NBER WORKING PAPER SERIES

DISTRIBUTION CAPITAL AND THE SHORT- AND LONG-RUN IMPORT DEMAND
ELASTICITY
Mario J. Crucini
J. Scott Davis
Working Paper 18753
http://www.nber.org/papers/w18753
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
February 2013This paper was begun while Davis was a visiting researcher at the Bank of Estonia and while Crucini
was a visiting Senior Fellow at the Globalization and Monetary Policy Institute, Federal Reserve Bankof Dallas. We would like to thank participants at the 2011 Midwest Macro Meetings and the 2012
meetings of the System Committee for International Economic Analysis at the Federal Reserve Bankof San Francisco, particularly our discussant Andrea Raffo. In addition we would like to thank George
Alessandria, Aurelijus Dabušinskas, Mick Devereux, Jonathan Heathcote, Finn Kydland, Sylvain Leduc,Jian Wang Lenno Uusküla and Mark Wynne for many helpful comments and suggestions. The viewsin this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve
Bank of Dallas, the Federal Reserve System, or the National Bureau of Economic Research. Mario
Crucini acknowledges the generous financial support of the National Science Foundation (SES #1030164).
NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official
NBER publications.
© 2013 by Mario J. Crucini and J. Scott Davis. All rights reserved. Short sections of text, not to exceed
two paragraphs, may be quoted without explicit permission provided that full credit, including © notice,is given to the source.

Distribution Capital and the Short- and Long-Run Import Demand Elasticity
Mario J. Crucini and J. Scott Davis
NBER Working Paper No. 18753
February 2013
JEL No. F1,F14,F44
ABSTRACTInternational business-cycle models assume that home and foreign goods are poor substitutes. International
trade models assume they are close substitutes. This paper constructs a model where this discrepancy
is due to frictions in distribution. Imports need to be combined with a local non-traded input, distribution
capital, which is slow to adjust. As a result, imported and domestic goods appear as poor substitutes
in the short run. In the long run this non-traded input can be reallocated, and quantities can shift following
a change in relative prices. Thus the observed substitutability between home and foreign goods getslarger as time passes.
Mario J. Crucini
Department of Economics
Vanderbilt University
Box 1819 Station B
Nashville, TN 37235-1819
and NBER
mario.j.crucini@vanderbilt.edu
J. Scott Davis
Research Department
2200 North Pearl Street
Dallas, TX 75201
Scott.Davis@dal.frb.org

The elasticity of substitution between home and foreign goods, also called the Armington elasticity, is one of the most important parameters in dynamic equilibrium models ofinternational trade and business cycles. The parameter determines how quantities adjust in
response to a change in relative prices, and thus determines how quantities of imports andexports adjust after a shift in the real exchange rate. Trade models rely on this parameterto determine the eﬀect of trade policy and tariﬀ rates on trade flows and welfare. Macromodels rely on this parameter to determine the business cycle eﬀects of certain macro shocks
and the business cycle properties of international macro models.
The problem, as highlighted in Ruhl (2005) is that the trade literature and the international macro literature don’t agree on the value of this parameter. Macro models, which areconcerned with short-run fluctuations, generally ascribe a low value to this parameter. In
the workhorse international real business cycle model, Backus, Kehoe and Kydland (1994)
assign a value of 1.5 to the Armington elasticity and discuss how the model fails to replicate
the negative co-movement between the terms of trade and net exports for values of the elasticity that are too high (above 3). In the calibration of their model, Kose and Yi (2006) use
this same value. Stockman and Tesar (1995) use a Cobb-Douglas specification, and thus anelasticity of 1, to aggregate home and foreign goods. Heathcote and Perri (2002) estimate theArmington elasticity from an equation that links changes in the real exchange rate to changes
in net exports and relative production. They estimate a vale of the Armington elasticity ofaround 0.9. Corsetti, Dedola and Luduc (2008) use a value of around 0.85. They arrive at
this value by calibrating their model to match certain features of the data, most notably thesecond moments of international relative prices like the real exchange rate and the terms oftrade. Enders, Müller and Scholl (2011) construct a model to specifically explain the path of
the real exchange rate and the terms of trade following either a productivity or government
spending shock. They find that the model calibrated with a high elasticity of substitution
yields counterfactual results as to the response of the real exchange rate following a shock.
Similarly in estimations using data on relative prices and import shares, Blonigen, Liebman and Wilson (1999) use quarterly data and find an average elasticity of about 0.81.
Hooper, Johnson and Marquez (1998) and Gallaway, McDaniel and Rivera (2003) use a regression framework that allows them to distinguish between short- and long-run elasticities.
They find that import demand elasticities are typically much larger in the long run thanthey are in the short run.
On the trade side, in their survey of the literature on trade costs, Anderson and van
Wincoop (2004) find that the import demand elasticity is generally found to lie between
5 and 10. Hillberry et al. (2001) find long run estimates of the elasticity between 4 and8. Hummels (1999) backs the elasticity parameter out of an estimated gravity model after2

estimating the elasticity of trade costs with respect to distance and finds the elasticity is
about 5. In a similar fashion, Obstfeld and Rogoﬀ (2000) find that when the elasticity of
substitution is equal to 6, the observed home bias in trade can be reconciled with estimatedinternational trade costs. Head and Reis (2001), Clausing (2001), and Romalis (2007) eachestimate the elasticity using U.S.-Canadian trade data from before and after the passage of
the Canada-U.S. Free Trade Agreement and find the elasticity is somewhere between 6 and11. Eaton and Kortum (2002) estimate a parameter that can be thought of as an importdemand elasticity and find a value of 8.
The discrepancy between short- and long-run estimates of the elasticity of substitution
is closely related to the literature on the J-curve. As noted in Junz and Rhomberg (1973)
and Magee (1973), after a change in international relative prices, like an exchange rate
depreciation, quantities do not always adjust instantaneously. This is closely related to thefamous Marshall-Lerner condition, which states that in order for a currency depreciation tolead to an improvement in the trade balance, the sum of the absolute values of the importdemand elasticity and export demand elasticity must be greater than one. If the sum of theelasticities is smaller than one in the short run then the currency depreciation will actuallylead to a worsening of the trade balance, but if the elasticities get larger with time, then the
trade balance should improve in the long run following an exchange rate depreciation.1
Junz and Rhomberg (1973) list five types of lags that may explain why quantities do notrespond quickly to a change in the exchange rate. These are a recognition lag, a decisionlag, a delivery lag, a replacement lag, and a production lag. More generally, these can begrouped into four categories.
Quantities may respond slowly to a change in relative price because consumers may
be slow to notice a change in relative prices or sellers who have some market power may
intentionally keep final goods prices from fluctuating following a transitory change in relative
prices. Drozd and Nosal (2012) construct a search model where sales require some marketing
capital. In this search framework, consumers initially may not notice a change in the relative
price of imported goods. In their model, marketing capital is acquired slowly but can belost quickly. As such, sellers have an incentive to keep transitory price changes from passing
through into final goods prices. This is consistent with the empirical literature detailing thelow pass through of exchange rate changes into import prices (see e.g. Campa and Goldberg(2005)).
1

See Bahmani-Oskooee and Bolhasani (2008) and Boyd, Caporale and Smith (2001) for empirical evidenceof a J-curve eﬀect and evidence that the Marshall-Lerner condition holds in the long run but may not holdin the short run. See also Rose (1991) for evidence that the Marshall-Lerner condition does not hold andthat the trade balance is largely independent of movements in the real exchange rate in at least the first two
years following a change in the exchange rate.

