Board of Governors of the Federal Reserve System
International Finance Discussion Papers
Number 826, February 2005--- Screen Reader
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Abstract:
A central puzzle in international finance is that real
exchange rates are volatile and, in stark contradiction to
efficient risk-sharing, negatively correlated with cross-country
consumption ratios. This paper shows that a standard international
business cycle model with incomplete asset markets augmented with
distribution services can account quantitatively for these
properties of real exchange rates. Distribution services, intensive
in local inputs, drive a wedge between producer and consumer
prices, thus lowering the impact of terms-of-trade changes on
optimal agents' decisions. This reduces the price elasticity of
tradables separately from assumptions on preferences.
Two very different patterns of the international transmission of
positive technology shocks generate the observed degree of
risk-sharing: one associated with improving, the other with
deteriorating terms of trade and real exchange rate. In both cases,
large equilibrium swings in international relative prices magnify
consumption risk due to country-specific shocks, running counter to
risk sharing. Suggestive evidence on the effect of productivity
changes in U.S. manufacturing is found in support of the first
transmission pattern, questioning the presumption that
terms-of-trade movements in response to supply shocks invariably
foster international risk-pooling.
Keywords: Incomplete asset markets, distribution cost, Backus-Smith's consumption-real exchange rate correlation puzzle
JEL classification: F32, F33, F41
Is consumption risk optimally hedged across countries? Despite the development of international financial markets in the last decades, the answer from a large body of financial and macroeconomic research appears to be "no".1 While the literature has analyzed many different facets of (the lack of) international risk sharing, a crucial testable implication is that, in a world economy characterized by large deviations from purchasing power parity, domestic households should consume more when their consumption basket is relatively cheap.2 As first shown by Backus and Smith [1993], this is clearly at odds with the data. For most OECD countries, the correlation between relative consumption and the real exchange rate (i.e., the relative price of consumption across countries) is generally low, and even negative. A striking illustration of such finding is presented in Figure 1, plotting (the log of) quarterly U.S. consumption relative to the other OECD countries and the U.S. real trade-weighted exchange rate in the period 1973-2001. The swings in the dollar in real terms are not associated with movements of the consumption ratio in the same direction; on the contrary the two variables tend to comove negatively.
An obvious element in the explanation is that international financial markets are not developed enough. Yet, theory offers convincing arguments to doubt that incomplete asset markets per se be sufficient to bring models in line with the Backus-Smith evidence on (the lack of) risk sharing. Several contributions have shown that the equilibrium allocation in economies that only trade in international, uncontingent bonds may be quite close to the first best (e.g. see Baxter and Crucini [1995]). Indeed, trade in bonds insures that the real rate of currency depreciation and the growth rate of relative consumption are highly and positively correlated in expectations -- although not necessarily period by period ex-post, as is the case when markets are complete. In addition, Cole and Obstfeld [1991] has called attention to the role of movements in the terms of trade in potentially insuring against production risk independently of trade in assets.
But do the observed swings in international relative prices necessarily foster risk sharing -- up to the point of partly offsetting the frictions and limitations of the asset markets? Could the Backus-Smith evidence instead indicate that in equilibrium these swings magnify (rather than reduce) consumption risk due to country specific shocks? In this paper, we study the link between high exchange rate volatility (the exchange rate volatility puzzle) and international consumption risk sharing (the Backus-Smith puzzle) in a two-country model of international business cycles. We adopt a model with traded and non traded goods similar to Stockman and Tesar [1995], except that we assume incomplete asset markets. Moreover, as in Burstein, Neves and Rebelo [2003], we introduce distribution services produced with the intensive use of local inputs. Combined with standard preferences across tradables, distribution services contribute to generate a realistically low price elasticity of tradables. In this setting, the terms of trade and the real exchange rate are highly volatile in response to productivity shocks and have large, uninsurable effects on relative wealth. Specifically, we show that large movements in international prices can actually hinder risk sharing, making the set of international assets available to agents less effective as instruments to hedge consumption risk against country-specific shocks.We conclude our paper by complementing our quantitative analysis of the model with statistical evidence on the responses of the real exchange rate and the terms of trade to innovations in productivity in the U.S. economy.
The theoretical and quantitative analysis in this paper yields two novel and important results. First, when we calibrate our model to match the U.S. real exchange rate volatility, we find that it generates large departures from efficient risk sharing. The predicted correlation between the real exchange rate and relative consumption is negative, while the comovements in aggregates across countries are broadly in line with those in the data. The main predictions of the model are reasonably robust to extensive sensitivity analysis.
Second, depending on the value of the price elasticity of tradables, our model predicts a low degree of risk-sharing for two very different patterns of the international transmission of productivity shocks, each corresponding to a plausible set of parameters values for preferences and technology. In our benchmark calibration, for a price elasticity slightly above 1/2, international spillovers in equilibrium are large and positive. A positive transmission is a standard prediction of the international business cycle literature: an increase in the productivity of the domestic tradable sector leads to a deterioration of the terms of trade and a depreciation of the real exchange rate. However, in our baseline economy the deterioration is so large on impact that relative domestic wealth decreases, driving foreign consumption above domestic consumption.For a price elasticity slightly below 1/2, instead, international spillovers are still large but -- strikingly -- negative. With a negative transmission, following a productivity increase, the home terms of trade and the real exchange rate appreciate, reducing relative wealth and consumption abroad. In both cases, large swings in international relative prices run counter to efficient risk sharing. But our numerical results suggest that the overall performance of the model is best under the negative transmission mechanism.
The latter pattern of international transmission is due to a combination of an unconventionally sloped demand curve, and nontrivial general equilibrium effects arising from market incompleteness. Because of home bias in consumption, domestic tradables are mainly demanded by domestic households. With a low price elasticity, a terms-of-trade depreciation that reduces domestic wealth relative to the rest of the world would actually result in a drop of the world demand for domestic goods -- the negative wealth effect in the home country would more than offset any global positive substitution and wealth effect. Therefore, for the world markets to clear, a larger supply of domestic tradables must be matched by an increase in their relative price, that is, an appreciation of the terms of trade -- driving up domestic wealth and demand.
To investigate whether the international transmission of productivity shocks to tradables in the U.S. data bear any resemblance to the above patterns, we close our paper with some suggestive evidence. Two findings stand out. First, we provide novel evidence in support of the prediction of a negative conditional correlation between relative consumption and the real exchange rate. Following a shock that increases permanently U.S. labor productivity in manufacturing (our measure of tradables) relative to the rest of the world, U.S. relative output and consumption increase, while the real exchange rate appreciates.3 Second, the same increase in productivity improves the terms of trade, as suggested by our model under the negative transmission.
In light of the results in this paper, the Backus-Smith evidence appears less puzzling yet more consequential for the construction of open-economy general-equilibrium models, with potentially strong implications for welfare and policy analysis. In fact, if the international transmission mechanism is such that a positive shock to productivity translates into a higher, rather than lower, international price of exports, foreign consumers will be negatively affected. Terms-of-trade movements will not contribute at all to consumption risk-sharing. Thus gains from international portfolio diversification may well be large relative to the predictions of standard open-economy models.
The paper is organized as follows.After providing a brief summary of the evidence on the correlation between relative consumption and the real exchange rate for industrialized countries, in the following section we derive some key implications for the link between these two variables in standard two-good open-economy models. In Section 3 we introduce the model, whose calibration is presented in Section 4. Section 5 explores the quantitative predictions of the model in numerical experiments. Section 6 presents suggestive evidence on the effects of shocks to productivity in the open economy. Section 7 summarizes and qualifies the paper's results, suggesting directions for further research.
In this section, we first restate the Backus and Smith [1993] puzzle, looking at the data for most OECD countries. Second, we reconsider the general equilibrium link between relative consumption and the real exchange rate in the framework of a simple endowment economy with incomplete markets and tradable goods only, in the spirit of Cole and Obstfeld [1991]. The goal of our exercise is to provide an intuitive yet analytical account of the determinants of the comovements between the real exchange rate and relative consumption conditional on endowment (supply) shocks. Using our framework, we will show that the link between these variables can have either sign depending on the price elasticity of tradables: a low elasticity can generate the negative pattern observed in the data. But since a low price elasticity also means that quantities are not very sensitive to price movements, a negative correlation between the real exchange rate and relative consumption will be associated with a high volatility of the real exchange rate and the terms of trade relative to fundamentals and other endogenous macroeconomic variables -- in accord with an important set of stylized facts of the international economy. These results shed light on the main mechanisms driving our quantitative results in the second part of our paper.
As pointed out by Backus and Smith [1993], an internationally efficient allocation implies that the marginal utility of consumption, weighted by the real exchange rate, should be equalized across countries:
![]() |
(1) |
where the real exchange rate (RER) is customarily defined as the
ratio of foreign (
) to domestic (
) price level, expressed in the same currency units (via
the nominal exchange rate),
(
) denotes the marginal
utility of consumption, and
and
denote domestic and foreign
consumption, respectively. Intuitively, a benevolent social planner
would allocate consumption across countries such that the marginal
benefits from an extra unit of foreign consumption equal its
marginal costs, given by the domestic marginal utility of
consumption times the real exchange rate
, i.e., the
relative price of
in terms of
.
If a complete set of state-contingent securities is available,
the above condition holds in a decentralized equilibrium
independently of trade frictions and goods market imperfections
(including shipping and trade costs, as well as sticky prices or
wages) that can cause large deviations from the law of one price
and purchasing power parity (PPP). It is only when PPP holds (i.e.,
) that efficient risk-sharing implies
equalization of the ex-post marginal utility of consumption
-- corresponding to the simple notion that complete markets imply a
high cross-country correlation of consumption.
Under the additional assumption that agents have preferences
represented by a time-separable, constant-relative-risk-aversion
utility function of the form
with
, (1) translates into
a condition on the correlation between the (logarithm of the) ratio
of domestic to foreign consumption and the (logarithm of the) real
exchange rate.4 Against the hypothesis of perfect
risk-sharing, many empirical studies have found this correlation to
be significantly below one, or even negative (in addition to Backus
and Smith [1993], see for instance Kollman [1995] and Ravn
[2001]).
Table 1 reports the correlation between real exchange rates and relative consumption for OECD countries relative to the U.S. and to an aggregate of the OECD countries, respectively. Since we use annual data, we report the correlations for both the HP-filtered and first-differenced series. As shown in the table, real exchange rates and relative consumption are negatively correlated for most OECD countries. The highest correlation is as low as 0.53 (Switzerland vis-à-vis the rest of the OECD countries), and most correlations are in fact negative -- the median of the table entries in the first two columns are -0.30 and -0.27, respectively.
Consistent with other studies, Table 1 presents strong prima facie evidence at odds with open-economy models with a complete set of state-contingent securities. Given that debt and equity trade, the most transparent means of consumption-smoothing, are far less operative across borders than within them, a natural first step to account for the apparent lack of risk-sharing is to assume that financial assets exist only on a limited number of securities. Restricting the set of assets that agents can use to hedge country-specific risk breaks the tight link between real exchange rates and the marginal utility of consumption implied by (1). It should therefore be an essential feature of models trying to account for the stylized facts summarized in Table 1.
Building on a simple setting similar to Cole and Obstfeld [1991], we now analyze the Backus-Smith correlation in a two-country, two-good endowment economy under the extreme case of financial autarky. We will refer to the two countries as 'Home' and 'Foreign', denoted H and F. For the Home representative consumer, consumption is given by the following CES aggregator
![]() |
(2) |
where
(
is the domestic
consumption of Home (Foreign) produced good,
is the share of the
domestically produced good in the Home consumption expenditure,
is the corresponding
share of imported goods, with
. Let
(
denote the price of
the Home (Foreign) good, and
the terms of trade, the relative price of Foreign goods in terms of
Home goods. Therefore, an increase in
implies a
depreciation of the terms of trade. The consumption-based price
index
is
![]() |
(3) |
Let
denote Home (tradable)
output. In financial autarky, consumption expenditure has to equal
current income, i.e.,
Domestic demand for Home goods can then be written:
where the demand's price elasticity coincides with the elasticity
of substitution across the two goods,
. Analogous
expressions can be derived for the Foreign country.
What is the link between international relative prices and the
world demand implied by this simple general equilibrium model?
Taking the derivative of
with respect to
:
![]() |
(4) |
makes it clear that the Home demand for the Home good
can be either
increasing or decreasing in the terms of trade
depending on
. When
, a fall in the relative price of
the domestic tradable -- an increase in
-- will
raise its domestic demand. This is the case when the positive
substitution effect (
) from lower prices is
larger in absolute value than the negative income effect
(
) from a lower valuation of
.5 Conversely, when
the negative income effect will
more than offset the substitution effect. Thus, a terms-of-trade
depreciation will reduce the domestic demand for the Home tradable.
