Stanford Econ 266: PhD International Trade Lecture 13: Firm-Level Heterogeneity (Empirics II)

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1 Stanford Econ 266: PhD International Trade Lecture 13: Firm-Level Heterogeneity (Empirics II) Stanford Econ 266 (Dave Donaldson) Winter 2016 (lecture 13) Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 1 / 50

2 Plan for Today s Lecture on Firm-Level Trade Empirics (Lecture II) 1 Trade flows: intensive and extensive margins 2 Exporting across multiple destinations Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 2 / 50

3 Plan for Today s Lecture on Firm-Level Trade Empirics (Lecture II) 1 Trade flows: intensive and extensive margins 2 Exporting across multiple destinations Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 3 / 50

4 Intensive and Extensive Margins in Trade Flows With access to micro data on trade flows at the firm-level, a question that has been explored is whether trade flows expand over time (or look bigger in the cross-section) along the: Intensive margin: the same firms (or product-firms) from country i export more volume (and/or charge higher prices we could also decompose the intensive margin into these two margins) to country j. Extensive margin: new firms (or product-firms) from country i are penetrating the market in country j. This is really just a decomposition we should expect trade to expand along both margins. Recently some papers have been able to look at this. A rough lesson from these exercises is that the extensive margin seems more important (in a purely accounting sense, not necessarily a causal sense). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 4 / 50

5 Bernard, Jensen, Redding and Schott (2007): Exporters Andrew B. Data from US manufacturing Bernard, J. Bradford firms. Jensen, The coefficients StephenJ. in Redding, columns and 2-4 Peter sum K. Schott 123 (across columns) to those in column 1. Table 6 Gravity and Aggregate U.S. Exports, 2000 Log of export Log of total Log of number of Log of number of value per exports value exporting firms exported products product per fir Log of GDP (0.04) (0.04) (0.03) (0.04) Log of distance (0.17) (0.16) (0.15) (0.19) Observations S Sources: Data are from the 2000 Linked-Longitudinal Firm Trade Transaction Database (LFTTD). Notes: Each column reports the results of a country-level ordinary least squares regression of the dependent variable noted at the top of each column on the covariates noted in the first column. Results for the constant are suppressed. Standard errors are noted below each coefficient. Products are defined as ten-digit Harmonized System categories. All results are statistically significant at the 1 percent level. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 5 / 50

6 Bernard, Jensen, Redding and Schott (2007): Importers 126 Journal of Economic Perspectives Data from US manufacturing firms. The coefficients in columns 2-4 sum (across columns) to those in column 1. Table 9 Gravity and Aggregate U.S. Imports, 2000 Log of total Log of number Log of import import of importing Log of number of value per value firms imported products product per firm Log of GDP 1.14*** 0.82*** 0.71*** -0.39*** (0.06) (0.03) (0.03) (0.05) Log of Distance -0.73*** -0.43*** -0.61*** 0.31 (0.27) (0.15) (0.15) (0.24) Observations R Sources: Data are from the 2000 Linked-Longitudinal Firm Trade Transaction Database (LFTTD). Notes: Each column reports the results of a country-level ordinary least squares regression of the dependent variable noted at the top of each column on the covariates listed on the left. Results for constants are suppressed. Standard errors are noted below each coefficient. Products are defined as ten-digit Harmonized System categories. *, **, and *** represent statistical significance at the 10, 5, and 1 percent levels, respectively. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 6 / 50

7 , ,96 2,48 0,88 0,51 0, ,03 1,60 0,68 0,39 0,18 0,00 CK (2010): Intensive margin Data from French manufacturing firms trading internationally, by domestic region j. Figure 1: Mean value of individual-firm exports (single-region firms, 1992) Importing country: Belgium Belgium Importing country: Switzerland Belgium Germany Germany Switzerland Switzerland Italy Italy Spain Spain Importing country: Germany Importing country: Spain Belgium Belgium Germany Germany Switzerland Switzerland Italy Italy Spain Importing country: Italy Belgium Spain Germany Switzerland Italy Spain Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 7 / 50

8 CK (2010): Extensive margin Data from French manufacturing firms trading internationally, by domestic region j. (NB: Extensive margin biased down by inclusion of only firms over 20 workers.) Figure 2: Percentage of firms which export (single-region firms, 1992) Importing country: Belgium Importing country: Switzerland Belgium Belgium Germany Germany Switzerland Switzerland Italy Italy Spain Spain Importing country: Germany Importing country: Spain Belgium Belgium Germany Germany Switzerland Switzerland Italy Italy Spain Importing country: Italy Belgium Spain Germany Switzerland Italy Spain Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 8 / 50

9 Crozet and Koenig (CJE, 2010) Data from French manufacturing firms trading internationally, by domestic region j. (Extensive margin biased down by inclusion of only firms over 20 workers.) Table 2: Decomposition of French aggregate industrial exports (34 industries countries to 1992) All firms Single-region firms > 20 employees > 20 employees (1) (2) (3) (4) Average Number of Average Number of Shipment Shipments Shipment Shipments ln (M kjt/n kjt) ln (N kjt) ln (M kjt/n kjt) ln (N kjt) ln (GDP kj) a a a a (0.007) (0.007) (0.007) (0.008) ln (Dist j) a a a a (0.013) (0.009) (0.012) (0.009) Contig j c a (0.035) (0.032) (0.038) (0.036) Colony j a a a a (0.032) (0.025) (0.035) (0.027) French j a a a a (0.029) (0.028) (0.032) (0.028) N R Note: These are OLS estimates with year and industry dummies. Robust standard errors in parentheses with a, b and c denoting significance at the 1%, 5% and 10% level respectively. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 9 / 50

