Trade Balance Dynamics and Exchange Rates: In Search of the J‐Curve Using a Structural Gravity Approach

This paper uses a structural gravity approach, specifying currency movements as trade cost component to derive an empirical trade balance model, which incorporates multilateral resistance terms and accounts for the cross&#8208;country variation in the exchange rate pass&#8208;through into import and export prices. The model is estimated using quarterly bilateral trade flows between 47 countries over the period 2010Q1 to 2017Q2, disaggregated into 97 commodity groups. Our results support the existence of an &#8220;aggregate&#8221; J&#8208;curve, pooled over commodity groups; at the same time they point to considerable heterogeneity in the trade balance dynamics across industries below the surface of aggregate data.

J-curve. The results of the estimates for the 97 commodity groups are less clear cut and show considerable heterogeneity, though their average closely resembles the results from the pooled estimation.
The remainder of the paper is structured as follows: Section 2 reviews a theoretically founded gravity model with exchange rate effects. Section 3 sets up a closely related, gravity based shortand long-run trade balance model. Section 4 presents the results from testing the J-curve hypothesis based on the corresponding empirical model, both pooled across and disaggregated for 97 commodity groups. Section 5 concludes.

| GRAVIT Y AND EXCHANGE RATES AS DETERMINANTS OF TRADE COSTS
In this section we consider a structural gravity model including the exchange rate, which builds the backbone of our empirical analysis.

| The basic gravity model
Specifically, our analysis builds on Anderson and Van Wincoop (2003). They use a multi-country monopolistic competition model to derive a gravity equation, which implies that the export shipment from country i to country j for commodity k at time t (X k ijt ) is given by where the bar over the dependent variable is meant to indicate that Equation 1 describes an equilibrium outcome for period t; Y k t is the world shipment from all origins to all destinations of commodity (group) k (total sales and expenditures), s k it is the share of world shipments of commodity k coming from origin i, b k jt is the share of world shipments of commodity k going from all origins to destination j, and Y k t s k it b k jt is the predicted frictionless trade flow of commodity k from country i to country j.
The second ratio is thus to be interpreted as the ratio of predicted trade (given trade costs) to predicted frictionless trade (Anderson, 2011), where the variable t k ijt depicts iceberg-type bilateral trade costs (equal to one under frictionless trade), and k is the elasticity of substitution parameter. Finally, Π k it and P k jt are the exporter (outward) and importer (inward) multilateral trade resistance terms (henceforth MRT), respectively, defined as that is, they can be regarded as income-share weighted average of the exporter's and importer's bilateral resistances (trade costs) with all trading partners. In a frictionless world with zero trade costs, Equation 1 simplifies to its first expression, that is, X k ijt = Y k t s k it b k jt , and trade flows solely depend on world output (sales/expenditures) and the exporter's sales and importer's expenditure shares therein. (1)