The foreign demand for Home tradables
, instead, will
always be increasing in
: independently of
, the substitution and income effects
in this case are both positive.6
As long as the negative income effects in the Home country is
not too strong, the world demand for Home goods
will be
decreasing in their relative price, i.e. increasing in
.7 For
sufficiently
high, then, the equilibrium Home terms of trade needs to depreciate
in response to a positive shock to Home output
. The international
transmission through terms of trade adjustment is therefore
positive: foreign consumption of Home tradables will rise,
responding to the fall in the relative price of imports. However,
when
is sufficiently below
and the Home bias in consumption is sufficiently high (i.e.,
is large relative to
), the response
of world demand for the Home goods to relative price movements will
be dominated by the strong negative income effects of its domestic
component: world demand will be falling in
. In
other words, the negative income effect of worsening terms of trade
on Home demand will more than offset any positive substitution
effects worlwide and income effects abroad.8 For a positive
supply shock to
to be matched by an
increase in world demand for the Home goods, the Home terms of
trade needs to appreciate. The international transmission in
this case is negative : a positive domestic supply shock has
a negative impact on consumption and welfare abroad.
To analyze the relation between international transmission and
price volatility, we take a log-linear approximation of the market
clearing condition for Home tradables (
) around a symmetric equilibrium (with
and
). The
equilibrium link between relative output (endowment) changes, and
the terms of trade/real exchange rate can be expressed as
follows:
![]() |
(5) |
![]() |
(6) |
where a "" represents a variable's
percentage deviation from the symmetric values. Consistent with our
analysis above, these expressions show that, for given movements in
relative output, the sign of the response of international relative
price changes depending on
. In addition,
they suggest that the volatility of the terms of trade and the real
exchange rate follows a hump-shaped pattern in
.
To see this, assume home bias in consumption (
). For a
sufficiently high elasticity of substitution, i.e.
, the real exchange rate and the terms of trade both depreciate in
response to a positive Home supply shock. This is the region of
parameters' values in which the world demand schedule is
conventionally sloped, and the international transmission is
positive. In this region, higher values of
reduce the coefficient relating
to
and
: the larger the price
elasticity, the lower the volatility of the real exchange rate and
the terms of trade relative in response to shocks to relative
output.
Conversely, for a sufficiently low price elasticity of imports,
that is, for
, a Home supply shock cause both the real exchange rate and the
terms of trade to appreciate in equilibrium. As shown above,
underlying this result is a weak substitution effect relative to
the income effect of changes in relative prices, so that the
domestic and world demand schedules for Home tradables are
negatively sloped. In this region of parameters' values, a higher
elasticity of substitution tends to raise the volatility of
international prices.
Note that the response of international relative prices to
output shocks tend to become stronger as
approaches
from either side, whereas the slope of the demand function becomes
flatter and flatter before changing sign. For
around the cutoff point, the coefficient relating
to
and
in the above expressions
becomes quite high in absolute value, driving up the volatility of
the real exchange rate and the terms of trade in response to shocks
to relative output. An important implication of our analysis is
that there will be two values of
(below and
above
)
that yield the same volatility of the terms of trade and real
exchange rate: one associated with positive, the other associated
with negative international transmission.
So far, we have shown that there can be different patterns of relative price movements in response to supply shocks, shaping the sign and magnitude of the international transmission mechanism. We can now derive the implications of our results for risk sharing and the equilibrium comovements between the real exchange rate and relative consumption . With incomplete markets the scope for insurance against country-specific shocks is limited, and equilibrium movements in international relative prices will expose consumers to potentially strong relative wealth shocks.
In our simple model with financial autarky, we can use the balanced-trade condition to derive an expression for relative consumption as a function of the terms of trade:
![]() |
(7) |
from this, we can then derive the following log-linearized relationship between the real exchange rate and relative consumption:
![]() |
(8) |
The relation between real exchange rates and relative consumption
can have either sign, depending on the values of
and
. Specifically, with home bias in consumption, it will
be negative when
.
We have seen above that, for a given change in the terms of
trade and the real exchange rate, the international transmission of
shocks can be positive or negative, depending on whether
is above or below
.
But this cutoff point is smaller than
. Hence, a
negative correlation between the real exchange rate and relative
consumption can correspond to different patterns of the
international transmission. Specifically, in response to a Home
supply shock, the Home terms of trade improves and the real
exchange rate appreciates, while Home consumption rises relative to
Foreign consumption, when
; the Home terms of trade and exchange rate depreciates, driving
Foreign consumption above domestic consumption, when
. Depending on the size of equilibrium movements in prices,
consumption at Home may or may not fall -- i.e., accounting for the
Backus Smith evidence in this case does not necessarily imply
'immiserizing growth.'
Contrast these results with the benchmark economy constructed by
Cole and Obstfeld [1991], which is a special case with and
. This
contribution -- as well as Corsetti and Pesenti [2001a] -- build
examples where productivity shocks to tradables bring about
relative price movements that exactly offset changes in
output, leaving cross-country relative wealth unchanged. Even under
financial autarky, agents can achieve the optimal degree of
international risk sharing, under the additional assumption of
logarithmic utility (
in (1).
But optimal risk sharing via terms-of-trade movements is likely
to be an extreme case, since according to the evidence, both the
magnitude of relative price movements and especially the sign of
the transmission appear to be different from what is required to
support an efficient allocation. Even when the international
transmission is positive -- as should be in the examples by Cole
and Obstfeld [1991] and Corsetti and Pesenti [2001a] -- equilibrium
fluctuations in real exchange rates and the terms of trade of the
magnitude of those observed in the data may be excessive
relative to the benchmark case of optimal transmission and hinder
international risk sharing, as is the case when
. Our analysis above unveils that an "excessively
positive" international transmission of productivity shock
generates an empirical pattern of low risk-sharing and can
therefore rationalize the Backus-Smith anomaly: large
terms-of-trade and real exchange rate depreciations will be
reflected in a reduction in relative consumptions.
Risk-sharing is clearly hindered by a negative transmission,
which prevails when
. In this case, a terms of trade appreciation in response to a
productivity shock raises domestic real import and consumption,
while reducing wealth abroad -- again in line with the Backus-Smith
evidence, but at odds with risk-sharing via relative price
movements.
The above stylized two-country, two-good model with financial
autarky and endowment shocks shows that, depending on the price
elasticity of tradables, the correlation between relative
consumption and the real exchange rate can have either sign. These
results emphasize a low price elasticity as a promising modelling
strategy to address the Backus-Smith anomaly. In what follows, we
pursue this strategy by developing a fully-fledged dynamic model
with capital accumulation and international trade in uncontingent
bonds. Different from standard models, however, a low price
elasticity of tradables will not be exclusively related to the
elasticity of substitution , but will be
an equilibrium implication of assuming a realistic structure of the
goods market, whereas we introduce distribution services.
It is worth stressing that our explanation of the Backus-Smith puzzle abstracts from nominal rigidities and demand shocks -- consistent with previous results from leading contributions. One may argue that the standard Mundell-Fleming-Dornbusch model also suggest a way to rationalize the Backus-Smith observation as a consequence of demand shocks. In this model, shocks to demand that drive domestic expenditure and consumption up appreciate the currency in real terms. Some external demand needs to be crowded out in order to make "more room" for domestic demand. This model thus appears to be consistent with the above evidence, but only to the extent that international business cycles and real exchange rate fluctuations can be described as mainly driven by demand shocks. Moreover, allowing for demand shocks (monetary and government spending shocks) in a two-country model with sticky prices (set by producers in the currency of the market of destination), Chari, Kehoe and McGrattan [2002] emphasize that the correlation between relative consumption and the real exchange rate remains close to 1 even when the only internationally traded asset is a nominal bond. In light of this result, in what follows we abstract from nominal rigidities altogether.9
In this and the next section, we develop our model, which will then be solved by employing standard numerical techniques. Our world economy consists of two countries of equal size, as before denoted H and F , each specialized in the production of an intermediate, perfectly tradable good. In addition, each country produces a nontradable good. This good is either consumed or used to make intermediate tradable goods H and F available to domestic consumers. In what follows, we describe our setup focusing on the Home country, with the understanding that similar expressions also characterize the Foreign economy -- whereas starred variables refer to Foreign firms and households.
Firms producing Home tradables (H) and Home nontradables (N) are perfectly competitive and employ a technology that combines domestic labor and capital inputs, according to the following Cobb-Douglas functions:
![]() |
![]() |
![]() |
![]() |
where
and
are exogenous random
disturbance following a statistical process to be determined below.
We assume that capital and labor are freely mobile across sectors.
The problem of these firms is standard: they hire labor and capital
from households to maximize their profits:
![]() |
![]() |
![]() |
![]() |
where
is the
wholesale price of the Home traded good and
is the price of the
nontraded good.
denote the wage rate, while
represents the capital rental rate.
Firms in the distribution sector are also perfectly competitive.
They buy tradable goods and distribute them to consumers using
nontraded goods as the only input in production. As in Burstein,
Neves and Rebelo [2003] and Corsetti and Dedola [2002], we assume
that bringing one unit of traded goods to Home (Foreign) consumers
requires units of the Home (Foreign) nontraded
goods.
The representative Home agent in the model maximizes the expected value of her lifetime utility, given by:
![]() |
(9) |
where instantaneous utility is a function of a
consumption index,
and leisure,
. Foreign agents' preferences are symmetrically
defined. It can be shown that, for all parameter values used in the
quantitative analysis below, these preferences guarantee the
presence of a locally unique symmetric steady state, independent of
initial conditions. 10
The full consumption basket, , in each
country is defined by the following CES aggregator
![]() |
(10) |
where
and
are the weights on the
consumption of traded and nontraded goods, respectively and
is the constant
elasticity of substitution between
and
. As in Section 2,
the consumption index of traded goods
is given by
(2).
A notable feature of our specification is that, because of
distribution costs, there is a wedge between the producer price and
the consumer price of each good. Let
and
denote the price of
the Home traded good at the producer and consumer
level, respectively. Let
denote the price of
the nontraded good that is necessary to distribute the tradable
one. With competitive firms in the distribution sector, the
consumer price of the traded good is simply
![]() |
(11) |
We hereafter write the utility-based CPIs, whereas the price index of tradables is given by (3):
![]() |
(12) |
Foreign prices, denoted with an asterisk and expressed in the same
currency as Home prices, are similarly defined. Observe that the
law of one price holds at the wholesale level but not at the
consumer level, so that
but
.
In the remainder of the paper, the price of Home aggregate
consumption
will be taken as the numeraire.
Hence, the real exchange rate will be given by the price of Foreign
aggregate consumption
in terms of
Home and Foreign agents hold an international bond,
, which pays in units
of Home aggregate consumption and is zero in net supply. Agents
derive income from working,
from renting capital to
firms,
, and from interest payments,
where
is the real bond's yield, paid at the
beginning of period
but known at time
. The individual flow budget constraint
for the representative agent in the Home country is
therefore:11
![]() |
(13) |
![]() |
We assume that investment is carried out in Home tradable goods and
that the capital stock, , can be freely reallocated
between the traded (
) and nontraded (
) sectors:12
As opposed to consumption goods, we assume that investment goods do
not require distribution services. The price of investment is
therefore equal to the wholesale price of the domestic traded good,
The
law of motion for the aggregate capital stock is given by:
![]() |
(14) |
The household's problem then consists of maximizing lifetime utility, defined by (9), subject to the constraints (13) and (14).
Let
denote the state of the world at time
where
. A competitive equilibrium is a set of Home agent's decision rules
a set of Foreign
agent's decision rules
a set of
Home firms' decision rules
a set of Foreign
firms' decision rules
a set of
pricing functions
such that
(i) the agents' decision rules solve the households' problems; (ii)
the firms' decision rules solve the firms' problems; and (iii) the
appropriate market-clearing conditions (for the labor market, the
capital market and the bond market) hold.
Table 2 reports our benchmark calibration, which we assume symmetric across countries. Several parameter values are similar to those adopted by Stockman and Tesar [1995], who calibrate their models to the United States relative to a set of OECD countries on annual data. Throughout the exercise, we will carry out sensitivity analysis and assess the robustness of our results under the benchmark calibration.
Productivity shocks We previously defined the exogenous state vector as
. We assume that disturbances to technology follow a
trend-stationary AR(1) process
![]() |
(15) |
whereas
has variance-covariance matrix
and
is a
matrix of coefficients describing the autocorrelation
properties of the shocks. Since we assume a symmetric economic
structure across countries, we also impose cross-country symmetry
on the autocorrelation and variance-covariance matrices of the
above sectoral process.
Consistent with our model and other open-economy studies (e.g., Backus, Kehoe and Kydland [1995]), we identify technology shocks with Solow residuals in each sector, using annual data in manufacturing and services from the OECD STAN database. Since hours are not available for most other OECD countries, we use sectoral data on employment. An appendix describes our data in more detail.