10 Hilberry and Hummels (EER, 2008) Data on intra-national US commodity shipping (zipcode-to-zipcode, with firm identifiers). Table 2. Decomposing Spatial Frictions (5-digit zip code data) value ( T ij ) # of shipments ( N ij ) dist dist 2 ownzip ownstate constant Adj. R 2 N ε D (0.009) (0.001) (0.030) (0.007) (0.026) (0.002) (0.000) (0.008) (0.002) (0.007) # of trading pairs F ( N ij ) (0.002) (0.000) (0.007) (0.002) (0.006) # of commodities k ( N ij ) avg. value ( PQ ij ) (0.001) (0.008) (0.000) (0.001) (0.003) (0.028) (0.001) (0.006) (0.003) (0.024) avg. price ( P ij ) (0.007) (0.001) (0.024) (0.006) (0.020) avg. weight ( Q ij ) (0.011) (0.001) (0.037) (0.009) (0.031) Notes: 1. Regression of (log) shipment value and its components from equations (7) and (8) on geographic variables. Dependent variables in left hand column. Coefficients in right-justified rows sum to coefficients in left justified rows. 2. Standard errors in parentheses. 3. ε D is the elasticity of trade with respect to distance, evaluated at the sample mean distance of 523 miles. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 10 / 50

11 Eaton, Kortum and Kramarz (2009) French Exporters: Extensive margin (i.e. N nf ) Figure 1: Entry and Sales by Market Size Panel A: Entry of Firms FRA # firms selling in market SIE BEL SWI GER NET ITAUNK SPA CAM POR GRE DENAUT TUN COTMOR ALG FIN NOR SWE CAN SEN IRE ISRHOK SAU AUL NIG TOG SIN EGY SOU CEN MAL BENBUK KUW MAD TUR YUG MAU MAS ZAI HUN CHA NIA CZE MEX ANG COL VEN IND JOR BRA SYRCHI ARG OMA PAK IRQ MAY NZE TAI KOR THA INO CHN URU BUL RWA KEN PAN PHI PER LIY ROM BUR GEE ETH DOM SUD ECU IRN PAR MOZGHA TAN LIB GUA COS ZIM CUB ZAM JAM TRI SRI BAN BOL HON ELS NIC VIE SOMAW PAP UGA AFG ALB NEP JAP USR USA market size ($ billions) arket share Panel B: Normalized Entry JAP USA CAN USR Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter GER AUL UNK 2016 (lecture 13) 11 / 50

12 # firms CHA BUR RWA ANG OMA URU COL KEN PAN PHI PER ECU LIY IRN SUD GHA Eaton, Kortum and Kramarz LIB PAR ETH DOM MOZ TAN GUA COS ZIM CUB ZAM HON SIE JAM TRI SRI BAN 100 BOL ELS NIC VIE SOM PAP ALB (2009) MAW NEP UGA AFG BUL ROM French Exporters: Extensive margin, normalized (i.e. N nf /(X nf /X n)) market size ($ billions) GEE entry normalized by French market share SIE Panel B: Normalized Entry CAN USR GER AUL SWI UNK GEE CHN BUL AUT FRA BEL NET SPA ITA DEN FIN NOR SWE TAI BRA NZE ISR SOU CZEROM ARG YUG IRE GRE MEX HUNVEN CHI MAY VIE HOK KOR POR SIN SAU IND CUB COL ALGTUR SUD COT EGY ZIMECU IRN CAM ALB MOR TAN COSTUN PAN PER TRI URU SYRPHI INO BUKSEN GUA ETH HON ELS DOM JOR PAK BOL PAR ZAI SRI KUW THA PAP NIA IRQ SOM LIY MAL NIG CHA TOG MAS OMA JAM BAN ANG RWABEN MAD UGA NIC KEN CEN BUR MOZ NEP ZAM GHA MAU LIB MAW AFG JAP USA market size ($ billions) arket ($ millions) 10 Panel C: Sales Percentiles CHNFRA USR LIY GEE ITA GER UNK USA NIC IRQ ALG EGY IND BELNET SPA GRE DEN FIN NOR SWE YUG BRA 1 TUR CZE MAW HUN MEX BUL AFG NIA CUB IRN INO KOR PAK SAU VEN JAP Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity SYR SIN THA(Empirics SOUAUT ROM ARG TAI AUL II) Winter 2016 (lecture 13) 12 / 50 SWI

13 entry normalized BUK BOL SEN GUA PAP PAR HON ZAI SOMTOG MAS OMA JAM BAN ANG NIA IRQ LIY MAL NIG Eaton, Kortum and CHA BEN MAD KEN RWA CEN BUR MOZ NEP UGA NIC ZAMKramarz LIB (2009) GHA MAU MAW AFG French Exporters: Intensive margin (sales per firm), by quantile 1000 SIE market size ($ billions) percentiles (25, 50, 75, 95) by market ($ millions) SIE Panel C: Sales Percentiles CHNFRA USR LIY GEE ITA GER UNK USA NIC IRQ ALG EGY IND BELNET SPA GRE DEN FIN NOR SWE YUG BRA TUR CZE MAW HUN BUL AFG NIA CUB IRN INO MEX KOR PAK SAU VEN JAP MOR IRE POR AUT ROM TUN SWI ETHANG PAN SYR SIN THA SOUARG TAI AUL PHI CAN ZAM MOZ KEN MAU GHALIB ZAI DOM BAN PER COL SUD CAM COT BUR MAL MAD GUA ELS COS CHI PAR ISR UGA BUK ALB NIG MAS SEN TAN HON ZIM SOM RWATOG BEN JAM TRI OMA JOR KUW MAY VIEHOK SRI ECU NEP PAP NZE URU CEN CHA BOL market size ($ billions) Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 13 / 50

