Lecture 13 Notes: Trade Theory with Firm-Level Heterogeneity (Cont.) - Empirics, Part II

14.581 International Trade Class notes on 3/20/2013 1 1 Intensive and Extensive Margins in Trade Flows • With access to micro data on trade flows at the firm-level, a key question to ask 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 can also de­ compose 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 can and 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). From Bernard, Andrew B., J. Bradford Jensen, et al. Journal of Economic Perspectives 21, no. 3 (2007): 105-30. Courtesy of American Economic Association. Used with permission. 1 The notes are based on lecture slides with inclusion of important insights emphasized during the class. 1 From Bernard, Andrew B., J. Bradford Jensen, et al. Journal of Economic Perspectives 21, no. 3 (2007): 105-30. Courtesy of American Economic Association. Used with permission. Figure 1: Mean value of individual-firm exports (single-region firms, 1992) Importing country: Switzerland Importing country: Belgium Belgium Belgium Germany Germany 32.61 Switzerland 25.57 3.45 2.32 1.32 0.56 Switzerland 0.75 0.46 0.10 0.02 0.00 Italy Italy Spain Spain Importing country: Germany Importing country: Spain Belgium Belgium Germany Germany 4,03 37.01 Switzerland 7.60 1,60 2.18 0,68 1,23 Switzerland 0,39 0,18 0.58 0,00 0.00 Italy Spain 0.25 Italy Importing country: Italy Spain Belgium Germany 8,96 2,48 0,88 Switzerland 0,51 0,22 Italy Spain Figure 1 from Crozet, M., and P. Koenig. "Structural Gravity Equations with Intensive and Extensive Margins." Canadian Journal of Economics/Revue canadienne d'économique 43 (2010): 41–62. © John Wiley And Sons Inc. All rights reserved. 2 Figure 2: Percentage of firms which export (single-region firms, 1992) Importing country: Belgium Importing country: Switzerland Belgium Belgium Germany Germany 92.85 92.59 60.00 61.53 Switzerland 34.21 46.87 Switzerland 38.00 23.71 16.66 0.00 26.92 9.37 Italy Italy Spain Spain Importing country: Germany Importing country: Spain Belgium Belgium Germany Germany 80.00 100.00 41.66 68.75 31.11 41.93 Switzerland Switzerland 32.05 25.00 22.85 18.42 5.00 0.00 Italy Italy Spain Spain Importing country: Italy Belgium Germany 80.00 46.15 33.33 Switzerland 25.00 18.18 6.66 Italy Spain Figure 2 from Crozet, M., and P. Koenig. "Structural Gravity Equations with Intensive and Extensive Margins." Canadian Journal of Economics/Revue canadienne d'économique 43 (2010): 41–62. © John Wiley And Sons Inc. All rights reserved. 3 Table 2: Decomposition of French aggregate industrial exports (34 industries - 159 countries ­ 1986 to 1992) ln (GDPkj ) All firms > 20 employees (1) (2) Average Number of Shipment Shipments ln (Nkjt ) ln (Mkjt /Nkjt ) 0.461a 0.417a (0.007) (0.007) Single-region firms > 20 employees (3) (4) Average Number of Shipment Shipments ln (Mkjt /Nkjt ) ln (Nkjt ) 0.421a 0.417a (0.007) (0.008) ln (Distj ) -0.325a (0.013) -0.446a (0.009) -0.363a (0.012) -0.475a (0.009) Contigj -0.064c (0.035) -0.007 (0.032) 0.002 (0.038) 0.190a (0.036) Colonyj 0.100a (0.032) 0.466a (0.025) 0.141a (0.035) 0.442a (0.027) Frenchj 0.213a (0.029) 23553 0.480 0.991a (0.028) 23553 0.591 0.188a (0.032) 23553 0.396 1.015a (0.028) 23553 0.569 N R2 Note: These are OLS estimates with year and industry dummies. Robust stan­ dard errors in parentheses with a , b and c denoting significance at the 1%, 5% and 10% level respectively. © John Wiley And Sons Inc. All rights reserved. Table 2. Decomposing Spatial Frictions (5-digit zip code data) dist dist2 ownzip ownstate constant Adj. R2 N SD value ( Tij ) -0.137 (0.009) -0.004 (0.001) 1.102 (0.030) -0.024 (0.007) -13.393 (0.026) 0.01 1290788 -0.187 # of shipments ( N ij ) -0.294 (0.002) 0.017 (0.000) 0.883 (0.008) 0.043 (0.002) -1.413 (0.007) 0.10 1290840 -0.081 -0.159 (0.002) 0.008 (0.000) 0.540 (0.007) 0.029 (0.002) -0.888 (0.006) 0.05 1290840 -0.059 -0.135 (0.001) 0.009 (0.000) 0.342 (0.003) 0.014 (0.001) -0.525 (0.003) 0.10 1290840 -0.022 0.157 (0.008) -0.021 (0.001) 0.219 (0.028) -0.067 (0.006) -11.980 (0.024) 0.00 1290788 -0.106 -0.032 (0.007) 0.036 (0.001) -0.115 (0.024) -0.154 (0.006) 0.021 (0.020) 0.08 1290788 0.419 0.189 (0.011) -0.058 (0.001) 0.334 (0.037) 0.087 (0.009) -12.001 (0.031) 0.05 1290788 -0.537 # of trading pairs F ( N ij ) # of commodities k ( N ij ) avg. value ( PQ ij ) avg. price ( Pij ) avg. weight ( Qij ) 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. S D is the elasticity of trade with respect to distance, evaluated at the sample mean distance of 523 miles. Courtesy of Russell Hillberry and David Hummels. Used with permission. 4 Panel A: Entry of Firms FRA # firms selling in market 100000 10000 1000 CEN 100 SIE BELSWI GER ITA UNK NETSPA CAN AUT SWE CAM COTMOR POR ALGDEN TUN GRE NOR SEN FIN SAU ISRHOK AUL IRE SIN EGY SOU TOG KUW BEN TUR YUG IND NIG MAL MADBUK TAI BRA KOR ZAI MAS NZE ARG JOR HUNVEN CHI THA MEX MAU MAY SYR PAK NIA CHN IRQ INO CZE OMA CHA ANG BUL URU KEN PER COL PAN PHI ROM IRN GEE RWA ECU LIY BUR SUD SRI CUB PAR ETH DOM ZIM COS MOZ GHALIB TRI BAN GUA TAN ZAM HON ELS VIE NIC BOLJAM PAP SOM ALB MAWUGA AFG NEP USA JAP USR 10 .1 1 10 100 market size ($ billions) 1000 10000 entry normalized by French market share Panel B: Normalized Entry 5000000 JAP USA 100000 10000 1000 CEN GER UNK AUL SWI CHN GEE ITA TAI SPABRA AUT BUL FRA NZE SWE NET ARG FIN YUG NOR SOU CZE BEL ROM ISRHOKDEN KOR MEX IND GRE VIE IRE HUN MAY SVEN AU SIN CHI CUB POR TUR COL ALG IRN EGY INO ECU SUD PER COT PHI ZIM CAMSYR PAN PAK TRI URU MOR ALB COS THA JORTUNKUW TAN DOM SRI ETH ELS UA BUKSEN BOL G HON ZAI OMA PAP PAR BAN NIA IRQ TOG MASJAM ANG LIY SOM CHAMAL KEN MAD NIC UGA BEN NEP RWA MOZ NIG BUR ZAM GHA LIB MAU MAW AFG SIE .1 percentiles (25, 50, 75, 95) by market ($ millions) USR CAN 1000000 1 10 100 market size ($ billions) 1000 10000 Panel C: Sales Percentiles 10 CHNFRA ITA UNK GER GEE IND EGY BRA IRQ ALG YUG KOR NET CZE BEL BUL INOVEN IRNHUN MEXSWE SPA TUR MAW AFG SAU PAKCUB NIA TAI DEN ARGAUL FIN ROM NOR THA SIN GRE AUT SYR PHI SWI PAN MOR CAN HOKSOU POR PERIRE COL ANG VIE BANTUN ETH ZAM KEN MOZ DOM KUWCHI MAY ISR NZE OMA JCOS OR CAM ZAI SRI PAR COT ECU SUD PAP LIB GUA MAU MAD ELS GHA TRI ZIM URU TAN UGA BUR MALNEP HON ALB MAS BUK SEN JAM NIG TOG RWABEN BOL SOM CHA LIY 1 .1 USR NIC SIE CEN USA JAP .01 .001 .1 1 10 100 market size ($ billions) 1000 10000 © The Econometric Society. All rights reserved. 2 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 an entire lecture on 5 estimating trade costs later in the course, and gravity equations will loom large. • HMR (2008) started wave of thinking about gravity equation estimation in the presence of extensive/intensive margins. – They use aggregate international trade (so this paper doesn’t tech­ nically belong in a lecture on ‘firm-level trade empirics’ !) to explore implications of a heterogeneous firm model for gravity equation esti­ mation. – The Melitz (2003) model—which you’ll see properly next week—is simplified and used as a tool to understand, estimate, and correct for biases in gravity equation estimation. 2.1 HMR (2008): Zeros in Trade Data • HMR start with the observation that there are lots of ‘zeros’ in interna­ tional trade data, even when aggregated up to total bilateral exports. – Baldwin and Harrigan (2008) and Johnson (2008) look at this in a more disaggregated manner and find (unsurprisingly) far more zeros. • Zeros are interesting. • But zeros are also problematic. – A typical analysis of trade flows is based on the gravity equation (in logs), which can’t incorporate Xij = 0 – Indeed, other models of the gravity equation (Armington, Krugman, Eaton-Kortum) don’t have any zeros in them (due to CES and un­ bounded productivities and finite trade costs). 