Carvalho, Carlos; Nechio, Fernanda
Working Paper
Aggregation and the PPP puzzle in a sticky-price
model
Staff Report, No. 351
Provided in Cooperation with:
Federal Reserve Bank of New York
Suggested Citation: Carvalho, Carlos; Nechio, Fernanda (2008) : Aggregation and the PPP
puzzle in a sticky-price model, Staff Report, No. 351, Federal Reserve Bank of New York, New
York, NY
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Federal Reserve Bank of New York
Staff Reports
Aggregation and the PPP Puzzle in a Sticky-Price Model
Carlos Carvalho
Fernanda Nechio
Staff Report no. 351
October 2008
Revised November 2008
This paper presents preliminary findings and is being distributed to economists
and other interested readers solely to stimulate discussion and elicit comments.
The views expressed in the paper are those of the authors and are not necessarily
reflective of views at the Federal Reserve Bank of New York or the Federal
Reserve System. Any errors or omissions are the responsibility of the authors.
Aggregation and the PPP Puzzle in a Sticky-Price Model
Carlos Carvalho and Fernanda Nechio
Federal Reserve Bank of New York Staff Reports, no. 351
October 2008; revised November 2008
JEL classification: F30, F41, E00
Abstract
We study the purchasing power parity (PPP) puzzle in a multisector, two-country,
sticky-price model. Firms’ price stickiness differs across sectors, in accordance with
recent microeconomic evidence on price setting in various countries. Combined with
local currency pricing, these differences lead sectoral real exchange rates to exhibit
heterogeneous dynamics. We show that in this economy, deviations of the real exchange
rate from PPP are more volatile and persistent when compared with a counterfactual
one-sector world economy that features the same average frequency of price changes and
is otherwise identical to the multisector world economy. When simulated with a sectoral
distribution of price stickiness that matches the microeconomic evidence for the U.S.
economy, the model produces a half-life of deviations from PPP of forty-five months.
In contrast, the half-life of such deviations in the counterfactual one-sector economy is
only slightly above one year. As a by-product, our model provides a decomposition of
this difference in persistence that allows a structural interpretation of the approaches
found in the empirical literature on aggregation and the real exchange rate. In particular,
we reconcile the apparently conflicting findings that gave rise to the “PPP strikes back”
debate (Imbs et al. [2005a, b] and Chen and Engel [2005]).
Key words: heterogeneity, aggregation, price stickiness, real exchange rates, PPP puzzle
Carvalho: Federal Reserve Bank of New York (e-mail: carlos.carvalho@ny.frb.org). Nechio:
Princeton University (e-mail: fnechio@princeton.edu). The authors would like to thank
participants at the NBER Summer Institute 2008 International Finance and Macroeconomics
Workshop, the 2008 SOEGW (Small Open Economies in a Globalized World) Conference,
and the New York Area Workshop on Monetary Economics at the Federal Reserve Bank of
New York, as well as seminar participants at Johns Hopkins University, Princeton University,
and the Federal Reserve Bank of New York for helpful comments. They are also grateful to
Gianluca Benigno, Roberto Chang, Michael Devereux, Gauti Eggertsson, Charles Engel,
Pierre-Olivier Gourinchas, Jean Imbs, Anthony Landry, Paolo Pesenti, Ricardo Reis, Hélène Rey,
Chris Sims, and Thomas Wu for comments and suggestions. The views expressed in this paper
are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank
of New York or the Federal Reserve System.
1 Introduction
Purchasing power parity (PPP ) states that, once converted to the same currency, price levels across
countries sh ould be equal. As a result, the real exchange rate between any two countries - the ratio
of their price levels in a common currency - should be constant and equal to unity. A more ‡exible
version of PPP postulates that real exchange rates should be constant, but not necessarily equal to
one. In contrast with the tight predictions of either version of PPP, in the data real exchange rates
display large and long-lived ‡uctuations around their average levels. Rogo¤’s (1996) survey of the
empirical literature on the subject reports a “consensus view”that places estimates of the half-life
of deviations from PPP in the range of 3 to 5 years. While he suggests that the high volatility of the
real exchange rate could be explained by a model with monetary shocks and nominal rigidities, so
far models of this type with plausible nominal frictions have failed to produce the large persistence
found in the data; hence, the puzzle.
