.

The paper is structured as follows. Section 2 will describe the model and the calibration

will be discussed in Section 3. We discuss the predictions of our model regarding the degree of

exchange-rate pass-through in Section 4. We then assess the performance of our framework and

that of empirical models of pass-through. The last section concludes.

2 The model

In this section, we develop our model. In the next section, we will employ standard numerical

techniques to solve it, with the specic goal of quantifying the degree of exchange-rate pass-

through in our economy when it is hit by monetary and productivity shocks.

Th ld i f i f l i H d F E h


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dierentiated nontradables, indexed by n 2 [0; 1]. Nontraded goods are either consumed or used

to make intermediate tradable goods h and f available to domestic consumers.

Firms producing tradable and nontraded goods are monopolistic suppliers of one brand of

goods only. These rms combine capital with dierentiated domestic labor inputs in a contin-

uum of unit mass. Each worker occupies a point in this continuum, and acts as a monopolistic

supplier of a dierentiated type of labor input to all rms in the domestic economy. House-

holds/workers are indexed by j 2 [0; 1] in the Home country and j 2 [0; 1] in the Foreign

country. Firms operating in the distribution sector, by contrast, are assumed to operate un-

der perfect competition.1 They buy tradable goods and distribute them to consumers using

nontraded goods as the only input in production.

In our baseline model, prices and wages will be assumed to be perfectly exible. In alternative

specications, we will introduce nominal price and wage rigidities, by assuming that workers and

rms face a quadratic cost of adjusting the nominal wage and the goods' prices, respectively.

2

In what follows, we describe our set up focusing on the Home country, with the understanding

that similar expressions also characterize the Foreign economy | whereas variables referred to

Foreign rms and households are marked with an asterisk.

2.1 The Household's Problem

2.1.1 Preferences

The representative Home agent in the model maximizes the expected value of her lifetime utility,

given by:

E

(1

Xt=0U

Ct;

Mt+1Pt

; Ltexp

"t1

X=0

U

Ct;

Mt+1Pt

; Lt#)

; (1)

where instantaneous utility U is a function of a consumption index, Ct; leisure, (1 Lt); and

real money balances Mt+1Pt

. This recursive specication of preferences, according to which the

discount factor is a function of past utility levels, guarantees the existence of a unique invari-


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ant distribution of wealth, independent of initial conditions.3 We assume that households are

monopolistically competitive and supply a dierentiated labor service to rms.

Households consume all types of (domestically-produced) nontraded goods, and both types

of traded goods. So Ct(n; j) is consumption of brand n of Home nontraded good by agent j at

time t; Ct(h; j) and Ct(f; j) are the same agent's consumption of Home brand h and Foreign

brand f. For each type of good, we assume that one brand is an imperfect substitute for all

other brands, with constant elasticity of substitution H and N > 1. Consumption of Home

and Foreign goods by Home agent j is dened as:

CH;t(j)

Z10

Ct(h; j)H1

H dh

HH1

, CF;t(j)

Z10

Ct(f; j)H1

H df

HH1

;

CN;t(j)

Z10

Ct(n; j)N1

N dn

NN1

:

The full consumption basket, Ct, in each country is dened by the following CES aggregator

Ct h

a1T CT;t + a1N CN;t

i 1

; < 1, (2)

where aT and aN are the weights on the consumption of traded and nontraded goods, respectively

and1

1 is the constant elasticity of substitution between CN;t and CT;t. The consumption

index of traded goods CT;t is given by the following CES aggregator

C = CT =h

a1H CH + a

1F C

F

i 1

; < 1: (3)

2.1.2 Budget constraints and asset markets

Home and Foreign agents hold an international bond, BH, which pays in units of Home currency

and is zero in net supply. Only domestic residents hold the Home currency,Mt. Households derive

income from working, WtLt; from renting capital to rms, RtKt, from previously accumulated

units of currency, and from the proceeds from holding the international bond, (1 + it)BH;t;

where it is the nominal bond's yield, paid at the beginning of period t in domestic currency but

known at time t 1 They pay non distortionary (lump sum) net taxes T denominated in Home


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to consume and invest. The individual ow budget constraint for the representative agent j in

the Home country is therefore:4

Mt(j) + BH;t+1(j) Mt1(j) + (1 + it)BH;t(j) + RtKt (j) (4)

+

Z10

(h; j)dh +

Z10

(n; j)dn +

Wt(j)Lt(j) Tt(j) PH;tCH;t(j) PF;tCF;t(j) PN;tCN;t(j) PH;tIt (j) PtACWt (j)

where Et is the nominal exchange rate, expressed as Home currency per unit of Foreign currency

andR

(h; j)dh+R

(n; j)dn is the agent's share of prots from all rms h and n in the economy.