The bottom panel of Table 2 reports our estimates of the parameters describing the process driving productivity. As found by previous studies, our estimated technology shocks are fairly persistent. On the other hand, in line with empirical studies, we find that spillovers across countries and sectors are not negligible.13
Preferences and production Consider first the preference parameters. Assuming a utility function of the form:
![]() |
(16) |
where
is a taste shock, we set
so that in steady state, one third of
the time endowment is spent working;
(risk
aversion) is set equal to 2. Following Schmitt-Grohe and Uribe
[2001], we assume that the endogenous discount factor depends on
the average per capita level of consumption,
, and hours worked,
, and has
the following form:
whereas is chosen such that the steady-state
real interest rate is 4 percent per annum, equal to 0.08. This
parameter also determines the speed of convergence to the unique
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. Stockman and Tesar [1995] estimate a
lower elasticity (0.44), but their sample includes both developed
and developing countries.
As regards the weights of domestic and foreign tradables in the
tradables consumption basket (
,
and
(normalized to
) are chosen
such that imports are 5 percent of aggregate output in steady
state. This corresponds to the average ratio of U.S. imports from
Europe, Canada and Japan to U.S. GDP between 1960 and 2002. The
weights of traded and nontraded goods,
and
, are chosen as to
match the share of nontradables in the U.S. consumption basket.
Over the period 1967-2002, this share is equal to 53 percent on
average. Consistently, Stockman and Tesar [1995] suggest that the
share of nontradables in the consumption basket of the seven
largest OECD countries is roughly 50 percent.
We calibrate and
the
labor shares in the production of tradables and nontradables, based
on the work of Stockman and Tesar [1995]. They calculate these
shares to be equal to 61 percent and 56 percent, respectively.
Finally, we set the depreciation rate of capital equal to 10
percent annually.
Distribution costs and the price elasticity of tradables The introduction of a distribution sector in our model is a novel feature relative to standard business cycle models in the literature. Before delving into numerical analysis, it is appropriate to discuss an important implication of this feature regarding the price elasticity of tradables. From the representative consumer's first-order conditions (regardless of frictions in the asset and goods markets), optimality requires that the relative price of the imported good in terms of the domestic tradable at consumer level be equal to the ratio of marginal utilities:
![]() |
(17) |
where
is equal
to the elasticity of substitution between Home and Foreign
tradables in the consumption aggregator
and thus to the
consumer price elasticity of these goods. Note that
is the
inverse of the ratio of real imports to nonexported tradable output
net of investment. In analogy to the literature, we can refer to
this ratio as the (tradable) import ratio.
Because of distribution costs, the relative price of imports in
terms of Home exports at the consumer level does not coincide with
the terms of trade
-- as in most standard models (e.g. Lucas [1982]). Let
denote the size of the distribution margin in steady
state, i.e.,
By log-linearizing (17), we get:
![]() |
(18) |
where the terms of trade is measured at the
producer-price level so that
can be thought of
as the producer price elasticity of tradables. Clearly, both
and
impinge
on the magnitude of the international transmission of
country-specific shocks through the equilibrium changes in the
terms of trade. It is well known that for any given change in
a lower
transpires into larger changes in the
terms of trade. In our model, a larger distribution margin
(i.e., a larger
) has
a similar effect. Accounting for distributive trade thus results
into an amplification of fluctuations in international relative
prices for any given variability in real quantities. So, for given
and
large
movements in the difference between the real consumption of
domestic and imported tradables
(the inverse of the import ratio) will be reflected in highly
volatile terms of trade and deviations from the law of one
price.14 Remarkably, it will be shown below
that in the U.S. data the absolute standard deviation of this ratio
is very close to that of the terms of trade (4.13 and 3.68 per
cent, respectively).15
There is considerable uncertainty regarding trade price
elasticities. Using time series data, empirical researchers have
found estimates that range from about 0.1 to 2 (see the
comprehensive study on G-7 countries by Hooper, Johnson and Marquez
[2000]). For instance, for the U.S. Taylor [1993] estimates a value
of 0.39, while Whalley [1985] finds it to be 1.5. For European
countries most empirical studies suggest values below 1.16
Correspondingly, there are differences in the quantitative
literature. For instance, in a model with traded and nontraded
goods similar to ours, Stockman and Tesar [1995] set the parameter
-- directly related to the price
elasticity with no distribution costs -- equal to 1. Following
Whalley [1985], in a model with only tradable goods Backus,
Kydland, and Kehoe [1995] set it equal to 1.5, whereas Heathcote
and Perri [2002] estimate it as low as 0.9. However, these authors
also report sensitivity analysis suggesting that much lower values,
in the range of 0.5, can improve their model performance in
accounting for features of the international business cycle like
the volatility of the terms of trade.
Given the uncertainty surrounding the appropriate parameter
value, and the key role this elasticity plays in open economy
models, we choose to follow a different route. First, we rely on
estimates in the trade literature on distribution costs to pick a
value for . 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 between 40 percent and 50 percent, depending on the
industrial sector. In their exhaustive survey on trade costs,
Anderson and van Wincoop [2004] report that in industrialized
countries representative local distribution costs account for over
55 percent of retail prices. Thus, we follow the calibration in
Burstein, Neves and Rebelo [2003] and set distribution costs to 50
percent.
Second, we set the elasticity of substitution to match the volatility of the U.S. real exchange rate
relative to that of U.S. output, equal to 3.28 (see Table 3 below).
Therefore, our quantitative analysis below can be interpreted as
investigating the link among international price movements, risk
sharing and the international transmission conditional on the model
being consistent with the observed volatility in real exchange
rates. In Section 2.2, we have used a simplified setup to show that
the volatility of international prices is hump-shaped in
, and discussed at length the
mechanism underlying this pattern. Consistently, we find two values
for the elasticity
such that the model
matches the volatility of the U.S. real exchange rate. In our
benchmark calibration these two values are
and
. Strikingly both values are
quite close to that assumed by Stockman and Tesar [1995], implying
similar consumers preferences across tradables for given consumer
prices. Most important, when combined with the calibrated value for
, the implied trade price elasticities
are well in the range of available estimates. While apparently
close to each other, however, the two possible values for
imply quite different dynamics and
international transmission patterns for shocks to tradables
productivity. These differences will become central to our
discussion of the evidence discussed at the end of the paper.
Our goal in this section is to verify whether our model can match the empirical evidence on the unconditional correlation between international prices and quantities, as well as the their relative volatilities. The evidence is summarized by the statistics reported in the first column of Tables 3 and 4. The statistics for the data -- all filtered using the Hodrick and Prescott filter -- are computed with the United States as the home country and an aggregate of the OECD comprising the European Union, Japan and Canada as the foreign country.17 Notably, the Backus Smith correlation between relative consumption and the real exchange rate is equal to -0.45.
In what follows, we will show that, different from standard open-economy models, our artificial economy performs quite well in this dimension. Throughout our exercises, we take a first-order Taylor series expansion around the deterministic steady state and simulate our model economy using King and Watson [1998]'s algorithm. We compute the model's statistics by logging and filtering the model's artificial time series using the Hodrick and Prescott filter and averaging moments across 100 simulations. Consistently with our dataset, in our simulations changes in aggregate GDP and consumption are computed using constant prices (precisely, we use relative steady state prices). The results for our baseline model and some variations on it are also shown in Tables 3 and 4.
The real exchange rate and the terms
of trade Using our framework, we can write the real exchange rate
() in the following log-linear form,
reflecting movements in the terms of trade as well as in the
relative price of non-traded goods:
![]() |
(19) |
where
and
represents the relative
price of nontradables.18 In our numerical results, the first
two components, arising from home bias in consumption and
deviations of the law of one price for the CPI of tradables,
dominate real exchange-rate movements.
In our baseline economy the real exchange rate and the terms of
trade are tightly related. Their correlation is positive (and equal
to 0.97 and 0.98, depending on our calibrated value of ), though higher than in the data (0.6). A positive
sign for this correlation is an important result relative to
alternative models that -- like ours -- allow for deviations from
the law of one price but do so by assuming sticky prices in the
buyer's currency. As argued by Obstfeld and Rogoff [2001], these
models can generate high exchange rate volatility as well, but at
the cost of inducing a counterfactual negative correlation between
the real exchange rate and the terms of trade.
The terms of trade is very volatile, even more than in the data.
The volatility of the terms of trade relative to output is 2.84
with
, and 4.47 with
, compared to 1.79 in the data.
In this sense, our model suggests that high volatility of the
international prices per se is not a measure of their
'disconnect' from fundamentals. To stress this point, consider the
volatility of the import ratio (IR), defined as the ratio of real
imports to nonexported tradable output net of investment
(empirically, we compute this ratio using manufacturing output). As
shown in Table 4, the standard deviation of the import ratio is
4.13 percent in the data. In our benchmark parametrization, it is
equal to 2.26 for the smaller
, but
increases to 4.33 percent for the larger
.19
Moreover, with
the model is consistent with the
ranking of variability in international prices observed in the
data: the real exchange rate is more volatile than the terms of
trade. The difference may be due either to the volatility of
deviations from the law of one price (which drives a wedge between
the terms of trade and relative prices at consumer levels) or to
the volatility of nontradable prices, or a combination of the two.
For this reason, the correct ranking of volatility is very hard to
replicate using models that abstract from the features above (see
Heathcoate and Perri [2002]).
We find that the relative price of nontradables across countries
is not the main force driving the high volatility of the model's
real exchange rate. Table 3 shows that the volatility of the
relative price of nontradables predicted by our model is quite in
line with that in the data: depending on ,
this volatility is 1.41 and 1.13, against an empirical estimate of
1.73. When we compute the ratio between the standard deviation of
the relative price of nontradables across countries, and the
standard deviation of the real exchange rate, this ratio is 40
percent and 33 percent, for the low and high
respectively. This figure is in line with that
estimated by Betts and Kehoe [2001], who find this ratio to be
between 35 and 44 percent using a weighted average of U.S.
bilateral real exchange rates.20
The Backus-Smith correlation An important novel result of our baseline model shown in Table 3
is that the correlation between relative consumption and the real
exchange rate is not only negative, but also quite close to its
empirical counterpart. With
and
, the correlation generated by
the model is respectively -0.48 and -0.45, against our empirical
estimate of -0.45. A similar pattern emerges for the terms of
trade: its correlation with relative consumption is -0.63 and -0.66
in the model, against an empirical estimate of -0.53.
Since our two values of are set so
that the model replicates the volatility of the real exchange rate
in the data, our results show that the price elasticity that is
consistent with a realistic volatility in international prices also
implies a realistic pattern of risk-sharing. 21 What generates a
negative Backus-Smith correlation is the mechanism linking
volatility and risk-sharing discussed in Section 2 in a very simple
setting under financial autarky. However, note that the simple
model predicts a perfectly negative correlation between relative
consumption and the real exchange rate. In our baseline economy
with capital accumulation and international borrowing and lending,
the same mechanism accounts for the quantitative result of a
negative but less than perfect correlation. It is instructive to
inspect the reason underlying this difference in detail. When
international asset trade is limited to uncontingent bonds, the
relation between the real exchange rate and marginal utilities of
consumption only holds in expected first-differences -- the
log-linearized Euler equations for the bond yield (abstracting from
the time-varying discount factor):
![]() |
(20) |
To the extent that the tight link between growth rates of variables is inherited by their levels, this expression suggests a mechanism that may prevent standard models allowing for borrowing and lending at international level to fit the Backus-Smith evidence. But in a stochastic environment, the international bond is traded only after the resolution of uncertainty, and does not provide households with ex-ante insurance against country-specific income shocks -- it only makes it possible to reallocate wealth and smooth consumption over time. The impact effect of a shock to tradables in a bond economy will thus be roughly the same as under financial autarky, moving relative consumption and the real exchange rate in a direction that will depend on the value of the price elasticity. Under our calibration, the Backus-Smith correlation will therefore be negative on impact, but positive in the aftermath of a shock, when the dynamics of relative consumption and the real exchange rate is determined by the above equation. For this reason, the Backus-Smith correlation in a bond economy will be less negative than under financial autarky.22 It will also become higher and closer to that implied by complete markets, the weaker the impact response (in absolute value) of the real exchange rate -- i.e., the less volatile the real exchange rate and the terms of trade on impact.23
International relative prices and business cycles Consider now the rest of the statistics for the baseline economy in Tables 3 and 4. As is well known, most open-economy models -- including those allowing for nominal rigidities and monetary shocks -- predict a strong and positive link between relative output and real exchange rates. As Stockman [1998] points out, this prediction is at variance with the data: the empirical correlation shown in Table 3 is -0.23. A similar shortcoming concerns the correlation between relative output and the terms of trade, which is negative in the data (and equal to -0.20), while it tends to be positive in quantitative models.
