Quality and Gravity in International Trade

Transcription

1 Quality and Gravity in International Trade FIW-Workshop "International Economics" Lisandra Flach Florian Unger University of Munich University of Munich 14. Juni 2016 Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 1 / 26

2 Introduction Motivation Quality in International Trade Quality sorting in international trade (Baldwin & Harrigan, 2011; Kugler & Verhoogen, 2012, Manova & Zhang, 2012, Flach, 2016, Antoniades, 2015) Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 2 / 26

3 Introduction Motivation Quality in International Trade Quality sorting in international trade (Baldwin & Harrigan, 2011; Kugler & Verhoogen, 2012, Manova & Zhang, 2012, Flach, 2016, Antoniades, 2015) Quality and gravity in international trade (Hallak, 2010; Feenstra & Romalis, 2014) Quality and distance e ect on exports? Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 2 / 26

4 Introduction Motivation Quality in International Trade Quality sorting in international trade (Baldwin & Harrigan, 2011; Kugler & Verhoogen, 2012, Manova & Zhang, 2012, Flach, 2016, Antoniades, 2015) Quality and gravity in international trade (Hallak, 2010; Feenstra & Romalis, 2014) Quality and distance e ect on exports? Martin & Mayneris (2015): distance with (almost) no e ect on high-end variety exports Ferguson (2012): R&D intensive industries less sensitive to trade costs Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 2 / 26

5 Introduction Motivation Quality in International Trade Quality sorting in international trade (Baldwin & Harrigan, 2011; Kugler & Verhoogen, 2012, Manova & Zhang, 2012, Flach, 2016, Antoniades, 2015) Quality and gravity in international trade (Hallak, 2010; Feenstra & Romalis, 2014) Quality and distance e ect on exports? Martin & Mayneris (2015): distance with (almost) no e ect on high-end variety exports Ferguson (2012): R&D intensive industries less sensitive to trade costs This project: E ect of quality di erentiation on elasticity of trade ows with respect to variable and xed costs? gravity equation of trade? Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 2 / 26

6 Quality and Gravity Introduction Overview Our contribution: E ect of distance on trade lower in industries with high quality di erentiation (export ows and extensive margin) Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 3 / 26

7 Quality and Gravity Introduction Overview Our contribution: E ect of distance on trade lower in industries with high quality di erentiation (export ows and extensive margin) Theory: Derivation of gravity equations Firm heterogeneity (Chaney, 2008; Melitz & Redding, 2014) Endogenous quality choice (Sutton, 2012; Kugler & Verhoogen, 2012) Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 3 / 26

8 Quality and Gravity Introduction Overview Our contribution: E ect of distance on trade lower in industries with high quality di erentiation (export ows and extensive margin) Theory: Derivation of gravity equations Firm heterogeneity (Chaney, 2008; Melitz & Redding, 2014) Endogenous quality choice (Sutton, 2012; Kugler & Verhoogen, 2012) Empirics: Estimation of gravity equations Aggregate trade data: COMTRADE, NBER-UN ) trade ows Firm-level data: Brazil, SECEX ) extensive margin Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 3 / 26

9 Quality and Gravity Introduction Overview Our contribution: E ect of distance on trade lower in industries with high quality di erentiation (export ows and extensive margin) Theory: Derivation of gravity equations Firm heterogeneity (Chaney, 2008; Melitz & Redding, 2014) Endogenous quality choice (Sutton, 2012; Kugler & Verhoogen, 2012) Empirics: Estimation of gravity equations Aggregate trade data: COMTRADE, NBER-UN ) trade ows Firm-level data: Brazil, SECEX ) extensive margin Parameter estimation: E ects of trade liberalization With vertical di erentiation: e ects on exports by 14% lower Heterogeneous e ects across industries: reduction between 2% and 31% Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 3 / 26

10 Introduction Overview Intuition Firm level: endogenous quality investment Increase in demand Endogenous sunk costs Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 4 / 26

11 Introduction Overview Intuition Firm level: endogenous quality investment Increase in demand Endogenous sunk costs Industry level: degree of quality di erentiation High quality di erentiation, high returns on investment Highly productive rms: large quality investment ) Low productivity rms face stronger competition Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 4 / 26