14 Helpman, Melitz and Rubenstein (QJE, 2008) What does the difference between intensive and extensive margins imply for the estimation of gravity equations? Gravity equations are often used as a tool for measuring trade costs and the determinants of trade costs we will see more of this in Lecture 15. HMR (2008) started wave of thinking about gravity equation estimation in the presence of extensive/intensive margins. They use aggregate international trade (so, technically, this paper doesn t belong in a lecture on empirical work on firm-level heterogeneity!) to explore implications of a heterogeneous firm model for gravity equation estimation. The Melitz (2003) model is simplified and used as a tool to understand, estimate, and correct for biases in gravity equation estimation. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 14 / 50

15 HMR (2008): Zeros in Trade Data HMR start with the observation that there are lots of zeros in international trade data, even when aggregated up to total bilateral exports. Baldwin and Harrigan (2008) and Johnson (2008) look at this in a more disaggregated (sectoral) manner and find (unsurprisingly) far more zeros. Zeros are also problematic. A typical analysis of trade flows is based on the gravity equation (in logs), which can t incorporate X ij = 0. Indeed, other models of the gravity equation (Armington, Krugman, Eaton-Kortum, Melitz-with-Pareto) don t have any zeros in them (due to symmetric CES demand, unbounded productivities, and finite trade costs). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 15 / 50

16 and the middle portion represents those that trade in one direction Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 16 / 50 HMR (2008) The extent of zeros, even at the aggregate export level ESTIMATING TRADE FLOWS 447 FIGURE I Distribution of Country Pairs Based on Direction of Trade Note. Constructed from 158 countries.

17 HMR (2008) The growth of 448 trade in recent QUARTERLY decades isjournal not dueof to ECONOMICS the death of zeros FIGURE II Aggregate Volume of Exports of All Country Pairs and of Country Pairs That Traded in Both Directions in 1970 Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 17 / 50

18 A Gravity Model with Zeroes HMR work with a multi-country version of Melitz (2003) similar to Chaney (2008). Set-up: Monopolistic competition, CES preferences (ε), one factor of production (unit cost c j ), one sector. Both variable (iceberg τ ij ) and fixed (f ij ) costs of exporting. Heterogeneous firm-level productivities 1/a drawn from truncated Pareto, G(a). This is the feature that allows for zeroes to exist (at finite trade costs). Some firms in j sell in country i iff a a ij, where the cutoff productivity (a ij ) is defined by: ( ) τij c j a 1 ε ij κ 1 Y i = c j f ij (1) P i Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 18 / 50

19 An Augmented Gravity Equation HMR (2008) derive an augmented gravity equation, for those observations that are non-zero, of the form: ln(m ij ) = β 0 + α i + α j γ ln d ij + w ij + u ij (2) Where: M ij is imports (into i from j) d ij is distance (or potentially other observable shifters of trade costs). w ij is the augmented part, which is a term accounting for selection. u ij represents unobserved components of trade costs Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 19 / 50

20 Two Sources of Bias The HMR (2008) theory suggests (and solves) two sources of bias in the typical estimation of gravity equations (which neglects w ij ). First: Omitted variable bias due to the presence of w ij : In a model with heterogeneous firm productivities and fixed costs of exporting (i.e. a Melitz (2003) model), only highly productive firms will penetrate distant markets. So distance (d ij ) does two things: it raises the price at which any firm can sell (thus reducing demand along the intensive margin) in a distant market; and it changes the productivity (and hence the price and hence the amount sold) of the firms entering a distant market. This means that d ij is correlated with w ij. Therefore, if one aims to estimate γ but neglects to control for w ij the estimate of γ will be biased (due to OVB). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 20 / 50

21 Two Sources of Bias The HMR (2008) theory suggests (and solves) two sources of bias in the typical estimation of gravity equations (which neglects w ij ). Second: A selection effect induced by only working with non-zero trade flows: HMR s gravity equation, like those before it, can t be estimated on the observations for which M ij = 0. The HMR theory tells us that the existence of these zeros is not as good as random with respect to d ij, so econometrically this selection effect needs to be corrected/controlled for. Intuitively, the problem is that far away destinations are less likely to be profitable, so the sample of zeros is selected on the basis of d ij. This calls for a standard Heckman (1979) selection correction. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 21 / 50

22 HMR (2008): Two-step Estimation Two-step estimation to solve bias 1 Estimate probit for zero trade flow or not: Include exporter and importer fixed effects, and d ij. Can proceed with just this, but then identification (in Step 2) is achieved purely off of the normality assumption. To strengthen identification, need additional variable that enters Probit in step 1, but does not enter Step 2. Theory says this should be a variable that affects the fixed cost of exporting, but not the variable cost. HMR use Djankov et al (QJE, 2002) s entry regulation index. Also try common religion dummy. 2 Estimate gravity equation on positive trade flows: Include inverse Mills ratio (standard Heckman procedure trick) to control for selection problem (Second source of bias) Also include empirical proxy for w ij based on estimate of entry equation in Step 1 (to fix First source of bias). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 22 / 50