Our baseline economy yields contrasting results on this issue.
The correlation between relative output and the real exchange rate
(the terms of trade) is high and positive -- equal to 0.93 and 0.98
respectively -- with
, but becomes strongly negative
with
. This is because, with the lower
, positive productivity shocks in the
tradable sector appreciate the terms of trade and the real exchange
rate -- a result that we will discuss in greater detail below. We
observe here that this very mechanism also accounts for the ability
of the model to match the observed positive correlation between
international relative prices and net exports, also shown at the
bottom of the table.
In Table 4, we see that the cross-country correlation of GDP in
the model (0.42 and 0.40 depending on ) is
very close to that in the data (0.49), and higher than that of
consumption. The cross-correlation of consumption is lower than in
the data (0.10 versus 0.32), while the cross-correlations of
investment and employment are higher. While positive comovements in
production mainly arise because of the positive cross-country
correlation of the shock innovations, the baseline model still does
relatively better in this dimension than the standard international
real business cycle model. It is well known that this class of
models predicts that consumption should be more correlated across
countries than output, largely independent of the shocks'
cross-country correlations, and that the correlation across
countries of investment and employment is negative, even under
financial autarky -- in Backus, Kehoe and Kydland [1995] this
empirical incongruity is dubbed the 'quantity anomaly'.
Finally, a discrepancy between the benchmark model and the data
is that -- relative to output -- consumption, investment, and
employment are slightly less volatile than in data; net exports are
about half as volatile in the model as in the data (0.25/0.38
against 0.63). However, note that our results with
account for countercyclical net
exports. Their correlation with GDP is -0.51 in the model, very
much in line with the data.
The Arrow-Debreu Economy The fourth column of Tables 3 and 4 reports results for an
economy with a complete set of Arrow-Debreu securities. Since in
such an economy the volatility of the real exchange rate is to a
large extent independent of the price elasticity of imports, we
only show numerical results for the lower value of -- basically replicating the parameterization in
Stockman and Tesar [1995]. As expected, including distribution
services in such an environment is not enough to account for the
Backus-Smith anomaly. The correlation between the real exchange
rate and relative consumption is approximately equal to one.
Moreover, the volatility of the real exchange rate, the terms of
trade, the import ratio and net exports is several times lower than
that in the data.
Nevertheless, this model generates a negative correlation between the real exchange rate and relative output, in line with the observed one. This is because productivity gains in the Home tradable sector raise relative output, worsen the Home terms of trade, but appreciate the real exchange rate -- the real appreciation reflecting a higher relative price of nontradables and a fall in relative consumption in the period following the shock, driven by a drop in the consumption of nontradables. On the other hand, contrary to the data, the correlation between the terms of trade and relative output is positive, while the real exchange rate and the terms of trade are basically uncorrelated (0.02).
We now assess the sensitivity of our results to (a) removing the distribution sector from our baseline economy; (b) setting a very high elasticity of substitution of tradables -- as to check whether the Backus-Smith correlation could be explained by a Balassa-Samuelson effect of productivity shocks on consumption and the real exchange rate; (c) removing cross-country spillovers from the process driving productivity shocks; (d) using different specifications of investment; and (e) introducing taste shocks. Results from these exercises are also shown in Tables 3 and 4.
Changing the distribution margin and
the elasticity of substitution When we abstract from distributive trade and set , the two values of
for which the
relative volatility of the real exchange rate in the model is the
same as in the data are 0.27 and 0.44, a good deal lower than
in our benchmark economy. As discussed in Section 4, the need to
combine tradables with retailing in our baseline economy makes the
price elasticity of imports lower than the value implied by the
preference parameter
. Without retailing, we
need to assume a lower elasticity of substitution between Home and
Foreign goods in agents' preferences for the model to fit the
volatility of the real exchange rate.
With a lower elasticity of substitution but no distribution
services, the model still performs remarkably well with respect to
the Backus-Smith anomaly: the correlation between the real exchange
rate and relative consumption is negative and equal to -0.22
(-0.81) for
(0.44). The underlying mechanism
has already been thoroughly discussed in sections 2.2 and 2.3.
With however, there are no deviations
from the law of one price, contradicting an important stylized fact
of the international economy (e.g., see Engel [1999]). As a
consequence, movements in the relative price of nontradables across
countries contribute to real exchange-rate fluctuations much more
than in our benchmark economy. The standard deviation of the
relative price of nontradables across countries is now 84 percent
of that of the real exchange rate when
and 56 percent when
, a significantly higher
fraction than in the data. Moreover, the relative price of
nontradables is more volatile than in the data and substantially
more volatile than under our benchmark economy (2.83 and 2.07
against 1.41 and 1.13). These results suggest that introducing a
distribution sector improves the performance of the model
independently of contributing to lower the trade elasticities
relative to what would be implied by preferences.
Balassa-Samuelson effects An interesting issue is whether the Backus-Smith anomaly could be accounted for by Balassa-Samuelson effects, linking exchange-rate fluctuations to movements in the relative price of nontradables. The idea is as follows. Consider a model in which domestic and foreign tradables are highly substitutable. A positive productivity shock to the tradable sector should appreciate the real exchange rate (terms of trade movements are tiny), and drive up domestic relative to foreign consumption. Is the Backus-Smith correlation driven mainly by this effect?
Our answer is no. In a numerical experiment, we abstract from
distributive trade ( and assume a rather
high value of
equal to
-- so
as to make tradables more homogeneous across countries and reduce
the role of the terms of trade in exchange-rate fluctuations
(results are the same for higher
). With such a
high elasticity of substitution, it is the correlation between the
real exchange rate and relative output that becomes very negative
(-0.54), but the corresponding correlation with relative
consumption remains close to one, i.e. as high as 0.84. In
addition, both the real exchange rate and the terms of trade are a
great deal less volatile than output (1.06 and 0.26), while their
cross-correlation is substantially lower than in the data
(0.13).
Absence of Spillovers As shown in Table 2, the process driving productivity that we
estimate and use in our model displays substantial cross-country
spillovers. How much of our results can be attributed to the
magnitude of such spillovers? It turns out that removing them
altogether in our numerical exercises does not substantially affect
our main conclusions. Adopting the productivity process without
spillovers, we again calibrate our economy such that the real
exchange rate is as volatile as in the data, obtaining
and
. The Backus-Smith correlation
remains close to the one in our baseline economy: -0.65 and -0.34.
However, one significant implication of removing spillovers is that
consumption becomes negatively correlated across countries for
.
Changing the investment specification In our baseline economy investment is carried out solely in domestically produced tradable goods. In our last exercise, we allow for a more general specification in which investment is a composite good comprising both Home and Foreign tradables. We assume that investment goods are given by the following CES aggregator
where
(
is the level of
investment in terms of the domestic (imported) traded good. As in
our baseline calibration, we set
and
such that imports
(which now also include investment) are 5 percent of aggregate
output in steady state. Since in this exercise investment goods
also include imports, we also introduce distribution services in
the price of investment to differentiate between trade-price
elasticities and preferences. But following Burnstein, Neves, and
Rebelo [2004], we set the share of distribution services in the
price of investment to be 16.7 percent. In Tables 3 and 4 results
are shown under the heading "CES Investment."
With the more general CES specification for investment, the
values of needed to reproduce the
volatility of the real exchange rate relative to that of output are
smaller than under our benchmark calibration. This is because
investment goods can now be imported from abroad, and investment
does not require as much distribution services as consumer goods
do. Thus, any given price elasticity of imports corresponds to a
lower elasticity of substitution relative to our baseline
specification. Nonetheless, the model still succeeds in generating
a significant departure from the complete markets outcome. Although
the real exchange rate and relative consumption are not as
negatively correlated as in our previous experiments, their
correlation remains well below zero. When
the model predicts a slightly
negative correlation of -0.34.24
Taste shocks The last two columns of Tables 3 and 4 report results from
introducing taste shocks in an economy with a complete set of
Arrow-Debreu securities and in our baseline economy, respectively.
We follow Stockman and Tesar [1995] and calibrate the taste shocks
in (16) assuming that
they are uncorrelated across countries and have a standard
deviation and serial correlation equal to the largest between the
two productivity shocks, 0.0089 and 0.961, respectively (see
Table 2).
The results in the last column in Tables 3 and 4 show the performance of our baseline economy accounting for these shocks. Interestingly, our results are broadly unchanged. The only significant difference is that, these shocks mainly affecting consumption, its cross-country correlation becomes too low, basically zero.
The results shown in the column before the last also show that assuming preference shocks to utility that are as volatile and persistent as productivity shocks, can improve the 'fit' of the complete market economy along a number of dimensions, including the Backus-Smith puzzle. Namely, the correlation between the real exchange rate and relative consumption is equal to -0.22; that between the terms of trade and relative consumption is negative as well, equal to -0.58. Moreover, the terms of trade and real exchange rate are now positively correlated (0.21), although less than in the data. However, while taste shocks in the Arrow Debreu economy also raise the volatility of the real exchange rate, the terms of trade, the import ratio and net exports, volatility is still much lower than in the data. Also, the cross-correlation of consumption becomes slightly negative. The correlation between net exports and GDP, and terms of trade and relative GDP is not as strongly negative as in the data.
The introduction of taste shocks in international business cycle models with complete markets weaken the links between relative consumption and relative marginal utility, thus being functional to generate a low or negative correlation between real exchange rates and relative consumptions. Yet, it is far from obvious that this approach can satisfactorily address the evidence of the low degree of risk sharing in other dimensions. Overall, we take these results as suggesting that the basic mechanism behind the Backus-Smith puzzle requires a combination of supply and demand effects, as implied by imperfect risk pooling.25
In our model, given a value for the distribution margin
there are two values of price
elasticity and thus of
that generate a real
exchange-rate volatility matching the evidence. In this subsection,
we analyze the difference between these two parameterizations by
looking at theoretical impulse responses to a shock to the traded
goods sector.
Our experiments consist of shocking the exogenous process for
sectoral productivity once by 1 percent at date 0, when both
countries are at their symmetric, deterministic steady state, and
let productivity be driven by the estimated autoregressive process
in (15).
Figure 2 draws the responses of the following economic variables:
(a) the real exchange rate; (b) the terms of trade; (c) relative
consumption; (d) relative aggregate output; (e) the ratio of net
exports to output. The two columns in Figure 2 report impulse
responses for
and
respectively. 26
Consider first the impulse responses under the higher
(first column in the figure). Since
for this value of the price elasticity world demand for Home
tradables is increasing in its relative price, the increase in the
supply of Home traded goods relative to the Foreign goods worsens
the Home country's terms of trade. Note that an adverse effect of
productivity shocks on the real exchange rate and the terms of
trade is predicted by all standard models with product
specialization and homothetic preferences (e.g., Lucas [1982] and
Backus et al. [1995]).27 The notable feature of our
specification with incomplete markets is that a relatively low
price elasticity of imports (also owing to the presence of
retailing) magnifies the deterioration of the Home terms of trade
and real exchange rate, increasing the ensuing negative wealth
effect for the domestic household. As a result, consumption abroad
rises by more than domestic consumption, while domestic output
rises relative to the foreign one. Thus, the real exchange rate,
the terms of trade and relative output on the one hand, and
relative consumption on the other move in the opposite direction,
as the large terms of trade worsening entails an excessively
positive transmission of the productivity shock in favor of the
Foreign country. Note that net exports increase following the rise
in productivity, which is consistent with the depreciations of the
real exchange rate and the terms of trade.
The response of the economy to an innovation in the productivity
of the domestic traded sector is widely different when
In this case, relative output
still rises, but the real exchange rate and the terms of trade now
appreciate. Recalls from Section 2 that for a low enough price
elasticity (low enough
), world demand for
Home tradables will be negatively sloped in the terms of trade,
owing to a prevailing negative income effect for the domestic
household. An increase in the relative supply of Home tradables
will thus require a terms-of-trade appreciation in equilibrium to
bring about market clearing. And as the terms of trade improve,
Home consumption rises by more than Foreign consumption. As a
result, the real exchange rate, the terms of trade and relative
consumption are again negatively correlated, but now relative
output will move in the same direction as relative consumption,
though by a lesser amount. Finally, the positive productivity shock
triggers a fall in net exports, which can account for its
well-known negative counter-cyclical movements.
To summarize, a productivity shock to the export sector always induces an increase in relative output and (conditional) negative comovements between the real exchange rate, the terms of trade and relative consumption. Depending on the strength of the price-elasticity of imports and thus on the slope of world demand, however, relative consumption can increase or fall in response to a positive shock.
In this section we study the comovements between the real exchange rate, the terms of trade, and relative consumption in response to productivity changes in the U.S. economy. Given our focus on time series evidence, we use VAR methods, extending work by Galí [1999] and Christiano, Eichenbaum and Vigfusson [2003] -- where technology shocks are identified via long-run restrictions -- to an open-economy context. We focus our study on the U.S. economy vis-à-vis an aggregate of other OECD countries.