12 Introduction Overview Intuition Firm level: endogenous quality investment Increase in demand Endogenous sunk costs Industry level: degree of quality di erentiation High quality di erentiation, high returns on investment Highly productive rms: large quality investment ) Low productivity rms face stronger competition Aggregate level: e ect of trade liberalization Lower trade barrier: entry of low productivity rms High quality di erentiation: entrants relatively small ) Smaller e ect on extensive margin and export ows Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 4 / 26

13 Introduction Overview Outline 1 Theoretical model 2 Estimation of gravity equations 3 Parameter estimation 4 Conclusion Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 5 / 26

14 Theoretical model Demand side Utility function N countries, i 2 N Homogenous good j = 0, di erentiated goods industries with j 1 Upper-tier Cobb-Douglas utility: U = J β j log X j, j=0 Sub-utility (CES) for di erentiated goods: J β j = 1, β j 0 (1) j=0 X j = " Z ω2ω j q j (ω) x j (ω) # σ j σ j 1 σ j 1 σ j dω, σ j > 1, j 1 (2) q j (ω): quality of variety ω; x j (ω): quantity of variety ω Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 6 / 26

15 Theoretical model Demand side Optimal demand One factor of production: labor L (mobile across industries, immobile across countries) Consumption on goods in industry j: Y j = β j Y = β j L Homogenous good sector: w j = w = 1 Demand for one variety ω: x j (ω) = A j q j (ω) σ j 1 p j (ω) σ j, A j = Y j P σ j 1 j (3) Quality-adjusted aggregate price: P j = " Z ω2ω j 1 pj (ω) 1 σj 1 σ j dω# (4) q j (ω) Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 7 / 26

16 Theoretical model Firm s maximization problem Supply side Quality investment Endogenous sunk costs: f q j (ω) = q j(ω) α j α j : convexity of investment costs Production costs: l j (ω) = f + q j(ω) θ j x j (ω) 0 < θ j < 1: sensitivity of marginal costs with respect to quality ϕ α j Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 8 / 26

17 Theoretical model Firm s maximization problem Supply side Quality investment Endogenous sunk costs: f q j (ω) = q j(ω) α j α j : convexity of investment costs Production costs: l j (ω) = f + q j(ω) θ j x j (ω) 0 < θ j < 1: sensitivity of marginal costs with respect to quality Pro ts of rm in country i and industry j: π ij = " N N π nij = 1 fxnij >0g p nij x nij n=1 n=1 ϕ α j θ q j nij τ ni ϕ x nij 1 α j q α j nij f ni # (5) f ni > 0: export xed costs, τ ni 1, τ ii = 1 Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 8 / 26

18 Theoretical model Supply side The role of quality di erentiation Quality-price ratio: q nij p nij = 1 θ j 1 θj A 1 θ j nj Sales relative to marginal exporter: σj 1 αj +1 θ j 1 ϕ αj α j (σ j 1)(1 θ j) σ j τ ni s nij (ϕ) s nij (ϕnij ) = ϕ ϕnij α j(σ j 1) α j (σ j 1)(1 θ j) Scope for vertical product di erentiation: Firm behavior Derivation 1 α q α j j nij (ϕ) = 1 θ j σ j 1 s nij (ϕ) α j σ j Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 9 / 26

19 Theoretical model Supply side The role of quality di erentiation Quality-price ratio: q nij p nij = 1 θ j 1 θj A 1 θ j nj Sales relative to marginal exporter: σj 1 αj +1 θ j 1 ϕ αj α j (σ j 1)(1 θ j) σ j τ ni s nij (ϕ) s nij (ϕnij ) = ϕ ϕnij α j(σ j 1) α j (σ j 1)(1 θ j) Scope for vertical product di erentiation: Firm behavior Derivation 1 α q α j j nij (ϕ) = 1 θ j σ j 1 s nij (ϕ) α j σ j If scope for vertical di erentiation is high (low α), high productivity rms: invest relatively more in (price-adjusted) quality, are relatively larger compared to low productivity rms. ) Low productivity rms face stronger competition Flach & Unger (LMU Munich) Quality and Gravity (University of Munich14. Juni University 2016 of Munich) 9 / 26

20 Gravity equation Theoretical model Gravity and predictions Gravity equation: S nij = 1 G ij ϕnij Z g ij (ϕ) M ij s nij (ϕ) dϕ (6) 1 G ij ϕiij ϕnij 1 G ij ϕnij Pareto distribution of productivity: g ij (ϕ) = ξ j ϕ ξ j 1 Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of10 Munich) / 26