3

Another reason for the slow adjustment of quantities lies on the production side. It takes
time for new producers to enter the export market following a favorable shift in relative prices.
For example, there may be a cost to entering the export market. Ruhl (2005) presents amodel where this entry cost is responsible for the discrepancy between macro and trade
estimates of the elasticity of substitution. Following a transitory change in relative prices,like a temporary TFP shock, the present value of entering the export market is relatively
low since the price advantage over foreign producers is only transitory. Thus the present
value of the gains from entering the export market do not exceed the one-time fixed cost ofexporting. However, following a permanent shock like a change in tariﬀ rates, the present
value is larger and thus more domestic firms will start exporting.
The third reason for the slow adjustment is due to frictions in replacement and inventory management. Alessandria, Kaboski and Midrigan (2010) present a model where fixedtransactions costs to importing make trade "lumpy" and importing firms use S-s style inventory management. In their framework, following an exchange rate appreciation that makes
foreign goods cheaper, importers will not immediately start buying more imports, especiallywhen inventory levels are already high.
The model developed in this paper highlights another reason why exports and imports
may be slow to respond to a change in relative prices, and thus why it may seem as if thesubstitutability of home and foreign goods is low in the short run relative to the long run.
Essentially, the local non-traded component is sluggish. If in response to a positive foreign
shock, home agents try to rapidly increase their purchases of imports, they strain the supplyof this local component and face a steeply increasing marginal cost curve. In the short run
the increasing marginal cost of the non-traded component largely cancels out the fall in theprice of the imported good. As a result, the final prices paid by consumers may barelychange in the short run in response to a change in relative price of imports. As time passes,
the supply of the non-traded component is able to adjust more easily and thus there is agreater response to the quantity of imports following a change in their relative price.
The manner in which we model the non-traded distribution sectors and the traded sectorsof national economies shares similarities with Burstein, Neves and Rebelo (2003), Burstein,
Eichenbaum and Rebelo (2005; 2007), Corsetti and Dedola (2005) and Corsetti, Dedola andLuduc (2008). These authors discuss how the observed import demand elasticity is diﬀerent
from the Armington elasticity of substitution when the cost of a local non-traded component
makes up a large part of the cost of an imported good.2 However these models cannot explain
the fact that observed elasticities are low in the short run but high in the long run, which
2

Anderson and van Wincoop (2004) report that distribution costs are responsible for 55% of the final
price of an imported good, Berger et al. (2012) argue that the distribution margin is between 50 − 70%.

4

is our focus. We accomplish this by modeling the local non-traded component of cost as afunction of both capital and labor. Labor can be reallocated within the period, but capitalused in the distribution sector is predetermined. This gives rise to a non-traded factor input
into domestic and imported final goods that is inelastically supplied in the short run, but
gradually adjusts across uses in response to international relative prices.
The rest of this paper is organized as follows. The model is presented in section 1. In theversion of the model without local non-traded inputs, the model collapses to the benchmark
IRBC model in Backus, Kehoe and Kydland (1994). The benchmark calibration of the modelis presented in section 2. Here we will pay particular attention to the calibration of the key
parameters involved in the distribution sector, and how the value of these parameters can beinferred from micro-data on prices. The results from the diﬀerent versions of the model arepresented in section 3. First we solve analytically for the observed import demand elasticity
following a change in the relative price of imports. We then compare the diﬀerent versions of
the model, the version with a high elasticity of substitution as measured in the international
trade literature, the version with the low elasticity as measured in the international macro
literature, and the version with the high elasticity of substitution but a local non-traded
component that is inelastically supplied in the short run. Only the version of the model witha high elasticity of substitution but an inelastically supplied local non-traded component canreplicate both the short-run properties of aggregate prices and quantities that we observein the data while also reproducing the observed long-run import demand elasticity. Finally,
section 4 concludes with some directions for further research.

1

The Model

1.1

Production

There are two countries, home and foreign. Foreign variables are written with an asterisk(∗) and home variables are not. In the following description of the model, foreign equations
are omitted for brevity.
An aggregate good is used by households for consumption,  , investment in production
capital,  , and investment in distribution capital,  . This aggregate good,  , is formed
through the combination of domestic and imported retail goods, which are combined in an
Armington (1969) aggregator function with an elasticity of substitution .
i 
h 1
−1
−1 −11.
 +  +  =  = ()  (̃ )  + (1 − )  (̃ ) 5(1)

where ̃ is the retail quantity of domestically produced goods and ̃ is the retail quantityof imported goods.
The demand for domestically produced or imported final goods as a function of aggregate
expenditure is:̃ =  (̃ )− (2)̃ = (1 − ) (̃ )− 
where ̃ (̃ ) is the retail price of domestic (imported) goods relative to the price of thehome consumption good.
Substituting these demand functions into the aggregator function in (1) yields:¤ 1£ (̃ )1− + (1 − ) (̃ )1− 1− = 1

The retail quantity of the domestic good, ̃ , is formed from the combination of aquantity of the domestic good,  , and good specific distribution services  .
i 
h
−1
−1 −11̃ = ( )  +   ( ) where  is the weight on distribution services, and  is the elasticity of substitution between
tangible goods and distribution. This same production technology is used to define ̃ :
i 
h
−1
−1 −11̃ = ( )+  ( )where  is the quantity of imported goods, and  are distribution services employedin the distribution of these imports. In the functions for ̃ and ̃ , when  = 0, thetechnology for domestic goods condenses to ̃ =  and ̃ =  , and the model
collapses to Backus et al. (1994). From this production function, the retail prices of domestic
and imported goods relative to the home aggregate price deflator are:£¤ 1( )1− +  ( )1− 1−£¤ 1= ( )1− +  ( )1− 1−̃ =
̃(3)

where  ( ) is the wholesale price of the domestic (imported) good, and  ( ) is
the cost of domestic (import) distribution services.
Wholesale goods are produced by firms engaged in perfect competition, and thus theprice of a home produced good is equal to its marginal cost of production,  , and the6price of a foreign produced good is equal to its marginal cost of production, ∗ . The
relative price of the domestic good in the home market is thus  =  while the relative∗, where  is the real exchange
price in the home market of the imported good is  = rate defined as the foreign price level divided by the home price level.
∗,
Wholesale goods used domestically or exported to the foreign country,  and exhaust current period production:∗=  1−  + (4)

where  and  are labor and capital employed in the production of home country goods,and  is a country specific total factor productivity parameter.
From this production function, the demand for labor and capital are given by  =
¡
¢
¡
¢

∗
∗

+

=

+


and


where  is the home real wage rate
(1 − ) 







(in terms of the home consumption good),  is the rental rate of physical capital employed¡  ¢1− ¡  ¢
.
in the production of home goods, and  = 1 1−Domestic distribution services employed in the final sales of domestic and imported goods, and  , are given by:



h
i 
−1
−1 −111=  (1 − ̂ ) ( )+ (̂ ) ( )
h
i 
−1
−1 −111=  (1 − ̂ ) ( )+ (̂ ) ( )(5)

where  and  are the labor and capital employed in the distribution of domestic
goods, and  and  are the labor and capital employed in the distribution of imported
goods.3
From the production functions for domestic and imported distribution services, the marginal costs of distribution are given by:¤ 1
1 £(1 − ̂ ) ( )1− + ̂ ( )1− 1−

¤ 1
1 £
=
(1 − ̂ ) ( )1− + ̂ ( )1− 1− =
(6)

where  is the rental rate of capital used for domestic distribution services,  is the rental3

̂ is the weight on capital in the production function, if the elasticity of substitution,  = 1, ̂ would
also be the share of distribution costs devoted to capital. When  6= 1, the capital share is instead a function
1−
 ()
of the steady state wage and rental rate,  = ̂ ()1−̂+(1−̂
1− . In section 2 where we calibrate this )()
parameter, to gain intuition we will calibrate capital’s share of distribution costs,  , but for a given steadystate wage and rental rate, there is a one-to-one relationship between the capital share,  , and the parameter
̂ .