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BADINGER AND FICHET DE CLAIRFONTAINE 2.2 | Exchange rate effects in the gravity model Following Anderson et al. (2016), the exchange rate is modeled as a time-variant per unit trade cost, where a depreciation could be equivalently interpreted as a tax on imports or subsidy on exports. Accordingly, bilateral trade costs in period t are defined as where k ij is the (bilateral) commodity-specific, time-invariant trade cost component, related to distance and contiguity and de facto time-invariant variables such as, for example, language, cultural or institutional differences or transport technology.
In Equation 3, the variable E ijt reflects the bilateral exchange rate between countries i and j; it is time-specific and hence introduces time variation into (total) bilateral trade costs t k ijt . It is defined such that an increase in the exchange rate is associated with a depreciation of country i's currency vis-à-vis country j's currency (price notation).
Of course, whether the decomposition of trade costs into a time-invariant component and the exchange rate as the only time-variant component is appropriate, depends on the time period considered. For our empirical analysis with a time span of 7 years, we argue that this approach can be reasonably justified.
Exchange rate changes matter for country i's exports only, if they translate into consumer prices of country j (i.e., country j's imports in domestic currency). Hence, another crucial determinant of trade costs is the variable k j , reflecting the exchange rate pass-through (ERPT) to country j's import prices. 2 According to Equation 3, a 1% depreciation of the exporter's currency relative to the importer decreases trade costs by (100 × k j )% in industry k, that is, if ERPT is complete, then k j = 1. On the other extreme, if exporters fully (have to) "absorb" the depreciation, import prices do not respond at all, k j = 0, and trade is invariant to exchange rate changes.
Substituting Equation 3 into Equation 1 yields the following augmented gravity equation: According to Equation 4, a country with a higher ERPT of the importer country will experience larger export effects of exchange rate changes. Note that with homogeneous ERPT, that is, k j = k i = k , the effects of exchange rate shocks on trade costs are fully symmetric, since E jit = E −1 ijt : that is, the effects of exchange rate changes on the exporter's and importer's trade costs are mirror images. Note that in Equation 4, ρ can only be interpreted as "pure" ERPT, if the (absolute) elasticity of country j's import demand with respect to prices is equal to (1 − k ) and hence invariant over destination countries j. We relax this assumption by replacing k j by k j Φ k j , where k j is the "pure" ERPT, which represents the amount of the change in exchange rates between currencies of i and j that is reflected in importing prices for country j, and where Φ k j (together with k ) reflects the (destination-country variant) elasticity of country j's import demand with respect to any changes in importing prices (which is assumed to be invariant across countries of origin i). As argued above, in case that Φ = 1, ρ = η. As a result, trade costs are redefined as and the augmented gravity model is given by Equation 7 shows that bilateral export flows depend positively on the exchange rate (increase with a depreciation) and that this relationship is stronger, when the ERPT ( k j ) is large and when the price elasticity (related to exchange rate changes) w.r.t. foreign products is large, that is, when Φ k j and k are large in magnitude.

| TRADE BALANCE GRAVIT Y, EXCHANGE RATES, AND THE J-CURVE
In the following, we translate the export gravity Equation 7 into a trade balance gravity equation, which will be used to test the J-curve hypothesis, according to which a depreciation is instantly followed by a deterioration of the trade balance (price effect) and a consecutive improvement (quantity effect) that is large enough make up for the incipient negative short-run effect.
In order to test the J-curve hypothesis, two modifications of the structural gravity equation defined in Equation 7 are required: First, the dependent variable of interest is the trade balance (TB) rather than exports. Second, Equation 7 does not distinguish between short-run and long-run effects of the exchange rate on the trade balance and therefore does not allow for opposite signs of short-and longrun effects, which is at the heart of the J-curve hypothesis.

| Trade balance gravity
Addressing the first issue, we define the bilateral trade balance TB k ij as the ratio of (commodity k) exports of country i to country j relative to the exports of country j to country i, that is, TB k ijt =X k ijt ∕X k jit . Making use of Equation 7, this yields the following trade balance version of the gravity model which specifies net exports as a function of relative income shares and relative (time-invariant and timevarying) trade costs, adjusted by the ratio of countries' MRTs. Since parameters s and b pertain to shows that an increase in the exchange rate E (depreciation) leads to an improvement of the trade balance, and the effect is larger, the greater the increase in exports and the decrease in imports. The effect on exports in turn is larger, the larger (in magnitude) the price elasticity of country j w.r.t. to foreign goods, that is, Φ k j ( k − 1), and the more exchange rate changes pass through to country j's consumer prices of country i's exports ( k j ). The effect on imports is larger, the larger (in magnitude) the price elasticity of country i w.r.t. to foreign goods, that is, Φ k it ( k − 1) and the more exchange rate changes pass through to consumer prices of country i's imports from country j ( k i ). Taking logs we obtain the following empirical model: which relates the trade balance (TB) to the exchange rate (E), interacted with importer ERPT ( j ) and exporter ERPT ( i ), relative trade costs ( k ji k ij ) and the ratios of countries' MRTs; finally, k ijt is an idiosyncratic error term.
Our trade balance gravity model expressed in Equation 9 can be interpreted as a generalization of the widely used J-curve model by Rose and Yellen (1989) and Bahmani-Oskooee and Brooks (1999), which establish a simple relationship between bilateral trade balances, exporter and importer GDP and (real) exchange rates. The latter can be retrieved from our model by imposing the following restrictions: First, assuming that both pass through to exporter's and importer's prices ( i and j ) are complete, and interpreting effects of changes in real exchange rate on the trade balance "as indicating approximate response of the trade balance to a nominal devaluation" (Himarios, 1985, p. 561). The variable of interest therefore becomes real instead of nominal exchange rate. Second, assuming bilateral trade costs to be symmetric, such that the second term within parentheses on the right-hand side of Equation 9 drops out. Third and most importantly, by omitting third country effects, and analyzing each bilateral trade balance separately, such that both MRT ratios in Equation 9 simplify to a ratio of demand over supply (i.e., b jt ∕s jt and s it ∕b it ), proxied in the literature by exporter and importer GDP.