A number of recent papers have investigated in a closed-economy framework the effects of technology shocks identified using long-run restrictions. This literature uses the basic insight from the standard stochastic growth model that only technology shocks should have a permanent effect on labor productivity to identify economy-wide technology shocks in the data. 28 However, since Galí [1999], several contributions have pointed out that these methods yield results that may be sensitive to assumptions about the particular VAR specification, e.g. the number and kind of variables included and the time series of properties of the variables. In this vein, Christiano, Eichenbaum and Vigfusson [2003] show that the findings in Gal í [1999] are turned around when variables like per capita hours worked are treated as a trend stationary process rather than as a difference stationary process, as does the latter author.
Following these insights, we thus examine the effects of technology shocks to the U.S. manufacturing sector (our proxy for traded goods), identified with long run restrictions, on the real exchange rate, the terms of trade, net exports and relative consumption and output, while carrying out several robustness checks. As Chang and Hong [2002] show that using total factor productivity (TFP) instead of labor productivity may affect results for the manufacturing sector, we also assess the robustness of our results to the use of (annual) TFP data. Moreover, the use of TFP provides a further check on the identification strategy, as it amounts to controlling for long-run effects on labor productivity brought about by changes in the long-run capital labor ratio.29 Leaving to the data appendix a more detailed description of data sources, hereafter we briefly describe our approach and discuss the main results.
Over the period 1970 to 2001, we estimate two specifications of the following structural VAR model
![]() |
(21) |
Here denotes the variable that is assumed
to be affected in the long run only by permanent technology shocks:
in our two different specifications, this variable is equal to (the
log of) U.S. quarterly manufacturing labor productivity and (the
log of) annual manufacturing TFP, respectively, both measured in
deviation from labor productivity in an aggregate of other OECD
countries. In the quarterly specification
is
a 5x1 vector of variables, including (the log of) U.S. aggregate
GDP and consumption relative to that of a composite of other OECD
countries, the U.S. ratio of net export over GDP, (the log of) the
U.S. real effective (trade-weighted) exchange rate, and (the log
of) the terms of trade (computed as the non-energy imports deflator
over the exports deflator). In the annual specification, in order
to save degrees of freedom
is 3x1. The
first two components of the quarterly specification are always
included, while the last three are included one by one.30
is a polynomial in the lag
operator;
denotes the technology
shock to manufacturing, and
the other structural,
non-technology shocks.31 In addition to the usual assumption
that the structural shocks are uncorrelated, positing that
is enough to
identify
. This restricts the
unit root in the variable
to originate
solely in the technology shock. Although not necessary for
identification, implicit in this benchmark specification is the
assumption that all the other variables also have a unit root; this
assumption is not rejected by the data over our sample. However,
following the suggestions in Christiano, Eichenbaum and Vigfusson
[2003], we also estimated specifications of the VAR with those
variables, like the real exchange rate, for which the unit root
null is not rejected only marginally, in levels. Our main findings
below, that a technology improvement leads to a persistent
terms-of-trade deterioration and real exchange-rate depreciation,
are basically unaltered. 32
Figure 3 shows the effects of the identified technology shocks on the levels of productivity, relative consumption, the real exchange rate, and the terms of trade. The first column is obtained from quarterly data, the second one from annual data. We report error bands for the significance levels of 68 percent and 90 percent (corresponding to the darker and lighter shaded areas, respectively).33
The first column in Figure 3 shows the impulse responses using
Galí's identification scheme, with
equal to (relative) U.S. manufacturing labor productivity.
Following a positive technology shock to manufacturing, U.S. total
consumption increases gradually but permanently relative to the
rest of the world. Moreover, the real exchange rate and the terms
of trade strongly appreciate on impact and remain permanently
stronger, by an amount that is larger in the case of the real
exchange rate, but that for both variables outsizes the increase in
productivity. Net exports fall following the positive productivity
shock, which is also consistent with the predictions of the model
under the negative transmission.
The second column in Figure 3 reports the effects of a technology shock identified as the only shock that permanently affects TFP in U.S. manufacturing. Our findings are broadly robust across different long-run identification schemes. In the annual data VAR also a positive technology shock to the U.S. production of tradables appears to lead to an increase in domestic consumption relative to the rest of the world, while improving the terms of trade and appreciating the real exchange rate for at least a year. As with quarterly data, the rise in productivity leads to a fall in net exports.34
Finally, we also checked whether these results were robust to using a different identification scheme, namely, assuming that a technology shock is the contemporaneous innovation to relative labor productivity in U.S. manufacturing, while keeping the same order of the variables as in (21) but in levels rather than first-differences. This identification scheme is closer in spirit to the assumption entertained in the calibration that labor productivity is basically an exogenous process. Again, as the results were very similar to those obtained above we do not report them here for the sake of brevity.35
To summarize, U.S. consumption relative to the rest of the world and the real exchange rate move in opposite directions, in sharp contrast with the predictions of the perfect risk-sharing hypothesis. Consistent with the Backus-Smith anomaly, the results in this section indicate that following changes in (relative) labor productivity in the traded goods sector real exchange rates and relative consumption can indeed be negatively correlated. Most interestingly, the appreciation of the real exchange rate, and especially the terms of trade, as well as the fall in net exports in response to a positive technology shock to domestic tradables, is qualitatively consistent with the transmission mechanism at work in our setup under the lower value of the price elasticity, but at odds with the presumption that an increase in the world supply of a good necessarily leads to a fall in its relative price.
It is worth stressing that we do not expect our empirical results for the U.S. -- a very large, rich and relatively closed economy -- to readily generalize to smaller and/or more open economies. Our theoretical model suggests that the wealth effects underlying the negative transmission of productivity shocks are rather unlikely in such economies. In this sense we see our findings as complementing the cross-sectional evidence provided by Acemoglu and Ventura [2003], showing that terms of trade changes are negatively related to output growth driven by capital accumulation. To reconcile the difference in our results it should be kept in mind that, first, we analyze time series for one country with quite distinctive features, as opposed to using cross-sectional data techniques. Second, we adopt a setting that directly tackles the problem of disentangling changes in technology from other factors, like those affecting demand.
Our model links the terms of trade appreciation in response to productivity shocks to price elasticities, in turn reflecting market structure and basic features of the economy, such as Home bias in consumption. In their empirical contribution based on panel data techniques, Debaere and Lee [2003] attribute terms of trade appreciation to quality and variety upgrading effects, proxied by variables such as income per capita and spending on research and development. While the creation of new and better goods varieties obviously runs against a fall in a country's terms of trade, the question is whether productivity improvements (that reduce marginal costs of production and/or marginal costs of creation of new varieties) could lead to both the creation of new varieties and an appreciation of the terms of trade. Some theoretical work in this area suggest that the answer in standard trade and macro models with endogenous creation of new goods is negative or ambiguous (see Acemoglu and Ventura [2003] and Corsetti, Martin and Pesenti [2004]).36
Many contributions to the literature have stressed that movements in the terms of trade in response to country-specific shocks may provide risk insurance to countries specialized in different types of goods. In this paper, we have reconsidered the link between exchange rate volatility and international consumption risk sharing, using a standard model with incomplete asset markets, where a low price elasticity of tradables arises from the presence of distribution services. In numerical exercises conducted under a plausible parameterization of our world economy, we find that the international transmission of productivity shocks envisioned in our model can actually account both for the high volatility of international prices and for the (unconditional) negative link between the real exchange rate and relative consumption observed in the data.
We complement our theoretical analysis with suggestive evidence supporting the prediction of a negative conditional correlation between relative consumption and international relative prices. Following a permanent positive shock to U.S. labor productivity in manufacturing (our measure of tradable goods), domestic output and consumption increase relative to the rest of the world, but both the terms of trade and the real exchange rate appreciate. Consistent with our model, productivity improvements do not lead to a drop in the international relative price of domestic tradables. This result is reasonably robust to the definition of the terms of trade and the use of TFP instead of labor productivity.
Our analysis suggests that large equilibrium terms-of-trade movements, reflecting trade frictions, may be much less effective in providing insurance against production risk -- and can even be counterproductive, in the sense of amplifying cross-country wedges in wealth stemming from asymmetric productivity shocks. In other words, international relative prices may move in ways that run counter to efficient risk sharing. Given the relevance of this issue to our understanding of the international transmission of supply shocks and the mechanism of international risk-sharing, further empirical and theoretical work would prove extremely helpful.
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This appendix describes the data used in this paper. The complete dataset is available from the authors upon request and covers the period 1970 to 2001, unless otherwise stated.
To calibrate the process of the shocks for the Home country labor productivity in tradables and nontradables we use the annual BLS series "Index of output per hour in manufacturing" and "Index of output per hour in private services," respectively. For the Foreign country we use an aggregation of the index of manufacturing output and output in services divided by sectoral total employment for an aggregate of OECD countries (Canada, Japan, EU-15) obtained from the OECD STAN sectoral database.
U.S. GDP, consumption and investment are annual chain-weighted 1996 dollar NIPA series from the BEA. World GDP, consumption and investment are annual constant 1995 PPP dollar series for Japan, Canada and EU-15 from the OECD Quarterly National Accounts. The U.S. labor input is the "Index of total hours in the non-farm business sector" from the BLS, while world labor input is aggregate employment for Japan, Canada and EU-15 from the OECD.
The series for U.S. imports and exports at current and constant prices are annual NIPA series from the BEA. The series for the U.S. real exchange rate is a trade-weighted measure of the real value of the dollar computed by J.P. Morgan vis-à-vis the main U.S. trading partners; the series for the U.S. (ex-oil) terms of trade is the ratio of the NIPA (non-oil) import price deflator over the export price deflator from the BEA. The relative price of nontradables in terms of tradables is computed as the ratio of the services CPI over the commodities CPI. Again all this are annual series.
In the estimation of the VAR models for the series on world labor productivity (quarterly) and total factor productivity (annual) we use the ratio between aggregate GDP and labor input for Japan, Canada and EU-15, and the index of TFP in the aggregate OECD countries from the OECD, respectively. In the quarterly VAR, the series for GDP, consumption, net exports, real exchange rate and terms of trade are the quarterly counterpart of the annual series described above.
Table 1: Correlations between real exchange rates and relative consumptionsa
Country | HP-Filtered: U.S. | HP-Filtered: OECD | First-Difference: U.S. | First-Difference: OECD |
---|---|---|---|---|
Australia | -0.01 | 0.05 | -0.09 | -0.13 |
Austria | -0.35 | -0.54 | -0.20 | -0.30 |
Belgium | -0.12 | 0.15 | -0.11 | 0.19 |
Canada | -0.41 | -0.10 | -0.20 | 0.02 |
Denmark | -0.16 | -0.27 | -0.20 | -0.21 |
E.U. | -0.30 | -0.10 | -0.23 | -0.04 |
Finland | -0.27 | -0.64 | -0.40 | -0.55 |
France | -0.18 | 0.12 | -0.21 | -0.01 |
Germany | -0.27 | -0.17 | -0.13 | 0.01 |
Italy | -0.26 | -0.51 | -0.27 | -0.31 |
Japan | 0.09 | 0.27 | 0.04 | 0.08 |
South Korea | -0.73 | -0.50 | -0.79 | -0.63 |
Mexico | -0.73 | -0.77 | -0.68 | -0.74 |
Netherlands | -0.41 | -0.20 | -0.30 | -0.19 |
New Zealand | -0.25 | -0.37 | -0.27 | -0.28 |
Portugal | -0.56 | -0.73 | -0.48 | -0.67 |
Sweden | -0.52 | -0.39 | -0.34 | -0.29 |
Spain | -0.60 | -0.66 | -0.41 | -0.38 |
Switzerland | 0.16 | 0.53 | 0.09 | 0.32 |
Turkey | -0.31 | -0.25 | -0.34 | -0.17 |
U.K. | -0.47 | -0.08 | -0.40 | -0.04 |
U.S. | N/A | -0.30 | N/A | -0.31 |
Medianb | -0.30 | -0.27 | -0.27 | -0.21 |
Cross-sectional 68 % CI | (-0.12,-0.56) | (0.12,-0.54) | (-0.11,-0.41) | (0.02,-0.55) |
a Consumption
and bilateral and effective real exchange rates are annual series
from the OECD Main Economic Indicators dataset, from 1973 to
2001.
b In
parenthesis the cross-sectional 68 percent confidence
interval.