21 Gravity equation Theoretical model Gravity and predictions Gravity equation: S nij = 1 G ij ϕnij Z g ij (ϕ) M ij s nij (ϕ) dϕ (6) 1 G ij ϕiij ϕnij 1 G ij ϕnij Pareto distribution of productivity: g ij (ϕ) = ξ j ϕ ξ j 1 Gravity equation with Pareto distributed productivity: S nij = S ij Ξ ij Y n P 1 σ j n! ξ j σ j 1 τ ξ j ni Exporter-industry FE: S ij Ξ ij ; Importer-industry FE: Gravity Estimation α j(σ j 1) ξ j[α j (σ j 1)(1 θ j)] α j(σ j 1) fni (7) Y n P 1 σ j n ξ j σ j 1 Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of10 Munich) / 26

22 Prediction 1 Theoretical model Gravity and predictions E ect of xed trade costs on aggregate trade ows: d ln S nij = 1 d ln f ni ξ j σ j 1 {z } Chaney (2008) + ξ j 1 θ j α j {z } Quality e ect (8) Scope for vertical product di erentiation: 1 α j q α j nij (ϕ) s nij (ϕ) = 1 θ j α j σ j 1 σ j Prediction 1: The elasticity of trade ows with respect to xed trade costs is lower in industries with high scope for vertical di erentiation. Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of11 Munich) / 26

23 Prediction 2 Theoretical model Gravity and predictions E ect of xed trade costs on share of exporters: d ln γ nij ξ j = + ξ j 1 θ j d ln f ni σ j 1 α j {z } {z } Chaney (2008) Quality e ect (9) Scope for vertical product di erentiation: Back to data 1 α j q α j nij (ϕ) s nij (ϕ) = 1 θ j α j σ j 1 σ j Prediction 2: The elasticity of the share of exporters with respect to xed trade costs is lower in industries with high scope for vertical di erentiation. Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of12 Munich) / 26

24 Data sources Empirical analysis Data and Statistics 1 Trade data Aggregate data: Bilateral world trade ows by SITC 4-digit from COMTRADE and NBER-UN Brazilian rm-level data from SECEX (Foreign Trade Secretariat) Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of13 Munich) / 26

25 Data sources Empirical analysis Data and Statistics 1 Trade data Aggregate data: Bilateral world trade ows by SITC 4-digit from COMTRADE and NBER-UN Brazilian rm-level data from SECEX (Foreign Trade Secretariat) 2 Industry-level degree of quality di erentiation (4-digit) "Quality ladder" from Khandelwal (2010) Quality ladder "ladder increases if price can rise without losing market share." R&D intensity from Kugler & Verhoogen (2012) Gollop-Monahan (1991) index: horizontal di erentiation R&D intensity Gollop Index Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of13 Munich) / 26

26 Data sources Empirical analysis Data and Statistics 1 Trade data Aggregate data: Bilateral world trade ows by SITC 4-digit from COMTRADE and NBER-UN Brazilian rm-level data from SECEX (Foreign Trade Secretariat) 2 Industry-level degree of quality di erentiation (4-digit) "Quality ladder" from Khandelwal (2010) Quality ladder "ladder increases if price can rise without losing market share." R&D intensity from Kugler & Verhoogen (2012) Gollop-Monahan (1991) index: horizontal di erentiation 3 Variable and xed trade costs R&D intensity Gollop Index Variable: Tari data from TRAINS-WTI Fixed: Bilateral distance and language from CEPII and administrative barriers from WB "Trading Across Borders". Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of13 Munich) / 26

27 Summary statistics Empirical analysis Data and Statistics Table: Summary statistics Variable Obs Mean Std. Dev. Sample for the analysis using bilateral world trade data, year 2000 ln S nij 420, ln Dist ni 420, Language ni 420, ladder j 420, R&D intensity 88, Gollop Monahan (GM) index 88, ln t_border ni 374, ln t_doc ni 425, Sample for the analysis of the share of Brazilian rms, year 2000 Share of rms γ nj 60, ln Dist n 60, ladder j 60, R&D intensity 14, GollopMonahan index 14, Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of14 Munich) / 26