6 Percent of country pairs 100 90 80 70 60 50 40 30 20 10 19 96 19 94 19 92 19 90 19 88 19 86 19 84 19 82 19 80 19 78 19 76 19 74 19 72 19 70 0 Trade in both directions Trade in one direction only No Trade Image by MIT OpenCourseWare. FIGURE I Distribution of Country Pairs Based on Direction of Trade Note. Constructed from 158 countries. 6,000 All country pairs Billions of 2000 U.S. dollars Trade in both directions in 1970 5,000 4,000 3,000 2,000 1,000 94 96 19 92 19 90 19 19 88 19 86 19 84 19 82 19 80 19 78 19 74 76 19 72 19 19 19 70 0 Year Image by MIT OpenCourseWare. FIGURE II Aggregate Volume of Exports of All Country Pairs and of Country Pairs That Traded in Both Directions in 1970 2.2 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 produc­ tion (unit cost cj ), one sector. 7 – Both variable (iceberg τij ) and fixed (fij ) costs of exporting. – Heterogeneous firm-level productivities 1/a drawn from truncated Pareto, G(a). • Some firms in j sell in country i iff a ≤ aij , where the cutoff productivity (aij ) is defined by: κ1 τij cj aij Pi 1−ε Yi = cj fij (1) • HMR (2008) derive a gravity equation, for those observations that are non-zero, of the form: ln(Mij ) = β0 + αi + αj − γ ln dij + wij + uij (2) • Where: – Mij is imports – dij is distance – wij is the ‘augmented’ part, which is a term accounting for selection. – Mij = 0 is possible here (even with CES preferences and finite vari­ able trade costs) because it is assumed that each country’s firms have productivities drawn from a bounded (truncated Pareto) distri­ bution. 2.3 Two Sources of Bias • The HMR (2008) theory suggests (and solves) two sources of bias in the typical estimation of gravity equations (which neglects wij ). • First: Omitted variable bias due to the presence of wij : – 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 (dij ) does two things: it raises the price at which any firm can sell (thus reducing demand along the intensive margin) in, and it changes the productivity (and hence the price and hence the amount sold) of the firms entering, a distant market. – This means that dij is correlated with wij . – Therefore, if one aims to estimate γ but neglects to control for wij the estimate of γ will be biased (due to OVB). 8 • The HMR (2008) theory suggests (and solves) two sources of bias in the typical estimation of gravity equations (which neglects wij ). • 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 Mij = 0. – The HMR theory tells us that the existence of these ‘zeros’ is not as good as random with respect to dij , 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 dij . – This calls for a standard Heckman (1979) selection correction. 2.4 HMR (2008): Two-step Estimation 1. Estimate probit for zero trade flow or not: • Include exporter and importer fixed effects, and dij . • 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 trick) to control for selection problem (Second source of bias) • Also include empirical proxy for wij based on estimate of entry equa­ tion in Step 1 (to fix First source of bias). 9 Benchmark Gravity and Selection into Trading Relationship 1986 Variables 1980's (Porbit) T m -1.176** (0.031) -0.263** (0.012) -1.201** (0.024) ij Distance (Porbit) m ij (Porbit) T ij T m ij ij -0.246** (0.008) -1.200** (0.024) ij -0.246** (0.008) Land border 0.458** (0.147) -0.148** (0.047) 0.366** (0.131) -0.146** (0.032) 0.364** (0.131) -0.146** (0.032) Island -0.391** (0.121) -0.136** (0.032) -0.381** (0.096) -0.140** (0.022) -0.378** (0.096) -0.140** (0.022) Landlock -0.561** (0.188) -0.072 (0.045) -0.582** (0.148) -0.087** (0.028) -0.581** (0.147) -0.087** (0.028) Legal 0.486** (0.050) 0.038** (0.014) 0.406** (0.040) 0.029** (0.009) 0.407** (0.040) 0.028** (0.009) Language 1.176** (0.061) 0.113** (0.016) 0.207** (0.047) 0.109** (0.011) 0.203** (0.047) 0.108** (0.011) Colonial ties 1.299** (0.120) 0.128 (0.117) 1.321** (0.110) 0.114 (0.082) 1.326** (0.110) 0.116 (0.082) Currency union 1.364** (0.255) 0.190** (0.052) 1.395** (0.187) 