23 HMR (2008): Results (traditional gravity estimation) 458 QUARTERLY JOURNAL OF ECONOMICS TABLE I BENCHMARK GRAVITY AND SELECTION INTO TRADING RELATIONSHIPS s (Probit) (Probit) (Probit) Variables mij Tij mij Tij mij Tij Distance (0.031) (0.012) (0.024) (0.008) (0.024) (0.008) Land border (0.147) (0.047) (0.131) (0.032) (0.131) (0.032) Island (0.121) (0.032) (0.096) (0.022) (0.096) (0.022) Landlock (0.188) (0.045) (0.148) (0.028) (0.147) (0.028) Legal (0.050) (0.014) (0.040) (0.009) (0.040) (0.009) Language (0.061) (0.016) (0.047) (0.011) (0.047) (0.011) Colonial ties (0.120) (0.117) (0.110) (0.082) (0.110) (0.082) Currency union (0.255) (0.052) (0.187) (0.026) (0.187) (0.026) FTA (0.222) (0.020) (0.213) (0.018) (0.214) (0.018) Religion (0.096) (0.025) (0.076) (0.016) (0.077) (0.016) WTO (none) (0.058) (0.013) WTO (both) (0.042) (0.013) Observations 11,146 24, , , , ,060 R Notes. Exporter, importer, and year fixed effects. Marginal effects at sample means and pseudo R 2 reported for Probit. Robust standard errors (clustering by country pair). + Significant at 10%. Significant at 5%. Significant at 1%. Stanford Econ 266 (Dave Donaldson) and introduce Firm-level both importing heterogeneity and exporting (Empirics country II) fixedwinter effects (lecture 13) 23 / 50

24 HMR (2008): Results (gravity estimation with correction) ESTIMATING TRADE FLOWS 463 TABLE II BASELINE RESULTS 1986 reduced sample Indicator variables (Probit) Variables Tij Benchmark NLS Polynomial 50 bins 100 bins Distance (0.016) (0.040) (0.049) (0.052) (0.070) (0.088) Land border (0.072) (0.165) (0.170) (0.166) (0.170) (0.170) Island (0.078) (0.269) (0.290) (0.258) (0.259) (0.258) Landlock (0.050) (0.189) (0.175) (0.187) (0.187) (0.187) Legal (0.019) (0.064) (0.065) (0.064) (0.065) (0.065) Language (0.021) (0.075) (0.087) (0.077) (0.079) (0.083) Colonial ties (0.130) (0.158) (0.257) (0.148) (0.152) (0.153) Currency union (0.038) (0.334) (0.360) (0.333) (0.337) (0.346) FTA (0.009) (0.247) (0.227) (0.197) (0.250) (0.348) Religion (0.034) (0.120) (0.136) (0.120) (0.124) (0.128) Regulation costs (0.036) (0.100) R. costs (days &proc.) (0.031) (0.124) δ (from ˆ w ij ) (0.043) ˆ η ij (0.099) (0.209) ˆ z ij (0.540) ˆ z ij (0.170) ˆ z ij (0.017) Observations 12,198 6,602 6,602 6,602 6,602 6,602 R mij Notes. Exporter and importer fixed effects. Marginal effects at sample means and pseudo R 2 reported for Probit. Regulation costs are excluded variables in all second stage specifications. Bootstrapped standard errors for NLS; robust standard errors (clustering by country pair) elsewhere. +Significant at 10%. Significant at 5%. Significant at 1%. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 24 / 50

25 Crozet and Koenig (CJE, 2010) CK (2010) conduct a similar exercise to HMR (2008), but with French firm-level data. This is attractive after all, the main point that HMR (2008) is making is that firm-level realities matter for aggregate flows. CK s firm data has exports to foreign countries in it (CK focus only on adjacent countries: Belgium, Switzerland, Germany, Spain and Italy). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 25 / 50

26 CK (2010): Identification But interestingly, CK also know where the firm is in France. So they try to separately identify the effects of variable and fixed trade costs by assuming: Variable trade costs are proportional to distance. Since each firm is a different distance from, say, Belgium, there is cross-firm variation here. Fixed trade costs are homogeneous across France for a given export destination. (That is, it costs just as much to figure out how to sell to the Swiss whether your French firm is based in Geneva or Normandy). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 26 / 50

27 CK (2010): The model and estimation I The model is deliberately close to Chaney (2008), which is a particular version of the Melitz (2003) model but with (unbounded) Pareto-distributed firm productivities (with shape parameter γ). In Chaney (2008) the elasticity of trade flows with respect to variable trade costs (proxies for by distance here, if we assume τ ij = θd δ ij where D = distance) can be subdivided into the: Extensive elasticity: ε EXT j D ij = δ [γ (σ 1)]. CK estimate this by regressing firm-level entry (ie a Probit) on firm-level distance D ij and a firm fixed effect. This is analogous to HMR s first stage. Intensive elasticity: ε INT j D ij = δ(σ 1). CK estimate this by regressing firm-level exports on firm-level distance D ij and a firm fixed effect. This is analogous to HMR s second stage. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 27 / 50

28 CK (2010): The model and estimation I Recall that γ is the Pareto parameter governing firm heterogeneity. The above two equations (HMR s first and second stage) don t separately identify δ, σ and γ. So to identify the model, CK bring in another equation which is the slope of the firm size (sales) distribution. In the Chaney (2008) model this will behave as: X i = λc [γ (σ 1)] i, where c i is a firm s marginal cost and X i is a firm s total sales. With an Olley and Pakes (1996) TFP estimate of 1/c i, CK estimate [γ (σ 1)] and hence identify the entire system of 3 unknowns. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 28 / 50

