International Trade and Intertemporal Substitution

March 8, 2022
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International Trade and Intertemporal Substitution

International Trade and Intertemporal Substitution

Trade. What’s the big deal?

Recently, an anti-trade rhetoric has entered the political arena. Anti-trade sentiments are actually not new, but very, very old. Known as mercantilism, these policies have widely been discussed by economists.

Briefly discuss and explain.

In this discussion, take a stance on how you think the government should handle international trade.

The collapse of international trade during the recent financial crisis exposed the failure of standard trade models to explain the response of trade volumes to changes in economic activity
during both normal and crisis episodes.1 For instance, the empirical elasticity of imports to
measures of economic output are well above one, yet standard models have a unitary income
elasticity. Similarly, while the empirical elasticity of import volumes to measures of relative
prices is well below one, typical calibrations of standard models use values that are well above
one. Moreover, accounting exercises that use static trade models to measure deviations between
predicted and observed fluctuations in imports find these deviations to be pro-cyclical.2
In this paper, we show that introducing dynamic considerations into a standard model of trade
can account for these puzzling features. The dynamic consideration we focus on is a time-toship friction to import goods and its interaction with a finite intertemporal elasticity of substitution.3 The time-to-ship friction makes the importing decision dynamic because resources today
must be sacrificed for the delivery of goods tomorrow. With a finite intertemporal elasticity
of substitution, the rate at which agents are willing to substitute across time—the intertemporal marginal rate of substitution—depends on the trade-off between consumption today versus expectations of consumption tomorrow. Our insight is that variation in the intertemporal
marginal rate of substitution with changes in income and relative prices breaks the unitary income elasticity, biases the estimated price elasticity relative to static trade models, and shows
up as a time-varying trade friction. Quantitatively, we show that this insight is able to account
well for these key features of U.S. cyclical import fluctuations.
We formalize these ideas by building a pure exchange, Armington model of trade. An agent
within a country receives a stochastic endowment of its own nationally differentiated good.
Agents have time-separable preferences of the constant relative risk aversion class over an aggregate consumption good. The aggregate consumption good is a composite of the nationally
differentiated goods, and the aggregator of the goods is of the constant elasticity of substitution
class. Agents take prices as given, and we model the evolution of relative prices as following a stochastic process. International purchases are subject to an ad-valorem trade cost. The
only other friction that agents face is that they must commit resources today for the delivery of
imported goods in subsequent periods.
1Examples of models of this type are those of Krugman (1980), Eaton and Kortum (2002), Anderson and van
Wincoop (2003), and Melitz (2003). This also includes international real business-cycle models as summarized in
Backus, Kehoe, and Kydland (1995).
2Houthakker and Magee (1969) is the seminal reference that documents the high income elasticity for the U.S.
and other countries at low frequencies. Jacks, Meissner, and Novy (2009) and Levchenko, Lewis, and Tesar (2010a),
building on the insights of Chari, Kehoe, and McGrattan (2007) emphasize the third fact’s role in accounting for
the decline in trade during the 2008-2010 recession.
3Hummels and Schaur (2013) document the time intensive nature of international trade and, thus, introducing
a time-to-ship friction is a natural way to introduce dynamics to the decision to import.
2
We use the model to answer the following quantitative question: Given a stochastic process
describing income and prices as in U.S. data, how do the time-to-ship friction and finite intertemporal elasticity of substitution shape the decision to import? To answer this question, we
estimate the stochastic process for endowments and prices from U.S. data. We then feed this
stochastic process into our model and walk through several exercises to study the quantitative
importance of our proposed mechanism.
The first exercise studies the model implied income and price elasticities. To compute these
measures, we simulate the model and estimate the model implied income and price elasticities
using simulated data under different assumptions about the intertemporal elasticity of substitution, the elasticity of substitution across goods, and the shipping technology. We find that
the model can quantitatively account for the high income elasticity and low price elasticity observed in U.S. time series data. For instance, with an intertemporal elasticity of substitution of
0.20 and an elasticity of substitution of 1.5, the income and price elasticities are 1.70 and -0.34;
in the data, they are 1.99 and -0.26. Performing the same exercise, but removing the time-toship friction or shutting down variation in the intertemporal marginal rate of substitution, we
find the estimated income elasticity is effectively one and the price elasticity is the same as our
calibrated elasticity of substitution.
The second exercise focuses on the ability of our model to account for the observed dynamics
of U.S. imports. To discipline this exercise, we calibrate the preference parameters of our model
to match features of the data over the first half of our sample. We then compute our model’s
predicted import series for the the un-targeted second half of our sample and compare it with
data. We find that our model accounts well for the dynamics in U.S. imports by correctly capturing the overall magnitude and timing of cyclical fluctuations (see Figure 5(a).) And that the
active intertemporal marginal rate of substitution is critical to accounting for these fluctuations.

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Finally, we provide supporting evidence of the mechanism by examining some cross-sectional
implications of our model. In particular, our model predicts that a country’s bilateral imports
should be more volatile when sourced from a partner with longer shipping times. This implication is a test of our model because static trade models (or our dynamic model with no active
intertemporal marginal rate of substitution) predict that the volatility of imports is independent
of to the time-to-ship/distance. Using data constructed by Hummels and Schaur (2013) and the
World Bank on shipping times, we find that US imports from countries with higher than average shipping times are considerably more volatile than imports from countries with lower than
average shipping times. We find these results to be supportive of the underlying mechanism at
work.
Our results have much to say about the large drop in trade during the 2008-2009 crisis.4 Our
4Much attention has focused on this episode. See, for example, the papers in Baldwin (2010); Alessandria,
3
explanation is simple: a very large shock unexpectedly reduced output, and agents became
unwilling to substitute (on the margin) across time periods. Because international trade is timeintensive, imports declined more than absorption resulting in a trade collapse. Quantitatively,
we find that our model accounts two-thirds of the peak-to-trough decline in imports in U.S.
imports (see Figure 6), when the parameters of the model are calibrated to pre-crisis events.
Our results complement alternative mechanisms proposed to explain the trade collapse. In
particular, an active intertemporal marginal rate of substitution would surely amplify the role
of financial fictions discussed in Amiti and Weinstein (2011) and Chor and Manova (2012),
inventory considerations in Alessandria, Kaboski, and Midrigan (2010b), or the future value of
manufactures as in Eaton, Kortum, Neiman, and Romalis (2013). The distinguishing feature of
our story, however, is that it does not rely on specifics about the 2008-2009 crisis but applies
broadly across time periods. This is a key implication of our second exercise which calibrated
the model parameters to pre-crisis events. Moreover, the lack of reliance on specifics of 2008-
2009 crisis is consistent with the evidence from Stock and Watson (2012) who find that the same
factors that explained previous postwar recessions also explain the most recent recession.
Trade elasticities play critical roles in formulating predictions and recommendations for policy
makers with regard to issues such as the effects of exchange rate fluctuations and policy (see,
e.g., Houthakker and Magee (1969) and Marquez (2002) for a discussion of this research). The
key questions surrounding the empirical estimates of trade elasticities concern their stability
(and, hence, their usefulness in making predictions) and the disconnect with the predictions
of standard trade models. We contribute to this literature by providing answers to these open
questions. First, we rationalize the disconnect between empirical trade elasticities and standard
trade models by introducing dynamics into the import decision. Moreover, while our model
does not have constant price and income elasticities, it retains the parsimony and performance
of statistical models. These two features—theoretical consistency and statistical performance—
suggest that our model can contribute to answering important forecasting and policy questions.

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