| Direct short-run and long-run effects
We next turn to a dynamic version of Equation 10 that is able to distinguish between direct short-and long-run effects on the trade balance with potentially different signs; by direct effects on the trade balance, we refer to short-and long-run effects as a result of exchange rate changes (translating into Electronic copy available at: https://ssrn.com/abstract=3619276 a change in the value of imports) and price changes related to the change in the exchange rate (and the implied import-and export-quantity effects, depending on the exchange rate pass-through and the demand responses), a point to which we will return after introducing the empirical model below.
A preliminary inspection of the time-series properties of our key variables-the trade balance and the exchange rate-indicates that around 88% of the 1,908 series contain a unit root for TB and 95% for E, when four lags are considered (the same applies when controlling for a time trend). This share drops with a shorter lag-length (particularly for TB), such that we conclude that most of our series are integrated of order one, with a small subset of stationary series.
Against this background, we opt for the dynamic fixed-effect estimator for non-stationary heterogeneous panels by Pesaran and Smith (1995). 3 Equation 11 will be estimated separately for each specific commodity group k (i.e., with cross-section dimension ij) as well as a panel that is pooled over commodity groups k, the latter case corresponding to Equation 11 with superscript k dropped (apart from k it , k jt , and k ij ) and with cross-section dimension ijk rather than ij.
In Equation 11, multilateral resistance terms ratios (Π it ∕P it and P jt ∕Π jt respectively) are controlled for by time-varying exporter-commodity ( it ) and importer-commodity fixed effects ( jt ). The time-invariant trade cost component is accounted for by the use of cross-section (exporter-importercommodity) fixed effects ( ij ).
This leaves the exchange rate (E ijt ), interacted with importer ERPT ( j ) and exporter ERPT ( i ), as key explanatory variable in our model. Ideally, ERPT would be measured at the commodity group level; unfortunately, for our sample, ERPT measures are only available at the country-level. Hence, the ERPT variables j and i are time invariant and country specific, both in the pooled estimation and in the estimation by commodity group. Provided there is cointegration (and the coefficients are significant), the long-run effect of a change in the exchange rate on the trade balance implied by Equation 11 is given by −( 2 + 3 )∕ 1 .
Short-run impacts are traced out by cumulatively summing up over time the estimates of the parameters associated with the lagged first differences of the exchange rate ( p + p ). An advantage of the ECM approach is that it gives us a direct estimate of long-run effects, allowing us to choose a parsimonious specification of Equation 11 for the short-run. If prices were completely flexible, the (negative) price effect would materialize immediately to its full extent; if for part of the exports, the exchange rate is contractually fixed for a certain period of time, the short-run effect will materialize with a delay. We opt for a maximum lag-length of eight quarters for the first differences of both the trade balance and the exchange rate, after which we assume the short-run price effect to have fully materialized. The total short-run effect is then obtained by summing over all short-run parameters ( ∑ 8 p = 0 ( p + p )). As argued above, the effects traced out by the parameters δ, ψ, and ω have to be interpreted as direct short-run and direct long-run effects on the trade balance, that is, effects of exchange rate changes and price changes in direct response to exchange rate changes, whereas subsequent price adjustments are not captured by these parameters but controlled for by the time-variant (commodity-)countryfixed effects k it and k jt . (11)