28 Empirical strategy Empirical analysis Estimation of gravity equations Log-linearized gravity equation: ln S nij = ξ j ln τ ni + + ln Sij Ξ ij 1 + ξ j σ j Test of Prediction 1: β 1 < 0, β 2 > 0 Gravity ξ j σ j 1 + ξ j(1 θ j) α j 1 ln Y n P 1 σ j n ln f ni ln S nij = β 1 fixedcosts ni + β 2 fixedcosts ni ln ladder j + x nij + ρ ij + µ nj + ε nij fixedcosts ni = e.g. language, bilateral distance (controlling for variable trade costs) ladder j = degree of quality di erentiation in industry j x nij = gravity covariates, tari s ρ ij and µ nj = exporter-industry and importer-industry xed e ects Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of15 Munich) / 26

29 Empirical analysis Estimation of gravity equations Results: distance and aggregate trade ows Table: Fixed costs and aggregate trade ows Dependent variable ln S nij (1) (2) (3) (4) (5) (6) ln Dist ni *** *** *** (0.0221) (0.0284) (0.0284) ln Dist ni ladder j *** *** 0.100*** 0.105*** 0.100*** 0.105*** ( ) ( ) (0.0122) (0.0122) (0.0122) (0.0122) τ nij ** *** ** ** (0.220) (0.206) (0.337) (0.339) τ nij ladder j (0.518) (0.554) Constant yes yes yes yes yes yes Industry-importer xed e ects yes yes yes yes yes yes Industry-exporter xed e ects yes yes yes yes yes yes Importer-exporter xed e ects no yes no yes no yes Observations 420, , , , , ,039 R-squared Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by importer-exporter pair. Estimation results Further proxies for xed costs Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of16 Munich) / 26

30 Empirical analysis Estimation of gravity equations Empirical strategy Log-linearized version for share of exporters: ln γ nij = ξ j ln τ ni ξ j 1 σ j 1 Test of Prediction 2: β 1 < 0, β 2 > 0 1 θ j fni α j ln f nn ln γ nj = β 1 fixedcosts n + β 2 fixedcosts n ln ladder j + ν j + ε nj fixedcosts n = e.g. bilateral distance between Brazil and destination n (controlling for tari s and additive trade costs) ladder j = degree of quality di erentiation in industry j v j = industry xed e ects Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of17 Munich) / 26

31 Empirical analysis Estimation of gravity equations Results: distance and share of exporters Table: Fixed costs and the share of exporters Dependent variable: γ nj (1) (2) (3) (4) (5) (6) ln Dist n *** *** *** ( ) ( ) ( ) ln Dist n ladder j *** *** ** *** ** *** ( ) ( ) ( ) ( ) ( ) ( ) τ nj (0.0277) (0.0277) (0.0202) (0.0420) τ nj ladder j (0.0348) (0.0221) Constant yes yes yes yes yes yes Importer xed e ects no yes no yes no yes Industry xed e ects yes yes yes yes yes yes Observations 60,032 60,032 30,646 30,646 30,646 30,646 R-squared Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by 4-digit industry. Further proxies for xed costs Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of18 Munich) / 26

32 Robustness checks Empirical analysis Estimation of gravity equations R&D intensity and the GM index for horizontal di erentiation: Alternative measure of vertical di erentiation: R&D intensity from Kugler & Verhoogen (2012) Controlling for horizontal di erentiation: GM index ) Interaction term is + for R&D intensity and - for GM Estimation results Comparison to Chaney Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of19 Munich) / 26

33 Robustness checks Empirical analysis Estimation of gravity equations R&D intensity and the GM index for horizontal di erentiation: Alternative measure of vertical di erentiation: R&D intensity from Kugler & Verhoogen (2012) Controlling for horizontal di erentiation: GM index ) Interaction term is + for R&D intensity and - for GM Estimation results Comparison to Chaney Variable trade costs using panel data From theory: Estimation: d ln S nij d ln τ ni = ξ j (no e ect of quality di erentiation!) ln S nijt = β 1 ln τ nijt + β 2 ln τ nijt ln ladder j + υ nij + ν t + ε nijt with β 1 < 0 and β 2 not signi cant. Tari data Estimation results Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of19 Munich) / 26