0.206** (0.026) 1.409** (0.187) 0.206** (0.026) FTA 0.759** (0.222) 0.494** (0.020) 0.996** (0.213) 0.497** (0.018) 0.976** (0.214) 0.495** (0.018) Religion 0.102 (0.096) 0.104** (0.025) -0.018 (0.076) 0.099** (0.016) -0.038 (0.077) 0.098** (0.016) WTO (none) -0.068 (0.058) -0.056** (0.013) WTO (both) 0.303** (0.042) 0.093** (0.013) 110,697 0.682 248,060 0.551 Observations R 11,146 0.709 2 24,649 0.587 248,060 0.551 110,697 0.682 Notes. Exporter, importer, and year fixed effects. Marginal effects at sample means and pseudo R2 reported for Probit. Robust standard errors (clustering by country pair). + Significant at 10% * Significant at 5% ** Significant at 1% Image by MIT OpenCourseWare. Baseline Results 1986 reduced sample Variables m ij (Probit) T ij Benchmark NLS Distance -0.213** (0.016) -1.167** (0.040) -0.813 (0.049) -0.847** (0.052) Land border -0.087 (0.072) 0.627** (0.165) 0.871 (0.170) 0.845** (0.166) Island -0.173* (0.078) -0.553* (0.269) -0.203 (0.290) -0.218 (0.258) -0.161 (0.259) Landlock -0.053 (0.050) -0.432* (0.189) -0.347* (0.175) -0.362+ (0.187) -0.352+ (0.187) Legal 0.049** (0.019) 0.535** (0.064) 0.431** (0.065) 0.434** (0.064) 0.407** (0.065) Language 0.101** (0.021) 0.147+ (0.075) -0.030 (0.087) -0.017 (0.077) -0.061 (0.079) Colonial ties -0.009 (0.130) 0.909** (0.158) 0.847** (0.257) 0.848** (0.148) 0.853** (0.152) Currency union 0.216** (0.038) 1.534** (0.334) 1.077** (0.360) 1.150** (0.333) 1.045** (0.337) FTA 0.343** (0.009) 0.976** (0.247) 0.124 (0.227) 0.241 (0.197) -0.141 (0.250) Religion 0.141** (0.034) 0.281* (0.120) 0.120 (0.136) 0.139 (0.120) 0.073 (0.124) Regulation -0.108** (0.036) -1.146 (0.100) -0.061* (0.031) -0.216+ (0.124) costs R costs (days & proc) Polynomial 100 bins -0.755** (0.070) -0.789** 0.892** 0.170) (0.088) 0.863** (0.170) -0.197 (0.258) -0.353+ (0.187) 0.418** (0.065) -0.036 (0.083) 0.838** (0.153) 1.107** (0.346) 0.065 (0.348) 0.100 (0.128) 0.840** (0.043) δ (from ω * ) ij 0.240* (0.099) ηij* 0.882** (0.209) * ij 3.261** (0.540) *2 ij *3 ij -0.712** (0.170) Observations R Indicator variables 50 bins 0.060** (0.017) 2 12,198 0.573 6,602 0.693 6,602 6,602 0.701 6,602 0.706 6,602 0.704 2 Notes: Exporter and importer fixed effects. Marginal effects at sample means and pseudo R 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%. Image by MIT OpenCourseWare. 3 Crozet and Koenig (CJE, 2010) • CK (2010) conduct a similar exercise to HMR (2008), but with French firm-level data. 10 – This is attractive—after all, the main point that HMR (2008) is mak­ ing 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). 3.1 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. (It costs just as much to figure out how to sell to the Swiss whether your French firm is based in Geneva or Normandy). 3.2 CK (2010): The model and estimation • The model is deliberately close to Chaney (2008), which is a particular ver­ sion of the Melitz (2003) model but with (unbounded) Pareto-distributed firm productivities (with shape parameter γ). We will see this model in detail in the next lecture. • In Chaney (2008) the elasticity of trade flows with respect to variable δ trade costs (proxies for by distance here, if we assume τij = θDij where D = distance) can be subdivided into the: EXT – Extensive elasticity: εDij j = −δ [γ − (σ − 1)]. CK estimate this by regressing firm-level entry (ie a Probit) on firm-level distance Dij and a firm fixed effect. This is analogous to HMR’s first stage. IN T – Intensive elasticity: εDij j = −δ(σ − 1). CK estimate this by regressing firm-level exports on firm-level distance Dij and a firm fixed effect. This is analogous to HMR’s second stage. • 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. 11 – In the Chaney (2008) model this will behave as: Xi = λ(ci )−[γ−(σ−1)] , where ci is a firm’s marginal cost and Xi is a firm’s total sales. – With an Olley and Pakes (1996) TFP estimate of 1/ci , CK estimate [γ − (σ − 1)] and hence identify the entire system of 3 unknowns. 