7

rate for capital used in import distribution. The demand functions for capital and´−in the³ labor,
distribution of both domestic and imported goods are given by  = (1 − ̂ ) 
1−

´−
³ ´−
³
´−
³





,  = ̂ 
,  = ̂ 
.
 = (1 − ̂ ) 
1−
1−
1−


1.2





Households

The one representative household per country derives utility from consumption and leisure.
The household in the home country maximizes expected lifetime utility given by:
0

∞
P

=



i1−
1 h
(1 −  ) ( )1−
1−

(7)

where  is the coeﬃcient of relative risk aversion and  =  +  +  .
We assume that international asset markets are complete. We can model this by assuming
households share one worldwide budget constraint:¡¢∗ +  +  +  ∗ + ∗ + 

(8)
¡ ∗ ∗
¢
∗
∗
∗
∗
=   +   +   +   +    + ∗ ∗ + + 



1.3

Capital Stocks

There are three separate types of capital in each country, capital used in production,  , andcapital used in distribution of either domestic or imported goods,  and  . Capital
employed in the production of goods evolves according to the usual capital accumulation
equation:(9)+1 = (1 − )  + Distribution capital is earmarked for domestic or imported distribution services. The twomarkets are segmented in the sense that capital cannot be reallocated between domestic andimported retail distribution, both capital stocks are also subject to adjustment costs.. The
two types of distribution capital each evolve according to their own capital accumulation
equation:+1+1

¶


= (1 − )  + 

¶
µ


= (1 − )  + 

µ

(10)

where the total investment in distribution capital,  , is allocated to investment in domestic8

or imported goods distribution,  =  +  .
The adjustment costs for distribution capital,  and  are described by the
concave function  (·) (0  0 and 00  0). The stock of domestic or imported distribution
capital is a state variable and cannot be changed in the current period. If there were no
adjustment cost (00 = 0) then reallocation could be completed in one period. However when
there are costs to adjusting the stocks of distribution capital, the optimal reallocation pathmay take multiple periods.

2

Calibration

The model described in the previous section is solved with a linear approximation andsimulated in order to produce moments and impulse responses of key variables.
In the next section, simulations of the model under diﬀerent values of the Armington
elasticity, , and the parameter controlling the distribution share, , are used to examine theimportance of the distribution sector in aﬀecting the substitutability of home and foreign
traded goods. The rest of the model’s parameters and their benchmark values are found in
table 1.
The first six parameters: , the exponent on leisure in the Cobb-Douglas utility function,
, the coeﬃcient of relative risk aversion, , the capital share, , the discount factor, , theweight on domestic goods in the Armington aggregator function, and , the capital depreciation rate, are all taken from Backus, Kehoe and Kydland (1994) and found throughout theinternational real business cycle literature.
The next four parameters, ,  , , and  are the key parameters in distribution.4 To
identify these parameters, we will calculate certain second moments of wholesale prices anddistribution margins from the data and then calibrate the value of these four parameters sothat the model can match specific moments of the data.
We use a panel data set of retail prices for over 300 goods in 123 cities where the priceof each good in each city is observed annually from 1990-2005. The data-set is described in
Crucini and Landry (2012). The dataset covers over 300 goods, but we exclude the goods
that are very close to the definition of a non-traded good (like domestic cleaning help), andaggregate the remaining goods into four sectors, grocery items, non-food consumer goods,
clothing, and transportation. The full list of goods in the dataset and how they are grouped
into four categories is presented in the appendix. We restrict our attention to 13 U.S. cities,4


describes
the  capitaladjustment cost for capital used in distribution.






    
0 

00





00   .
= 0  

 


9

Specifically  =the list of these 13 cities is also presented in the appendix.
Before we discuss how the data is used, consider the price indices for the retail price andthe marginal cost of distribution in (3) and (6). If we linearize these price indices, then thefluctuations in the final good price, ̃ , can be expressed as a combination of the fluctuationsin the wholesale price, ̂ , the wage rate (non-sector specific input into distribution), ̂ , andthe rental rate for sector specific distribution capital, ̂ :̃ = (1 − ) ̂ +  (1 −  ) ̂ +  ̂where  measures the steady state distribution margin,  = 

³


̃

´1−

=

³


̃

´1−

.

In the data set we observe ̃ , the retail price of the good from sector  in city  attime . Crucini and Landry (2012) also provide data on the distribution margin for eachgood in the dataset,  .5 Given these prices and the distribution margins we can estimate
the following regression:(11)̃ = (1 −  )  +   +  where  is sector specific fixed eﬀect intended to capture variation in wholesale prices (̂ ),and  is a city-fixed eﬀect intended to capture variation in the city, but not good specificcomponent of distribution (̂ ). Furthermore we can calculate the total distribution cost,̃ −(1− )
̂ =     .
With time series of ̂ , ̂ , ̂ we can calculate the variance, the persistence, and the comovement of each one of the components of the retail price. These statistics are presented intable 2. In this table, these statistics are computed using a few diﬀerent detrending methods.
The price data, ̃ , is nominal, so the first step is to remove the nominal trend. In columns
1-3, the nominal trend is removed by including a time dummy in the regression in equation(11). In columns 4-6, the nominal trend is removed by dividing all prices by the consumer
price index, and in columns 7-9, there is no nominal detrending. Comparing each set ofthree columns shows that nominal detrending really doesn’t have much of an eﬀect on thesestatistics. This is due to the fact that the data is taken from 13 U.S. cities over the period
1990-2005, a period when inflation was low and stable.
But even after taking out a nominal trend, over this period there have been shifts in relative productivity between sectors, which would lead to non-stationary relative price changes
that we would want to filter out before using the data to calibrate a stationary model (e.g.
productivity improvements in the technology sector have led to a non-stationary fall in therelative price of computers over this period). To account for these non-stationary shifts in
sectoral prices, we can either filter the sectoral price data, ̃ , using an HP filter (with5

The distribution margins,  , are good specific, but is common across all locations and time.

10smoothing parameter 100 for annual data) or taking first-diﬀerences. Thus within each setof three columns in table 2, the first column filters each sectoral price with an HP filter, thesecond uses first-diﬀerences, and the third does nothing.
The first thing to notice is that the wholesale goods price, ̂ , is extremely volatile when
no filter is used. This is due to non-stationary shifts in relative prices across sectors. Once
we use a filter to remove these non-stationary shifts in relative prices, the results in thetable are largely invariant to which filter we use. The only noticeable diﬀerence is that thefirst-order autocorrelation coeﬃcient is much lower using the first-diﬀerenced data, but allother statistics are largely the same. Thus in the following calibration exercise, we simply
use the first column, the data using the time dummy for nominal detrending and the HP
filter for additional detrending, as the benchmark set of statistics.
Simulated method of moments are employed to find the combination of ,  ,  and that minimizes the squared distance between the moments presented in the first column oftable 2 and the corresponding moments from simulations of the model. These estimatedparameters are listed in the bottom four rows of table 1.
The the optimal combination of ,  ,  and  is chosen by varying all four parameterssimultaneously, but to gain some intuition about the separate role of each of these fourparameters related to the distribution sector, in tables 3 and 4 we vary one of these fourparameters, while holding the other three constant.
The eﬀect of varying the elasticity of substitution between tangible goods and distribution services, , is shown in columns 2-6 of table 3. The simulated method of moments
exercise finds that the optimal value of  is 002, implying that tangible goods and distribution services are nearly perfect compliments. The table reports the eﬀect of increasing 
while holding all other parameters constant. As  increases, there is very little change ineither the volatility or the persistence of the wage rate, ̂ . However, the relative volatilityof both the wholesale price and distribution costs falls as  increases. In the data, bothwholesale prices, ̂ , and distribution costs, ̂ , are about two-thirds as volatile as the wage
rate. When wholesale goods and distribution services are nearly perfect compliments, themodel is able to replicate these relative volatilities. As  increases and the two become more
substitutable, these relative volatilities fall, when  = 08, the price of wholesale goods andthe cost of distribution are both about a third as volatile as the wage rate. Hence,  must be
small, implying that wholesale goods and distribution services are compliments, to replicate
the volatility of prices that we see in the data. Our estimates of a near perfect complementarity between wholesale goods and distribution services largely validate the calibration by
Burstein, Neves and Rebelo (2003) and Burstein, Eichenbaum and Rebelo (2007).
In columns 7-11 of the same table we vary  , the labor share in the production of11