34 Empirical analysis Estimation of gravity equations Robustness checks Estimation strategy: Poisson Maximum Likelihood Product weights and income per capita: Alchian-Allen e ect and home market e ect Alternative proxies for xed costs: Common language from CEP II Administrative barriers from the World Bank Trading Across Borders: Time (importer and exporter) spent for documentary compliance t_doc ni and border compliance t_border ni "The Tip of the Iceberg": Additive trade costs as in Irarrazabal, Moxnes and Opromolla (2015) Poisson Income, weights Proxies for xed costs Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of20 Munich) / 26

35 Parameter estimation Parameter estimation: 3-step procedure E ects of trade liberalization with and without quality? 3 Unknowns: Pareto shape parameter ξ j, Elasticity of substitution σ j, R&D intensity 1 θ j α j Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of21 Munich) / 26

36 Parameter estimation Parameter estimation: 3-step procedure E ects of trade liberalization with and without quality? 3 Unknowns: Pareto shape parameter ξ j, Elasticity of substitution σ j, R&D intensity 1 3 Steps of estimation: 1 Trade elasticity of exports: 2 Distance elasticity of exports: β 1 = d ln S nij d ln f ni = 1 α j θ j d ln S nij d ln τ ni = ξ j ) Crozet & Koenig (2010) ξ j σ j 1 + ξ j(1 θ j ) α j 3 R&D intensity (Kugler & Verhoogen, 2012): β 2 = σ j 1 σ j 1 θ j α j ) σ j = 1+β 1 +ξ j 1+β 1 +ξ j β 2 Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of21 Munich) / 26

37 Parameter estimates Parameter estimation 1 θ Industry ξ j σ j j α j Builder s carpentry and joinery Newsprint Printing paper and writing paper Paper and paperboard Packing containers, box les of paper Paper pulp, paper, paperboard Textile yarn, synthetic bres, not for retail Machinery, equipment for heating and cooling Filtering, purifying machinery, for liquids, gases Parts of purifying and ltering machinery Valves for pipes boiler shells Shaft, crank, bearing housing, pulley Precious jewellery Sound recording tape, discs Orthophaedic appliances, hearing aids Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of22 Munich) / 26

38 Parameter estimation E ects of trade liberalization Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of23 Munich) / 26

39 Parameter estimation Relative e ects of trade liberalization Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of24 Munich) / 26

40 Parameter estimation E ects of trade liberalization With quality di erentiation: Smaller e ects of trade liberalization (10% decrease xed trade costs) Export ows by industry: on average by 14% lower Share of exporters: on average by 6% lower Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of25 Munich) / 26

41 Parameter estimation E ects of trade liberalization With quality di erentiation: Smaller e ects of trade liberalization (10% decrease xed trade costs) Export ows by industry: on average by 14% lower Share of exporters: on average by 6% lower Heterogeneous e ects across industries: Exports: between -2% and -31% Extensive margin: between -0.9% and -11% Correlation between R&D intensity and relative trade e ect: Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of25 Munich) / 26

42 Parameter estimation E ects of trade liberalization With quality di erentiation: Smaller e ects of trade liberalization (10% decrease xed trade costs) Export ows by industry: on average by 14% lower Share of exporters: on average by 6% lower Heterogeneous e ects across industries: Exports: between -2% and -31% Extensive margin: between -0.9% and -11% Correlation between R&D intensity and relative trade e ect: Result: Gravity models without quality di erentiation overestimate the e ects of trade liberalization, especially in industries with high scope for vertical di erentiation and large rm heterogeneity. Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of25 Munich) / 26

43 Conclusion Summary E ect of distance on trade lower in industries with high scope for quality di erentiation Theory: Derivation of gravity equations Endogenous quality Firm heterogeneity Empirics: Estimation of gravity equations Aggregate trade ows: COMTRADE Extensive margin: Brazilian rm-level data Estimation: E ects of trade liberalization With vertical di erentiation: e ects on exports by 14% lower Heterogeneous e ects across industries: reduction between 2% and 31% Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

44 Appendix Optimal rm behavior Optimal price: p nij (ϕ) = Quality level: q nij = Zero-pro t condition: σ j σ j 1 τ ni q θ j nij ϕ 1 θ j Anj σj σ j 1 σj 1 1 σj τni α j (σ j 1)(1 θ j) ϕ π nij (ϕ nij ) = 0, s nij(ϕ nij ) = Free entry condition: α j σ j f ni α j 1 θ j σj 1 (10) N Z π nij (ϕ)g ij (ϕ) = f Ei (11) n=1 ϕnij Role of quality Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