29 CK (2010): Results (each industry separately) Table 3: The structural parameters of the gravity equation (Firm-level estimations) (1) (2) (3) (4) (5) (6) P [Export > 0] Export value Pareto # Industry Code δγ δ(σ 1) [γ (σ 1)] γ σ δ Iron and steel a a Steel processing a a Metallurgy a a Minerals a a Ceramic and building mat a a Glass a a Chemicals a a Speciality chemicals a a Pharmaceuticals a Foundry a a Metal work a a Agricultural machines a a Machine tools a a Industrial equipment a a Mining/civil egnring eqpmt a a Office equipment a Electrical equipment a Electronical equipment a a Domestic equipment a a Transport equipment a a Ship building a a Aeronautical building a Precision instruments a Textile a -0.3 a Leather products a a Shoe industry a a Garment industry a Mechanical woodwork a -0.2 a Furniture a a Paper & Cardboard a a Printing and editing a -0.7 a Rubber a -0.8 a Plastic processing a a Miscellaneous a a Trade-weighted mean a, b and c denote significance at the 1%, 5% and 10% level respectively. # : All coefficients in this column are significant at the 1% level. Estimations include the contiguity variable. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 29 / 50

30 CK (2010): Results (do the parameters make sense?) NB: the Broda and Weinstein (2003) here is to Broda and Weinstein (QJE, 2006) Figure 3: Comparison of our results for σ and δ with those of Broda and Weinstein (2003) (a) (b) Broda & Weinstein s sigma (log scale) US-Canada freight rates (log scale) sigma (log scale) Delta (log scale) Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 30 / 50

31 CK (2010): Results (what do the parameters imply about the two margins?) Figure 4: The estimated impact of trade barriers and distance on trade margins, by industry (a) Impact of distance on trade margins Intensive Margin δ(σ 1) Extensive Margin δ(γ (σ 1)) Shoe Electronical equip. Miscellaneous Domestic equip. Speciality chemicals Textile Metal work Leather product Plastic processing Rubber Industrial equip. Machine tools Mining/Civil egnring equip. Transport equip. Printing and editing Furniture Paper & cardboard Steel processing Foundry Chemicals Agricultural mach. Mechanical woodwork Metallurgy Glass Ceram. & Building mat. Minerals Ship building Iron and Steel (b) Impact of a tariff on trade margins Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 31 / 50

32 Ceram. & Building mat. CK (2010): Results (what do the parameters Minerals imply about Ship building Iron and Steel the two margins?) Metallurgy Glass (b) Impact of a tariff on trade margins Intensive Margin (σ 1) Extensive Margin (γ (σ 1)) Mechanical woodwork Textile Chemicals Miscellaneous Iron and Steel Speciality chemicals Electronical equip. Printing and editing Domestic equip. Leather product Plastic processing Ceram. & Building mat. Metallurgy Glass Mining/Civil egnring equip. Furniture Industrial equip. Agricultural mach. Metal work Transport equip. Paper & cardboard Minerals Machine tools Foundry Steel processing Ship building Rubber Shoe Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 32 / 50

33 Plan for Today s Lecture on Firm-Level Trade Empirics (Lecture II) 1 Trade flows: intensive and extensive margins 2 Exporting across multiple destinations Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 33 / 50

34 Eaton, Kortum and Kramarz (Ecma, 2011) EKK (2011) construct a Melitz (2003)-like model in order to try to capture key features of French firms exporting behavior: Whether to export at all. (Simple extensive margin). Which countries to export to. (Country-wise extensive margins). How much to export to each country. (Intensive margin). They uncover some striking regularities in the firm-wise sales data in (multiple) foreign markets. These power law like relationships occur in many settings (e.g. Gabaix (ARE, 2009; JEP, 2016)). Most famously, they occur for domestic sales within one market. In that sense, perhaps it s not surprising that they also occur market by market abroad. (Since scale invariance is at the heart of power laws.) They then (very nicely) show how these moments can be used to estimate a quantitative Melitz-like model and use the estimated model to answer counterfactual questions. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 34 / 50

35 EKK (2011): Stylised Fact 1: Market Entry (averages across countries) Normalization in Panel B: N nf /(X nf /X n) Figure 1: Entry and Sales by Market Size Panel A: Entry of Firms FRA # firms selling in market SIE CEN BEL SWI GER NET ITAUNK SPA CAM POR GRE DENAUT TUN COTMOR ALG FIN NOR SWE CAN SEN IRE ISRHOK SAU AUL NIG TOG SIN EGY SOU MAL BENBUK KUW MAD TUR YUG MAU MAS ZAI HUN CHA NIA CZE MEX ANG COL VEN IND JOR BRA SYRCHI ARG OMA PAK IRQ MAY NZE TAI KOR THA INO CHN URU BUL RWA KEN PAN PHI PER LIY ROM BUR GEE ETH DOM SUD ECU IRN PAR MOZGHA TAN LIB GUA COS ZIM CUB ZAM JAM TRI SRI BAN BOL HON ELS NIC VIE SOMAW PAP UGA AFG ALB NEP JAP USR USA market size ($ billions) entry normalized by French market share Panel B: Normalized Entry JAP USA CAN USR GER AUL SWI UNK GEE CHN AUT FRA BEL NET SPA ITA DEN NOR SWE IRE GRE FIN BUL TAI BRA NZE ISR SOU CZEROM ARG YUG MEX HUNVEN CHI MAY VIE HOK KOR POR SAU IND SIN CUB COL ALGTUR SUD COT EGY ZIMECU IRN CAM ALB MOR TAN COSTUN PAN PER TRI URU SYRPHI INO BUKSEN GUA ETH HON ELS DOM JOR PAK KUW THA BOL SRI PAP PAR ZAI NIA IRQ SOM LIY MAL NIG CHA TOG MAS OMA JAM BAN ANG RWABEN MAD UGA NIC KEN CEN BUR MOZ NEP ZAM GHA MAU LIB MAW AFG 1000 SIE market size ($ billions) percentiles (25, 50, 75, 95) by market ($ millions) Panel C: Sales Percentiles 10 CHNFRA USR LIY GEE ITA GER UNK USA NIC IRQ ALG EGY IND BELNET SPA GRE DEN FIN NOR SWE YUG BRA 1 TUR CZE MAW HUN BUL AFG NIA CUB IRN INO MEX KOR PAK SAU VEN JAP MOR IRE POR AUT ROM TUN SWI MOZ ETHANG PAN SYR SIN THA SOUARG TAI AUL PHI CAN ZAM KEN MAU GHALIB ZAI DOM BAN PER COL SUD CAM COT BUR MAL MAD GUA ELS COS CHI PAR ISR UGA BUK ALB NIG MAS SEN TAN HON ZIM TOG BEN JAM TRI OMA JOR KUW MAY VIEHOK SRI ECU NEP PAP NZE URU.1 SIE SOM RWA CEN CHA BOL market size ($ billions) Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 35 / 50