distribution services from 016 to 056. Again we see that varying  has little eﬀect on thevolatility or persistence of the wage rate. Allowing the labor share to increase does havesome eﬀect on the relative volatilities of the wholesale price and the distribution costs, but
the major eﬀect of increasing  is in the co-movement between the wage rate and wholesale
prices or between the wage rate and distribution costs. In the data, the correlation between
the wage rate and the cost of distribution is about 034. When  is small, and thus there isvery little labor used in distribution, the model predicts that the co-movement between thetwo should be almost 0. As  increases and thus there is more labor used in distribution,
the correlation between the two will increases. However, as  gets too big, the correlation
between the two gets too large, so to replicated the positive but modest correlation between
the wage rate and the cost of distribution,  should be about 036.
Similarly, in the data, the correlation between the wage rate and wholesale prices is about−027. In the model, when  is small, the two are nearly uncorrelated, but as  increases,
this correlation falls, but again, to replicate the negative, but modest, correlation,  shouldbe about 036.
In columns 2-6 of table 4 we vary , the elasticity of substitution between capital andlabor in the production of distribution services. Again we see that allowing  to vary has little
eﬀect on the volatility or the persistence of the wage rate. However, as  increases capitaland labor in distribution become more substitutable, and the relative volatilities of both the
distribution cost and the wholesale price falls. When  is small, and capital and labor in
distribution are nearly perfect compliments, both distribution costs and the wholesale prices
should be about as volatile as the wage rate. When  is higher and capital and labor arecloser substitutes, these two prices are about half as volatile as the wage rate, in order tomatch the relative volatilities that we observe in the data,  should be about 04.
Finally, columns 7-11 of table 4 present the results from simulation of the model where, the distribution capital adjustment cost parameter varies. Again, allowing  to vary
has little eﬀect on the volatility or the persistence of the wage rate. Note that in contrast
to the other three cases in tables 3 and 4, only when we vary  do we see any significant
eﬀect on persistence. In the data, both the distribution cost and the wholesale price have afirst-order autocorrelation coeﬃcient of about 082. When  = 0, implying that there are nocosts to adjusting the stocks of distribution capital, the persistence of these two variables iscounterfactually low. Similarly, when  is low, the relative volatilities of the two prices is
too low, the correlation between the wage rate and the cost of distribution is too low, andthe correlation between the wage rate and wholesale prices is too high. In order to replicate
the moments we observe in the data, the model needs a modest investment adjustment cost
parameter of 018.
12

2.1

Shock Process

In this real business cycle model, fluctuations in total factor productivity drive business cycle
fluctuations. The  and ∗ variables in (4) are exogenous country specific shocks. Using
data on gross value added, total employment, and gross fixed capital formation from theOECD’s STAN database, we estimate two series of total factor productivity for the UnitedStates and the combination of Germany, France, Italy, the Netherlands, Belgium, Austria,
and Finland from 1977-2007. The data is available at annual frequency, we first estimate
a VAR(1) with the two series using the annual data, and then we impose symmetry andconvert this annual process to a quarterly process. The resulting quarterly shock process forthe model is:
"

+1
∗+1

#

=

"

083 00 083

#"


∗

#

+

"


∗

#

where var( ) =var(∗ ) = 012 and corr(  ∗ ) = 031.
This shock process assumes that TFP is the same across both the production sector
and the distribution sector within a country, as in the production functions in (4) and (5).
Alternatively we can assume that there is a separate TFP process for the distribution sector,
and thus the  in (5) is replaced with  . There are now four TFP processes to estimate, sowith the STAN data, instead of considering total value added, total employment, and total
capital formation in order to find aggregate TFP, we can consider these same series separated
into industry and service sectors. Thus using both industrial and service sector TFP for boththe U.S. and Europe, we can estimate a VAR(1) with the four TFP variables,  , ∗ ,  ,and ∗ . Again, this data is available at an annual frequency, so after estimating the annual
process, imposing symmetry across countries, and converting to a quarterly process, theresulting shock process for the model is:where A =

h



∗



∗


i0

A+1 = ρA + εand  (ε ε0 ) = Ω, where13⎡078 006
007⎢⎢ 006 078 −019
ρ = ⎢⎢ 000 002
084⎣
002 000 −007and⎡692 063⎢⎢ 063 692
Ω = 10−1 × ⎢⎢ 032 033⎣
033 032

⎤
−019
⎥
007 ⎥⎥−007 ⎥
⎦
084
032
077
097
047

⎤
077
⎥
032 ⎥⎥
047 ⎥⎦
097

3

Results

3.1

Distribution costs and the observed elasticity of substitution

The elasticity of substitution between home and foreign goods is defined as the percentagechange in relative quantities divided by the percentage change in relative prices:
 ln
 =
 ln

³

³






´

´

(12)

To find this elasticity in terms of the model’s
parameters, consider the demand´³ structural̃functions in (2) and find an expression for ln ̃ :6
µ

̃
ln
̃

¶

µ

1−
= ln


¶

µ

̃
−  ln̃¶

If ̃ =  and ̃ =  , then the elasticity,  equals the structural parameter .
If however, the price of imports relative to domestic goods at the wholesale level varies overtime relative to that at the retail level, then the elasticity  becomes a function of otherparameters in the model, and generally time varying.
To see this, expand the elasticity expression in (12):6

The model is calibrated such that , the elasticity of substitution between intermediate goods anddistribution services is equal to zero. In thisof´
³ the ´observed elasticity of substitution we are using³ derivation̃. If instead   0, then the expression linking
that fact in order to simplify and say  ln ̃ =  ln wholesale quantities and retail quantities will be more complicated, but the intuition is the same.

14

 ln
 =
 ln

³

³

̃
̃
̃
̃

´

´

 ln
 ln

³

³

̃
̃



´

´ =

 ln
 ln

³

³

̃
̃



´
´

Thus the change in relative quantities following a change in wholesale prices is the Armington elasticity of substitution between home and foreign goods, , multiplied by the elasticity of relative prices at the consumer level with respect to changes in relative prices at thewholesale level.7 Given the expressions for the final consumer prices in (3), this elasticity
can be written as:
 ln
 ln

³

³

´

̃
̃

(1 − )  ln

´≈




³




 ln

³

´

+  ln
´




³




´

Thus the observed elasticity of substitution between domestic and imported goods following a change in wholesale prices is:⎛ =  ⎝(1 − ) + 

 ln
 ln

³

³






´⎞
´⎠

In response to a change in relative wholesale prices, the market will react by shifting
resources from one type of distribution to another. Specifically, if domestic´ become³ goods
relatively more expensive than imported goods at the wholesale level,  ln   0, thenthe quantity demanded of imported goods should increase and the quantity demanded ofdomestic goods should fall.
There are two inputs into the production of distribution services, non-sector specific laborand sector specificcapital. From equation (6), fluctuations in the ratio of the two distribution´³

margins,  ln  , can be written as:
µ


 ln


¶

µ


=   ln


¶

µ


+ (1 −  )  ln


¶

µ


= (1 −  )  ln¶Thus the observed elasticity of substitution,  , is:⎛ =  ⎝(1 − ) +  (1 −  )

 ln
 ln

³

³






´⎞
´⎠

(13)

Following the shift in the quantity demanded of imported and domestic wholesale goods,
7

See Crucini and Yilmazkuday (2009) for empirical evidence using micro-level price data of how distribution costs lead to a long-run disconnect between producer and consumer prices.