45 Appendix Scope for vertical product di erentiation: Firm sales: s nij (ϕ) = " 1 θ j 1 θj A α j σ j 1 nj σj σ j 1 σ # j 1 θj 1 α j τnij αj α j (σ j 1)(1 θ j) ϕ Investment costs: 1 α j q α j nij (ϕ) = 1 α j α σj σj j τnij 1 σj α 1 θ j (σ j 1)(1 θ j Anj j) σ j 1 ϕ Scope for vertical product di erentiation: 1 α j q α j nij s nij (ϕ) = 1 θ j σ j 1 α j σ j Back to Model Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

46 Appendix Gravity equation with Pareto distribution S nij = S ij Ξ ij Y n P 1 σ j n! ξ j σ j 1 τ ξ j ni f α j(σ j 1) ξ j[α j (σ j 1)(1 θ j)] α j(σ j 1) ni Total sales of industry j in country i: S ij = n S nij! ξ j α j(σ j 1) ξ j[α j (σ j 1)(1 θ σ j 1 j)] α j(σ j 1) Ξ ij = n Y nj P 1 σ j nj τ ξ j ni Log-linearized version of gravity equation: Sij ln S nij = ln + ξ j σ j 1 ln Y n Gravity Ξ ij f ni P 1 σ j n! ξ j ln τ ni + α j σ j 1 ξ j αj σ j 1 1 θ j α j σ j 1 ln f ni Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

47 Appendix Comparison to Chaney (2008) E ect of xed trade costs on share of exporters: d ln γ nij ξ j = + ξ j 1 θ j d ln f ni σ j 1 α j {z } {z } Chaney (2008) Quality e ect Comparison vertical vs. horizontal di erentiation: Vertical (low α) Horizontal (low σ) Degree competition high low New entrants relatively small relatively large E ect of trade weak on EM strong on EM Robustness checks Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

48 Welfare Appendix Price index: P j = Welfare: N i=1 M nij R ϕ nij 1 pnij (ϕ) 1 σj 1 σ j µnij (ϕ)dϕ q nij (ϕ) W j = P 1 = Ω nnj β j L i 1 σ j 1 ϕ nnj (12) 1 θ j 1+αj αj θj (σj 1)(1 θj) α σj Ω iij = 1 θ j 1 α j α j (1 θ j)(σ j 1) α j(σ j 1) j σ j α j σ j f nn Domestic cuto productivity: with χ j = ϕ ξ j iij = χ j n α j(σ j 1) ξ j [α j (σ j 1)(1 θ j)] α j(σ j 1) ξ j[α j (σ j 1)(1 θ j)] f ni τ ξ j fni α j(σ j 1) f ni Ei f nn Welfare e ect (13) Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

49 Appendix Gollop-Monahan measure of horizontal di erentiation Gollop-Monahan (1991) measure: GM k = ω jt j,k,t i s ijkt 2 s ikt! 1 2 i = inputs, j = plants, k = 5-digit industries, t = years s ijkt = expenditure share on input i of plant j in industry k and year t s ikt = average expenditure share measure of dissimilarity of input mixes ω jt = share of revenues Back to data Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

50 Appendix Khandelwal measure and quality di erentiation Khandelwal-type expression of sales: Log quality-price: ln s nij (ϕ) = ln A nj + σ j 1 ln q nij ln p nij σj ln q nij ln p nij = (1 θ j)[ln(1 θ j)+ln A nj]+(θ j 1 α j) ln σ j 1 +α j(ln ϕ ln τ nij) α j (σ j 1)(1 θ j) Quality ladder depends on: Ladder j (α j ) = with Ladder j(α j ) α j < 0 Back to data α j σ j 1 α j σ j 1 1 θ j Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

51 Appendix Results: Fixed costs and aggregate trade ows Table: Aggregate trade ows, R&D intensity and horizontal di erentiation Dependent variable ln S nij (1) (2) (3) (4) (5) (6) ln Dist ni *** *** *** *** (0.0319) (0.0365) (0.0355) (0.0406) ln Dist ni R&D Intensity *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ln Dist ni GM Index *** *** *** (0.0316) (0.0473) (0.0466) Constant yes yes yes yes yes yes Industry xed e ects yes no no yes no no Importer xed e ects yes no no yes no no Exporter xed e ects yes no no yes no no Industry-importer xed e ects no yes yes no yes yes Industry-exporter xed e ects no yes yes no yes yes Importer-exporter xed e ects no no yes no no yes Observations 88,789 88,789 88,789 88,789 88,789 88,789 R-squared Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by importer-exporter pair. Back to estimation Robustness checks Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