Table 2: Parameter values - Benchmark Model
Preferences and Technology
Risk aversion | ![]() |
---|---|
Consumption share |
![]() |
Elasticity of substitution between: Home and Foreign traded goods |
![]() |
Elasticity of substitution between: traded and non-traded goods |
![]() |
Share of Home Traded goods |
![]() |
Share of non-traded goods |
![]() |
Elasticity of the discount factor with respect to ![]() ![]() | ![]() |
Distribution Margin | ![]() |
Labor Share in Tradables | ![]() |
Labor Share in Nontradables |
![]() |
Depreciation Rate |
![]() |
Productivity Shocks
Variance-Covariance Matrix (in percent)
Table 3: Exchange rates and prices in the theoretical
economiesa
Benchmark Economy and Variations on the Benchmark Economy
Statistics | Data | Benchmark Economy: ω = 0.95 | Benchmark Economy: ω = 1.14 | Variation: Arrow-Debreu Economy: ω = 0.95 | Variation: No Spillover: ω = 0.93 | Variation: No Spillover: ω = 1.17 | Variation: CES Investment: ω = 0.50 | Variation: CES Investment: ω = 0.75 | Variation: No Distribution: ω = 0.27 | Variation: No Distribution: ω = 0.44 | Variation: No Distribution: ω = 10 | Variation: Taste Shocks (I): ω = 0.95 | Variation: Taste Shocks (II): ω = 0.82 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Standard deviation relative to GDP: Real exchange rate | 3.28 | 3.28 | 3.28 | 0.79 | 3.28 | 3.28 | 3.28 | 3.28 | 3.28 | 3.28 | 1.06 | 1.26 | 3.28 |
Standard deviation relative to GDP: Terms of trade | 1.79 | 2.84 | 4.47 | 0.78 | 3.18 | 4.20 | 2.53 | 4.41 | 2.68 | 4.92 | 0.26 | 1.38 | 3.39 |
absolute: Relative price of nontradables | 1.73 | 1.41 | 1.13 | 0.91 | 1.44 | 1.25 | 1.10 | 0.83 | 2.83 | 2.07 | 1.95 | 0.95 | 1.41 |
Cross-correlations: Between real exchange rate and Relative GDPs | -0.23 | -0.94 | 0.93 | -0.14 | -0.99 | 0.84 | -0.79 | 0.89 | -0.57 | 0.68 | -0.54 | -0.56 | -0.87 |
Cross-correlations: Relative consumptions | -0.45 | -0.48 | -0.45 | 0.98 | -0.65 | -0.34 | -0.11 | 0.18 | -0.22 | -0.81 | 0.84 | -0.34 | -0.73 |
Cross-correlations: Net exports | 0.39 | 0.95 | 0.95 | -0.64 | 0.94 | 0.95 | 0.92 | 0.97 | 0.98 | 0.99 | 0.63 | 0.69 | 0.94 |
Cross-correlations: Terms of trade | 0.60 | 0.98 | 0.97 | 0.02 | 0.96 | 0.96 | 0.99 | 0.99 | 0.99 | 0.99 | 0.53 | 0.71 | 0.96 |
Cross-correlations: Between terms of trade and Relative GDPs | -0.20 | -0.98 | 0.98 | 0.89 | -0.94 | 0.95 | -0.82 | 0.86 | -0.52 | 0.70 | 0.25 | -0.19 | -0.82 |
Cross-correlations: Relative consumptions | -0.53 | -0.63 | -0.66 | 0.18 | -0.81 | -0.56 | -0.19 | 0.06 | -0.21 | -0.85 | 0.88 | -0.64 | -0.86 |
Cross-correlations: Net exports | 0.43 | 0.98 | 0.99 | 0.73 | 0.99 | 0.99 | 0.95 | 0.99 | 0.98 | 0.99 | 0.99 | 0.92 | 0.99 |
a denotes the elasticity of substitution
between Home and Foreign traded goods. The data reported under the
heading "Data" are those of the U.S. vis-à-vis the rest of
the OECD countries. Simulation
results of the Arrow-Debreu economy and the benchmark economy with
taste shocks are reported under Taste Shocks (I) and (II),
respectively. See the text for a description of the variations on
the benchmark economy.
Table 4: Business cycle statistics in the theoretical economiesa
Statistics | Data | Benchmark Economy: ω = 0.95 | Benchmark Economy: ω = 1.14 | Variation: Arrow-Debreu Economy: ω = 0.95 | Variation: No Spillover: ω = 0.93 | Variation: No Spillover: ω = 1.17 | Variation: CES Investment: ω = 0.50 | Variation: CES Investment: ω = 0.75 | Variation: No Distribution: ω = 0.27 | Variation: No Distribution: ω = 0.44 | Variation: No Distribution: ω = 10 | Variation: Taste Shocks (I): ω = 0.95 | Variation: Taste Shocks (II): ω = 0.82 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Standard deviation relative to GDP: Consumption | 0.92 | 0.54 | 0.55 | 0.49 | 0.56 | 0.46 | 0.50 | 0.49 | 0.47 | 0.67 | 0.44 | 0.59 | 0.68 |
Standard deviation relative to GDP: Investment | 4.25 | 3.13 | 3.14 | 3.14 | 3.28 | 3.28 | 3.15 | 2.62 | 3.15 | 3.17 | 3.28 | 2.93 | 2.91 |
Standard deviation relative to GDP: Employment | 1.09 | 0.49 | 0.51 | 0.49 | 0.54 | 0.55 | 0.45 | 0.39 | 0.49 | 0.51 | 0.54 | 1.00 | 1.00 |
absolute: Import ratio | 4.13 | 2.26 | 4.33 | 0.62 | 2.67 | 4.47 | 1.02 | 2.59 | 1.23 | 3.67 | 4.70 | 1.20 | 2.60 |
absolute: Net Exports over GDP | 0.63 | 0.25 | 0.38 | 0.04 | 0.30 | 0.38 | 0.06 | 0.11 | 0.23 | 0.41 | 0.33 | 0.16 | 0.32 |
Cross-correlations: Between foreign and domestic GDP | 0.49 | 0.42 | 0.40 | 0.43 | 0.52 | 0.50 | 0.40 | 0.49 | 0.43 | 0.40 | 0.28 | 0.31 | 0.29 |
Cross-correlations: Consumption | 0.32 | 0.10 | 0.10 | 0.37 | -0.22 | 0.12 | 0.33 | 0.54 | 0.45 | -0.25 | 0.48 | -0.001 | -0.23 |
Cross-correlations: Investment | 0.08 | 0.35 | 0.31 | 0.34 | 0.51 | 0.49 | 0.04 | 0.59 | 0.33 | 0.29 | 0.08 | 0.28 | 0.28 |
Cross-correlations: Employment | 0.32 | 0.27 | 0.19 | 0.28 | 0.53 | 0.46 | 0.13 | 0.62 | 0.29 | 0.21 | -0.02 | 0.08 | 0.05 |
Cross-correlations: Between net exports and GDP | -0.51 | -0.51 | 0.52 | 0.34 | -0.45 | 0.48 | -0.49 | 0.38 | -0.32 | 0.32 | -0.15 | -0.23 | -0.46 |
a denotes the elasticity of substitution
between Home and Foreign traded goods. The data reported under the
heading "Data" are those of the U.S. vis-à-vis the rest of
the OECD countries. Simulation
results of the Arrow-Debreu economy and the benchmark economy with
taste shocks are reported under Taste Shocks (I) and (II),
respectively. See the text for a description of the variations on
the benchmark economy.
Figure 1: U.S. Real exchange rate and relative consumption
The real exchange rate is eP*/P, where the nominal exchange rate e is the U.S. dollar price of a basket of OECD currencies, P* is an aggregate of OECD CPIs, and P is the U.S. CPI. See the Appendix for the sources.
Figure 2: Theoretical Responses to a Technology Shock in the Traded-Goods Sector
All series are in percent.
Data for Figure 2 - Panel A: Low Elasticity
Period | RER | TOT | C - C* | Y - Y* | NX / Y |
---|---|---|---|---|---|
1 | -2.9080 | -2.4929 | 0.1927 | 0.7567 | -0.1213 |
2 | -2.6032 | -2.4045 | 0.3731 | 0.5617 | -0.1239 |
3 | -2.4124 | -2.3687 | 0.4839 | 0.4344 | -0.1260 |
4 | -2.2962 | -2.3646 | 0.5484 | 0.3477 | -0.1277 |
5 | -2.2290 | -2.3789 | 0.5825 | 0.2859 | -0.1290 |
6 | -2.1937 | -2.4035 | 0.5966 | 0.2397 | -0.1300 |
7 | -2.1790 | -2.4330 | 0.5978 | 0.2037 | -0.1308 |
8 | -2.1774 | -2.4643 | 0.5909 | 0.1746 | -0.1314 |
9 | -2.1839 | -2.4953 | 0.5791 | 0.1504 | -0.1318 |
10 | -2.1951 | -2.5248 | 0.5646 | 0.1299 | -0.1321 |
11 | -2.2087 | -2.5523 | 0.5489 | 0.1122 | -0.1323 |
12 | -2.2233 | -2.5772 | 0.5329 | 0.0969 | -0.1325 |
13 | -2.2378 | -2.5996 | 0.5172 | 0.0836 | -0.1325 |
14 | -2.2516 | -2.6194 | 0.5022 | 0.0719 | -0.1325 |
15 | -2.2644 | -2.6368 | 0.4881 | 0.0617 | -0.1325 |
16 | -2.2761 | -2.6519 | 0.4751 | 0.0527 | -0.1325 |
17 | -2.2864 | -2.6648 | 0.4631 | 0.0448 | -0.1324 |
18 | -2.2954 | -2.6758 | 0.4522 | 0.0378 | -0.1323 |
19 | -2.3032 | -2.6850 | 0.4423 | 0.0317 | -0.1322 |
20 | -2.3097 | -2.6926 | 0.4333 | 0.0263 | -0.1320 |
21 | -2.3152 | -2.6988 | 0.4253 | 0.0216 | -0.1319 |
22 | -2.3196 | -2.7037 | 0.4180 | 0.0174 | -0.1317 |
23 | -2.3230 | -2.7074 | 0.4115 | 0.0138 | -0.1316 |
24 | -2.3257 | -2.7102 | 0.4057 | 0.0106 | -0.1314 |
25 | -2.3275 | -2.7120 | 0.4004 | 0.0078 | -0.1312 |
Data for Figure 2 - Panel B: High Elasticity
Period | RER | TOT | C - C* | Y - Y* | NX / Y |
---|---|---|---|---|---|
1 | 2.1696 | 3.4215 | -0.6570 | 0.7862 | 0.1770 |
2 | 2.4723 | 3.5070 | -0.4695 | 0.5945 | 0.1743 |
3 | 2.6602 | 3.5388 | -0.3525 | 0.4698 | 0.1719 |
4 | 2.7726 | 3.5382 | -0.2822 | 0.3854 | 0.1697 |
5 | 2.8356 | 3.5184 | -0.2429 | 0.3255 | 0.1679 |
6 | 2.8660 | 3.4878 | -0.2240 | 0.2809 | 0.1663 |
7 | 2.8752 | 3.4517 | -0.2184 | 0.2462 | 0.1648 |
8 | 2.8709 | 3.4133 | -0.2213 | 0.2183 | 0.1636 |
9 | 2.8582 | 3.3749 | -0.2294 | 0.1951 | 0.1626 |
10 | 2.8404 | 3.3375 | -0.2405 | 0.1755 | 0.1616 |
11 | 2.8199 | 3.3019 | -0.2530 | 0.1586 | 0.1608 |
12 | 2.7983 | 3.2685 | -0.2661 | 0.1439 | 0.1600 |
13 | 2.7765 | 3.2374 | -0.2790 | 0.1312 | 0.1593 |
14 | 2.7551 | 3.2087 | -0.2914 | 0.1200 | 0.1587 |
15 | 2.7345 | 3.1822 | -0.3030 | 0.1101 | 0.1581 |
16 | 2.7150 | 3.1579 | -0.3137 | 0.1015 | 0.1576 |
17 | 2.6967 | 3.1356 | -0.3234 | 0.0938 | 0.1570 |
18 | 2.6796 | 3.1152 | -0.3322 | 0.0871 | 0.1566 |
19 | 2.6636 | 3.0963 | -0.3400 | 0.0812 | 0.1561 |
20 | 2.6488 | 3.0791 | -0.3470 | 0.0760 | 0.1557 |
21 | 2.6350 | 3.0631 | -0.3531 | 0.0714 | 0.1553 |
22 | 2.6222 | 3.0484 | -0.3585 | 0.0674 | 0.1549 |
23 | 2.6103 | 3.0347 | -0.3632 | 0.0638 | 0.1545 |
24 | 2.5992 | 3.0221 | -0.3673 | 0.0607 | 0.1541 |
25 | 2.5888 | 3.0103 | -0.3709 | 0.0580 | 0.1538 |
Figure 3: Impulse Responses to a Technology Shock in the Traded-Goods Sector
The first column describes the responses from a 6-variable VAR, using quarterly data. The variables are labor productivity, the real exchange rate, the terms of trade, relative consumption, relative output, and net exports. The second column shows the responses from a 4-variable VAR, using annual data. The variables are TFP, relative consumption, relative output, and alternatively, the real exchange rate, the terms of trade, and net exports. All series are in percent.
