Long-Run Price Elasticity of Trade and the
Trade-Comovement Puzzle ∗
Lukasz A. Drozd† and Jaromir B. Nosal‡
July 7, 2008
ABSTRACT
Recent studies have found significant support for the positive link between bilateral trade intensity
and business cycle comovement of output and TFP in a cross-section of industrialized country
pairs. Since this feature of the data is not reproduced by the workhorse model of international
business cycle, it is referred to as the trade-comovement puzzle. In the paper, we show that the
puzzle is intimately related to the failure of the standard theory to account for the high long-run
price elasticity of trade flows. We do so by enriching the standard theory with frictions of building
market shares and establishing trade relations, which generate low short-run price elasticity of trade
coexisting with the high long-run price elasticity. We show that when the low short-run elasticity is
generated by explicitly modeled frictions of building market shares, the theory can account for 50%
and 78% of the trade-comovement relation in the data for output and TFP, respectively.
JEL: E32, F31
Keywords: international correlations, trade-comovement puzzle, international business cycle
∗We thank V.V. Chari, Patrick Kehoe and Fabrizio Perri for valuable advice and encouragement. All remaining
errors are ours.
†University of Wisconsin-Madison, Department of Economics, 1180 Observatory Drive, SSC Bldg., Madison,
WI 53706. Contact: ldrozd@ssc.wisc.edu
‡Columbia University, Department of Economics, 1022 International Affairs Building 420 West 118th Street,
New York, NY 10027, Contact: jnosal@columbia.edu

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1. Introduction
The conventional wisdom about the international comovement of business cycles is that coun-
tries which trade more with each other should have more synchronized output fluctuations.
The logic behind this assertion is that shocks in one country, by demand complementarity,
spillover to demand for goods produced in major trade partner countries, and in effect lead
to an increased correlation of their GDPs. The link suggested by this intuition has been
extensively studied empirically, and shown to be consistent with the data. By running cross-
country regressions Frankel & Rose (1998), Clark & van Wincoop (2001), Calderon, Chong &
Stein (2002), Otto, Voss & Willard (2001), Baxter & Kouparitsas (2005), Kose & Yi (2006)
all find that, among industrialized bilateral country pairs, more trade is associated with more
synchronized business cycle fluctuations.
In a series of papers, Kose and Yi (2001, 2006) show that the conventional wisdom
and the above pattern in the data are at odds with the standard model of international
macroeconomics (Backus, Kehoe & Kydland (1995))1. Kose and Yi show that in the standard
model there is an additional opposing force to the complementarity effect, potent enough to
reverse the relationship between trade and comovement. This force is the resource-shifting
effect, which in this model environment makes productive resources (capital and labor) shift
over the business cycle towards the most productive country, and thereby tends to reduce
international correlation of output.
The reason why resource-shifting effect affects the trade-comovement relation implied
by the standard model is because its intensity varies with trade. The mechanism behind it
is as follows. When countries trade little with each other, which in the model corresponds
to high assumed bilateral trade barriers in the long-run, it is costly to produce goods in a
country different from the one in which these goods are eventually consumed. This effect
acts as a counterforce to the resource shifting motive because shifting resources (production)
towards the most productive country implies that either vast amount of resources are wasted
in transportation (due to high trade barriers) or there is a departure from international
1Even in the best scenario of financial autarky and exogenously assumed correlation of the primitive
productivity shocks increasing with trade intensity as in the data, the standard model accounts for merely
30% of the relationship. Under complete markets, the standard model gives the opposite prediction to the
data.