The price indexes as as follows: PH;t and PH;t denote the price of the Home traded good at

the producer and consumer level, respectively, PF;t is the consumer price of Home imports; PN;t

is the price of nontraded goods; Pt is the consumer price index. Following Kim [2000], the

wage-adjustment cost is given by the following quadratic function:5

ACWt (j) =w

2

Wt(j)

Wt1(j)

2 WtPt

:

We assume that investment is carried out in Home tradable goods and that the capital stock,

K, can be freely reallocated between the traded (KH) and nontraded (KN) sectors:

K = KH

+ KN

:

Moreover, contrary to the consumption of tradables, we assume that investment is not subject

to distribution services. The price of investment is therefore the wholesale price of the domestic

traded good, PH;t: The law of motion for the aggregate capital stock is given by:

Kt+1 = It + (1 )Kt (5)

The household's problem then consists of maximizing lifetime utility, dened by (1), subject

to the constraints (4) and (5).


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2.2 Firms' optimization and optimal price discrimination

International price discrimination is a key feature of the international economy captured by

our model. In what follows we show that, even if Home and Foreign consumers have identical

constant-elasticity preferences for consumption, the need for distribution services intensive in

local nontraded goods implies that the elasticity of demand for the h (f) brand at wholesale

level be not generally the same across markets. Firms will thus want to charge dierent prices at

Home and in the Foreign country. We will focus our analysis on Home rms | optimal pricing

by Foreign rms can be easily derived from it.

Firms producing Home tradables (H) and Home nontradables (N) are monopolist in their

variety of good; they employ a technology that combines domestic labor and capital inputs,

according to the following Cobb-Douglas functions:

Y (h) = ZK(h)1 L (h)

Y (n) = ZK(n)1L (n) ;

where Z is an economy-wide random disturbance following a statistical process to be determined

below. We assume that capital and labor are freely mobile across sectors.

Let L(h; j) denote the demand for labor input of type j by the producer of good h. By the

same token, L(n; j) denotes the corresponding demand for labor input j. Aggregate labor input

in the production of the Home traded and nontraded goods are, respectively:

Lt(h) =

Z10

Lt(h; j)L1

L dj

LL1

; Lt(n) =

Z10

Lt(n; j)L1

L dj

LL1

; (6)

where L is the elasticity of substitution among labor inputs, which is the same across sectors.

Our specication of the distribution sector is in the spirit of the factual remark by Tirole

([1995], page 175) that \production and retailing are complements, and consumers often consume

them in xed proportions". As in Erceg and Levin [1995] and Burstein, Neves and Rebelo [2001],

we thus assume that bringing one unit of traded goods to consumers requires units of a basket

of dierentiated nontraded goods


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goods required to distribute tradable goods to consumers will have the same composition as the

basket of nontradable goods consumed by the representative domestic household.6

With exible prices, the problem of these rms is standard: they hire labor and capital from

households to maximize their prots:

t (h) = pt (h) Dt (h) WtLt (h) RtKt (h)

t (n) = pt (n) Dt (n) WtLt (n) RtKt (n)

where pt (h) is thewholesale

price of the Home traded good and pt (n) is the price of thenontraded good. Wt denote the aggregate wage rate, while Rt represents the capital rental rate.

Consider rst the optimal pricing problem faced by rms producing nontradables for the

Home market. The demand for their product is

D(n) + (n) = [pt(n)]N PNN;t

DN;t +

Z10

Dt(h)dh +

Z10

Dt(f)df

; (8)

where DN;t is the (consumer) aggregate demand for non-traded goods. It is easy to see that

their optimal price will result from charging a constant markup over marginal costs:

pt(n) = PN;t =N

N 1M CN;t

= PN;t =N

N 1

Wt R1t

ZN,t(9)

Note that nominal wage rigidities do not translate into price rigidities: the price of the nontraded

good pt(n) in fact moves inversely with productivity in the sector.

Now, let pt(h) denote the price of brand h expressed in the Home currency, at producer level.

With a competitive distribution sector, the consumer price of good h is simply

pt(h) = pt(h) + PN;t: (10)

In the case of rms producing tradables, \pricing to market" derives endogenously from the

solution to the problem of the Home representative rm in the sector:

M axp(h);p(h) [pt(h)Dt(h) + Etp

t (h)D

t (h)] Wt R

1t

ZH;t[Dt(h) + D

t (h)] (11)


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where

Dt(h) = PH;t

pt(h) + PN;t!H

DH;t; D

t (h) = PH;t

p

t (h) + P

N;t!H

DH;t: (12)

Making use of (9), the optimal wholesale prices p(h) and p(h) are:

pt(h) =H

H 1

1 +

H

NN 1

ZH;tZN;t

Wt R1t

Wt R1t

!Wt R

1t

ZH;t; (13)

Etp(h) =

H

H

1

1 +

H

N

N

1

ZH;tZ

N;t

EtWt R

1t

Wt

R1t

!Wt R

1t

ZH;t; (14)

where Et is the nominal exchange rate, expressed in units of home currency units. Unlike the

case of nontraded goods (9), in this case the markups charged by the Home rms include a

state-contingent component | in brackets in the above expression | that varies as a function

of productivity shocks, monetary innovations (aecting the exchange rate) and relative wages.

