Abstract
US imports and exports respond little to exchange rate changes in the short run. Firms’ pricing behavior is thought central to explaining this response: If local prices do not respond to exchange rates, neither will trade flows. Sticky prices, strategic complementarities, and imported intermediates can reduce the trade response, and they are necessary to match newly available international micro price data. Using trade flow data, I test models designed to match these trade price data. Even with significant pricing frictions, the models imply a stronger trade response to exchange rates than found in the data. Moreover, despite substantial crosssector heterogeneity, differential responses implied by the model find little to no support in the data.
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Notes
 1.
Bussiere (2013) shows evidence that aggregate US export prices respond more to appreciations, but finds less evidence for asymmetries in US import prices.
 2.
See Burstein and Gopinath (2014) for a more comprehensive overview.
 3.
Landry (2010) demonstrates the effects of statedependent pricing in a DSGE setting with two countries.
 4.
It is also common in the literature, where generating plausible exchange rate volatility is difficult in general equilibrium. See, e.g., Alessandria and others (2010).
 5.
Note that each of these papers addresses either exports or imports.
 6.
By contrast, a timedependent Calvo price framework can be implemented in the same model by making this menu cost stochastic, taking a zero value a small portion of the time and a prohibitively high value otherwise.
 7.
See Gopinath and Itskhoki (2010) for details on this approximation.
 8.
Sectoral demand is held constant and assumed to be independent of the exchange rate shocks. This is broadly consistent with the exchange rate disconnect literature, e.g., Obstfeld and Rogoff (2000).
 9.
The average exchange rate volatility in the sample of OECD countries is somewhat higher.
 10.
The underlying confidential BLS microdata identify the country of origin/destination, but the data are still insufficiently detailed to construct reliable price indices for each bilateral pair by sector.
 11.
Though trade data are obviously available at a more disaggregated bilateral level for the USA, HS4level analysis is a tradeoff between sectoral heterogeneity and the noisiness of more disaggregated data. There are over 1200 distinct HS4 categories. Using SITC4 categories, which provide a comparable level of disaggregation and are used for the substitutability exercises, leads to very similar results.
 12.
Feenstra and others (2014) estimate elasticities between foreign partners separately from the usual home–foreign elasticity, and report that the foreign–foreign elasticity is significantly higher. This further supports the benchmark calibration of the elasticity parameter to be more in line with trade estimates.
 13.
At this level of disaggregation, there are a significant number of zeros in the data set. Traditional gravity equation estimations tend to drop these zeros, but this can lead to inconsistent estimates as argued by Silva (2006). Since the estimating strategy here uses (log) differences, I conduct robustness exercises using an alternative difference formula which explicitly allows for zero observations; this follows from work in the labor literature, including Davis and others (2006). The log differences are replaced by \(2\frac{x_{ij,t}  x_{ij,t1}}{x_{ij,t} + x_{ij,t1}}\). The estimates are generally similar to those with log differences, which I report for ease of interpretation. In addition, since foreign GDP encompasses net exports, I reestimate (8) omitting \(\Delta \ln y_{jt}\) and \(\Delta \ln y_{jt1}\), which could in principle be correlated with \(\Delta \ln \textit{Trade}_{ijt}\). The resulting \(\hat{\beta }_{e,k}\) are basically unaffected. Detailed results available upon request.
 14.
While these proxies are not perfect, they are implied by most international business cycle models as indicators of supply and demand changes.
 15.
That said, Balke and others (2013) show that shortrun movements in exchange rates remain difficult to explain by observed fundamentals.
 16.
For example, Goldberg and Campa (2010) document the variation in imported intermediates across OECD countries along with variation in distribution margins, another source of destination currency production costs. Amiti and others (2014) focus on a combination of larger, more productive firms optimally choosing a larger share of imported intermediates to reduce its owncurrency production costs.
 17.
Note that this calculation is an upper bound of imported intermediates coming from the destination market, as many imported intermediates can come from a third country.
 18.
Three additional exercises are provided in “Appendix.” Given fixed capital, sectors which use labor relatively more should be more responsive to exchange rate changes. In addition, consumers are likely to be more cost sensitive toward durable goods purchases; they can substitute both between suppliers and over time. Neither of these explanations can reasonably explain the small response of trade to exchange rate changes. The final exercise considers whether relatedparty trade might explain the lack of a response. This does not appear to be the case, as sectors with a relatively higher share of relatedparty trade have a similar trade response as other sectors.
 19.
I report summarized regression coefficients in “Appendix E in ESM.”
 20.
These confidence bands are generated by asymptotic Waldbased tests of the summed coefficients, where the standard errors of the coefficients are calculated clustering by HS category. Experiments with clusterbased bootstrapped confidence intervals yielded similar results.
 21.
On the other hand, the timedependent Calvo framework produces a very muted response, though exporters are free to adjust their prices by a greater magnitude when they are allowed to change their price.
 22.
It is important to keep in mind that the demand curve itself is changing in \(\epsilon\), and exporting firms face a tradeoff between paying the menu cost to adjust their price to prevent full passthrough or facing the significantly lower demand by having a toohigh price.
 23.
\(\hat{\mu }_4\) is roughly equal to \(\hat{\mu }_3\) in practice, suggesting that the model’s ability to generate aggregate asymmetric responses in the sectoral price level is limited.
 24.
Quantitatively, the US I–O tables are not comparable across trading partners, so this cannot be directly translated to US imports. Using the bins only as a measure of ranking across sectors still reveals little difference in the trade response between the sectors that use the least imported intermediates compared to those that use the most. Results are available upon request.
 25.
1.5 is often used for the elasticity of home versus foreign goods, rather than between foreign goods as considered here.
 26.
The same holds for flexible and Calvopriced models, not shown.
 27.
Preunification Germany observations are dropped.
 28.
I also experimented with collocation methods, but the value functions were not well approximated by the commonly used Chebyshev polynomials, requiring spline interpolation; the computational speed was substantially slower than the more common discretization method with relatively few benefits in numerical precision.
 29.
I thank Gita Gopinath and Oleg Itskhoki for making their model’s code available for comparison.
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*Logan T. Lewis is a Principal Economist at the Federal Reserve Board. This paper was previously circulated as “Menu Costs, Trade Flows, and Exchange Rate Volatility.” Contact: logantlewis@ltlewis.net. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff. I thank Jen Baggs, Wenjie Chen, Andrei Levchenko, Jaime Marquez, Andrew McCallum, Brent Neiman, Todd Pugatch, Jagadeesh Sivadasan, Philip Sauré, Linda Tesar, Rob Vigfusson, Jing Zhang, the editor, two anonymous referees, and seminar participants at the Banque de France, Federal Reserve Board, DC Area Trade Study Group, Drexel, George Washington University, NBER IFM Fall Meetings, NBER ITI Winter Meetings, Rocky Mountain Empirical Trade Conference, Society for Economic Dynamics, Swiss National Bank/IMF Conference on External Adjustment, and Washington Area International Trade Symposium for their comments and suggestions. I gratefully acknowledge the support of the Robert V. Roosa Dissertation Fellowship. All errors are mine.
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Appendices
Appendix 1: Data Appendix
Bilateral, nominal trade value data are collected from the USITC at the HS4 and SITC4 level from 1989 through 2009. The partner countries defined as OECD for the purposes of this exercise are: Australia, Austria, Belgium, Canada, the Czech Republic, Denmark, Finland, France, Germany,^{Footnote 27} Greece, Hungary, Iceland, Ireland, Italy, Japan, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, Spain, Sweden, Switzerland, Turkey, and Great Britain. These countries have been members of the OECD since at least 1995. Nominal GDP data, in foreign currency terms, and the nominal exchange rate are collected from the IMF International Financial Statistics database.
Broda and Weinstein (2006) report import demand elasticities using US trade data for SITC 4digit categories. Rauch (1999) classifies goods by SITC categories, The “conservative” classification is used (categories are more likely to be classified as “differentiated” or “referencepriced”).
Appendix 2: Computational Algorithm
The computational model in Section II is solved via discretization of the state space and value function iteration for each set of calibrated parameters.^{Footnote 28} The basic solution method is similar to Gopinath and Itskhoki (2010).^{Footnote 29} The (log) sectoral price level is centered around \(\ln \left( \theta /(\theta  1)\right)\), with 81 grid points used for the individual firm price, 75 for the sectoral price level, 31 for the exchange rate, and 15 for the idiosyncratic productivity. The AR (1) processes for the exchange rate and productivity have grid points and transition matrices calculated with the method described in Jerome and Cooper (2003).
The Klenow–Willis demand function has the potential to be negative for a sufficiently large relative price, so I follow Gopinath and others (2010) and set demand to be nil if the price is sufficiently high. Profits are denominated and maximized in the destination currency, though the results are similar to profits maximized in the exporter’s currency.
The procedure is iterative, as follows:

1.
Guess values for \(\mu _1\), \(\mu _2\), \(\mu _3\), and \(\mu _4\). In practice, I start with \(\mu _1 = 0\), \(\mu _2 = 1\), \(\mu _3 = 0\), \(\mu _4 = 0\).

2.
Solve for four value functions via iteration: \(\lbrace V^a,V^n \rbrace\) for an exporter and \(\lbrace V^a,V^n\rbrace\) for a domestic firm competing with the exporter.

3.
Simulate \(N_f\) exporters and \(N  N_f\) domestic competitors for 2100 months, dropping the first 100. In each quarter, endogenously determine the aggregate price index as the geometric average of firms’ prices as expressed in the destination currency.

4.
Regress the price index on its lag, the exchange rate, and a constant, as in (5).

5.
If the assumed values for \(\mu\) are all within 1 percent of the estimated values, continue. Otherwise, update the guess for \(\mu\) and go back to step 2.

6.
Reestimate the model for M independent countries, each of which have 376 months, dropping the first 100 (leaving 23 years).

7.
Calculate price statistics for the importers/exporters in each country and average over them.

8.
Aggregate the trade flows to quarterly frequency, and run (8) on the pooled sample.
In practice, the value functions in step 2 converge quickly after the first time by using the previous value function.
Appendix 3: Regression Equivalence: Prefiltering Exchange Rate
The regression model (8) is equivalent to one in which the exchange rate series are prefiltered with time dummies to remove their common component. This common component can be thought of as a US and global component. This relationship is obvious for the case in which only the contemporaneous exchange rate is included in (8), but less obvious that the sectortime dummies included there fully replicate the case in which the exchange rate series are prefiltered.
To consider that case, I ignore sectoral heterogeneity for notational convenience. Suppose that instead of (8), one first prefilters the exchange rate series by running:
where \(\mathbb {I}_l\) is an indicator variable taking the value 1 if \(l = t\), and 0 otherwise. The filtered series is then \(\epsilon _{it}\). With this series, we can run the following regression:
Substituting in for \(\epsilon _{itk}\) with equation (10), one obtains:
Compare this to the estimation without prefiltering, which (abstracting from the GDP entries) takes the form:
Thus, \(\tau _l =  \sum _{k=0}^8 \beta _{k}\gamma _{lk} + \alpha _j\), and the estimates of \(\beta\) are unchanged.
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Lewis, L.T. How Important Are Trade Prices for Trade Flows?. IMF Econ Rev 65, 471–497 (2017). https://doi.org/10.1057/s4130801700371
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JEL
 F14
 F31
 F32
 E31