Data for Figure 3 - Productivity
Period | Quarterly: low 90 | Quarterly: low 68 | Quarterly: response | Quarterly: high 68 | Quarterly: high 90 | Annual: low 90 | Annual: low 68 | Annual: response | Annual: high 68 | Annual: high 90 |
---|---|---|---|---|---|---|---|---|---|---|
1 | 0.325 | 0.384 | 0.553 | 0.534 | 0.587 | 0.249 | 0.377 | 0.781 | 0.982 | 1.129 |
2 | 0.409 | 0.479 | 0.691 | 0.689 | 0.765 | 0.770 | 0.987 | 1.459 | 1.594 | 1.869 |
3 | 0.427 | 0.514 | 0.716 | 0.742 | 0.837 | 1.186 | 1.432 | 1.961 | 2.047 | 2.336 |
4 | 0.619 | 0.701 | 0.972 | 0.992 | 1.123 | 1.123 | 1.498 | 2.247 | 2.418 | 3.068 |
5 | 0.778 | 0.880 | 1.189 | 1.212 | 1.344 | 1.153 | 1.381 | 2.361 | 2.777 | 3.295 |
6 | 0.809 | 0.901 | 1.242 | 1.324 | 1.432 | 1.019 | 1.337 | 2.375 | 2.886 | 3.704 |
7 | 0.832 | 0.968 | 1.311 | 1.386 | 1.519 | 1.108 | 1.174 | 2.350 | 3.173 | 3.498 |
8 | 0.800 | 0.938 | 1.345 | 1.481 | 1.592 | 1.073 | 1.132 | 2.321 | 3.289 | 3.739 |
9 | 0.753 | 0.979 | 1.369 | 1.474 | 1.667 | 1.077 | 1.136 | 2.302 | 3.291 | 3.848 |
10 | 0.792 | 0.943 | 1.392 | 1.559 | 1.686 | 1.072 | 1.164 | 2.293 | 3.262 | 3.898 |
11 | 0.746 | 0.970 | 1.379 | 1.505 | 1.734 | 1.078 | 1.237 | 2.292 | 3.086 | 3.866 |
12 | 0.753 | 0.930 | 1.377 | 1.551 | 1.733 | 1.073 | 1.237 | 2.294 | 3.082 | 3.825 |
13 | 0.756 | 0.864 | 1.389 | 1.684 | 1.778 | 1.113 | 1.241 | 2.296 | 3.078 | 3.740 |
14 | 0.751 | 0.897 | 1.385 | 1.617 | 1.792 | 1.114 | 1.240 | 2.298 | 3.086 | 3.745 |
Data for Figure 3 - RER
Period | Quarterly: low 90 | Quarterly: low 68 | Quarterly: response | Quarterly: high 68 | Quarterly: high 90 | Annual: low 90 | Annual: low 68 | Annual: response | Annual: high 68 | Annual: high 90 |
---|---|---|---|---|---|---|---|---|---|---|
1 | -1.626 | -1.433 | -1.337 | -0.697 | -0.281 | -4.470 | -3.613 | -3.013 | -1.143 | -0.300 |
2 | -2.181 | -1.949 | -1.777 | -0.952 | -0.472 | -6.806 | -5.596 | -4.426 | -1.418 | -0.355 |
3 | -2.670 | -2.343 | -2.078 | -1.166 | -0.432 | -7.578 | -6.027 | -4.699 | -0.987 | 0.145 |
4 | -3.022 | -2.583 | -2.234 | -1.186 | -0.409 | -8.318 | -5.856 | -4.455 | -0.579 | 1.083 |
5 | -3.509 | -3.128 | -2.551 | -1.160 | -0.466 | -7.714 | -6.129 | -4.115 | -0.043 | 0.970 |
6 | -3.784 | -3.382 | -2.786 | -1.303 | -0.747 | -7.733 | -5.371 | -3.869 | -0.301 | 1.104 |
7 | -4.024 | -3.666 | -2.941 | -1.295 | -0.829 | -8.057 | -5.540 | -3.750 | -0.116 | 1.299 |
8 | -4.053 | -3.579 | -2.920 | -1.401 | -0.761 | -7.929 | -5.077 | -3.722 | -0.603 | 1.140 |
9 | -4.261 | -3.625 | -3.004 | -1.479 | -0.750 | -7.939 | -5.553 | -3.737 | -0.264 | 1.092 |
10 | -4.264 | -3.644 | -3.045 | -1.479 | -0.856 | -7.882 | -5.584 | -3.762 | -0.342 | 1.043 |
11 | -4.644 | -3.689 | -3.013 | -1.412 | -0.560 | -7.863 | -5.666 | -3.781 | -0.325 | 1.083 |
12 | -4.478 | -3.686 | -2.960 | -1.326 | -0.605 | -7.821 | -5.366 | -3.790 | -0.592 | 1.012 |
13 | -4.513 | -3.582 | -2.912 | -1.324 | -0.580 | -7.860 | -5.455 | -3.793 | -0.540 | 1.088 |
14 | -4.561 | -3.697 | -2.870 | -1.155 | -0.520 | -7.924 | -5.453 | -3.792 | -0.548 | 1.122 |
Data for Figure 3 - TOT
Period | Quarterly: low 90 | Quarterly: low 68 | Quarterly: response | Quarterly: high 68 | Quarterly: high 90 | Annual: low 90 | Annual: low 68 | Annual: response | Annual: high 68 | Annual: high 90 |
---|---|---|---|---|---|---|---|---|---|---|
1 | -0.407 | -0.276 | -0.075 | 0.157 | 0.339 | -2.245 | -1.665 | -1.375 | -0.451 | 0.221 |
2 | -0.772 | -0.580 | -0.308 | 0.077 | 0.352 | -2.795 | -2.289 | -1.753 | -0.427 | 0.240 |
3 | -0.979 | -0.838 | -0.516 | -0.011 | 0.139 | -3.121 | -2.476 | -1.706 | -0.137 | 0.555 |
4 | -1.039 | -0.795 | -0.501 | -0.039 | 0.263 | -3.324 | -2.294 | -1.567 | -0.069 | 0.829 |
5 | -1.394 | -1.084 | -0.857 | -0.343 | 0.037 | -3.182 | -2.223 | -1.458 | 0.036 | 0.870 |
6 | -1.672 | -1.419 | -1.186 | -0.573 | -0.252 | -3.139 | -2.212 | -1.403 | 0.078 | 0.811 |
7 | -1.933 | -1.813 | -1.416 | -0.586 | -0.414 | -3.149 | -2.176 | -1.385 | 0.043 | 0.808 |
8 | -2.196 | -1.949 | -1.608 | -0.782 | -0.494 | -3.247 | -2.328 | -1.386 | 0.110 | 0.850 |
9 | -2.386 | -1.950 | -1.723 | -0.985 | -0.518 | -3.253 | -2.273 | -1.392 | 0.048 | 0.845 |
10 | -2.442 | -2.125 | -1.794 | -0.946 | -0.607 | -3.266 | -2.236 | -1.398 | 0.004 | 0.833 |
11 | -2.618 | -2.254 | -1.883 | -0.985 | -0.597 | -3.211 | -2.207 | -1.401 | -0.003 | 0.784 |
12 | -2.691 | -2.300 | -1.913 | -1.002 | -0.607 | -3.211 | -2.206 | -1.402 | 0.011 | 0.785 |
13 | -2.714 | -2.251 | -1.934 | -1.078 | -0.639 | -3.286 | -2.203 | -1.402 | 0.009 | 0.843 |
14 | -2.828 | -2.304 | -1.964 | -1.077 | -0.624 | -3.265 | -2.239 | -1.402 | 0.015 | 0.832 |
Data for Figure 3 - C - C*
Period | Quarterly: low 90 | Quarterly: low 68 | Quarterly: response | Quarterly: high 68 | Quarterly: high 90 | Annual: low 90 | Annual: low 68 | Annual: response | Annual: high 68 | Annual: high 90 |
---|---|---|---|---|---|---|---|---|---|---|
1 | -0.224 | -0.121 | -0.022 | 0.068 | 0.164 | -0.016 | 0.092 | 0.231 | 0.325 | 0.387 |
2 | -0.210 | -0.107 | -0.003 | 0.083 | 0.167 | 0.280 | 0.413 | 0.655 | 0.768 | 0.854 |
3 | -0.258 | -0.147 | -0.006 | 0.105 | 0.208 | 0.365 | 0.519 | 0.984 | 1.219 | 1.319 |
4 | -0.099 | 0.037 | 0.244 | 0.338 | 0.448 | 0.344 | 0.580 | 1.161 | 1.406 | 1.649 |
5 | -0.097 | 0.024 | 0.266 | 0.388 | 0.490 | 0.194 | 0.497 | 1.219 | 1.568 | 2.023 |
6 | -0.043 | 0.104 | 0.346 | 0.469 | 0.572 | 0.206 | 0.381 | 1.213 | 1.756 | 2.033 |
7 | 0.064 | 0.162 | 0.488 | 0.638 | 0.712 | 0.210 | 0.291 | 1.186 | 1.960 | 2.085 |
8 | 0.083 | 0.231 | 0.578 | 0.737 | 0.841 | 0.197 | 0.310 | 1.162 | 1.926 | 2.116 |
9 | 0.158 | 0.345 | 0.666 | 0.792 | 0.926 | 0.162 | 0.381 | 1.148 | 1.805 | 2.270 |
10 | 0.165 | 0.333 | 0.736 | 0.908 | 1.038 | 0.162 | 0.327 | 1.143 | 1.937 | 2.303 |
11 | 0.172 | 0.361 | 0.773 | 0.946 | 1.103 | 0.198 | 0.329 | 1.143 | 1.947 | 2.172 |
12 | 0.156 | 0.398 | 0.830 | 1.006 | 1.204 | 0.131 | 0.384 | 1.145 | 1.841 | 2.421 |
13 | 0.179 | 0.372 | 0.866 | 1.093 | 1.246 | 0.131 | 0.382 | 1.147 | 1.837 | 2.419 |
14 | 0.187 | 0.447 | 0.884 | 1.046 | 1.282 | 0.149 | 0.382 | 1.148 | 1.840 | 2.382 |
Data for Figure 3 - Y - Y*
Period | Quarterly: low 90 | Quarterly: low 68 | Quarterly: response | Quarterly: high 68 | Quarterly: high 90 | Annual: low 90 | Annual: low 68 | Annual: response | Annual: high 68 | Annual: high 90 |
---|---|---|---|---|---|---|---|---|---|---|
1 | -0.185 | -0.098 | 0.026 | 0.131 | 0.213 | -0.246 | -0.057 | 0.285 | 0.544 | 0.629 |
2 | -0.274 | -0.166 | -0.012 | 0.132 | 0.238 | 0.266 | 0.569 | 0.975 | 1.203 | 1.370 |
3 | -0.322 | -0.251 | -0.050 | 0.151 | 0.206 | 0.607 | 0.991 | 1.569 | 1.806 | 2.087 |
4 | -0.218 | -0.088 | 0.118 | 0.262 | 0.364 | 0.657 | 1.019 | 1.937 | 2.345 | 2.689 |
5 | -0.175 | -0.040 | 0.204 | 0.358 | 0.463 | 0.549 | 1.036 | 2.094 | 2.540 | 3.132 |
6 | -0.106 | 0.026 | 0.289 | 0.441 | 0.557 | 0.474 | 0.775 | 2.120 | 2.918 | 3.399 |
7 | -0.107 | 0.082 | 0.370 | 0.532 | 0.680 | 0.475 | 0.664 | 2.089 | 3.150 | 3.402 |
8 | -0.017 | 0.165 | 0.446 | 0.582 | 0.732 | 0.403 | 0.696 | 2.051 | 3.109 | 3.657 |
9 | 0.000 | 0.173 | 0.510 | 0.679 | 0.846 | 0.358 | 0.713 | 2.025 | 3.148 | 3.861 |
10 | 0.011 | 0.214 | 0.553 | 0.716 | 0.894 | 0.375 | 0.720 | 2.012 | 3.153 | 3.849 |
11 | 0.020 | 0.224 | 0.571 | 0.737 | 0.915 | 0.476 | 0.687 | 2.010 | 3.235 | 3.636 |
12 | 0.041 | 0.228 | 0.600 | 0.780 | 0.941 | 0.492 | 0.717 | 2.012 | 3.195 | 3.625 |
13 | 0.019 | 0.273 | 0.621 | 0.780 | 1.009 | 0.477 | 0.710 | 2.015 | 3.228 | 3.633 |
14 | -0.007 | 0.276 | 0.636 | 0.806 | 1.062 | 0.414 | 0.709 | 2.017 | 3.224 | 3.801 |
Data for Figure 3 - NX / Y
Period | Quarterly: low 90 | Quarterly: low 68 | Quarterly: response | Quarterly: high 68 | Quarterly: high 90 | Annual: low 90 | Annual: low 68 | Annual: response | Annual: high 68 | Annual: high 90 |
---|---|---|---|---|---|---|---|---|---|---|
1 | -0.075 | -0.046 | -0.017 | 0.027 | 0.054 | -0.379 | -0.319 | -0.235 | -0.061 | 0.043 |
2 | -0.100 | -0.069 | -0.027 | 0.037 | 0.059 | -0.626 | -0.563 | -0.445 | -0.163 | -0.072 |
3 | -0.119 | -0.078 | -0.028 | 0.044 | 0.084 | -0.846 | -0.736 | -0.587 | -0.224 | -0.095 |
4 | -0.150 | -0.096 | -0.051 | 0.026 | 0.078 | -0.976 | -0.844 | -0.645 | -0.184 | -0.076 |
5 | -0.196 | -0.132 | -0.087 | 0.003 | 0.061 | -1.018 | -0.881 | -0.670 | -0.209 | -0.100 |
6 | -0.218 | -0.167 | -0.102 | 0.008 | 0.056 | -1.074 | -0.910 | -0.680 | -0.199 | -0.080 |
7 | -0.211 | -0.177 | -0.115 | -0.005 | 0.023 | -1.105 | -0.870 | -0.682 | -0.252 | -0.083 |
8 | -0.230 | -0.192 | -0.132 | -0.022 | 0.016 | -1.129 | -0.866 | -0.682 | -0.254 | -0.099 |
9 | -0.273 | -0.211 | -0.158 | -0.045 | 0.018 | -1.160 | -0.924 | -0.682 | -0.199 | -0.088 |
10 | -0.289 | -0.245 | -0.185 | -0.059 | -0.006 | -1.177 | -0.919 | -0.681 | -0.208 | -0.088 |
11 | -0.339 | -0.279 | -0.208 | -0.068 | -0.010 | -1.183 | -0.914 | -0.681 | -0.212 | -0.090 |
12 | -0.371 | -0.291 | -0.222 | -0.079 | 0.001 | -1.163 | -0.919 | -0.680 | -0.208 | -0.104 |
13 | -0.381 | -0.311 | -0.235 | -0.078 | -0.010 | -1.164 | -0.819 | -0.680 | -0.298 | -0.102 |
14 | -0.390 | -0.318 | -0.246 | -0.087 | -0.022 | -1.166 | -0.912 | -0.680 | -0.217 | -0.103 |
* We thank our discussants Larry Christiano, Mick Devereux, Fabrizio Perri, Cédric Tille, and V.V. Chari, Marty Eichenbaum, Peter Ireland, Paolo Pesenti, Morten Ravn, Sergio Rebelo, Stephanie Schmitt-Grohé, Alan Stockman, Martín Uribe, along with seminar participants at the AEA meetings, the SED meetings, Boston College, the Canadian Macro Study Group, Duke University, the Ente Einaudi, the European Central Bank, the European University Institute, the Federal Reserve Bank of San Francisco, IGIER, the IMF, New York University, Northwestern University, the University of Pennsylvania, the University of Rochester, the University of Toulouse, the Wharton Macro Lunch group, and the workshop "Exchange rates, Prices and the International Transmission Mechanism" hosted by the Bank of Italy, for many helpful comments and criticism. Corsetti's work on this paper is part of a research network on "The Analysis of International Capital Markets: Understanding Europe's Role in the Global Economy," funded by the European Commission under the Research Training Network Programme (Contract No. HPRN-CT-1999-00067). Part of Dedola's work on this paper was carried out while he was visiting the Department of Economics of the University of Pennsylvania, whose hospitality is gratefully acknowledged. The views expressed here are those of the authors and do not necessarily reflect the positions of the ECB, the Board of Governors of the Federal Reserve System, or any other institution with which the authors are affiliated. Contact: Giancarlo Corsetti, Via dei Roccettini 9, San Domenico di Fiesole 50016, Italy; email: Giancarlo.Corsettiiue.it. Luca Dedola, Postfach 16 013 19, D-60066 Frankfurt am Main, Germany; email: luca.dedolaecb.int. Sylvain Leduc, 20th and C Streets, N.W., Stop 23, Washington, DC 20551; email: Sylvain.Leduc.frb.gov. Return to text