Let mkH;t and mkH;t denote the state contingent component of markups:

mkH;t = 1 +

H

NN 1

ZH;tZN;t

Wt R1t

Wt R1t

; (15)

mkH;t = 1 +

H

NN 1

ZH;tZN;t

EtWt R

1t

Wt R1t

: (16)

Since in general mkH;t will not equal mkH;t, even when

H = H, the optimal wholesale price

of tradable goods will not obey the law of one price (pt(h) 6= Etp

t (h)). This result reects the

dierence in the elasticity of demand faced by the upstream monopolist at Home and abroad

brought about by any asymmetry in relative productivity and/or factor prices.

Sticky Prices To study the impact of local currency pricing on the degree of exchange-rate

pass-through, in alternative specications of our benchmark model we allow for the possibility

that goods prices are sticky. Following Rotemberg [1982] and Dedola and Leduc [2001], rms in

the traded and non-traded goods sectors are assumed to face a quadratic cost when adjusting

their prices (costs which are set equal to zero in steady state). Firms do not face price-adjustment

costs in steady state. Firms pay this adjustment cost by purchasing a CES aggregated basket


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and

ACpt (n) =pN2

pt(n)

pt1(n)

2

DN;t:

Since rms producing traded goods can price dierently according to the destination market,

they incur a cost when they change prices in either the Home or the Foreign market. Note that,

rather innocuously, we assume that both ACpH;t (h) and ACpH;t (h) are denominated in units of

domestic traded goods.

2.2.1 Price indexes

A notable feature of our specication is that, because of distribution costs, there is a wedge

between the producer price and the consumer price of each good. With competitive rms in the

distribution sector, the consumer price of the Home traded good PH;t is simply the sum of the

price of Home traded goods at producer level PH;t and the value of the nontraded goods that

are necessary to distribute it to consumers

PH;t = PH;t + PN;t: (17)

We hereafter write the price index of tradables and the utility-based CPIs:

PT;t = haHPH;t

1 + aFPF;t

1

i1

Pt =

aTPT;t

1 + aNPN;t

1

1

:

Foreign prices, denoted with an asterisk and expressed in the same currency as Home prices, are

similarly dened. Observe that the law of one price holds at the wholesale level but not at the

consumer level, so that PH;t = P

H;t but PH;t 6= P

H;t.

3 Calibration

Table 1 reports our benchmark calibration, which we assume symmetric across countries. Several


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Productivity shocks Let the vector Z fZ; Zg represent the economy-wide technology

shocks in the domestic and foreign economies. We assume that disturbances to technology

follow a trend-stationary AR(1) process

Z0

= Z + u; (18)

whereas u (u; u) has variance-covariance matrix V(u); and is a 2x2 matrix of coecients

describing the autocorrelation properties of the shocks. Since we assume a symmetric eco-

nomic structure across countries, we also impose symmetry on the autocorrelation and variance-

covariance matrices of the above process. Following Backus, Kehoe, and Kydland [1992], we set

the autocorrelation and cross-correlation of shocks to be equal to 0.906 and 0.088, respectively.

The standard deviation of the innovations is set to 0.00852 and their correlation to 0.252 (see

bottom panel of Table 1).

Monetary policy In the benchmark economy, monetary policy is set according to an interest-

rate feedback rule. Our baseline interest-rate rule is similar to that estimated by Clarida, Gal

and Gertler [2000] and used in a similar setting by Chari, Kehoe and McGrattan [2002]:

it = it1 + (1 )(t

e) + (1 )y(Yt

eY) + "i;t; (1)

where e and eY are steady-state levels of ination and output. Following Chari, Kehoe andMcGrattan [2002], we set to 0:79, to 2:15, and y to 0:93=4. The innovation, "i, is

assumed to be independently normally distributed with a standard deviation of 0.2 percent.

Preferences and production Consider rst the preference parameters. Assuming a utility

function of the form:

U

Ct;

Mt+1Pt

; `t

=

C1t1

+

Mt+1Pt

11

+ (1 `t)

1

1 ; > 0; (19)

we set so that in steady state, one third of the time endowment is spent working; (risk


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depends on the average per capita level of consumption, Ct, real money balances,Mt+1Pt

, and

hours worked, `t, and has the following form:

U

Ct;

Mt+1Pt

; `t

=

8>: ln

1 + h

Ct + Mt+1Pt

+ (1 `t)i

6= 1

ln

1 + h

ln Ct + lnMt+1Pt

+ ln(1 `t)i

= 1;

whereas is chosen such that the steady-state real interest rate is 1 percent per quarter, i.e.

equal to 0.006. This parameter also pins down the speed of convergence to the nonstochastic

steady state.