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consumption smoothing (and risk sharing). As a result, when trade barriers are high, the
resource-shifting effect is weak. On the other hand, when countries trade more and trade
barriers are lower, resource shifting intensifies and lowers business cycle synchronization. In
the standard model this effect quantitatively dominates and we observe a negative correlation
between trade and comovement of business cycles.
To address this puzzle, in this paper we keep the complete asset market assumption
intact, and model trade frictions which lead to a disconnect between the short-run and the
long-run price elasticity of trade flows. These frictions allow us to be consistent with the long-
run oriented trade literature in assuming that domestic and foreign goods are intrinsically
closely substitutable and still have a low short-run elasticity in consistency with the business
cycle literature2. Our main finding is that such explicit modeling of the disconnect between
the long-run and short-run price elasticity of trade, even under the worst case scenario of
complete asset markets, can account for about half of the trade-comovement relation in the
data. We conjecture that a mild restriction on asset market incompleteness would be enough
in our model to match the data exactly.
The reason why our theory successfully accounts for the trade-comovement pattern is
twofold. First, short-run search and matching frictions involved in trade in goods generate an
additional complementarity effect similar to the one generated by the Armington aggregation
with low elasticity of substitution between the domestic and foreign goods. Second, the high
intrinsic elasticity of substitution between domestic and foreign goods effectively dampens
the influence of the resource shifting effect on the trade-comovement relation predicted by
the theory. This is because when domestic and foreign goods are closely substitutable in
the long-run, much smaller variation in the assumed bilateral trade barriers is required to
replicate in the model 3 the differences of trade intensities seen in the cross-section of bilateral
country pairs. A smaller variation of trade barriers across bilateral country pairs leads to a
smaller variation of the motive to produce goods in the country where they are consumed,
and a smaller variation of the intensity of the resource-shifting effect. As a result, in the cross-
section of bilateral country pairs simulated from our model, the resource shifting motive varies
2See Ruhl (2005) for more details.
3 In our simulations, tariffs vary from 0% to 64%.
2

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much less, and the still present complementarity effect then dominates.
The additional complementarity effect in our framework is implied by search and
matching frictions involved in trade in goods. Unlike in frictionless environments, in our
model producers need to first establish long-lasting trade relations with their customers in
order to sell their goods, and the build-up of such relationships is time consuming. This
introduces sluggishness in market shares of producers and thus sluggishness in the consumed
ratio of domestic products and imports. As a result, after a positive productivity shock,
a larger number of searching customers in the domestic country increases the demand for
imported goods in the short-run in proportion to the initial market share of foreign importers
– just like in a model with complementarity built into preferences.
The high intrinsic elasticity of substitution between domestic and foreign goods, crucial
for our results, finds strong support in the long-run oriented trade literature. Numerous
studies confirm that long-run elasticity of trade with respect to permanent tariff changes is
very large (see for example Head & Ries (2001), Eaton & Kortum (2002), Clausing (2001)),
and large values of elasticity are needed to account for the evolution of world trade in the last
century (Yi (2003)). The measurement of long-run elasticity in the literature exactly aligns
with the type of exercise performed to account for the trade-comovement relation, which
further reinforces the need to use a high value of elasticity.
The rest of the paper is organized as follows. In Section 2.
, we present an overview of
empirical evidence reported in the literature. Section 3.presents the setup and discusses the
features of the model. Calibration and results are presented in Section 3. Section 5.presents
the results. Section 6.concludes.
2. Link Between Trade and Comovement in the Data
In this section, we set a quantitative target for the model. For this purpose, we explore
the empirical relation between trade and comovement of business cycles in a sample of 20
industrialized countries over the period 1980Q1 - 2004Q2. Countries in our sample constitute
about 79% of world GDP and 62% of world trade (as of year 1994).
More specifically, we perform a simple data study that we will later mimic in the
model. The result of this study gives us the estimates of the regression coefficients between
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bilateral trade intensity and bilateral correlations of output and TFP. We find that coefficients
for both output and TFP are positive and statistically significant. The robustness of these
results to the use of instrumental variables and various controls has been widely documented
in the literature (see for example Kose & Yi (2006), Baxter & Kouparitsas (2005) or the
extensive analysis in Clark & van Wincoop (2001)), and so we will not repeat it here.
In Table 1, we report results from simple regressions of correlations of GDP and
TFP on trade intensity, in a cross-section of bilateral country pairs. In the exercise, we
use quarterly data from 20 industrialized countries for the years 1980Q1 - 2004Q2, divided
into 2 subperiods4: 1980Q1-1993Q4 and 1994Q1-2004Q4. The list of countries included in
our sample is: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany,
Ireland, Italy, Japan, Korea, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland,
United Kingdom, United States. The reported statistic is the estimated β coefficient of the
x
equation
corr(xi, xj)τ = α + β trade
x
ij,τ + εij,τ ,
(1)
where, corr(xi, xj)τ is the correlation between countries i and j in subperiod τ of the logged
and HP-filtered series of real GDP or Solow residuals.The variable tradeij,τ is a measure of
bilateral trade intensity of countries i and j in subperiod τ , given by the log of
IMij,τ + IMji,τ ,
GDPi,τ + GDPj,τ
where IMij,τ are nominal imports (in US dollars) by country i from country j at the beginning
of subperiod τ , and GDPi,τ is the nominal GDP (in US dollars) of country i at the beginning5
of subperiod τ . Bilateral trade intensity in our sample ranges from 0.019% to 7.37%. In total,
we have 392 observations.
Table 1 reports regression coefficients together with 5% significance intervals.
As
we can see, both coefficients are statistically significant and indicate a positive relationship
4Not all years of data are available for all countries. For a detailed description of the data we use, see
Appendix.
5The coefficients do not change significantly when we use end of subperiod statistics of trade intensity.
They both remain significant on a 95% level, the coefficient for GDP increases to 0.0708, and the coefficient
for Solow residuals decreases to 0.0269.
4