36 EKK (2011): Stylised Fact 1: Market Entry (averages across countries) All exporters export to at least one of these 7 places. But it s not a strict hierarchy as one would see in pure Melitz (2003) model. Table 1 - French Firms Exporting to the Seven Most Popular Destinations Country Belgium* (BE) Number of Exporters 17,699 Fraction of Exporters Germany (DE) 14, Switzerland (CH 14, Italy (IT) 10, United Kingdom (UK) 9, Netherlands (NL) 8, United States (US) 7, Total Exporters 34,035 * Belgium includes Luxembourg Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 36 / 50

37 Netherlands (NL) 8, United States (US) 7, EKK Total Exporters (2011): Stylised Fact 1: Market 34,035 Entry (averages * Belgium includes Luxembourg across countries) For 27% of exporters, a strict hierarchy is observed over these 7 destinations. Within these firms, foreign market entry is not independent. Table 2 - French Firms Selling to Strings of Top Seven Countries Number of French Exporters Under Export String Data Independence Model BE* 3,988 1,700 4,417 BE-DE 863 1, BE-DE-CH BE-DE-CH-IT BE-DE-CH-IT-UK BE-DE-CH-IT-UK-NL BE-DE-CH-IT-UK-NL-US 2, ,840 Total 9,260 4,532 9,648 * The string "BE" means selling to Belgium but no other among the top 7, "BE-DE" means selling to Belgium and Germany but no other, etc. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 37 / 50

38 EKK (2011): Stylised Fact 2: Sales Distributions (across all firms) Surprisingly similar shape (with mean shift) in each destination market (including home). Power laws (at least in upper tails upper left, here). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 38 / 50

39 EKK (2011): Stylised Fact 3: Export Participation and Size in France Big firms at home are multi-destination exporters. Figure 3: Sales in France and Market Entry average sale in France ($ millions) Panel A: Sales and Markets Penetrated minimum number of markets penetrated average sale in France ($ millions) Panel B: Sales and # Penetrating Multiple Markets # firms selling to k or more markets 1 average sales in France ($ millions) Panel C: Sales and # Selling to a Market UGA MAWBOL ALB SOM SIE JAM ELS AFG NIC VIE ZAM HON GHA GUA COS PAP LIB TAN BAN MOZ ZIM DOM ETH SRI SUD LIY ECU GEE NEP TRIPAR CUB BUR IRN ROM KEN PER RWA PHI COL CHN PAN URU BUL ANG OMA INO CZE IRQ USR NIA PAK SYR MAY MEX CHI THA VEN HUN JOR MAU ARG CHANZE MAS ZAI KOR BRA TAI MAD MAL CEN NIG YUG IND TUR BUK KUW EGY BEN TOG SOU SIN IRE HOK AUL ISR SAU FIN SEN NOR GRE TUN JAP ALG DEN POR COT MOR CAM AUT SWE CAN SPA USA NET UNK ITA SWI GER BEL FRA # firms selling in the market percentiles (25, 50, 75, 95) in France ($ millions) Panel D: Distribution of Sales and Market Entry MAW UGABOL ALB SOM SIE JAM ELS ZAM PAP NIC HON GUA COS VIELIB AFG GHA MOZ BAN ZIM DOM ETH PAR SRI SUD LIY CUB BUR ECU GEE IRN KEN PER PHI NEP TAN TRI RWA ROM PAN URU BUL ANG COL INO CHN CHA OMA CZE IRQ USR NIA PAK SYR MAY MAU MEX CHI THA VEN HUN JOR ARG NZE MAS ZAI KOR BRA TAI MAD MAL CEN YUG IND TUR NIG BUK BEN KUW EGY TOG SOU SIN IRE HOK AUL ISR SAU FIN SEN NOR GRE TUN JAP ALG DEN POR COT MOR CAM AUT SWE CANSPA USA NET UNK ITA SWI GER BEL # firms selling in the market FRA Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 39 / 50

40 EKK (2011): Stylised Fact 4: Export Intensity Firm-level ratio of sales at home to abroad (X nf (j)/x FF (j)) relative to the average ( X nf / X FF ). Characteristics of distribution across j s plotted here. Figure 4: Distribution of Export Intensity, by Market percentiles (50, 95) of normalized export intensity USA GER USR ITA JAP ALG UNK CHNKOR SAU NET SWI BEL AFG NIC LIY GEE EGY SPA BUL IND NORSWE CAN CUB PAN CZE NIA BRA HOK AUL PAR TAI KUW TUN DEN MOR AUT IRN VEN PHI IRQ PAK ANG MEX HUN ZAI YUGSOU SIN FIN GRE CAM OMA INO SYR TUR IRE POR PAPVIE LIB MOZ COL ISR THAMAL COT SIE ROM MAY MAU CHI ARG NZE MAD BUK TAN GHA BEN SEN ALB HON ZAM BAN ZIM DOM BUR ECU KEN URU JOR MAS NIG BOL TRIETH SRI PER CHA TOG ELSGUA NEP COS SUD CEN MAW JAM RWA UGA SOM # firms selling in the market Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 40 / 50