15the demand for imported goods distribution services will increase and the demand for domestic goods distribution services will fall. Labor used in the production of distribution services
can be reallocated within the period, but in the short run distribution capital cannot bereallocated. Thus following a change in relative wholesale prices that leads to an increased
demand for imports and a decreased demand for domestic goods, there is an excess demandfor imported goods distribution capital and an excess supply of domestic goods distribution
capital. This implies that the equilibrium cost of domestic goods distribution capital should
fall and the cost of imported goods distribution capital should rise. Thus the following
inequality should hold in the short run:8
 ln
 ln

³

³






´

´ 0

Given this excess demand in one market and the excess supply in another, agents willchange their future investment plans. Investment in imported goods distribution capital will
increase and investment in domestic good distribution capital will decrease.
If there are no adjustment costs in the capital accumulation equations in (10) then plansfor investment in new domestic or import distribution capital are changed and the capitalstocks reach their new eﬃcient level in the next period. If there are capital adjustment costs
then the adjustment may be slower and it may take multiple periods to clear out any excess
demand or supply in the market for distribution services and reach a point where  =  .
Given this change in the relative distribution costs, in the short run   (1 − ) , andas time passes and capital is reallocated,  approaches (1 − ) .
If  = 1, non-sector specific labor is the only input into distribution. Given that labor
may be reallocated across uses within the period, the cost of distribution services must be
the same for both domestic goods and imports,  =  . In this case  = (1 − )  for all.
The path of the observed elasticity of substitution following a productivity shock ispresented in figure 1. The figure presents the path of the observed elasticity of substitution,
as measured by (12) for 40 quarters following a shock in the three diﬀerent cases. The firstis where the Armington elasticity of substitution between home and foreign goods is equal
to 4 and there is no distribution sector, in the second case the Armington elasticity is equal
to 09 and there is no distribution sector, and in the third the Armington elasticity is equal
to 8 but distribution costs make up approximately 50% of the final cost of a good, as in
8

Empirically, Goldberg and Campa (2010) find that following a 1% exchange rate depreciation that results
in a 1% increase in the price of foreign currency denominated imports at the dock, the distribution costs ofimports falls by 047%.

16

Corsetti and Dedola (2005). Given that  = 05 and  = 8, the observed long run elasticity
of substitution is equal to 4.
In the two cases where there is no distribution sector the observed elasticity of substitution
is simply equal to the Armington elasticity. In the case where there is a distribution sector,
the observed elasticity is initially close to zero since distribution capital is a state variable
and cannot be instantaneously reallocated from the domestic goods sector to the imported
goods sector, and the elasticity of substitution between capital and labor in the distributionsector is low, meaning that some labor is shifted into the high demand sector, but not
much. Agents cannot reallocate existing capital but can change investment plans subject
to investment adjustment costs, so over time capital in one sector is allowed to depreciate
without replacement while the stock of distribution capital increases in the other. Thus overtime as the stocks of distribution capital change, the observed substitutability between homeand foreign goods increases.

3.2

Impulse Responses

The responses of home and foreign GDP and its components to a positive home TFP shock
are presented in figures 2 and 3. Figure 2 presents the responses of home and foreign GDP
and investment under three cases mentioned earlier, where the Armington elasticity, , isequal to 4 and the distribution margin is equal to 0, where the Armington elasticity is equal
to 09 and the distribution margin is equal to 0, and where the Armington elasticity is equal
to 8 but the distribution margin is set to 50%. Figure 3 does the same for consumption andnet exports.
For the case where the elasticity is equal to 4 but there are no distribution costs, thefigures show the familiar result that in an international real business cycle model with complete international asset markets and a high degree of substitutability between home andforeign goods. Following a productivity shock in the home country, there is a sharp increasein home investment demand. The foreign country does not have the same increase in investment demand and any increase in foreign investment is tempered in order to ship goods tofuel the productivity induced investment boom in the home country. Thus in the immediate
aftermath of the shock, before the benefits of the shock in terms of increased home production are felt, the home country runs a current account deficit and the foreign country runs
a current account surplus.
Within a few quarters there is a reversal in the current account as the higher production
leads to increased saving in the home country, some of this increased savings is shippedabroad in the form of high home current account surpluses. Thus after the first few quarters,17the home country runs a large and persistent current account surplus and the foreign country
runs a large and persistent deficit.
The current account dynamics change in significant ways when home and foreign goods
are less substitutable. When the elasticity of substitution is equal to 09, the foreign goods
can’t as easily be used to fuel a home country investment boom, so there is more of an increasein foreign investment in the aftermath of the shock. Furthermore, once the increased home
productivity leads to an increase in home production and home saving, foreign agents can’t
as easily consume the benefits of the productivity fueled boom in the home country and thus
do not run large current account deficits when substitutability is low.
The responses from the model with distribution costs are very similar to the responses
when the technological elasticity of substitution is equal to 09. The observed long-run
elasticity of substitution between home and foreign goods may be equal to 4, but in the
short run, home and foreign goods are not highly substitutable. The figure shows that there
is more of an increase in foreign investment in the immediate aftermath of the shock as
foreign goods are not as easily diverted for use in the home country investment boom. And
since without adequate distribution channels, foreign agents cannot as easily substitute theexcess production from the home country for their own goods, foreign agents import less andthus run a smaller trade deficit.
Following a shock to productivity in one country, prices and quantities need to adjust to
restore equilibrium. Figures 2 and 3 show that when there is low substitutability between
home and foreign goods, there is not much response to net exports following a shock, so it
must be that most of the burden of adjustment falls on international relative prices, namely
the terms of trade and the real exchange rate.9
Figure 4 shows the responses of the home country terms of trade and the real exchange
rate following a positive home TFP shock. When the technological elasticity of substitution
is equal to 4 and there are no distribution costs there is little movement in either the termsof trade or net exports following a shock. When the elasticity of substitution is equal to 09,
there is much more movement in both the terms of trade and the real exchange rate. Similarly
when the Armington elasticity of substitution is equal to 8 but there are distribution costs
there is significant movement in both the terms of trade and the real exchange rate following
the shock. Thus when there are distribution costs and a distribution sector that is slow toadjust, the economy with a high elasticity of substitution but distribution costs acts a lot
like the economy with a low elasticity of substitution, following a shock, quantity variables
9

A similar argument (but one that relied on incomplete pass-through to explain the low substitutability)
is given in Devereux and Engel (2002) to explain the high volatility of exchange rates that we observe in the
data.

18

like like exports and imports cannot adjust quickly to restore equilibrium, so the burden of
adjustment falls on prices like the terms of trade and the real exchange rate.