12 3.3 CK (2010): Results (each industry separately) The Structural Parameters of the Gravity Equation (Firm-level Estimations) Export value P[Export > 0] Pareto# γ σ δ 10 11 Iron and steel Steel processing -5.51* -1.5* -1.71* -0.99* -1.36 -1.74 1.98 5.1 1.62 4.36 2.78 13 14 15 Metallurgy -2.14* -0.73* -1.85 2.82 1.97 0.29 0.76 Minerals Ceramic and building mat. -2.98* -2.63* -0.91* -0.76* -2.86 -1.97 4.11 2.76 2.25 1.79 0.72 0.95 16 17 18 Glass Chemicals Speciality chemicals -2.33* -1.81* -0.97* -0.58* -0.76* 0.34* -2.13 -1.09 -1.39 2.84 1.89 2.13 1.7 1.8 1.74 0.82 0.95 0.46 19 20 21 Pharmaceuticals Foundry Metal work -1.19* -1.72* -1.19* -0.14 -0.85* -0.36* -1.4 -2.37 -2.43 4.68 3.48 3.31 2.05 0.37 0.34 22 23 Agricultural machines Machine tools -2.06* -1.29* -0.57* -0.48* -2.39 -2.47 3.31 3.92 1.92 2.45 0.62 0.33 24 Industrial equipment -1.25* -0.48* -1.97 3.21 2.24 0.39 25 Mining / civil egnring eqpmt -1.37* -0.46* -1.9 2.86 1.96 0.48 27 Office equipment -0.52* -1.02 -1.57 28 29 30 31 32 33 Electrical equipment Electronical equipment Domestic equipment Transport equipment Ship building Aeronautical building -0.8* -0.77* -0.94* -1.4* -3.69* -0.78* -0.14 -0.24* -0.14* -0.55* -2.67* -0.13 -2.34 -1.63 -2.13 -2.23 -1.52 -3.27 2.34 2.51 3.69 5.53 1.71 1.37 2.46 5.01 0.33 0.38 0.38 0.67 34 Precision instruments -1.07* 0.08 -1.63 44 45 46 47 48 Textile Leather products Shoe industry Garment industry Mechanical woodwork -1.17* -1.24* -0.42* -0.33* -2.14* -0.3* -0.44* -0.29* 0.13 -0.2* -1.37 -1.63 -2.3 -1.04 -1.5 1.84 2.53 7.31 1.47 1.9 6.01 0.64 0.49 0.06 1.65 1.15 1.29 49 Furniture -1.43* -0.37* -2.25 3.04 1.79 0.47 50 51 Paper & Cardboard Printing and editing -1.45* -1.4* 0.76* 0.7* -1.76 -1.24 3.71 2.46 2.95 2.22 0.39 0.57 52 53 Rubber Plastic processing Miscellaneous -1.26* -1.24* -0.91* 0.8* 0.51* -0.33* -2.52 -1.6 -1.22 6.93 2.7 1.92 5.41 2.11 1.7 0.18 0.46 0.47 Tread weighted mean -1.41 -0.53 -1.86 3.09 2.25 0.58 Industry Code 54 -δ(σ−1) -δγ −[γ−(σ−1)] *,** and ***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. Image by MIT OpenCourseWare. CK (2010): Results (do the parameters make sense?) 40 50 Broda and Weinstein's sigma (log scale) 30 20 10 11 31 25 44 48 30 53 14 24 21 51 13 23 18 1722 20 28 10 45 49 45 20 52 32 1 2 3 4 US-Canada freight rate (log scale) 3.4 22 2 1.5 1 .5 14 48 50 11 52 16 21 45 50 44 13 25 21 30 52 11 25 51 29 24 54 32 23 31 5 15 1 Sigma (log scale) 10 17 2 3 Delta (log scale) Image by MIT OpenCourseWare. Figure 3: Comparison of our results for σ and δ with those of Broda and Weinstein (2003) 3.5 CK (2010): Results (what do the parameters imply about margins?) Figure 4: The estimated impact of trade barriers and distance on trade margins, by industry Impact of Distance on Trade Margins 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 and cardboard Steel processing Foundry Chemicals Agricultural mach. Mechanical woodwork Metallurgy Glass Ceram. and building mat. Minerals Ship building Iron and Steel Intensive Margin -δ(σ-1) Extensive Margin −δ(γ−(σ−1)) 6 4 2 0 Image by MIT OpenCourseWare. 13 Impact of a Tariff on Trade Margins Mechanical woodwork Textile Chemicals Miscellaneous Iron and Steel Speciality chemicals Electronical equip. Printing and editing Domestic equip. Leather product Plastic processing Ceram. and bulding mat. Metallurgy Glass Mining/Civil egnring equip. Furniture Industrial equip. Agricultural mach. Metal work Transport equip. Paper and cardboard Minerals Machine tools Foundry Steel processing Ship building Rubber Shoe Intensive Margin −(σ-1) Extensive Margin −(γ−(σ−1)) 8 6 4 2 0 Image by MIT OpenCourseWare. 