BADINGER AND FICHET DE CLAIRFONTAINE
Controlling for "indirect" price (and their trade balance) effects by fixed effects is perfectly consistent with our aim to test the J-curve hypothesis, which rests on an immediate effect of the exchange rate change on the value of imports and the quantity responses owing to price changes triggered by the change in the exchange rate. In the long(er)-run, allowing for indirect price effects (on the trade balance), the existence of a J-curve is much less certain; according to purchasing power parity theory, for example, these price adjustments would exactly offset the initial change in the exchange rate, such that the real exchange rate would return to 1 and the trade balance to its initial state.
Having clarified the notion of direct short-run and long-run effects, we define our estimation results to be indicative of the existence of a J-curve, if the cumulative direct short-run effect of a depreciation is significant and negative for any of the lag-lengths considered and the (cointegrating) direct long-run effect given by −( 2 + 3 )∕ 1 is significant and positive.

| ESTIMATION RESULTS
In order to trace out the trade balance dynamics in response to exchange rate changes and to test for J-curve effects, we use quarterly data over the period 2010 to 2017. The use of high frequency data is important, since with yearly data, offsetting effects might occur within the same time period, potentially giving a distorted picture of the shape of the reaction function. 4 Bilateral trade flows are extracted from the UN Comtrade database, quarterly exchange rates are taken from the European Central Bank data warehouse and defined as quarterly average of units of foreign currency in domestic currency. Country-specific data for the exchange rate pass-through (ERPT) is taken from Bussiere, Gaulier, and Steingress (2016), who provide estimates of the exchange rate pass-through to import prices for 51 economies. Unfortunately their ERPT-estimates are time invariant and not disaggregated into commodity groups.
We end up with an unbalanced panel of 47 advanced and emerging economies and a total of 97 commodity groups, following the two-digit Harmonized System (HS) classification (2012 revision). 5 This yields an average of 24,944 observations (of potentially 64,860) per commodity group and 2,419,613 observations in total.
To test for a long-run (cointegrating) relationship between TB and E (interacted with importer and exporter ERPT), we carry out Pedroni (1999) panel cointegration tests for each of the 97 commodity groups. The testing procedure consists of seven statistics, four based on a pooled panel (the "within dimension"), three based on a group-mean approach, allowing parameter heterogeneity over crosssectional units (the "between dimension"). 6 Detailed results are reported in Table A1 in the Appendix. All of the 679 tests (seven tests, 97 commodity groups) reject the null hypothesis of no cointegration. This is strong evidence for the existence of a long-run cointegrating relationship between the trade balance and the exchange rate for all 97 commodity groups (and thereby indirectly also for an overall long-run relationship in the "average" panel that is pooled across commodity groups). Of course, sign and significance of the link between TB and E remain to be determined in the estimation of the error-correction model (11).

| Results for pooled panel
To illustrate our empirical approach, Equation 1 is first estimated as a panel, which is pooled for all 97 commodity groups and can hence be considered as analysis of the aggregate trade balance.
Cross-section (exporter-importer-commodity) fixed effects and exporter-commodity-time and importer-commodity-time are included in the estimation. The cross-sectional dimension comprises 92,816 exporter-importer-commodity combinations and the time dimension ranges from 2010Q1 to 2017Q2 (30 quarters). As outlined above, the maximum number of lags of the first differences of TB and E, that is, the short-run terms, is set equal to eight quarters in line with earlier studies typically using up to six or eight quarterly lags (see, for instance, Bahmani-Oskooee & Kanitpong, 2017).
The lag-length is then determined by minimizing the joint F-test on the short-run coefficients of E and minimizing the mean-squared prediction error (MSE). In case of conflicting outcomes of these two approaches, we select the smaller number of lags for the sake of parsimony. 7 For the pooled estimation of Equation 11, the number of lags obtained is one for ΔTB and four for ΔE (interacted with both ERPT), yielding an ECM (1, 4). Table 1 shows the estimation results for Equation 11. The first panel reports the long-run coefficients, related to the lagged level of the TB ( 1 ) and E, interacted with importer ERPT ( 2 ) and exporter ERPT ( 3 ). The second panel reports the (short-run) coefficients of the lagged first difference of TB and of four lags of the first difference of E (along with the contemporaneous difference), interacted with importer ERPT ( p ) and exporter ERPT ( p ). Additionally, the third and fourth panels report