The value of is selected based on the available estimates for the elasticity of substitution

between traded and nontraded goods. We use the estimate by Mendoza [1991] referred to a

sample of industrialized countries and set that elasticity equal to 0.74.

According to the evidence for the U.S. economy in Burstein, Neves and Rebelo [2003], the

share of the retail price of traded goods accounted for by local distribution services ranges be-

tween 40 percent and 50 percent, depending on the industrial sector. We follow their calibration

and set it equal to 50 percent.

As regards the weights of domestic and foreign tradables in the tradables consumption basket

(Ct), ah and af (normalized ah+af = 1) are chosen such that imports are 15 percent of aggregate

output in steady state, which corresponds to the same ratio for the U.S. in the recent period.

The weights of traded and nontraded goods, at and an, are chosen as to match the share of

nontradables (i.e. services) in the U.S. consumption basket, which is around 50 percent when

energy goods are excluded.

Due to lack of better evidence, we calibrate and ; the labor shares in the production

of tradables and nontradables, based on the work of Stockman and Tesar [1995]. They calcu-

late these shares to be equal to 61 percent and 56 percent, respectively. Finally, we set thedepreciation rate of capital equal to 10 percent annually.

A key role in our model is played by the markup in the tradable sector. Note, however,

that in the presence of distribution costs, the sectoral markups will not be equal in steady state


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where M Cn and M Ch are the marginal costs in the non-traded and traded-goods sector, respec-

tively. We set the gross steady-state markup for domestic goods to 1.15. This implies that n

(and n) is equal to 7.7. We then parametrize the elasticity of substitution between domestic

traded goods, h and

f, so that the steady-state markup is identical across sectors, for the given

calibrated value of the distribution margin. Finally, we assume that the gross markup for im-

ported goods is 1.35, higher than that for domestic tradable goods, and accordingly parameterize

f and

h:

In our specication with nominal price rigidity, we calibrate the price-adjustment cost pa-rameters, h and n, by noting that a typical Calvo price-setting model implies a stochastic

dierence equation for ination of the form t = Ett+1 + mct; where mct is the rm's real

marginal cost of production, and = (1q)(1q)

q ; with q being the constant probability that

a rm must keep its price unchanged in any given period and the discount factor (see Gal

and Gertler [1999]). The quadratic adjustment-cost model gives a similar dierence equation

for ination, but with = J1pJ2

; J=H,N. In line with the evidence reported by Bils and Klenow

[2004] for the U.S., showing that the average duration between price changes is 4.3 months, we

set the values of pH; pH ; and

pN equal to 8.6, 3.7, and 4.0, respectively. These values imply

that the reduced form coecient multiplying real marginal costs is the same across all goods.

Moreover, we also simulate our model assuming that prices are set for four quarters, since this

is the value often used in the sticky-price literature.7

The elasticity of substitution between the dierent labor inputs, l; is set to 4.3. Following

the same reasoning as before, assuming that wage contract are xed for four quarters on average,

as in Chari, Kehoe and McGrattan [2002], translates into a value for the wage-adjustment cost

parameter of 65.8.

The elasticity of substitution between Home and Foreign tradables The quantitative

literature has proposed a variety of values for the elasticity of substitution between traded goods.

For instance, Backus, Kydland, and Kehoe [1995] set it equal to 1.5, whereas Heathcote and


17/33

partners) relative to that of U.S. GDP, equal to 2.24 (see Table 2).8 In our benchmark economy,

we nd that ! is around 0.9, which (accounting for distribution costs) implies a steady state

price elasticity of import of 0.51.9

4 Business cycle properties of exchange rates and prices

We report on the H-P{ltered statistics for the data, the exible price economy, and some

variations on that economy in Table 2. The statistics for the data are all computed with the

United States as the home country and the rest of the world as the foreign country. Thus, all

the numbers that refer to import and export prices, the CPI and so on are from U.S. data, while

the nominal (real) exchange rate, for example, refers to the trade-weighted exchange rate for

the United States (deated with CPIs) relative to its trading partners, based on data reported

by the OECD. In the statistics for exchange rates, the standard deviations are normalized by

the standard deviation of U.S. output. Throughout our exercises, we take a rst-order Taylor

series expansion around the deterministic steady state and solve our model economy using King

and Watson [1998]'s algorithm. We compute the model's statistics by logging and ltering the

model's articial time series using the Hodrick and Prescott lter and averaging moments across

100 simulations. Table 2 reports the results from several versions of our model: a benchmark

exible-price economy, and three economies with nominal rigidities: a) two with dierent degrees

of local currency price stickiness (LCP), b) one with both LCP and nominal wage rigidities.