3.3

Volatility and co-movement of certain macro variables

The standard deviation and co-movement of GDP, the components of GDP, and international
prices like the terms of trade and the real exchange rate are listed in table 5. The first twocolumns of the table list these moments calculated from the data either for the U.S. or theEuro area. The data is quarterly from 1984 to 2007. The rest of the table presents these
moments as calculated from simulations of the model. In the first three columns of data fromsimulations of the model (Model 1), exports and imports (and thus net exports and GDP)
are measured with prices that are allowed to vary over the cycle. Exports and imports aremeasured with constant (steady-state) prices in the last three columns of the table (Model
2).
The simulations of the model are conducted under the three alternative parameterizations
that were used in the impulse response analysis. The table shows that when the Armington
elasticity of substitution is equal to 4 but there are no distribution costs the model predicts
too little volatility in both consumption and international prices like the terms of tradeor the real exchange rate. The model also predicts a low cross-country co-movement inproduction side variables like output and employment, and a high cross-country co-movement
in consumption.
These features of the model where shown earlier in the impulse response analysis. Following a positive shock in one country, the country that experienced the positive shock caneasily export their surplus production to the less productive country. This leads to too muchconsumption smoothing, and since quantities adjust so easily in order to clear markets internationally, there is not much movement in either the terms of trade or the real exchange
rate. The high substitutability of home and foreign goods means that agents are very willingto have changes in the composition of their consumption and take advantage of productivity diﬀerentials across countries to maximize total consumption, and this results in a low
cross-country correlation in production and a high cross-country correlation in consumption.
When the elasticity of substitution between home and foreign goods is 09, the low
substitutability between home and foreign goods means that the country that experiences
a positive shock cannot as easily export their surplus production to the foreign country.
This implies that net exports are less volatile and consumption is more volatile. Lower
substitutability means that production responsibilities cannot as easily be "shared" between
countries, so cross-country output co-movement is higher and cross country consumption

19

co-movement is lower. Given that net exports are less volatile when home and foreign goods
are not as easily substitutable, international prices like the real exchange rate and the termsof trade must move more to restore equilibrium following a shock.
The table shows that in the version of the model where the Armington elasticity of substitution between home and foreign goods is equal to 8 but there are distribution costs, thevolatility and co-movement from simulations of the model are very close to the moments
predicted from the model with the low Armington elasticity. Even though the Armington
elasticity is high, since distribution channels cannot be adjusted quickly following a shock, atshort horizons home and foreign goods are much less substitutable. As a result, net exports
are not very volatile, and the model with distribution costs is able to predict the high volatility of the real exchange rate and the terms of trade even when the observed long run elasticity
of substitution between home and foreign goods is equal to 4. Since home and foreign goods
cannot be easily substituted in the short run, there is less consumption smoothing, lower
cross-country consumption correlation, and higher cross-country correlation in output andinvestment.
In the last three columns of the table exports and imports are measured with constant(steady state) prices. In this model, frictions in distribution may severely hamper the abilityof export and import volumes to respond following a shock. Measuring exports and imports
with constant prices allows us to study the behavior of trade quantities, and ensure thatthese results are not simply driven by changes in the terms of trade.
The table shows that measuring exports and imports with constant price has little eﬀect
on most variables in the model. None of the variances or co-movements involving GDP, net
exports, exports, or imports are significantly aﬀected. The volatility of exports and imports
drops when measured with constant prices. In the model, the volatility of the volume ofexports and imports is highest when goods are very substitutable. This volatility falls in
the model where goods are less substitutable. When there are frictions in the distribution
margin, the volatility of export and import volumes predictably lies between these two
extremes.10
3.3.1

The S-curve

As discussed in Backus, Kehoe and Kydland (1994), the contemporaneous correlation between international relative prices like the terms of trade or the real exchange rate and net
10
It should be noted that the volatility of exports and imports in the model is very low compared to what
we observe in the data. As discussed in Engel and Wang (2011), this feature of the data is due to the factthat much trade seems to be concentrated in the more volatile durable goods sector. Since this model does
not provide a special role for durable goods trade over non-durable trade, export and import volumes shouldin the model should still be below what they are in the data.

20

exports is low and maybe even negative. The last two rows of table 5, show that the correlation between the terms of trade and net exports or between the real exchange rate andnet exports is negative in the United States. The same correlations are positive but close tozero in the Euro Area. Furthermore, the table shows that simulations of the model where
the Armington elasticity is equal to 4 but there are no distribution costs predict a high contemporaneous correlation between relative prices and net exports, that is the model predicts
that when there is a depreciation in the real exchange rate or the terms of trade that makes
home goods relatively less expensive than goods produced abroad, there is an instantaneous
improvement in the trade balance.
The table shows that when home and foreign goods are less substitutable, either because
the Armington elasticity is equal to 09 or because there are distribution costs in the model,
the contemporaneous correlation between relative prices and net exports falls. The models
with a low substitutability between home and foreign goods predict that the contemporaneous correlation between the terms of trade and net exports is about −036. In the model
without distribution costs the real exchange rate is perfectly correlated with the terms oftrade, and thus the correlation between the real exchange rate and net exports is also −036.
In the model with distribution costs the real exchange rate and the terms of trade are nolonger perfectly correlated, but the model still predicts a low correlation between the realexchange rate and net exports.11
Backus et al. go on to describe the S-curve. The fact that the correlation between theterms of trade at time  and net exports at time + looks like a horizontal letter S as  goesfrom some negative integer to some positive integer. Most importantly, the S-curve shows
the fact that the contemporaneous correlation between net exports and international relative
prices is negative, but the correlation between relative prices today and net exports at time
 +  is positive for some positive , implying that the immediate impact of an exchange
rate depreciation may be a fall in the trade balance, but a depreciation eventually leads toan increase in net exports.
This S-like relationship between relative prices like the real exchange rate or the termsof trade and lags or leads of net exports is presented in figure 5. The figure shows the11

The fact that the contemporaneous correlation between the terms of trade and the trade balance may bepositive or negative is related to the famous Marshall-Lerner condition. When there is a depreciation in theterms of trade, the relative price of imports increases, this means that the quantity demanded of imports willcertainly fall and the quantity demanded of a country’s exports will certainly rise. Thus when measuring net
exports with constant (steady-state) prices, there will certainly be a positive correlation between the termsof trade and the trade balance, as shown in the results for Model-2. However, when the prices that are used
to calculated the trade balance also vary, the relative price of imports may increases, and thus the quantity
demanded of imports will fall, but if the import demand elasticity is less than 1 then the fall in quantity
demanded is not as great as the rise in the price, so the total spending on imports will actually increase,resulting in a negative contemporaneous correlation between the terms of trade and the trade balance.

21

correlation between relative prices at time  and net exports at time  +  as observed in thedata for the United States and the Euro Area, and as predicted by the three versions of themodel.
As observed from the S-curves in the data, the correlation between relative prices attime  and net exports at time  +  is increasing as  increases. Thus there is a negative
contemporaneous correlation between either the terms of trade or the real exchange rate
and the current value of net exports, but this correlation increases for future values of net
exports. When the technological elasticity of substitution is equal to 4 and there are no
distribution costs, the model cannot replicate this finding. Counterfactually the model findsthat the correlation between relative prices at time  and net exports at time  +  falls as increases.
However, when the short-run substitutability of home and foreign goods is low, either
because the Armington elasticity is low or because frictions in the distribution sector hamper
substitutability in the short run, the model can replicate the fact that the correlation between
relative prices at time  and net exports at time  +  starts at an initially low level andincreases as  increases.
3.3.2

Separate shocks in the production and distribution sectors

The results presented so far have assumed that both the production and distribution sectors
within a country are aﬀected by the same country-specific TFP shock. This was done
to ensure that the results from the model without the distribution sector could be easily
compared with the results from the model with a distribution sector. However, as mentioned
in section 2, it may be more realistic to assume that within each country there are two shocks,
a production sector shock,  , that aﬀects the manufacturing sector, and a service sector
shock,  , that aﬀects the distribution sector. We use data from the OECD’s STAN databaseto calculate country and sector specific TFP processes for both the manufacturing sector andthe service sector, and the results from the estimation of this VAR(1) process with these four
shocks was presented in section 2.
The results from simulations of this model are presented in table 6. Now the comparison
between the model with no distribution sector and the model with a distribution sector is
not as easy. Since the shocks to the production sector are more volatile than shocks to theservices sector, it is not as clear-cut to compare a model where all of the economy is engaged
in manufacturing to one where half is manufacturing and half is distribution.
That said, in the model with both sector- and country-specific shocks, most of the samefeatures of the model with only country-specific shocks continue to hold. Namely the factthat in the model with a high technological elasticity of substitution, consumption volatility
22will be counterfactually low, the volatility of the terms of trade and the real exchange rate will
be too low, cross-country GDP co-movement will be too low, and cross-country consumption
correlation will be too high. These key failings of the model were brought on by the factthat home and foreign goods were too highly substitutable, and thus home and foreign
agents could too easily smooth consumption following a county-specific shock. The modelwith both sector- and country-specific TFP shocks can still lead to key improvements in theability of the model to match the data since frictions in the distribution sector still hamper
the substitutability of home and foreign goods in the short run.