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Table 1: OLS estimates of β
x
βx
0.0616
Gross Domestic Product
(0.0332, 0.09)
0.0297
Total Factor Productivity
(0.0035, 0.0559)
between trade intensity and correlation of GDPs and TFPs, consistent with results reported
by other authors. These values imply that doubling trade intensity is associated with an
increase of correlation of GDP of about 0.043, and correlation of TFP of about 0.021. Given
the dispersion of trade intensities in our dataset, this implies that the difference in correlation
of output between 10th and 90th percentile of bilateral trade intensities is about 0.2. We
now proceed with the presentation of the model.
3. Model
Time is discrete, t = 0, 1, 2..., and horizon infinite. The world is comprised of three countries.
The first two countries, labeled domestic (D) and foreign (F), are symmetric and of equal size,
and the third country, labeled rest of the world (W), is allowed to differ in size. The size of a
country is determined by the population size of atomless households residing in the country.
Labor and capital, supplied by the households are assumed to be immobile across countries,
and are used by local producers to produce goods. Goods are differentiated by the country
of origin and tradable. The good produced in the domestic country is labeled D, the good
produced in the foreign country is labeled F, and the good produced in the rest of the world
is labeled W . Households in each country use these goods for consumption and investment
in physical capital. Their preferences are characterized by imperfect substitutability between
each type of good, and a preference bias towards the locally produced good. Financial markets
are assumed to be complete.
As far as trade in goods is concerned, we follow here Drozd & Nosal (2008) and
introduce search and matching frictions involved in trade in goods. These frictions are critical
to our analysis. The detailed description of these frictions is as follows. In each country
5

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we introduce a sector of local retailers who purchase tradable goods from domestic and
foreign producers and locally resell them to the households. Retailers search for producers
of goods (foreign and domestic), and producers accumulate marketing capital to attract
searching retailers. Trade between households and retailers is assumed perfectly competitive
and frictionless. Trade between producers and retailers is subject to the matching friction
and prices are determined by bargaining.
A. Technology and Notation
The source of uncertainty in the model is the random productivity shock affecting the produc-
tion technology in each country. The history of shocks up to and including period t is denoted
by st = (s0, s1, ...st), where st ≡ (εit)i∈{D,F,W } and εit is an iid random variable. The initial re-
alization s0, as well as time invariant probability measure µ over the three dimensional shock
space S are given.
Each country i = D, F, W has access to a constant returns to scale production tech-
nology zi(st)Fi (ki(st), li(st)) , which uses country-specific capital and labor, and is subject
to country-specific technology shock zi. The technology shock zi is given by an exogenous
AR(1) process
log(zi(st)) = ψ log(zi(st−1)) + εit,
where 0 < ψ < 1 is the shock persistence parameter, and εit is Normally distributed i.i.d.
random variable with zero mean.
Since the production function is assumed to be constant returns to scale, we sum-
marize production constraints by an economy-wide marginal cost vi(st). Given factor prices
wi (st) , ri (st) and the shock zi (st) , the marginal cost in each country can be defined as
follows
vi st ≡ min wi st l + ri st k | zi st F (k, l) = 1 .
(2)
k,l
B. Households
The problem of the households is standard. Each country i = D, F, W is populated by a fixed
measure Li of identical and infinitely lived households. Households supply production factors
6