The main feature of our models is their ability to account for the correlation between inter-

national prices and quantities, as well as their relative volatilities, that we observe in the data.

Namely, when we calibrate each specic version of the model as to match the volatility of the

real exchange rate, it can account for the negative Backus-Smith correlation between relative

8There is considerable uncertainty regarding the true value of trade elasticities, directly related to this para-

meter. For instance, Taylor [1993] estimates the value for the U.S. to be 0.39, while Whalley [1985], in the study

quoted by Backus et al. [1995], reports a value of 1.5. For European countries most empirical studies suggest a

value below 1. For instance, Anderton et al. (2004) report values between 0.5 and 0.81 for the Euro area.9


18/33

consumption and the real exchange rate, of the order of -0.8. The analysis of the economy with

exible prices is fully developed in Corsetti Dedola and Leduc [2003]. Relative to the exible

prices benchmark, in this paper we highlight that this important feature of our model also

characterize our specications including nominal price and wage rigidities.

Overall, we nd that in general our economies generate exchange rates and international

prices that match the data qualitatively: international price movements are volatile, persistent,

and highly correlated. Moreover, the correlation of the nominal exchange rate with consumer

prices is generally low. However, quantitatively, some specications of the model do less wellthan others along some dimensions. Namely, while with a limited degree of price rigidities the

volatility of exchange rates is about right , the persistence in exchange rate movements is too

little, the volatility in the terms of trade too much. More precisely, the following results emerge.

First, the volatility of the nominal exchange rate and international prices is as high as (or

higher than) in the data (recall that the model is calibrated to match the volatility of the real

exchange rate (relative to GDP)). Observe that the addition of a limited degree of price stickiness

to our benchmark specication lowers the volatility of both the nominal exchange rate and the

terms of trade, bringing it more in line with the data. However, the specications with a higher

degree of LCP generate a nominal exchange rate that is too little volatile.

Second, the nominal exchange rate is positively correlated with both the real exchange rate

and the terms of trade (a weaker currency is associated with a worsening of the terms of trade).

A positive comovements of the nominal exchange rate and the terms of trade is stressed by

Obstfeld and Rogo [2001] as evidence against the so called `local currency pricing', i.e. the idea

that export prices are completely sticky in the short run due to nominal rigidities. In light of the

debate following the point by Obstfeld and Rogo, the high correlation that we obtain in our

simulations (even excessive relative to the data) is an intriguing result, because it is obtained

under the assumption that export prices are indeed sticky in buyer's currency. Observe however

that in our dynamic setup prices can change already in the rst period in which rms are hit

by a shock, provided they are ready to pay the price adjustment costs. Hence, our model does


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Third, standard models with price rigidities but perfect pass-through predict a perfectly

positive correlation between the exchange rate and the import price index: a depreciation of

the currency translates into higher \imported ination" for the domestic economy. In our sim-

ulations, instead, this correlation is positive but much below one, as in the data: the highest

correlation, in the exible price economy, is 0.61, and the lowest is 0.35, in the economy with

limited LCP, against 0.51 in the data (excluding oil imports). By the same token, standard

models with nominal rigidities and complete pass-through would predict a zero correlation be-

tween the exchange rate and the export price index, since the latter is predetermined in theshort run. In our results, this correlation is around 0.9, and is therefore much higher than that

in the U.S. data, standing at only 0.16.

Finally, a low (endogenous) import price elasticity and distributive trade imply that both

the consumer prices and ination are only tenuously correlated with the nominal exchange rate

across all specications | in accord to the evidence. In particular, the correlation with the

CPI level across all specications with nominal rigidities is as low and negative as that in the

data, standing at -0.13 (excluding energy), while that with ination never exceeds 0.1 in the

theoretical economies, only slightly lower than the actual value of 0.19.

5 Structural and empirical pass-through equations

The textbook denition of exchange pass-through (henceforth, ERPT) is the percentage change

in import prices denominated in local currency resulting from a one percent change in the

bilateral exchange rate between the exporting and the importing country, other things equal.

Textbook models of the balance of payments, as well as a host of papers in the New open-economy

macroeconomics literature, assume a one-for-one response of import prices to exchange rates,

namely full or complete ERPT. Notably, complete ERPT obtains if (i) markups over costs are

constant, and (ii) marginal costs are also constant.10

Under these two conditions, the elasticity of demand for imports is a crucial determinant

f h f h d b l i h h A l i l i


20/33

of particular interest in a world with incomplete nancial markets and lies at the core of the

external adjustment and the cross-border transmission of ination.