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BADINGER AND FICHET DE CLAIRFONTAINE the short-run quarterly aggregate effects of E, defined as ( p + p ), and the cumulative effect of E, obtained by summing up the aggregate effects of E over time.
Considering specification tests of our model, note that a panel Breusch-Pagan test rejects the null hypothesis of homoskedasticity. Heteroskedasticity has been a main issue in the OLS estimation of gravity equations and our application does not make an exception. 8 In the pooled regression, the Wooldridge (2010) test for serial autocorrelation turns out significant at the 1% level. With a view to our (preferred) estimates by commodity group, we repeated the test for subsets of our sample, namely importer-exporter by commodity, importer-commodity by exporter, and exporter-commodity by importer. The corresponding results indicate that the null hypothesis of uncorrelated disturbances cannot be rejected for 79.2%, 76.6%, and 78.4% of the estimates, respectively. These results, pointing to a lack of serial correlation for the large majority of our residual series, will be enforced by our serial correlation tests of the estimates by commodity group.
To address both the presence of heteroskedasticity and serial correlation (in a subset of our series), we follow the approach suggested by Baltagi (2001) and Wooldridge (2010) and use cross-section clustered standard errors for inference.
Turning to the results, the estimate of the speed of adjustment parameter ( 1 ), that is, the coefficient related to level TB, is equal to −0.706 and significantly different from zero, thus indicating a relatively quick return to equilibrium following a shock on the trade balance. The long-run effect of a depreciation passed through to export prices amounts to −(0.376/−0.706) = 0.532, since demand for exports goes up as a result of a decrease in prices (which in turn depends on the importer ERPT ( j )). The longrun effect materializing through increased import prices of the exporting country ( i × E) is given by −(0.341/−0.706) = 0.483. Interestingly, we find that the responses to the price effects passed through to exports and imports are equal in size, that is, the hypothesis that 2 ∕ 1 = 3 ∕ 1 cannot be rejected.
Summing up, our results for the long run suggest a positive (cointegrating) relationship between the trade balance and the exchange rate (indicating that the Marshall-Lerner condition is fulfilled for aggregate trade on average), and that the import and export channels are quantitatively of equal importance, conditional on the exchange rate pass-through.
Regarding the short-run, the coefficients of the lagged differences Δ( j × ln E) and Δ( i × ln E) are negative and significant at lag zero for the former and at the first quarter lag for the latter. The significant negative effect of Δ( i × ln E) is consistent with an immediate price effect on country i's imports from country j, which increase in value and hence deteriorate the trade balance. The significant negative effect of Δ( j × ln E) is consistent with the immediate price effect on the exporter's side, which is due to the decrease of exports' trade value that deteriorates the trade balance; this suggests that part of exports is contracted in foreign currency and that part of the depreciation is borne by the exporter. 9 By symmetry, from the importing country j's perspective, the change in the exchange rate would be associated with an appreciation and a positive price effect through a larger value of exports to country i and a smaller value of imports from country i.
Furthermore, it is worth noting that ignoring the importer and exporter ERPT by setting i = j = 1 yields a positive long-run coefficient of E equal to 0.733 (not reported in the table), which is close to the sum of both estimates from the first panel of Table 1 but turns out insignificant. Moreover, in this specification, none of short-run coefficients of the lagged differences of the (interacted) exchange rate are significant, such that the existence of a negative short-run (price) effect would be concealed. We conclude that accounting for the ERPT is important in the analysis of trade balance dynamics and that its omission from the analysis (as in most previous studies) may yield misleading estimates.
Remaining short-run coefficients are also negative until the last lag considered though they turn out statistically insignificant. However, if we restrict the parameters of Δ( i × E) and Δ( j × E) to equality and consider the combined effect of a change in the exchange rate (which can be justified by F-tests statistically), the effects reported in the third panel, that is, the overall short-run effect of change in exchange rate through both the export and import channel, show a longer lasting (negative) short-run effect up to the fourth quarter lag. The persistence of this short-run TB deterioration, measured by the cumulative sum of short-run coefficients in the fourth panel, lasts up to four quarters following the depreciation with a total sum equal to −2.017. There is therefore no evidence of a strong short-run recovery (or quantity effect) already in the first year after the shock. However, in light of the large standard error (0.754) and the fact that several coefficients turned out insignificant when considered separately, the magnitude of the negative cumulative short-run effect should not be overstressed.
Overall, with aggregate trade data, the J-curve hypothesis receives support by negative short-run (price) effects (reflected in negative single, aggregated and cumulative sums of short-run coefficients), which are followed by long-run quantity adjustments leading to an overall improvement of the trade balance (reflected in the positive cointegration relationship between the exchange rate and the trade balance).
It is worth emphasizing that estimation results strongly differ, when Equation 11 is misspecified by omitting proxies for the MRT ratios (time-varying exporter-commodity ( it ) and importer-commodity fixed effects ( jt )), proxies for time-invariant asymmetric trade costs ratio (cross-section (exporter-importer-commodity) fixed effects ( ij )), or both. Misspecification leads to contradictory results as well as to a severe lack of significance of the TB responses to changes in E. Omitting MRT ratios' proxies leads to a mix of positive and negative short-run depreciation effects on the TB. Omitting country-pair fixed effects as proxies of asymmetric trade costs ratio yields a inverted J-curve, that is, small but negatively significant long-run responses of the TB to a depreciation with positive effects in the short-run. Finally, omitting both proxies also leads to an inverted J-curve with significant negative long-run effects following a depreciation and most of the (positive) short-run effects working through the exporter's ERPT.