4

Summary and Conclusion

The international macro literature uses a low elasticity of substitution between home andforeign goods since a low substitutability is needed to explain short business cycle fluctuations, particularly movements in international relative price and the real exchange rate. Theinternational trade literature measures this elasticity using data on the longer term change
in trade patterns following a changes in relative prices, for instance after an exogenous tariﬀ
reduction.
This paper presents a model that can explain these two apparently contradictory results.
The true elasticity of substitution between home and foreign goods is high, like in the trade
literature. However in the short run there are frictions in distribution that makes home andforeign goods appear much less substitutable in the short run. The model is parameterized
to produce this high long-term elasticity, but simulations of the model show that in the
short run it behaves like an international macro model parameterized with a low elasticity
of substitution. Specifically, the model is able to replicate the short-run volatility of the realexchange rate and the terms of trade. The model can also replicate the negative co-movement
between relative prices and both GDP and net exports.
Thus frictions in distribution are one possible reason for the discrepancy between tradeand macro estimates of the elasticity of substitution. Other reasons for this low short run
elasticity and high long run elasticity include frictions in price setting, frictions in firm entry
and exit, and frictions in inventory management. It is left as an interesting direction forfurther research to empirically measure the relative weights of these competing explanations
in explaining the elasticity puzzle.

23

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26

5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0

0

5

10

15

20
Quarters

25

30

35

40

Figure 1: Observed Elasticity of Substitution following a TFP shock. The solid line is where
the structural elasticity is equal to 4 and there is no distribution. The dashed line is where
the structural elasticity is equal to 0.9 and there is no distribution. The line with stars iswhere the structural elasticity is equal to 4 and there is distribution.

Table 1: Parameter Values
Symbol
θ
σ
α
β
ω
δ
γ
αd
η
χ

Value
0.66
2
0.36
0.99
0.85
0.025
0.02
0.36
0.40
0.18

Description
weight on leisure in the household’s utility function
coeﬃcient of relative risk aversion
capital share in the production of traded goods
discount factor
exogenous preference for home goods
capital depreciation rateelasticity of substitution between wholesale goods and distribution services
capital’s share in distribution costs
elasticity of substitution between capital and labor in distribution
capital adjustment cost parameter for capital used in distribution

27

Home GDP

Foreign GDP

0.7

0.2

0.6
0.15

0.5
0.4

0.1
0.3
0.2

0.05

0.1
0

0

10

20

30

0

40

0

Home Investment

10

20

30

40

Foreign Investment

2.5

0.4

2

0.3

1.5
0.2
1
0.1
0.5
0

0
−0.5

0

10

20
Quarters

30

−0.1

40

0

10

20
Quarters

30

40

Figure 2: The responses of home and foreign GDP and investment to a positive home
TFP shock. The solid line is where the structural elasticity is equal to 4 and there is no
distribution. The dashed line is where the structural elasticity is equal to 0.9 and there isno distribution. The line with stars is where the structural elasticity is equal to 4 and there
is distribution.

28

Home Consumption

Foreign Consumption

0.14

0.06

0.12

0.05

0.1

0.04

0.08
0.03
0.06
0.02

0.04

0.01

0.02
0

0

10

20

30

0

40

0

Home Net Exports
0.08

0.02

0.06

0

0.04

−0.02

0.02

−0.04

0

−0.06

−0.02

0

10

20
Quarters

30

20

30

40

Foreign Net Exports

0.04

−0.08

10

−0.04

40

0

10

20
Quarters

30

40

Figure 3: The responses of home and foreign consumption and net exports to a positive
home TFP shock. The solid line is where the structural elasticity is equal to 4 and there isno distribution. The dashed line is where the structural elasticity is equal to 0.9 and there isno distribution. The line with stars is where the structural elasticity is equal to 4 and there
is distribution.

29

Home Terms of Trade

Real Exchange Rate

0.25

0.09
0.08

0.2

0.07
0.06

0.15

0.05
0.04

0.1

0.03
0.02

0.05

0.01
0

0

10

20

30

0

40

0

10

20
Quarters

30

40

Figure 4: The response of the home country terms of trade and the real exchange rate to a
positive home TFP shock. The solid line is where the structural elasticity is equal to 4 andthere is no distribution. The dashed line is where the structural elasticity is equal to 0.9 andthere is no distribution. The line with stars is where the structural elasticity is equal to 4
and there is distribution.

30

Correlation between NX(t+n) and TOT(t)1
USEuro Area

Correlation between NX(t+n) and TOT(t)
1

0.5

0.5

0

0

−0.5

−0.5

−1

−5

0
n

−1

5

Correlation between NX(t+n) and RER(t)1
USEuro Area

0.5

0

0

−0.5

−0.5

−5

0
n

0
n

5

Correlation between NX(t+n) and RER(t)
1

0.5

−1

−5

−1

5

−5

0
n

5

Figure 5: The correlation between relative prices and lagged values of net exports. The solidline is where the structural elasticity is equal to 4 and there is no distribution. The dashedline is where the structural elasticity is equal to 0.9 and there is no distribution. The linewith stars is where the structural elasticity is equal to 4 and there is distribution.

31

32

ŵt
p̂it
ĉit

Autocorrelation

Correlation p̂it , ŵtĉit , ŵtp̂it , ĉit

p̂it
ĉit

St. Dev. relative
to ŵt
0.80
0.16
0.66

0.84
0.72
0.96
0.95
0.93

19.81
0.69

−0.27 −0.15
0.33
0.34
0.25
0.30
−0.44 −0.32 −0.01

0.90
0.82
0.82

0.69
0.65
0.79
0.45
0.64

0.65
0.82
0.96
0.96
0.93

17.85
0.72

−0.44 −0.36 −0.20
0.74
0.69
0.72
−0.36 −0.30 −0.15

0.91
0.81
0.82

0.56
0.70
0.80
0.66
0.65

0.66
0.82

0.96
0.95
0.93

16.88
0.72

−0.42 −0.21 −0.26
0.74
0.68
0.72
−0.35 −0.21 −0.19

0.91
0.80
0.82

0.56
0.70

Table 2: The price data used to calibrate the distribution parameter values under various detrending methods.
Remove nominal trend:
Use Time dummy
Remove CPI
Do nothing
Additional ﬁltering:
HP
Diﬀ
None
HP
Diﬀ
None
HP
Diﬀ
None
St. Dev.
ŵt 12.12 12.10 22.35
12.07 11.87 22.88
12.07 11.98 22.80

33

ŵt
p̂it
ĉit
ŵt
p̂it
ĉit

p̂it , ŵtĉit , ŵtp̂it , ĉit

St. Dev.