4 Eaton, Kortum and Kramarz (2009) • EKK (2009) construct a Melitz (2003)-like model in order to try to capture the key features of French firms’ exporting behavior: – Whether to export. (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 (mul­ tiple) foreign markets. – These ‘power law’ like relationships occur all over the place (Gabaix (ARE survey, 2009)). – 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. (At the heart of power laws is scale invariance.) 14 4.1 EKK (2009): Stylised Fact 1: Market Entry (averages across countries) Figure 1: Entry and Sales by Market Size Panel A: Entry of Firms FRA # firms selling in market 100000 10000 1000 CEN 100 SIE BELSWI GER ITA UNK NETSPA CAN AUT SWE CAM COTMOR POR ALGDEN TUN GRE NOR SEN FIN SAU ISRHOK AUL IRE SIN EGY SOU TOG KUW BEN TUR YUG IND NIG MAL MADBUK TAI BRA KOR ZAI JOR MAS NZE ARG HUN VEN CHI THA MEX MAU MAY SYR PAK NIA CHN IRQ INO CZE OMA CHA ANG BUL URU KEN PER COL PAN PHI ROM IRN GEE RWA ECU LIY BUR SUD SRI CUB PAR ETH DOM ZIM COS MOZ TRI BAN LIB GUA TAN ZAM GHA HON ELS VIE NIC BOLJAM PAP SOM ALB MAWUGA AFG NEP USA JAP USR 10 .1 1 10 100 market size ($ billions) 1000 10000 entry normalized by French market share Panel B: Normalized Entry 5000000 JAP USA 100000 10000 1000 CEN GER UNK AUL SWI CHN GEE ITA TAI SPABRA AUT BUL FRA NZE SWE NET ARG FIN YUG NOR SOU CZE BEL ROM ISRHOKDEN KOR MEX IND GRE VIE IRE HUN MAY SVEN AU SIN CHI CUB POR TUR COL ALG IRN EGY ECU SUD PER INO COTSYRPHI ZIM CAM PAN TRI URU MORPAK THA ALB COS KUW JORTUN TAN DOM SRI ETH ELS GUA BUKSEN BOL PAR HON ZAI OMA PAP BAN NIA IRQ MASJAM ANG LIY SOMTOG CHAMAL KEN MAD NIC UGA NEP RWABEN NIG MOZ BUR ZAM GHA LIB MAU MAW AFG SIE .1 percentiles (25, 50, 75, 95) by market ($ millions) USR CAN 1000000 1 10 100 market size ($ billions) 1000 10000 Panel C: Sales Percentiles 10 1 .1 SIE CEN CHNFRA LIY ITA UNK GER GEE IND BRA EGY IRQ ALG YUG KOR NET NIC CZE BEL BUL INOTUR IRNHUN MEX SWE SPA VEN MAW AFG SAU PAKCUB NIA TAI DEN ARGAUL FINAUT ROM NOR THA SIN GRE SYR PHI SWI PAN MOR CAN HOKSOU POR PERIRE COL ANG VIE BANTUN ETH ZAM KEN MOZ DOM KUWCHI MAY ISR NZE OMA COS JOR CAM ZAI SRI PAR COT ECU SUD PAP GUA ELS MAU MAD GHALIB TRI ZIM TAN UGA BUR MALNEP HONURU ALB MAS BUK SEN JAM NIG TOG RWABEN BOL SOM CHA USR USA JAP .01 .001 .1 1 10 100 market size ($ billions) 1000 10000 © The Econometric Society. All rights reserved. French Firms Exporting to the Seven Most Popular Destinations Country Number of exporters Fraction of exporters Belgium* (BE) 17,699 0.520 Germany (DE) 14,579 0.428 Switzerland (CH) 14,173 0.416 Italy (IT) 10,643 0.313 United Kingdom (UK) 9,752 0.287 Netherlands (NL) 8,294 0.244 United States (US) 7,608 0.224 Total Exporters 34,035 * Belgium includes Luxembourg Image by MIT OpenCourseWare. 15 French Firms Selling to Strings of Top Seven Countries Number of French exporters Export string Under independence Data BE* Model 3,988 1,700 4.417 BE-DE 863 1,274 912 BE-DE-CH 579 909 402 BE-DE-CH-IT 330 414 275 BE-DE-CH-IT-UK 313 166 297 BE-DE-CH-IT-UK-NL 781 54 505 BE-DE-CH-IT-UK-NL-US 2,406 15 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. Image by MIT OpenCourseWare. 4.2 EKK (2009): Stylised Fact 2: Sales Distributions (across all firms) Sales Distributions of French Firms Sales in market relative to mean Belgium-Luxembourg France 1000 100 10 1 .1 .01 .001 Ireland United States 1000 100 10 1 .1 .01 .001 .00001 .0001 .001 .01 .1 1 .00001 .0001 .001 .01 .1 1 Fraction of firms selling at least that much Image by MIT OpenCourseWare. 4.3 EKK (2009): Stylised Fact 3: Export Participation and Size in France Sales in France and Market Entry Sales and Markets Penetrated Sales and # Penetrating Multiple Markets 100 10 ($ millions) Average sale in France 1000 1000 ($ millions) Average sale in France 1000 110 108 123 105 12134125 423513424531 2513 541 224 15 3354 2 5345 112112322 3 4135424653 5766647758 879886 211 322 8 91997 433544 9 1 655 2 766 3 877 4 988 5 199 6 27 318 429 531642753 6492 81 753 81 64 92 753 8 164 9 275364 28 81975 39 16 438 27 5 149 6 25 36 17 47 28 1 58 39 2 69 43 765 54 876 987 99886 974 5329 187 65 4 1000 100 10 1 2 4 8 16 32 64 1 1 128 10 Minimum