In this section, we use our model (in dierent specications) to derive structural expressions

for pass-through coecients in the short- and the long-run. These expressions can be used in

specifying empirical regression models which are consistent with alternative theoretical views of

pass-through. Moreover, based on these expressions, we will be able to study the performance

of empirical regression models which, because of data availability, do not exactly conform with

our structural equations. We will also provide a quantitative assessment of the resulting bias.

5.1 Inspecting the mechanism(s): structural ERPT equations

5.1.1 ERPT and price discrimination

Let us consider rst our specications with exible prices. The log-linear expression for the price

of imports is: bPf;t = 11 + (mkf 1)

bEt + [M Cf;t + (mkf 1)1 + (mkf 1)

dM Cn;t (20)where mkf is the total markup (including both distribution and standard markup) in the home

import sector and is the distribution margin. As long as is strictly above zero, the coecient

on the exchange rate will be less than one, and so will be ERPT.

In our benchmark calibration, plausible markups and structural parameters value imply that

the EPRT coecient is equal to 0.85. Because of the presence of distribution services, the impact

of changes in the nominal exchange rate on the prices that consumers pay for import will be

lower:

bPf;t = (1 )b

Pf;t + bPn;t

With a distribution margin as high as 50 percent, pass-through to consumer prices (of imports)

falls to 43 percent. As noted by the literature, the implications of distributive trade for local

currency pricing is quite remarkable even in models with perfect price exibility.


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imposing symmetry and log-linearizing around a steady state , we obtain:

bPf;t = bEt + [M Cf;t1 + (mkf 1) + pF2 (mkf 1) (1 + ) + (mkf 1)

1 + (mkf 1) + pF

2 (mkf 1) (1 + )bPn;t +

pF2 (mkh 1)

1 + (mkf 1) + pF

2 (mkf 1) (1 + )

EtbPf;t+1 + bPf;t1 ;

whereas the nominal marginal cost M Cf;t is equal to(Wt )

(Rt )1

Zf,t, and as before mkf denotes

the total markup (including both distribution and standard markup) in the imported Home

tradable sector.

The above equation highlights the two mechanisms of imperfect pass-through embedded in

our analysis. In the short run, even if prices are fully exible { corresponding to pF = 0 { the

pass-through coecient is less than 1 per eect of distributive trade { corresponding to > 0.

When there are no distribution costs ( = 0), the short-run pass-through coecient is less than

1 only when there are nominal rigidities.

The low pass-through coecient in the short run mostly reects nominal price rigidities. In

our benchmark calibration, the short run coecient can be as low as 2 percent for a high degree

of nominal rigidities. Calibrating the model using the results from Bils and Klenow [2004], for

an average nominal price rigidities of 4.3 months, the short run coecient is 14 percent. In the

long run, nominal rigidities are obviously irrelevant, and imperfect pass-through can only be

attributed to the implications of distribution for the price elasticity of imports. Depending on

the degree of monopolistic distortions, in our model the long-run EPRT is 85 percent. Recall

that with a distribution margin of 50 percent, pass-through onto consumer prices will be half

the degree of pass-through onto prices at the dock, namely:

bPf;t = (1 )bPf;t + bPn;t= (1 )

bEt + [M Cf;t1 + (mkf 1) +

pF

2 (mkf 1) (1 + )+


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sistent specication of the regression model would call for the inclusion of the expected value

of Et

bPf;t+1. Its omission is bound to result into omitted-variable bias. We will return on this

point below.

Observe that the log linear equation for the domestic prices abroad is:

cP

f;t =[M Cf;t

1 + (mkf 1) + pF

2 (mkf 1) (1 + )+

(mkf 1)

1 + (mkf 1) + pF

2 (mkf 1) (1 + )cPn;t +

pF 2 (mkf 1)1 + (mkf 1) +

pF

2 (mkf 1) (1 + )EtcPf;t+1 + cPf;t1 ;

Combining equations (assuming symmetry) we obtain a structural equation of the determinant

of deviations from the law of one price at wholesale (border) level:

bEt + cP

f;t bPf;t = (mkf 1) + (mkf 1)

pF

2 (1 + )

1 + (mkf 1) + p

F

2 (mkf 1) (1 + )! bEt +(mkf 1)

1 + (mkf 1) + pF

2 (mkf 1) (1 + )

cPn;t bPn;t +(mkf 1)

pF

2

1 + (mkf 1) + pF

2 (mkf 1) (1 + )Etc

P

f;t+1 +cP

f;t1

EtbPf;t+1 + bPf;t1

As pointed out by Corsetti and Dedola [2005], these deviations are a function of the degree of

monopolistic distortions (markup), as well as the price of nontraded goods and services employed

in distribution (for > 0). Our dynamic analysis also point out a role for ination and price

adjustment costs.