41 EKK (2011): Model The above relationships fit the Melitz (2003) model (with G(.) being Pareto) in some regards, but not all. EKK (2011) therefore add some features to Melitz (2003) in order to bring this model closer to the data. Most of these will take the flavor of firm-specific shocks/noise. The shocks smooths things out, allows for unobserved heterogeneity, and answer the structural econometrician s question of where does your regression s error term come from?. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 41 / 50

42 EKK (2011) Model Shocks: Firm (i.e. j)-specific productivity draws (in country i): z i (j). This is Pareto with parameter θ. Firm-specific demand draw α n (j). The demand they face in market n (if they sell at p there) is thus: X n (j) = α n (j)fx n ( p P n ) (σ 1), where f will be defined shortly. Firm-specific fixed entry costs E ni (j) = ε n (j)e ni M(f ), where ε n (j) is a firm-specific fixed exporting cost shock, E ni is the fixed exporting term that appears in Melitz (2003) or HMR (2008) (i.e. constant 1 (1 f )1 1/λ across firms). And M(f ) = 1 1/λ, which, following Arkolakis (JPE, 2010), is a micro-founded marketing function that captures how much firms have to pay to access f consumers (this is a choice variable). EKK allow for g(α, ε) to take any form, but it needs to be the same across countries n, iid across firms, and within firms independent from the Pareto distribution of z. (In practice, they use a bivariate log-normal distribution.) Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 42 / 50

43 EKK (2011) Model: Entry The entry condition is similar to Melitz (2003). Enter if cost c ni (j) = w i τ ij z i (j) satisfies: ( ηxn c c ni (η) σe ni ) 1/(σ 1) P n m (3) Here η n (j) αn(j) ε n(j). And X n is total sales in n, P n is the price index in n, and m is the (constant) markup. Integrating this over the distribution g(η) we know how much entry (measure of firms) there is: J ni = κ 2 κ 1 π ni X n σe ni (4) This therefore agrees well with Fact 1 (normalized entry is linear in X n ). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 43 / 50

44 EKK (2011): Stylised Fact 1: Market Entry (averages across countries) Normalization : N nf /(X nf /X n) Figure 1: Entry and Sales by Market Size Panel A: Entry of Firms FRA # firms selling in market SIE CEN BEL SWI GER NET ITAUNK SPA CAM POR GRE DENAUT TUN COTMOR ALG FIN NOR SWE CAN SEN IRE ISRHOK SAU AUL NIG TOG SIN EGY SOU MAL BENBUK KUW MAD TUR YUG MAU MAS ZAI HUN CHA NIA CZE MEX ANG COL VEN IND JOR BRA SYRCHI ARG OMA PAK IRQ MAY NZE TAI KOR THA INO CHN URU BUL RWA KEN PAN PHI PER LIY ROM BUR GEE ETH DOM SUD ECU IRN PAR MOZGHA TAN LIB GUA COS ZIM CUB ZAM JAM TRI SRI BAN BOL HON ELS NIC VIE SOMAW PAP UGA AFG ALB NEP JAP USR USA market size ($ billions) entry normalized by French market share Panel B: Normalized Entry JAP USA CAN USR GER AUL SWI UNK GEE CHN AUT FRA BEL NET SPA ITA DEN NOR SWE IRE GRE FIN BUL TAI BRA NZE ISR SOU CZEROM ARG YUG MEX HUNVEN CHI MAY VIE HOK KOR POR SAU IND SIN CUB COL ALGTUR SUD COT EGY ZIMECU IRN CAM ALB MOR TAN COSTUN PAN PER TRI URU SYRPHI INO BUKSEN GUA ETH HON ELS DOM JOR PAK KUW THA BOL SRI PAP PAR ZAI NIA IRQ SOM LIY MAL NIG CHA TOG MAS OMA JAM BAN ANG RWABEN MAD UGA NIC KEN CEN BUR MOZ NEP ZAM GHA MAU LIB MAW AFG 1000 SIE market size ($ billions) percentiles (25, 50, 75, 95) by market ($ millions) Panel C: Sales Percentiles 10 CHNFRA USR LIY GEE ITA GER UNK USA NIC IRQ ALG EGY IND BELNET SPA GRE DEN FIN NOR SWE YUG BRA 1 TUR CZE MAW HUN BUL AFG NIA CUB IRN INO MEX KOR PAK SAU VEN JAP MOR IRE POR AUT ROM TUN SWI MOZ ETHANG PAN SYR SIN THA SOUARG TAI AUL PHI CAN ZAM KEN MAU GHALIB ZAI DOM BAN PER COL SUD CAM COT BUR MAL MAD GUA ELS COS CHI PAR ISR UGA BUK ALB NIG MAS SEN TAN HON ZIM TOG BEN JAM TRI OMA JOR KUW MAY VIEHOK SRI ECU NEP PAP NZE URU.1 SIE SOM RWA CEN CHA BOL market size ($ billions) Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 44 / 50