In this paper, we study the PPP puzzle in a multi-sector, two-country, sticky-price model. We
depart from the existing literature by introducing heterogeneity in the freque ncy of p rice changes
across sectors, in accordance with recent microeconomic evidence on price setting for various coun-
tries (e.g. Bils and Klenow 2004; Dhyne et al. 2006 for the E uro area). Combined with local
currency pricing, these di¤erences in the extent of price stickiness lead sectoral real exchange rates
to have heterogeneous dynamics, which are also evident in the data (Imbs et al. 2005a).
We isolate the role of heterogeneity by comparing the dynamic behavior of the aggregate real
exchange rate in such a multi-sector economy with the behavior of the real exchange rate in an
otherwise identical one-sector world economy with the same average frequency of price changes.
We refer to this auxiliary econ omy as the counterfactual one-sector world economy. We show that,
in response to nominal shocks, the aggregate real exchange rate in the heterogeneous economy is
more volatile and persistent than in the counterfactual one-sector world economy, and that the
di¤erence can be arbitrarily large.
We then investigate whether quantitatively our multi-sector model can solve the PPP puzzle,
i.e. produce highly volatile and persistent real exchange rates in response to monetary disturbances,
under a plausible parametrization. In particular, to discipline our analysis we use a cross-se ctional
distribution of the frequency of price ch anges that matches the recent microeconomic evidence
for the U.S. economy. We ask the same question in the counterfactual one-sector world economy.
Our multi-sector model produces a half-life of deviations from P PP of 45 months, well within
the consensus view of 3 to 5 years. In contrast, su ch deviations in the one-sector world economy
are short-lived, with a h alf-life only slightly above one year. In order to produce deviations f rom
PPP with a half- life of 45 months, the one-sector model requires …rms to change prices much less
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frequently - on average once every 20-21 months. The volatility of the real exchange rate is also much
higher in the heterogeneous economy (by a factor that ranges from 2:5 to more than 5, depending on
the speci…cation of the model). These results obtain in the absence of strategic comp lementarities
in price-setting decisions. Thus, heterogeneity in price stickiness can lead nominal disturbances to
have very persistent e¤ects on real exchange rates, without the need for the propagation mechanism
that such complementarities provide.
Our quantitative …ndings reveal that the counterfactual one-sector world economy is a poor
representation of the multi-sector model. As a result of cross-sectional aggregation of sectoral
exchange rates with heterogeneous dynamics, the aggregate real exchange rate in the multi-sector
economy displays much richer dynamics than the real exchange rate in the counterfactual one-
sector model. As our analytical results show, the volatility and persisten ce of real exchange rates
are convex functions of the frequency of price adjustments, which leads the counterfactual one-sector
model to understate both quantities relative to the underlying heterogeneous economy.
We start by presenting our multi-sector general equilibrium model in Section 2. It has two
countries trading intermediate goods produced by monopolistically competitive …rms, which are
divided into sectors that di¤er in the frequency of price changes. Firms can price-discriminate
across the two countries, and set prices in the currency of the market in which the good is sold.
Consumers supply labor to these intermediate …rms and consume the non-traded …nal good, which
is produced by competitive …rms that bundle the intermediate goods from the two countries.
Using common assumptions about preferences and nominal shocks, Section 3 presents analytical
results that show that the volatility and persistence of the aggregate real exchange rate in the multi-
sector economy are larger than in the counterfactual one-sector model. It provides a decomposition
of such di¤eren ce in persistence into two terms: an aggregation e¤ect - de…ned as the di¤eren ce
between the persistence of the aggregate real exchange rate of the heterogeneous economy and the
(weighted) average persistence of sectoral exchange rates; and a counterfactuality e¤ect - de…ned as
the di¤erence between the former weighted average and the persistence of the real exchange rate in
the counterfactual one-sector world ec onomy. This decomposition clari…es the role of heterogeneity
and aggregation in accounting for the di¤erence in real exchange rate persistence across the two
world economies.
Section 4 presents results from simulations of the model using the cross-sectional distribution
of the frequency of price changes from Nakamura and Steinsson (2008). It shows that in response
to monetary shocks our multi-sector model generates much higher volatility and persistence than
the counterfactual one-sector model. The counterfactuality e¤ect accounts for well over 90% of this
di¤erence in persistence, whereas the aggregation e¤ect explains the residual di¤erence. We also
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