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to firms, accumulate physical capital, and consume. After each history st, the households
choose their allocation, which consist of the level of consumption ci (st) , investment in physical
capital ii (st), labor supply li (st), purchases of tradable goods Di (st), Fi (st) , Wi(st), and
purchases of a set of one period state-contingent bonds bi (st+1|st) , to maximize their expected
discounted lifetime utility given by
∞
βt
ui ci st , 1 − li st
µ dst ,
(3)
t=0
St
where the instantaneous utility function u is parameterized by
(cη(1 − l)1−η)1−σ
ui(c, l) =
, σ > 0, 0 ≤ η ≤ 1.
1 − σ
The preferences towards D, F , and W goods are described by a CES aggregator Gi with
the elasticity of substitution γ and home bias parameters ωj,
i
γ
γ−1
γ−1
γ−1
γ−1
γ
G
γ
γ
i (D, F, W ) =
ωDD
+ ωF F
+ ωW W
, γ ≥ 0,
ωj = 1.
(4)
i
i
i
i
j=D,F,W
The composite output is used for consumption and investment in physical capital,
ci st + ii st = Gi Di st , Fi st , Wi st
.
(5)
Given the sequence of investment ii(st), physical capital in country i follows the standard law
of motion with a constant depreciation rate δ
ki st = (1 − δ) ki st−1 + ii st , 0 < δ ≤ 1.
(6)
The budget constraint of the household can be defined sequentially. After each history
7

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st, households in each country face a budget constraint given by
P D st D
st F
st W
i
i
st + P F
i
i
st + P W
i
i
st
(7)
+
Qi(st+1|st)bi(st+1|st)µ(dst+1)
S
= bi st + wi st li st + ri st ki st−1 + Πi st , i = D, F, W
On the expenditure side, the budget constraint includes purchases of goods in the retail
market at retail prices P i, and purchases of the set of one-period state contingent bonds
j
bi(st+1|st) traded at state contingent prices given by Qi(st+1|st). On the income side, it
includes income from maturing bonds bi (st) purchased in the previous period, labor income
wi (st) li (st), physical capital rental income ri (st) ki (st−1), and profits paid by the domestic
firms Πi(st).
In the formulation of the household problem we normalize the prices at each st so that
the composite consumption good ci is the numeraire in each country. We do so by setting
the level of CPI6 price index in each country equal to 1.
In addition, because the world asset market is assumed to be fully integrated, there is
a spot price which translates country i’s numeraire to country j’s numeraire xj(st), and must
i
satisfy the following non-arbitrage condition
xj(st+1)
Q
i
j (st+1|st) =
Qi(st+1|st).
(8)
xj(st)
i
This price is the real exchange rate as the numeraire in each country are the consumption
baskets. The above condition is standard under complete markets and says that one cannot
profit by trading assets denominated in the other country numeraire unit.
Summarizing, given the initial values for ki(s−1) and bi(s−1), households choose their
6The CP Ii is defined as the lowest cost of acquiring a unit of consumption, and thus solves
CP Ii = min P DD + P F F + P GW
i
i
i
D,F,W
subject to
Gi(D, F, W ) = 1.
8

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allocations to maximize (3) subject to the aggregation constraint (5), the law of motion
for physical capital (6), the budget constraints (7), the no-Ponzi scheme condition, and the
numeraire normalization. The following necessary conditions characterize the household’s
problem:
(i) consumption/leisure choice
uil (st) = −wi st ,
(9)
uic (st)
(ii) Euler equation
uic st = βEst[uic st+1
(1 − δk) + ri st+1 ],
(iii) demand equations
P j st = G
i
ij
st ,
(10)
(iv) pricing kernels
u
Q
ic (st+1)
i(st+1|st) = β
,
(11)
uic (st)
(v) non-arbitrage condition
xj(st+1)
Q
i
j (st+1|st) =
Qi(st+1|st)
xj(st)
i
where uil (st) , uic (st) , GiD (st) denote derivatives of the instantaneous utility function and
the Armington aggregator function with respect to the subscripted arguments7.
C. Producers
Tradeable goods are country specific and are produced by a unit measure of atomless compet-
itive producers residing in each country. Producers employ local capital and labor to produce
these goods using the production technology available in their country of residence. In order
to sell the goods, producers must match with retailers who become their customers. This
7By comparing side-by-side (iv) and iterating backwards to state s0, one can obtain a simpler condition
for the real exchange rate
ujc (st)
xj st =
xj s0 .
i
u
i
ic (st)
The above equation is referred to as the efficient risk sharing equation.
9

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Document Outline

• Introduction
• Link Between Trade and Comovement in the Data
• Model
  • Technology and Notation
  • Households
  • Producers
  • Retailers
  • Equilibrium
• Parameterization
• Quantitative Analysis
  • Bilateral Pairs
  • European Case
  • Explanation of the Results
• Conclusion
  • National Accounts in the Model
  • Estimation of the Productivity Shock Process
  • Data Sources

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