# From Micro to Macro: Demand, Supply, and Heterogeneity in the Trade Elasticity

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5 degree of competition on this market), a firm-level gravity equation can be derived: ( ) σ ln x n (α) = (1 σ) ln + (1 σ) ln(αw) + (1 σ) ln τ n + ln A n + ln ɛ n (α) (2) σ 1 Our objective is to estimate the trade elasticity, 1 σ identified on cross-country differences in applied tariffs (that are part of τ n ). This involves controlling for a number of other determinants ( nuisance terms) in equation (2). First, it is problematic to proxy for A n, since it includes the ideal CES price index P n, which is a complex non-linear construction that itself requires knowledge of σ. A well-known solution used in the gravity literature is to capture (A n ) with destination country fixed effects (which also solves any issue arising from omitted unobservable n-specific determinants). This is however not applicable here since A n and τ n vary across the same dimension. To separate those two determinants, we use a second set of exporters, based in a country that faces different levels of applied tariffs, such that we recover a bilateral dimension on τ. A second issue is that we need to control for firm-level marginal costs (αw). Again measures of firm-level productivity and wages are hard to obtain for two different source countries on an exhaustive basis. In addition, there might be a myriad of other firm-level determinants of export performance, such as quality of products exported, managerial capabilities... which will remain unobservable. We use a ratio-type estimation, inspired by Hallak (2006), Romalis (2007) and Head et al. (2010), that removes observable and unobservable determinants for both firm-level and destination factors. This method uses four individual export flows to calculate ratios of ratios: an approach referred to as tetrads from now on. We now turn to a presentation of this method. 2.2 Microfoundations of a ratio-type estimation To implement tetrads at the micro level, we need firm-level datasets for two origin countries reporting exports by firm-product and destination country. Second, we also require information on bilateral trade costs faced by firms when selling their products abroad that differ across exporting countries. We combine French and Chinese firm-level datasets from the corresponding customs administration which report export value by firm at the hs6 level for all destinations in The firm-level customs datasets are matched with data on effectively applied tariffs to each exporting country (China and France) at the same level of product disaggregation by each destination. Focusing on 2000 allows us to exploit variation in tariffs applied to each exporter country (France/China) at the product level by the importer countries since it precedes the entry of China into WTO at the end of We also exploit the variation of tariffs applied to France and China within products and destinations over time from 2000 to Estimating micro-level tetrads implies dividing product-level exports of a firm located in France to country n by the exports of the same product by that same firm to a reference country, denoted k. Then, calculate the same ratio for a Chinese exporter (same product and countries). Finally the ratio of those two ratios uses the multiplicative nature of the CES demand system to get rid of all the nuisance terms mentioned above. Because there is quite a large number of exporters, taking all possible firm pair combinations is not feasible. We therefore concentrate our identification of the largest exporters for each product. 5 5 Section A.1.2. presents an alternative strategy that keeps all exporters and explicitly takes into account selection issues. 5

9 Table 1: Average percentage point difference between the applied tariff to France and China across industries by Germany and Japan (2000) Reference importer: Germany Japan Full Tetrad Full Tetrad sample regression sample sample regression sample Agriculture Food Textile Wearing apparel Leather Wood Paper Edition Coke prod Chemical Rubber & Plastic Non Metallic Basic metal products Metal products Machinery Office Electrical Prod Equip. Radio, TV Medical instruments Vehicles Transport Furniture

10 Figure 1: Average percentage point difference between the applied tariff to France and China across industries by Germany and Japan (2000) Importer: DEU Wearing apparel Food Textile Agriculture Vehicles Basic metal products Equip. Radio, TV Leather Non Metallic Rubber & Plastic Wood Transport Chemical Edition Metal products Medical instruments Furniture Electrical Prod Machinery Office Paper Coke prod Full sample Tetrad regression sample Importer: JPN Office Equip. Radio, TV Vehicles Transport Agriculture Medical instruments Machinery Edition Electrical Prod Coke prod Non Metallic Food Metal products Paper Basic metal products Furniture Rubber & Plastic Chemical Wood Textile Wearing apparel Leather Source: Authors calculation based on Tariff data from WITS (World Bank). 3.2 Estimating sample As explained in the previous section, we estimate the elasticity of exports with respect to tariffs at the firm-level relying on a ratio-type estimation. The dependent variable is the log of a ratio of ratios of firm-level exports of firms with rank j of product p to destination n. The two ratios use the French/Chinese origin of the firm, and the reference country dimensions. Firms are ranked according to their export value for each hs6 line and reference importer country. We first take the ratio of ratios of exports of the top 1 French and Chinese firms and then we complete the missing export values for hs6 product-destination pairs with the ratio of ratios of exports of the top 2 to the top 10 firms. The final estimating sample is composed of 99,645 (37,396 for the top 1 exporting firm) hs6-product, destination and reference importer country pairs observations in the year