St. Dev. relative
to ŵt

Autocorrelation

Correlation

0.96
0.86
0.86
−0.32
0.29
−0.99

−0.27
0.34
−0.44

0.69
0.65

0.90
0.82
0.82

0.69
0.65

−0.33
0.29
−0.99

0.96
0.88
0.87

0.57
0.52

−0.33
0.28
−0.98

0.95
0.89
0.89

0.50
0.44

−0.32
0.26
−0.98

0.95
0.90
0.90

0.44
0.39

−0.31
0.25
−0.98

0.95
0.90
0.90

0.40
0.34

−0.06
0.04
−0.99

0.98
0.85
0.84

0.87
0.84

−0.19
0.16
−0.99

0.97
0.85
0.85

0.78
0.75

−0.32
0.29
−0.99

0.96
0.86
0.86

0.69
0.65

Table 3: Calibrating the value of the parameters used in distribution
Data
γ = .02 γ = .2 γ = .4 γ = .6 γ = .8
αd = .16 αd = .26 αd = .36
12.12
0.58
0.59
0.60
0.61
0.61
0.59
0.58
0.58

−0.46
0.42
−0.99

0.95
0.87
0.87

0.60
0.55

αd = .46
0.58

−0.59
0.56
−0.98

0.94
0.90
0.89

0.52
0.45

αd = .56
0.59

34

ŵt
p̂it
ĉit
ŵt
p̂it
ĉit

p̂it , ŵtĉit , ŵtp̂it , ĉit

St. Dev.

St. Dev. relative
to ŵt

Autocorrelation

Correlation

0.98
0.82
0.82
−0.21
0.19
−0.99

−0.27
0.34
−0.44

0.90
0.86

0.90
0.82
0.82

0.69
0.65

−0.28
0.25
−0.99

0.97
0.84
0.84

0.77
0.73

−0.32
0.29
−0.99

0.96
0.86
0.86

0.69
0.65

−0.36
0.32
−0.99

0.95
0.88
0.87

0.63
0.58

−0.39
0.35
−0.99

0.95
0.89
0.89

0.58
0.53

0.15
−0.23
−0.92

0.97
0.46
0.39

0.43
0.37

−0.21
0.16
−0.98

0.97
0.83
0.82

0.62
0.57

−0.32
0.29
−0.99

0.96
0.86
0.86

0.69
0.65

−0.40
0.37
−0.99

0.96
0.88
0.87

0.74
0.69

−0.45
0.43
−0.99

0.95
0.89
0.88

0.77
0.73

Table 4: Calibrating the value of the parameters used in distributionDataη = .10 η = .25 η = .40 η = .55 η = .70
χ = 0 χ = .09 χ = .18 χ = .27 χ = .36
12.12
0.56
0.57
0.58
0.59
0.59
0.64
0.60
0.58
0.56
0.55

35
C
I
NX
N
Ex
Im
Tot
Q

C
I
N
Ex
Im
Tot
Q

Correlation

Tot,NX
Q,NX

Cross-country GDP
co-movement C
I
NEx

Co-movement
with
GDP

Volatility
Relative
to GDP

0.85
0.90
0.02
0.87
0.91
0.90
0.31
0.66

0.74
2.64
0.61
3.26
3.40
3.86
5.16

−0.13 0.18
−0.05 0.21

0.52
0.76
0.67
0.47
0.63

0.84
0.91
−0.41
0.81
0.54
0.82
0.29
−0.02

0.89
3.14
0.85
3.86
3.37
2.14
4.14

0.51
3.18
0.45
1.01
1.11
0.84
0.59

0.49
0.55
0.15
0.47
0.47
0.78 −0.36
0.78 −0.36

0.23
0.77
−0.02
0.04
−0.28

0.81
0.83
0.89
0.94
0.09 −0.46
0.93
0.90
0.58
0.59
0.50
0.99
0.46
0.36
0.46
0.36

0.43
3.13
0.49
1.31
1.17
0.34
0.24

−0.46
−0.08

0.44
0.50
0.25
0.45
−0.39

0.86
0.93
−0.22
0.93
0.43
0.75
0.52
0.48

0.61
2.10
0.27
1.23
1.28
1.18
0.75

0.48
3.03
0.43
0.98
0.98
0.80
0.56

0.84
0.84

0.17
0.77
−0.02
0.04
−0.32

0.40
0.40

0.34
0.55
0.15
0.47
0.41

0.80
0.84
0.88
0.93
0.19 −0.13
0.93
0.87
0.60
0.62
0.29
0.76
0.50
0.46
0.50
0.46

0.42
3.06
0.47
1.31
1.31
0.33
0.23

0.15
0.52

0.31
0.50
0.25
0.45
−0.03

0.86
0.93
0.11
0.93
0.64
0.48
0.58
0.54

0.58
2.00
0.26
1.17
1.17
1.12
0.71

Table 5: Volatility and co-movement of GDP and its components in the data and from simulations of the model under diﬀerent
elasticities of substitution and distribution costs.
Model - 2
Model - 1
Data
Distribution
No
No
Yes
No
No
Yes
US
EA
Elasticity
4
0.9
4
4
0.9
4
St. Dev.
GDP
0.92 0.89
1.08
0.98
0.84
1.10
1.03
0.88
NX
0.28 0.40
0.31
0.16
0.12
0.35
0.16
0.11

36
C
I
NX
N
Ex
Im
Tot
Q

C
I
N
Ex
Im
Tot
Q

Correlation

Tot,NX
Q,NX

Cross-country GDP
co-movement C
I
NEx

Co-movement
with
GDP

Volatility
Relative
to GDP

0.85
0.90
0.02
0.87
0.91
0.90
0.31
0.66

0.74
2.64
0.61
3.26
3.40
3.86
5.16

−0.13 0.18
−0.05 0.21

0.52
0.76
0.67
0.47
0.63

0.84
0.91
−0.41
0.81
0.54
0.82
0.29
−0.02

0.89
3.14
0.85
3.86
3.37
2.14
4.14

0.51
3.18
0.45
1.01
1.11
0.84
0.59

0.49
0.55
0.15
0.47
0.47
0.78 −0.36
0.78 −0.36

0.23
0.77
−0.02
0.04
−0.28

0.81
0.83
0.89
0.94
0.09 −0.46
0.93
0.90
0.58
0.59
0.50
0.99
0.46
0.36
0.46
0.36

0.43
3.13
0.49
1.31
1.17
0.34
0.24

−0.66
0.05

0.45
0.45
0.40
−0.08
−0.15

0.85
0.91
0.01
0.22
0.13
0.12
0.15
0.50

0.60
2.06
0.54
1.79
1.77
3.00
0.76

0.48
3.03
0.43
0.98
0.98
0.80
0.56

0.84
0.84

0.17
0.77
−0.02
0.04
−0.32

0.40
0.40

0.34
0.55
0.15
0.47
0.41

0.80
0.84
0.88
0.93
0.19 −0.13
0.93
0.87
0.60
0.62
0.29
0.76
0.50
0.46
0.50
0.46

0.42
3.06
0.47
1.31
1.31
0.33
0.23

0.56
0.63

0.29
0.45
0.40
−0.08
−0.29

0.83
0.93
0.31
0.10
0.73
0.23
0.35
0.57

0.57
1.95
0.51
1.37
1.37
2.84
0.72

Table 6: Volatility and co-movement of GDP and its components in the data and from simulations of the model under diﬀerent
elasticities of substitution and distribution costs. Simulated assuming separate shocks for the production and distribution sectos.
Model - 1
Model - 2
Data
Distribution
No
No
Yes
No
No
Yes
EA
Elasticity
4
0.9
4
4
0.9
4
US
St. Dev.
GDP
0.92 0.89
1.08
0.98
0.89
1.10
1.03
0.94
NX
0.28 0.40
0.31
0.16
0.17
0.35
0.16
0.15