| Results by commodity group
Having obtain results from a bird eye's perspective on the aggregate trade balance dynamics, we next estimate Equation 11 using disaggregated data for 97 two-digit HS commodity groups, using the same time period and following the same approach as for the pooled estimation described above. 10 At this level of aggregation, the number of observations varies considerably across commodity groups, with a maximum of 33,256 observations for "Iron and steel", and a minimum of 3,456 observations for "Vegetable plaiting materials".
Optimal lag structures for the 97 estimations are again determined by minimized joint F-test on short-run exchange rate coefficients and MSE criterion as defined above. There is substantial variation in the short-run dynamics across commodity groups: 14 groups include only the contemporaneous change in exchange rate (period t) while 14 others include the maximum number of lags (from period t to t−8). The average number of first-differenced lags of E is four, which corresponds to the number of quarterly lags used in the pooled regression, and two for the first-differenced lags of TB. Table 2 summarizes the parameter estimates of the long-run and of the short-run effect of an exchange rate depreciation, with each line representing the results for a specific commodity group. To improve readability, Table 2 shows only the short-run coefficients significant at least at the 10% level.
Overall, the fit of the models is satisfactory with an average adjusted R-squared of 0.533.
Residual diagnosis indicate that heteroskedasticity remains an issue in 58 commodity groups and serial correlation in 35 commodity groups. As in the pooled estimation, we use cross-section clustered standard errors to take these issues into account.
Before turning to detailed results, we take a look at the mean effects of the exchange rate on the trade balance, obtained by averaging the coefficients across the 97 commodity groups. The overall | 1279

T A B L E 2 Estimates of Trade Balance Model for 97 Commodity Groups, Equation 11
Long-run coefficients