13 We do that in Figure 4 for the 184 products that have at least 30 destinations in common in our sample for French and Chinese exporters. The coefficient is again very large in absolute value and highly significant. The next section presents regression results with the full sample, both dimensions of identification, and the appropriate set of gravity control variables which will confirm this descriptive evidence and, as expected reduce the steepness of the estimated response. 4.2 Baseline results This section presents the estimates of the trade elasticity with respect to applied tariffs from equation (7) for all reference importer countries (Australia, Canada, Germany, Italy, Japan, New Zealand, Poland and the UK) pooled in the same specification. Standard errors are clustered by destination-reference importing country. Columns (1) to (3) of Table 2 show the results using as dependent variable the ratio of the top 1 exporting French and Chinese firm. Columns (2) presents estimations on the sample of positive tetraded tariffs and column (3) controls for the tetradic terms of Regional Trade Agreements (RTA). Columns (4) to (6) of Table 2 present the estimations using as dependent variable the ratio of firm-level exports of the top 1 to the top 10 French and Chinese firm at the hs6 product level. These estimations yield coefficients for the applied tariffs (1 σ) that range between and Note that In both cases, the coefficients on applied tariffs are reduced when including the RTA, but that the tariff variable retains statistical significance, showing that the effect of tariffs is not restricted to the binary impact of going from positive to zero tariffs. Estimations in Table 2 exploit the variation in tariffs applied to France and China across both products and destination countries. We now focus on the variation of tariffs within hs6-products across destination countries. To that effect, Table 3 includes hs6 product - reference importer country fixed effects and standard errors are clustered by destination-reference country pair. The coefficients for the applied tariffs (1 σ) range from -6 and -3.2 for the pair of the top 1 exporting French and Chinese firms (columns (1) to (3)). Columns (4) to (6) present the results using as dependent variable the pair of the top 1 to the top 10 firms. In this case, the applied tariffs vary from -4.1 to While RTA has a positive and significant effect, it again does not capture the whole effect of tariff variations across destination countries on export flows. Note also that distance and contiguity have the usual and expected signs and very high significance, while the presence of a colonial link and of a common language has a much more volatile influence. 13

15 Table 2: Intensive margin elasticities. Top 1 Top 1 to 10 Dependent variable: firm-level exports firm-level exports (1) (2) (3) (4) (5) (6) Applied Tariff a a a a a a (0.76) (0.81) (0.71) (0.60) (0.61) (0.54) Distance a a a a a a (0.03) (0.03) (0.04) (0.02) (0.02) (0.03) Contiguity 0.58 a 0.75 a 0.52 a 0.60 a 0.75 a 0.54 a (0.08) (0.08) (0.07) (0.08) (0.07) (0.07) Colony c a (0.29) (0.32) (0.29) (0.15) (0.18) (0.15) Common language a a (0.09) (0.09) (0.09) (0.08) (0.07) (0.07) RTA 1.06 a 1.07 a (0.12) (0.09) Observations R rmse Notes: Standard errors are clustered by destination-reference importing country. All estimations include a constant that is not reported. Applied tariff is the tetradic term of the logarithm of applied tariff plus one. Columns (2) and (5) present estimations on the sample of positive tetraded tariffs. a, b and c denote statistical significance levels of one, five and ten percent respectively. 15