5.2 Empirical models of ERPT: an assessment using simulated time series

Empirical research on ERPT focuses on the adjustment of prices to an exchange rate change

for transactions between an exporting and importing country. According to the taxonomy in

Goldberg and Knetter (1997), the typical ERPT regression can be written as


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competing prices or income in the importing country), as well as lagged values of the dependent

variable to capture dynamics, and Et is the nominal exchange rate (importer's currency per unit

of exporter's currency). The coecient is referred to as the pass-through coecient. ERPT

| conditional on controls Xt and Ct | is full or complete if = 1 and is incomplete if < 1:

Provided one can nd an accurate measure of marginal cost Ct; the coecient measures only

the variable markup component of the textbook denition of pass-through.

The typical pass-through regression treats marginal costs as directly observable, but includes

cost indices. These indices may be reasonable measures of average costs incurred domestically,but are unlikely to be good measures of marginal costs, which is the relevant concept in specifying

optimal pricing by prot maximizing rms. Furthermore, measurement errors in cost indices may

be correlated with exchange rates in ways that bias the coecients toward nding incomplete

pass-through and excess markup adjustment.

The research on pricing-to-market (henceforth PTM) has addressed this issue including prices

in both the origin and the destination markets, as well as costs, in the empirical regressions.

In terms of (21), Pt is the export price, Ct is the domestic price of the same good, while Yt

includes other cost factors and demand shifters in both markets. Costs, and thus errors in costs,

inuence the export price relative to the domestic price only when there is a dierence in the

convexity of demand in the two markets (e.g., see Marston [1990]).11

To shed light on the quantitative importance of dierent potential sources of biases in the

empirical studies of pass-through, we run two types of regressions on the articial data simulated

using our theoretical economies. We dub the rst one `ERPT regression':

Pf;t = + Et + W

t + 1Yt + 2Pf;t1; (22)

In terms of (21), the ERPT regression includes Foreign nominal wages, W

t ; to control for mar-ginal costs in the exporting country, and Home real GDP, Yt; to control for demand conditions in

the importing country. We also include one lag of the dependent variable to capture dierences

between short run and long run pass-through that are relevant in the economy with nominal


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rigidities. Thus, the exchange-rate coecient represents the estimate of the short-run ERPT

coecient, while

1 2will be the estimate of the long-run ERPT coecient.

The second regression, which we dub the `PTM regression', has the following specication:

Pf;t = + Et + P

f;t + 1Ph;t + 2Pf;t1; (23)

In line with the insights from the PTM literature, this regression includes the domestic price

of Foreign exports, P

f;t; to control for marginal cost in the exporting country, and the Home

PPI of tradables, Ph;t; to control for demand conditions in the importing country. As above, we

also include the lagged dependent variable, so that represents the short-run ERPT coecient,

while

1 2will be our estimate of the long-run ERPT coecient. Moreover, in line with the

PTM literature we impose the constraints: = (e.g., see Anderton [2003]):

Both regressions are clearly misspecied in the context of our theoretical models, as they do

not control for the eect of the cost of distribution on the markup, and suer from measurement

error problems, as they rely on proxies of the generally unobservable marginal costs. Precisely,

(22) only includes nominal wages, but omit the price of capital and measures of technology

shocks. By the same token, the inclusion of the Foreign price of Home imports among the

regressors in (23) is a potential source of bias, as this price includes a Foreign market time-

varying markup.12

But how far are these empirical regression models from the true values of the structural

coecients? The answer to this question is crucial for the empirical literature, given that the

problems discussed above are likely to plague virtually all applied papers trying to estimate

structural ERPT empirically. Moreover, it is worth keeping in mind that the accuracy of ERPT

estimates has an important policy dimension: these estimates are an important input into

projections of exchange rate changes onto prices and output which underlie monetary policy

decision making.

Table 3 presents the results of the ERPT and PTM regressions run on our simulated time

series. The table also shows a control regression in which the import price is regressed only on


25/33

in the table are averages over 100 simulations of 88 quarters (a typical sample size). For each

theoretical economy, the table shows the true value of the short run and long run coecients

and

1 2 in the two rows under the heading Structural. As shown above, these coecients

reect the value of the structural parameters in the log-linearized rst order conditions of the

monopolistic Foreign exporter. Thus, in the benchmark model with exible prices the short

run and long run coecients coincide, and their level, equal to 0.85, is fully determined by the

steady state level of the markup in the import sector, mkh; and the distribution margin, :

Conversely, in the sticky price model short run and long run ERPT coecients dier. Becauseof the destination-specic price adjustment cost, the short run coecient is equal to 0.14, the

long run coecient is 0.85, as in the benchmark. Notably, these values are well in the range of

the estimates for the U.S. and in general the industrialized countries (see Anderton [2003] and

Campa and Goldberg [2002], respectively).