45 EKK (2011) Model: Firm Sales The firm sales (conditional on entry) condition is similar to Arkolakis (2010): [ ( ) ] c λ(σ 1) ( ) c (σ 1) X ni (j) = ε 1 σe ni. (5) c ni (η) c ni (η) There is more work to be done, but one can already see that this will look a lot like a Pareto distribution (c is Pareto, so c to any power is also Pareto) in each market (as in Figure 2). [ ( ) ] λ(σ 1) But the 1 c c ni (η) will cause the sales distribution to deviate from Pareto in the lower tail (also as in Figure 2). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 45 / 50

46 EKK (2011): Stylised Fact 2: Sales Distributions (across all firms) Surprisingly similar shape (with mean shift) in each destination market (including home). Power laws (at least in upper tails top left, here). Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 46 / 50

47 EKK (2011) Model: Sales in France Conditional on Foreign Entry The amount of sales in France conditional on entering market n can be shown to be (where v nf (j) is a term that reflects the ratio of a firm s cost own cost draw to its own entry threshold (where that threshold depends on the α(j) and η(j) draws it got)): [ X FF (j) n = α ( F (j) 1 v nf (j) λ/ θ NnF η n (j) N FF v nf (j) 1/ θ ( NnF N FF ) 1/ θ κ 2 κ 1 X FF. ) λ/ θ ( ) ] ηn (j) λ η F (j) Since N nf /N FF is close to zero (everywhere but in France) the dependence of this on N nf is Pareto with slope 1/ θ. As in Figure 3. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 47 / 50

48 EKK (2011): Stylised Fact 3: Export Participation and Size in France Big firms at home are multi-destination exporters. Figure 3: Sales in France and Market Entry average sale in France ($ millions) Panel A: Sales and Markets Penetrated minimum number of markets penetrated average sale in France ($ millions) Panel B: Sales and # Penetrating Multiple Markets # firms selling to k or more markets 2 1 average sales in France ($ millions) Panel C: Sales and # Selling to a Market UGA MAWBOL ALB SOM SIE JAM ELS AFG NIC VIE ZAM HON GHA GUA COS PAP LIB TAN BAN MOZ ZIM DOM ETH SRI SUD LIY ECU GEE NEP TRIPAR CUB BUR IRN ROM KEN PER RWA PHI COL CHN PAN URU BUL ANG OMA INO CZE IRQ USR NIA PAK SYR MAY MEX CHI THA VEN HUN JOR MAU ARG CHANZE MAS ZAI KOR BRA TAI MAD MAL CEN NIG YUG IND TUR BUK KUW EGY BEN TOG SOU SIN IRE HOK AUL ISR SAU FIN SEN NOR GRE TUN JAP ALG DEN POR COT MOR CAM AUT SWE CAN SPA USA NET UNK ITA SWI GER BEL FRA # firms selling in the market percentiles (25, 50, 75, 95) in France ($ millions) Panel D: Distribution of Sales and Market Entry MAW UGABOL ALB SOM SIE JAM ELS ZAM PAP NIC HON GUA COS VIELIB AFG GHA MOZ BAN ZIM DOM ETH PAR SRI SUD LIY CUB BUR ECU GEE IRN KEN PER PHI NEP TAN TRI RWA ROM PAN URU BUL ANG COL INO CHN CHA OMA CZE IRQ USR NIA PAK SYR MAY MAU MEX CHI THA VEN HUN JOR ARG NZE MAS ZAI KOR BRA TAI MAD MAL CEN YUG IND TUR NIG BUK BEN KUW EGY TOG SOU SIN IRE HOK AUL ISR SAU FIN SEN NOR GRE TUN JAP ALG DEN POR COT MOR CAM AUT SWE CANSPA USA NET UNK ITA SWI GER BEL # firms selling in the market FRA Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 48 / 50

49 EKK (2011) Model: Normalized Export Intensity This can can be shown to be: X nf (j) X FF (j) / X nf X FF = α n(j) α F (j) 1 v nf (j) λ/ θ 1 v nf (j) λ/ θ ( NnF N FF ) λ/ θ ( ηn(j) η F (j) ) λ ( ) 1/ θ NnF N FF Since N nf /N FF is close to zero (everywhere but in France) the dependence of the square bracket on N nf is negligible. So we are left with the dependence driven by the term outside the square bracket, i.e. Pareto with slope 1/ θ. As in Figure 4. Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 49 / 50

50 EKK (2011): Stylised Fact 4: Export Intensity Firm-level ratio of sales at home to abroad (X nf (j)/x FF (j)) relative to the average ( X nf / X FF ). Characteristics of distribution across j s plotted here. Figure 4: Distribution of Export Intensity, by Market percentiles (50, 95) of normalized export intensity USA GER USR ITA JAP ALG UNK CHNKOR SAU NET SWI BEL AFG NIC LIY GEE EGY SPA BUL IND NORSWE CAN CUB PAN CZE NIA BRA HOK AUL PAR TAI KUW TUN DEN MOR AUT IRN VEN PHI IRQ PAK ANG MEX HUN ZAI YUGSOU SIN FIN GRE CAM OMA INO SYR TUR IRE POR PAPVIE LIB MOZ COL ISR THAMAL COT SIE ROM MAY MAU CHI ARG NZE MAD BUK TAN GHA BEN SEN ALB HON ZAM BAN ZIM DOM BUR ECU KEN URU JOR MAS NIG BOL TRIETH SRI PER CHA TOG ELSGUA NEP COS SUD CEN MAW JAM RWA UGA SOM # firms selling in the market Stanford Econ 266 (Dave Donaldson) Firm-level heterogeneity (Empirics II) Winter 2016 (lecture 13) 50 / 50