16 Figure 4: Unconditional tetrad evidence: averaged over top products Average export tetrad CUB GAB BEL ESPBGR CHE CHE EST ITA FIN DNK PRT IRL CHE SAU BRN AUT AUT BEL PRT SWE PRT BEL DEU DNK AUTGTM IRL SWE FIN ITA DEU ESP GRC BRN GBR NLD PER MAR CZE LBN NZL BGR BRN DEU IRL CHE MAR ESPEST PRT ARG CZE GBR NLD CYP MLT URY CHL COL PER MLT MLT DNK SWE GRCGTM ITAAUT AUS CZE IRL PER GBR FINLBNKEN BRA JOR ARG CYP LKA CHE BGR BGDBRA CZE BRN GTM BEL GBR MEX THA KEN COL MEX MAR EST PRY ITA USA LKA PRY SAU CYP PRT ESP SWE GRC DEUBRA USA URY MLT LBN MAR NZL NLD THA IRN SLV MLT NZL CHE ITA CHE PAN SAU DNK CHL USA BGR AUS GHA PHL NLD CHE PHL VEN IDN COL IRN ARG IDN PER BRA CRI THA SAU EST MEX NGA IRNSAU CYP JPN CZE CYP ARG JOR NPL GAB EST BRB NLDAUT MAR CZE MEX COL TZA FINBEL IRN CHL TWN JAM URY TWN CHL USA PHLIRN JPN SAU ARG PHL PER TZA DEU GAB JOR SLV EST SWE BGR BRACZE KEN VEN DNK VEN LKA DOM NGA ESTPER SAU BRA MEX PHL DOM MAR KEN DOM GHA JOR GBR MAR YEM JPN IRL TWN MLT LKA LBN GHA CRI GRC GHA URY DOM TZAPRY IRN BGD BRA CYP LBN CYP MEX LBN URY BOL VENCOL CZE MEX COL MAR MLT NZL GTM BGRARG TWN CYP GUY THA CRI THA NICHND IDNSLV JAM NZL AUS JPN PAN IDN IRN BGR ARG TWN MEX URY IRN EST LKA AUS USA DOM NGA CRI LKA HNDGAB IDN ARG TWN PRY CUB PAN LKA NGA PRY LBN GHA AUS CUB CHL URYJPN BRN SAU GTM USA AUS NZL VEN PRY SLV DOM YEM THA COL IDN GAB HND NGA PER NZL BGD USA CHL LKA CUB AUS JAMCRI PHL THA PER COL CHL JOR PAN SLV YEM JAM GAB TWN BGD VEN MLT PHL VEN YEM JPN NGA GHA PHL IDN GAB JPN JOR PAN BRB BGDCUB PRY NGA NIC CRI GTMSLV TZA THA HND CUB JOR BGD UGA NPL KEN DOM BOL VEN KEN GTM HND URY YEM TZA PRY HND PAN IDN SLV SLV YEM KEN TZA BOLPAN CRI NPL VCT YEM BOL BRB JAM Ref. countries: AUS CRI BRBMDA JAM BGD JAM NPL JPN NZL JAM HND NPL GHA UGA DEU UGA GBR HND ITA BLR Average tariff tetrad Note: Tetrads are averaged over the 184 products with at least 30 destinations in common. The coefficient is with a standard error of Table 3: Intensive margin elasticities. Within-product estimations. Top 1 Top 1 to 10 Dependent variable: firm-level exports firm-level exports (1) (2) (3) (4) (5) (6) Applied Tariff a a a a a b (0.79) (1.07) (0.79) (0.72) (0.75) (0.68) Distance a a a a a a (0.03) (0.03) (0.04) (0.03) (0.03) (0.03) Contiguity 0.93 a 0.97 a 0.84 a 1.00 a 0.94 a 0.93 a (0.08) (0.09) (0.07) (0.07) (0.09) (0.07) Colony 0.56 a 0.48 c a (0.21) (0.29) (0.21) (0.10) (0.15) (0.11) Common language a a (0.07) (0.08) (0.06) (0.06) (0.07) (0.06) RTA 1.08 a 0.94 a (0.11) (0.07) Observations R rmse Notes: All estimations include hs6-reference importing country fixed effects Standard errors are clustered by destination-reference importing country. All estimations include a constant that is not reported. Applied tariff is the tetradic term of the logarithm of applied tariff plus one. Columns 16 (2) and (5) present estimations on the sample of positive tetraded tariffs. a, b and c denote statistical significance levels of one, five and ten percent respectively.