number of markets penetrated 100 1000 10000 10000 500000 #Firms selling to k or more market Sales and # Selling to a Market Distribution of Sales and Market Entry 1000 CHA LMB SEB DEL PAN CHA DEL LMB CHA SEB NEP LMB BRA AFG PAN SEB AFG LMBPAN NEP BRA DEL AFG PAN BRA CHA AFG DEL LMB NEP BRA SEB NEP BRA LMB AFG SEB PAN CHA DEL NEP LMB BRA AFG BRA PAN CHA AFG DEL LMB BRA LMB AFG PAN CHA DEL LMB SEB SEB NEP BRA BRA PAN AFG CHA AFG DEL LMB SEB NEP BRA LMBPAN AFG PAN CHA DEL BRA CHA AFG SEB NEP BRA LMB SEB NEP BRA AFG BRA PAN CHA AFG DEL SEB LMB SEB SEB NEP BRA AFG PAN PAN CHA DEL SEB CHA DEL NEP BRA AFG SEB NEP BRA BRA DEL 100 10 FRA 1 20 100 1000 10000 100000 500000 #Firms selling in the market France ($ millions) 10000 Percentiles (25, 50, 75, 95) in ($ millions) 2 1 1 Average sales in France 3 JAW LMB JAN DEL BRI CHA DEL DEL CHA DEL CHA LMB CHA PAN DEL PAN AFG DEL LMB LMB PAN CHA CHA BRA AFG AFG LMBAFG CHA SEB AFG NEP PAN CHA CHA DEL BRA LMB LMB NEP PAN LMB BRA PAN CHA SEB CHA NEP AFG BRA CHA DEL BRA LMB SEB AFG PAN CHA CHA TAN PAN LMB NEP DEL DEL TRY LMBPAN LMB DEL SEB NEP NEP BRA NEP AFG AFG SEB CHA SEB BRA CHA AFG DEL LMB SEB NEP SEB PAN NEP BRA LMB AFG PAN CHA PAN DEL PAN NEP LMB CHA DEL SEB NEP BRA AFG SEB BRA AFG NEP AFGSEB NEP SEB BRA BRA DEL 1000 100 10 FRA 1 .1 20 100 1000 10000 100000 500000 #Firms selling in the market Image by MIT OpenCourseWare. 4.4 EKK (2009): Stylised Fact 4: Export Intensity 16 • EKK (2009) 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?”. • The remaining slides describe some of the features of the EKK model, and how the model matches the data. I include them here just for your interest as they won’t make much sense until you’ve learned the Melitz (2003) model—see the next lecture! • Shocks: – Firm (ie j)-specific productivity draws (in country i): zi (j). This is Pareto with parameter θ. – Firm-specific demand draw αn (j). The demand they face in market −(σ−1) n is thus: Xn (j) = αn (j)f Xn Ppn , where f will be defined shortly. – Firm-specific fixed entry costs Eni (j) = εn (j)Eni M (f ), where εn (j) is the firm-specific ‘fixed exporting cost shock’, Eni is the fixed ex­ porting term that appears in Melitz (2003) or HMR (2008) (ie con­ 1−1/λ ) stant across firms). And M (f ) = 1−(1−f , which, following 1−1/λ Arkolakis (2008), is a micro-founded ‘marketing’ function that cap­ tures how much firms have to pay to ‘access’ f consumers (this is a choice variable). – EKK assume that g(α, ε) can take any form, but it needs to be the same across countries n, iid across firms, and within firms indepen­ dent from the Pareto distribution of z. • The entry condition is similar to Melitz (2003). Enter if cost cni (j) = satisfies:  1/(σ−1) ηXn Pn c ≤ c̄ni (η) ≡ m̄ σEni – Here ηn (j) ≡ wi τij zi (j) (3) αn (j) εn (j) . – And Xn is total sales in n, Pn is the price index in n, and m̄ is the (constant) markup. 17 • Integrating this over the distribution g(η) we know how much entry (mea­ sure of firms) there is: κ2 πni Xn Jni = (4) κ1 σEni • This therefore agrees well with Fact 1 (normalized entry is linear in Xn ). Figure 1: Entry and Sales by Market Size Panel A: Entry of Firms FRA # firms selling in market 100000 10000 1000 CEN 100 SIE BELSWI GER ITA UNK NETSPA CAN SWE AUT CAM COTMOR POR ALGDEN TUN GRE NOR SEN FIN SAU ISRHOK AUL IRE SIN EGY SOU TOG KUW BEN TUR YUG IND NIG MAL MADBUK TAI BRA KOR ZAI MAS NZE ARG JOR HUNVEN CHI THA MEX MAU MAY SYR PAK NIA CHN IRQ INO CZE OMA CHA ANG BUL URU KEN PER COL PAN PHI ROM IRN GEE RWA ECU LIY BUR SUD SRI CUB PAR ETH DOM ZIM COS MOZ TRI BAN LIB GUA TAN ZAM GHA HELS ON VIE NIC BOLJAM PAP SOM ALB MAWUGA AFG NEP USA JAP USR 10 .1 1 10 100 market size ($ billions) 1000 10000 entry normalized by French market share Panel B: Normalized Entry 5000000 JAP USA 100000 10000 1000 CEN GER UNK AUL SWI CHN GEE ITA TAI SPABRA AUT BUL FRA NZE SWE NET ARG FIN YUG NOR SOU CZE BEL ROM ISRHOKDEN KOR MEX IND GRE VIE