Short-run ΔE coefficients
Industry

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BADINGER AND FICHET DE CLAIRFONTAINE mean long-run depreciation effect of the exchange rate on the trade balance amounts to 0.852 (and 1.457 when taking only coefficients significant at 10% into account). Hence, the magnitude of the estimated average long-run effect is well in line with the results from the pooled estimation (1.015). The estimated mean short-run effects of the exchange rate and their cumulative sum reveal interesting aspects of the short-run trade balance dynamics. The cumulative sum of the mean values of the short-run coefficients is illustrated in Figure 1. The contemporaneous and first lags are characterized by a deterioration of the trade balance and are then followed by consecutive quarters of short-run TB improvements before this effect vanishes in the last quarter (t−8). Combined with a mean long-run effect of E amounting to 0.852, this pattern is indicative of the presence of an average J-curve. Moreover, the implied inter-temporal shape of the TB dynamics is in line with the pooled estimation, though the latter suggests that the improvement of the trade balance starts after lag four (rather than after lag two).
We next take a closer look at the commodity-specific estimates. Summarizing the key long-run results, a depreciation is linked to an improvement of the trade balance in 26 commodity groups, as reflected in significant and positive sum of long-run coefficients for the exchange rate interacted with importer and exporter ERPT ( 2 + 3 ). In twelve groups, a depreciation is associated with a long-run deterioration of the trade balance, for the remaining 59 commodity groups, the long-run effect of the exchange rate on the trade balance is insignificant.
Significant short-run effects, as measured by the sum of the short-run coefficients for the difference of the interacted exchange rate (η + ω) show up primarily within the first four quarters (including the contemporaneous quarter), following the change in the exchange rate. The peak in the number of significant short-run coefficients appears in the second-quarter lag with a total of 20 commodity groups. The number then falls throughout the remaining four quarters with a maximum of eleven coefficients at the fifth-quarter lag and a minimum of three coefficients at the eighth-quarter lag. This suggests that short-run trade balance deviations from the equilibrium caused by a change in the exchange rate occur mainly within a year. In total, 42 significant negative short-run coefficients and 33 significant positive short-run coefficients are obtained for our sample in the first year following the depreciation. The highest frequency of negative short-run effects, 13, occurs contemporaneously (t), while the highest frequency of positive short-run effects (twelve) is observed for the third quarter (t−2). F I G U R E 1 Mean of cumulative short-run reaction of TB to E. Notes. Mean (over all 97 commodity groups) of cumulative values of the sum of the coefficients of ( i ×Δ ln E) and ( j ×Δ ln E) for all eight quarterly lags. All insignificant coefficients have been set equal to zero Turning to significant cumulative short-run effects (not reported in the table), 77 of them are negative and 49 positive. Alike the significant single short-run coefficients, they are mainly observed within the first year following the depreciation. Also worth noting, with the exception of two commodity groups, no significant cumulative effects are found within the last three quarters of the second year. It is an indication that, in our sample, short-run trade balance dynamics triggered by exchange rate changes fade out after five quarters.
Overall, out of the subset of 26 commodity groups with positive long-run effects of the exchange rate, eleven J-curves are found with solely negative short-run coefficients. 11 Furthermore, for eight commodity groups 12 the long-run effects are positive with no short-run trade balance deterioration after the change in the exchange rate. 13 A total of six commodity groups are characterized by both a significant short-run and long-run deterioration of the trade balance, where quantity adjustments seem absent. 14 A total of 59 commodity groups with no long-run depreciation effect are identified, where 17 solely exhibit negative short-run effects (thus no sign of quantity adjustment in the short-run) and 18 positive effects (thus no sign of a price effect in the short-run). Out of this subset of 59 commodity groups without long-run depreciation effect, 20 are characterized by "short-run J-curve" dynamics, where negative short-run coefficients are followed by positive ones. For these commodities the depreciation effect seems to be only temporary and vanishes after 2 years.

| CONCLUDING REMARK S
The literature on the J-curve hypothesis has offered a variety of approaches on how to estimate intertemporal responses of the trade balance to exchange rate shocks. While most studies focus on the investigation of bilateral relationships, the present study provides a multilateral and sectoral perspective in a gravity framework for a sample of 47 countries and 97 commodity groups over the period 2010Q1 to 2017Q2.
We build on Anderson et al. (2016) and derive a structural trade balance gravity equation that includes the exchange rate and its pass through to prices as a component of trade costs. The inter-temporal aspects of the empirical relationship between the trade balance and the exchange rate are investigated with an error-correction model, modeling the long-run cointegrating relationship between the trade balance and the exchange rate as well as short-run effects.
A test of the J-curve hypothesis for the 47 countries (2162 country-pairs, pooled across all 97 commodity groups) reveals that on average, there is a negative short-run (price) effect materializing "immediately" within the first two quarters and significantly deteriorating the trade balance. The negative effect persists throughout the entire short-run period of eight quarters considered. A long-run improvement of the trade balance is indicated by the existence of a long-run cointegrating relationship, suggesting that a 1% depreciation is associated with a 1.04% improvement of the trade balance. Hence, for our country and commodity sample and period of investigation, the trade balance dynamics seems to follow a J-curve pattern on average. The analysis at the commodity level yields a much more diverse picture. A positive long-run effect is obtained only for a subset of 26 of the 97 commodity groups (of which eleven show a J-curve pattern), for 59 groups there is no significant long-run effect (20 of which show a short-run J-curve pattern).
Overall, in light of the anything but clear-cut long-run relationship between the exchange rate and the trade balance at the sectoral level and the anything but uniform short-and long-run patterns of T A B L E A 2 (Continued)