17 As a more demanding specification, still identifying trade elasticity across destinations, we now restrict the sample to countries applying non-mfn tariffs to France and China. The sample of such countries contains Australia, Canada, Japan, New Zealand and Poland. 12 Table 4 presents the results. Common language, contiguity and colony are excluded from the estimation since there is no enough variance in the non-mfn sample. Our non-mfn sample also does not allow for including a RTA dummy. In estimations reported in columns (1) and (2), standard errors are clustered by destination-reference country. Estimations in columns (3) and (4) include a fixed effect identifying the product-reference country and standard errors are clustered by destinationreference importer country as in the baseline specifications discussed in the previous section. Columns (2) and (4) present estimations on the sample non-mfn and positive tetraded tariffs. Table 4: Intensive margin: non-mfn sample. Dependent variable: Top 1 to 10 firm-level exports (1) (2) (3) (4) Applied Tariff a a a a (1.09) (1.14) (1.09) (1.03) Distance a a a a (0.03) (0.03) (0.05) (0.05) Observations R rmse Notes: Estimations in columns (1) and (2) standard errors are clustered by destination and reference importing country. Estimations in columns (3) and (4) include a fixed effect identifying the hs6 product-reference importing country and standard errors are clustered by destination-reference importer country. All estimations include a constant that is not reported. Applied tariff is the tetradic term of the logarithm of applied tariff plus one. Columns (2) and (4) present estimations on the sample of positive tetraded tariffs. a, b and c denote statistical significance levels of one, five and ten percent respectively. 4.3 Alternative specifications Identification across products Preceding section s estimations on the intensive margin trade elasticity exploit variation of applied tariffs within hs6 products across destination countries and exporters (firms located in France and China). This section presents a set of estimations on alternative specifications that exploits the variation of applied tariffs within destination countries across hs6-products. Table 5 reports the results from estimations including a destination-reference importer country fixed effect. In this case, standard errors are clustered by hs6-reference importer country. Including 12 We exclude EU countries from the sample of non-mfn destinations since those share many other dimensions with France that might be correlated with the absence of tariffs (absence of Non-Tariff Barriers, free mobility of factors, etc.). Poland only enters the EU in

18 these fixed effects implies that the source of identification comes from variations within destination countries across hs6-products in applied tariffs to both origin countries, France and China, by the reference importer countries. Columns (1) and (3) present estimations on the full sample, while columns (2) and (4) report estimations on the sample of positive tetraded tariffs. The trade elasticity ranges from to Estimations in columns (5) and (6) restrict the destination countries to be the ones applying non-mfn duties and in column (7) to EU destination countries including countries with EU-trade agreements as Norway and Switzerland. The sample size drops radically, with the trade elasticities remaining of the expected sign and order of magnitude, but losing in statistical significance. Table 5: Intensive margin elasticities. Within-country estimations. Top 1 Top 1 to 10 Dependent variable: firm-level exports firm-level exports Sample: Full Full non-mfn EU (1) (2) (3) (4) (5) (6) (7) Applied Tariff a a a a a a a (1.07) (1.26) (0.70) (0.83) (0.83) (0.94) (0.61) Observations R rmse Notes: All estimations include destination-reference importing country fixed effects Standard errors are clustered by hs6-reference importing country. All estimations include a constant that is not reported. Applied tariff is the tetradic term of the logarithm of applied tariff plus one. Columns (5) and (6) present the estimations for the non-mfn sample. Columns (2), (4) and (6) present estimations on the sample of positive tetraded tariffs. a, b and c denote statistical significance levels of one, five and ten percent respectively Cross-section estimations in 2001 and 2006 Results up to this point have focused on cross-sectional analysis of the year 2000 (before entry of China into WTO). We now turn to additional cross-section evidence after China entry into WTO (2001) and for the final year of our sample (2006), in Table 6. Estimations in columns (1) and (3) include a fixed effect identifying the product-reference country combination while columns (2) and (4) include a fixed effect identifying the destination-reference importing country. As expected the coefficients on tariffs are lower since the difference of tariffs applied to France and China by destination countries is reduced after The implied values of σ range from -3.6 to almost

19 Table 6: Intensive margin: cross-section 2001 and 2006 Dependent variable: Top 1 to 10 firm-level exports (1) (2) (3) (4) Applied Tariff a a b b (0.64) (0.68) (0.42) (0.61) Distance a a (0.02) (0.02) Contiguity 0.75 a 0.98 a (0.08) (0.06) Colony a (0.09) (0.07) Common language b (0.06) (0.05) Observations R rmse Notes: Estimations in columns (1) and (3) include a fixed effect identifying the hs6 product-reference importing country and standard errors are clustered by destination-reference importer country. Estimations in columns (2) and (4) include a fixed effect identifying the destination-reference importing country and standard errors are clustered by hs6 product-reference importer country. All estimations include a constant that is not reported. Applied tariff is the tetradic term of the logarithm of applied tariff plus one. a, b and c denote statistical significance levels of one, five and ten percent respectively Panel estimations Our dataset spans over the period. This dimension allows us to identify the variation of tariffs within product-destination over time and across reference countries. Table 7 reports results. Columns (1) and (3) present the baseline estimation for the period, columns (2) and (5) present estimations on the sample of non-mfn destinations and columns (3) and (6) on the sample of EU destination countries. All estimations include productdestination, year and importing reference country fixed effects. The coefficients of the intensive margin elasticity are close to the findings from the cross-section estimations of 2000, and they range from to

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