VEN HUN IRE MAY SAU SIN CHI CUB POR TUR COL ALG IRN EGY ECU SUD PER INO COT PHI ZIM CAMSYR PAN TRI URU MORPAK THA ALB COS KUW JORTUN TAN DOM SRI ETH ELS GUA BOL BUK SEN PAR HON ZAI OMA PAP BAN NIA IRQ MASJAM ANG LIY SOMTOG CHAMAL KEN MAD NIC UGA NEP RWABEN NIG MOZ BUR ZAM GHA LIB MAU MAW AFG SIE .1 percentiles (25, 50, 75, 95) by market ($ millions) USR CAN 1000000 1 10 100 market size ($ billions) 1000 10000 Panel C: Sales Percentiles 10 1 .1 SIE CEN CHNFRA LIY ITA UNK GER GEE IND EGY BRA IRQ ALG YUG KOR NET NIC CZE BUL INOVEN IRNHUN MEXBEL SWE SPA MAW AFG STUR AU PAKCUB NIA TAI DEN ARGAUL FIN ROM NOR THA SIN GRE AUT SYR PHI SWI PAN MOR CAN HOKSOU POR PERIRE COL ANG VIE BANTUN ETH ZAM KEN MOZ DOM KUWCHI MAY ISR NZE OMA JCOS OR CAM ZAI SRI PAR COT ECU SUD PAP GUA MAU MAD ELS GHALIB NEP TRI ZIM TAN UGA BUR MAL HONURU ALB MAS BUK SEN JAM NIG TOG BEN RWA SOM BOL CHA USR USA JAP .01 .001 .1 1 10 100 market size ($ billions) 1000 10000 © The Econometric Society. All rights reserved. • The firm sales (conditional on entry) condition is similar to Arkolakis (2008): Xni (j) = ε 1 −  c c̄ni (η) λ(σ−1)  c c̄ni (η) −(σ−1) σEni . (5) • 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). • But the 1 −  c c̄ni (η) λ(σ−1) will cause the sales distribution to deviate from Pareto in the lower tail (also as in Figure 2). 18 Sales Distributions of French Firms Sales in market relative to mean Belgium-Luxembourg France 1000 100 10 1 .1 .01 .001 Ireland United States 1000 100 10 1 .1 .01 .001 .00001 .0001 .001 .01 .1 1 .00001 .0001 .001 .01 .1 1 Fraction of firms selling at least that much Image by MIT OpenCourseWare. • The amount of sales in France conditional on entering market n can be shown to be: "  λ/θ/  λ # αF (j) ηn (j) λ/θ/ NnF XF F (j)|n = 1 − vnF (j) ηn (j) NF F ηF (j)  −1/θ/ κ2 ¯ / NnF XF F . × vnF (j)−1/θ κ1 NF F • Since NnF /NF F is close to zero (everywhere but in France) the dependence of this on NnF is Pareto with slope −1/θe. As in Figure 3. 19 Sales in France and Market Entry Sales and Markets Penetrated Sales and # Penetrating Multiple Markets 100 10 ($ millions) Average sale in France 1000 1000 ($ millions) Average sale in France 1000 110 108 123 105 12134125 423513424531 2513 541 224 15 3354 2 5345 112112322 3 4135424653 5766647758 879886 211 322 8 91997 433544 9 1 655 2 766 3 877 4 988 5 199 6 27 318 429 531642753 6492 81 753 81 64 92 753 8 164 9 275364 28 81975 39 16 438 27 5 149 6 25 36 17 47 28 1 58 39 2 69 43 765 54 876 987 99886 974 5329 187 65 4 1000 100 10 1 2 4 8 16 32 64 1 1 128 10 Minimum number of markets penetrated 100 1000 10000 10000 500000 #Firms selling to k or more market Sales and # Selling to a Market Distribution of Sales and Market Entry 1000 100 10 FRA 1 20 100 1000 10000 100000 France ($ millions) 10000 CHA LMB SEB DEL PAN CHA DEL LMB CHA SEB NEP LMB BRA AFG PAN SEB AFG LMBPAN NEP BRA DEL AFG PAN BRA CHA AFG DEL LMB NEP BRA SEB NEP BRA LMB AFG SEB PAN CHA DEL NEP LMB BRA AFG BRA PAN CHA AFG DEL LMB BRA LMB AFG PAN CHA DEL LMB SEB SEB NEP BRA BRA PAN AFG CHA AFG DEL LMB SEB NEP BRA LMBPAN AFG PAN CHA DEL BRA CHA AFG SEB NEP BRA LMB SEB NEP BRA AFG BRA PAN CHA AFG DEL SEB LMB SEB SEB NEP BRA AFG PAN PAN CHA DEL SEB CHA DEL NEP BRA AFG SEB NEP BRA BRA DEL Percentiles (25, 50, 75, 95) in ($ millions) 2 1 1 Average sales in France 3 JAW LMB JAN DEL BRI CHA DEL DEL CHA DEL CHA LMB CHA PAN DEL PAN AFG DEL LMB LMB PAN CHA CHA BRA AFG AFG LMBAFG CHA SEB AFG NEP PAN CHA CHA DEL BRA LMB LMB NEP PAN LMB BRA PAN CHA SEB CHA NEP AFG BRA CHA DEL BRA LMB SEB AFG PAN CHA CHA TAN PAN LMB NEP DEL DEL TRY LMBPAN LMB DEL SEB NEP NEP BRA NEP AFG AFG SEB CHA SEB BRA CHA AFG DEL LMB SEB NEP SEB PAN NEP BRA LMB AFG PAN CHA PAN DEL PAN NEP LMB CHA DEL SEB NEP BRA AFG SEB BRA AFG NEP AFGSEB NEP SEB BRA BRA DEL 1000 100 10 FRA 1 .1 20 500000 #Firms selling in the market 100 1000 10000 100000 500000 #Firms selling in the market Image by MIT OpenCourseWare. 20