From Table 3, it appears that the overall performance of the ERPT and PTM specication

is in general satisfactory, although the coecient estimates are somewhat biased. First, both

specications are always able to distinguish between short run and long run coecients when

they are truly dierent, and correctly set their estimates equal when they are the same. This is

most apparent in comparison with the "naive" specication, in which the inclusion of the lagged

dependent variable alone is not enough to estimate the same short run and long run coecients

in the case of the exible price model (see rst column of Table 3)

Second, the PTM specication does very well in recovering the correct value of the long run

structural coecient, regardless of the presence of nominal rigidities. However, its performance

deteriorates with price stickiness, as a systematic upward bias shows up in the estimation of the

short run coecient across all model variations. Moreover, the unbiasedness of the long run

estimates highlights that the short run upward bias in the estimated is basically oset by acorresponding downward bias in the coecient on the lagged dependent variable, 2, that will

adversely aect the inference of the dynamics eects of the exchange rate on import prices.

Third, although the ERPT specication never recovers the exact structural coecients, it


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error in the proxy for foreign marginal costs included in this specication, i.e. nominal wages, is

too large to be oset by the variability in the other regressors of interest, notably the exchange

rate. Thus, this bias is at least as serious as that arising from omitted variables in the "naive"

specication.

It is worthwhile to stress that the estimated coecients for the economy with a limited

degree of LCP are pretty close to those found in the empirical literature; for instance Campa

and Goldberg [2002] nd that on average across OECD countries, exchange rate pass-through

into import prices is 46% in the short run and 64% over the long run. In light of the aboveresults documenting the reliability of these regressions, it seems reasonable to conclude that only

a limited amount of nominal rigidities is required for the theoretical economy to be consistent

with this dimension of the actual data.

5.3 ERPT coecient and pass-through

What conclusions that can be drawn from estimating ERPT coecients? We close our analysis

with an important caveat. Even if econometricians were able to recover precise estimates of

structural pass-through coecients, there will still be a question about their use in policy-

oriented exercises addressing the impact of specic shocks on import prices or, more in general,

on the CPI.

The main issue is that, in general, structural pass-through coecients are not a complete

description of the actual properties of the model as regards the link between import prices and

exchange rates. In each particular period, this link will be determined conditional on the specic

shocks causing exchange rate uctuations. To clarify this point: in all our specications import

prices responds one-to-one to monetary shocks in the long run | and also in the short run in

the benchmark economy where prices are exible. Hence, conditional on monetary disturbances,

long-run ERPT is perfect.

Even the exchange rate coecient in the pass-through equation is lower than one, perfect

pass through from monetary shocks will eventually results because such disturbances will bring


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increase in the nominal price of distribution services. Putting all elements together, it is easy to

verify that import prices will eventually rise one-to-one with the exchange rate. The lesson is

that using structural equations to forecast the impact of a nominal shock, but failing to control

for the general equilibrium eects of such shocks, would produce an underestimation of the

response of import prices to fundamental changes in exchange rates.

6 Concluding remarks

Why do prices respond only partially, if at all, to changes in the nominal exchange rate? This

paper develops a quantitative, dynamic, open-economy model to assess the contributions of price

discrimination and local currency pricing with nominal rigidity to the low degree of ERPT.

Because of the presence of distribution services, the elasticity of demand is market specic,

which leads rms to price-discriminate across countries. In our model, the combination of price

discrimination and local currency pricing with nominal rigidity can account for the variable

degree of ERPT over dierent horizons. As a result of price discrimination, our model predicts

exchange-rate pass-through coecients that are dierent than one in the long run: 85% and

43% on import and consumer prices. Moreover, we nd that a very small amount of nominal

rigidities lower these values to 10% and 5% in the short run, respectively. Finally, we compare the

performance of regression models commonly used in the empirical literature, with the structuralfeatures of the model. We nd that the regression models perform surprisingly well, displaying

relatively small bias in the estimated pass-through coecients.

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Table 1. Parameter values

Benchmark Model

Preferences and Technology

Risk aversion = 2

Disutility of labor = 1:13

Velocity parameter = 0:1

Elasticity of substitution between:

Home and Foreign traded goods 11 = 0:89

traded and non-traded goods 11 = 0:74

Home non-traded goods N = 7:7

Home traded goods H = 15:3

labor inputs L = 4:3

Share of Home traded goods aH = 0:38

Share of non-traded goods aN = 0:48

Elasticity of the discount factor

with respect to C and L = 0:006

Distribution margin = 0:5 ( = 1:13)

Labor share in tradables = 0:61

Labor share in nontradables = 0:56Depreciation rate = 0:025

Pice-adjusment cost N = H = 5:6

Wage-adjusment cost W = 63

Monetary Policy

Coecient of autocorrelation = 0:93

Coecient on ination = 1:66

Coecient on output y = 0:14

Standard deviation of the shock " = 0:0013


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