1. See the surveys by Lewis [1999] and Obstfeld and Rogoff [2001]. Return to text
2. As discussed in the next section, under standard assumptions on the utility function this is the main implication of efficient risk-sharing in the presence of real exchange rate (PPP) fluctuations -- as opposed to a high cross-country correlation of consumption. See also Engel's [2000] discussion of Obstfeld and Rogoff [2001]. Return to text
3. Conditional on a productivity increase in tradables, an appreciation of the real exchange rate and an increase in domestic consumption are also predicted by the Balassa-Samuelson model with no terms-of-trade effect (because of perfect substitutability of domestic and foreign tradables). Yet, as shown by our numerical experiments, a model with a high price elasticity of tradables cannot generate either enough volatility of the real exchange rate and terms of trade or replicate the negative Backus-Smith unconditonal correlation. Return to text
4. Lewis [1996] rejects nonseparability of preferences between consumption and leisure as an empirical explanation of the low correlation of consumption across countries. Return to text
5. Formally, by a straightforward
derivation of the Slutsky equation, the substitution effect is
obtained from the compensated demand function
Return to text
6. Using self-explanatory notation:
Return to text
7. We are grateful to Fabrizio Perri for suggesting this line of exposition. Return to text
8. In this simple setting, strong income effects raise the possibility of multiple steady states (e.g., see the discussion in Corsetti and Dedola [2002]). It is worth stressing, however, that the specification of preferences in the model we use in our numerical exercises below always ensure a unique steady state. Return to text
9. Nonetheless, one can still envision shocks, e.g., taste shocks to utility, that move the level of consumption and the marginal utility of consumption in opposite directions, thus mechanically attenuating the link between the real exchange rate and relative consumption in (1) also in models assuming complete asset markets. While Chari, Kehoe and McGrattan [2002] cast doubts on this perfunctionary rationalization of the Backus-Smith puzzle by showing that traditional demand shocks can hardly match the effects of those unobservable taste shocks, in Section 5 we will conduct sensitivity analyisis to the inclusion of taste shocks, following Stockman and Tesar [1995]. Return to text
10. A unique invariant distribution of wealth under these preferences will allow us to use standard numerical techniques to solve the model around a stable nonstochastic steady state when only a non-contingent bond is traded internationally (see Obstfeld [1990], Mendoza [1991], and Schmitt-Grohe and Uribe [2001]). Return to text
11.
denotes the Home
agent's bonds accumulated during period
and
carried over into period
. Return to text
12. We also conduct sensitivity analysis on our specification of the investment process, below. Return to text
13. See Costello [1993]. The persistence of the estimated shocks, though in line with estimates both in the closed (e.g., Cooley and Prescott [1995]) and open-economy (Heathcote and Perri [2002]) literature, is higher than that reported by Stockman and Tesar [1995]. The difference can be attributed to the fact that they compute their Solow residuals from HP-filtered data - while we and most of the literature compute them using data in (log) levels. Return to text
14. In particular, the tradable import ratio will display more variability, ceteris paribus, when changes in absorption of domestic and imported tradables have opposite signs. Return to text
15. Note that under financial autarky the
counterpart of condition (4) in our
fully-specified model with distribution services is:
A positive distribution margin reduces the
substitution effect (
) from a deterioration in
the terms of trade, while making the income effect (
) more negative, as the presence of distributive trade
causes the consumer price to fall less than one-to-one relative to
the relative price of domestic tradables. Return to text
16. Ruhl [2003] shows a way to reconcile these time series estimates with the contrasting evidence on the large growth in trade volumes resulting from changes in tariffs. Return to text
17. Here we follow Heathcote and Perri [2002]. See the Data Appendix for details. Return to text
18. Namely,
where
denotes a steady-state value
and
is the elasticity of
substitution between tradables and nontradables. Return to text
19. Remarkably, the data supports the
tight and negative link between the terms of trade and the real
exchange rate, on the one hand, and the import ratio, on the other
hand, predicted by the theory. In the data these correlations stand
at -0.68 and -0.41, respectively, against -1 predicted by the model
for either value of . Return to text
20. Following a different procedure, Engel [1999] finds that deviations from the law of one price in traded goods virtually account for all of the volatility of the U.S. real exchange rate. Return to text
21. The model can also generate a negative
Backus-Smith correlation when we calibrate as
to match the empirical volatility of the terms of trade (rather
than the real exchange rate) relative to volatility of output.
Following this approach, we obtain a value of
equal to
corresponding to a
Backus-Smith correlation equal to -0.23. In this exercise the
predicted volatility of the real exchange rate is about 74 percent
of what is found in the data. Return to
text
22. Interestingly, the model can also
replicate the Backus-Smith correlation even when welook at
first-differenced data. In our economy this correlation
ex-post is -0.47 (-0.56) when equals
0.95 (1.14). Return to text
23. The same mechanism holds in an economy in which the consumption share of nontradables is set to zero, so that they are used only in distribution, and their production function is not subject to thechnology shocks. In this case, we find that the Backus-Smith correlation is around -0.90. Return to text
24. We also analyzed an economy without capital accumulation, whose results are not reported for the sake of space. Excluding capital does not substantially change the match of the model with the data along most dimensions. However, consumption becomes more volatile than output, while the volatility and cross-country correlation of employment tend to be very low. Return to text
25. Another avenue would be to explore richer preferences. Interestingly, however, Chari, Kehoe and McGrattan [2002] show that allowing for habits formation in consumption, which has proved useful in understanding other puzzles (for instance, the equity premium puzzle), cannot account for the Backus-Smith anomaly. Return to text
26. Although not reported in the charts,
all variables ultimately return to their steady-state values
following this one-time shock, because of the endogeneity of the
discount factor. As we mentioned previously, the slow convergence
is due to the low value of the parameter
required to match the steady state real interest
rate. Return to text
27. This result is seldom highlighted in
models with traded and nontraded goods. A possible explanation is
that in these models tradables are very often assumed to be
perfectly homogeneous across countries, i.e..
so that there are
no terms of trade fluctuations (see e.g., Stockman and Dellas
[1989] and Tesar [1993]). With this specification, a technological
advance in the traded-good sector typically brings about an
appreciation of the domestic currency owing to an increase in the
domestic relative price of nontradables, according to the
Balassa-Samuelson hypothesis. Note, however, that these models
obviously leave unexplained the terms of trade
behavior. Return to text
28. See Shapiro and Watson [1988], Francis and Ramey [2003] and Chang and Hong [2002], among others. Some open-economy papers, following Blanchard and Quah [1989], use long-run restrictions derived in the context of the traditional aggregate demand and aggregate supply framework. For instance, Clarida and Galí [1994] identify supply shocks by assuming that demand and monetary shocks do not have long-run effects on relative output levels across countries. While monetary shocks satisfy this assumption in most models, fiscal or preference shocks do not, since they can have long-run effects on output (and hours) in the stochastic growth model. Return to text
29. For instance, Uhlig [2003] argues that a unit root in labor productivity may results not only from the standard RBC shock to TFP, but also from permanent shocks to the capital-income tax. . Return to text
30. We also estimated specifications of the model including more U.S. and international variables, like investment, real wages and hours worked, and different definitions of the terms of trade. Since very similar results to those discussed in the text are obtained, they are not included to save on space. They are available from the authors upon request. Return to text
31. We include up to four lags for quarterly data and one for annual data, based on a BIC criterion and tests of residual serial correlation. Return to text
32. These results are not included in the paper to save on space, but they are available upon request. Return to text
33. The standard error bands were computed using a bootstrap Monte Carlo procedure with 5000 replications. We thank Yongsung Chang for graciously providing us with his bootstrapping codes. Return to text
34. Notice that the terms of trade appreciation cannot be easily rationalized with the well-known bias in measured import prices that arises from a lack of adjustment to an increasing number of imported goods (see Feenstra [1994]). As shown by Ruhl [2003], this bias is negatively correlated with the level of imports, as the (mis)measured price index fails to fall as much as the correct price index, thus biasing results against finding a terms of trade appreciation. Return to text
35. Consistently with our results, Alquist and Chinn [2002] find, with cointegrating techniques, that each percentage point increase in the U.S.-Euro area economy-wide labor productivity differential results in a 5-percentage-point real appreciation of the dollar in the long run. Return to text
36. A theoretical attempt to build a model encompassing a discussion of both elasticities and creation of new goods is provided by Ruhl [2003]. Return to text
This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to text