52 Appendix Results: Fixed costs and share of exporters Table: Share of exporters, R&D intensity and horizontal di erentiation Dependent variable: γ nj (1) (2) (3) (4) ln Dist n ** (0.0119) (0.0130) ln Dist n R&D Intensity *** *** *** *** ( ) ( ) ( ) ( ) ln Dist n * GM Index *** *** (0.0133) (0.0134) Constant yes yes yes yes Destination country xed e ects no no yes yes Product xed e ects yes yes yes yes Observations 13,990 13,990 13,990 13,990 R-squared Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by 4-digit industry. Robustness checks Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

53 Appendix Results: Alternative xed costs and aggregate trade ows Table: Aggregate trade ows, alternative proxies for xed costs Dependent variable ln S nij (1) (2) (3) (4) (5) (6) ln t_border ni *** (0.0269) ln t_border ni ladder j ** *** ( ) ( ) ln t_doc ni *** (0.0284) ln t_doc ni ladder j *** *** ( ) ( ) language ni 1.072*** (0.0768) language ni ladder j *** *** (0.0112) (0.0104) Constant yes yes yes yes yes yes Industry-importer xed e ects yes yes yes yes yes yes Industry-exporter xed e ects yes yes yes yes yes yes Importer-exporter xed e ects no yes no yes no yes Observations 374, , , , , ,120 R-squared Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by importer-exporter pair. Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

54 Appendix Results: Alternative xed costs and share of exporters Table: Share of rms, alternative proxies for xed costs Dependent variable γ nj (1) (2) (3) (4) ln t_border n *** ( ) ln t_border n ladder j ** * ( ) ( ) ln t_doc n *** ( ) ln t_doc n ladder j *** *** ( ) ( ) Constant yes yes yes yes Destination country xed e ects no yes no yes Industry xed e ects yes yes yes yes Observations 43,802 43,802 42,647 42,647 R-squared Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by importer-exporter pair. Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

55 Appendix Results: Income and weights for aggregate trade ows Table: Aggregate trade ows, alternative proxies for xed costs Dependent variable ln S nij (1) (2) (3) (4) ln Dist ni ladder j *** *** ( ) ( ) ln Dist ni R&D *** *** ( ) ( ) ln Dist ln kg_value nij *** *** ( ) ( ) ln CGDP ni ladder j -1,993 (1,711) ln CGDP ni R&D *** ( ) Constant yes yes yes yes Industry-importer xed e ects yes yes yes yes Industry-exporter xed e ects yes yes yes yes Importer-exporter xed e ects yes yes yes yes Importer xed e ects no no no no Industry xed e ects no no no no Observations 317,771 67, ,107 91,872 R-squared Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by importer-exporter pair. Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

56 Appendix Results: Income and weights for share of rms Table: Share of rms, alternative proxies for xed costs Dependent variable γ nj (1) (2) (3) (4) ln Dist ni ladder j *** *** ( ) ( ) ln Dist ni R&D *** *** ( ) ( ) ln Dist ln kg_value nij 7.95e e-05 (5.63e-05) ( ) ln CGDP ni ladder j ( ) ln CGDP ni R&D ( ) Constant yes yes yes yes Industry-importer xed e ects no no no no Industry-exporter xed e ects no no no no Importer-exporter xed e ects no no no no Importer xed e ects yes yes yes yes Industry xed e ects yes yes yes yes Observations 55,845 13,095 59,681 13,889 R-squared Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by importer-exporter pair. Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

57 Appendix Summary statistics tari data Table: Summary statistics Sample for the analysis of variable trade costs using panel data Variable Obs Mean Std. Dev. ln S nijt 798, ladder j 798, τ nijt 798, Robustness checks Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

58 Appendix Results: Variable trade costs and aggregate trade ows Dependent variable: ln S nijt (1) (2) (3) (4) ln τ nijt *** *** ** *** (0.0555) (0.0537) (0.170) (0.0992) ln τ nijt ladder j (0.0833) ln τ nijt ln ladder j (0.139) Observations 798, , , ,131 R-squared Number of nij groups 310, , , ,971 Constant yes yes yes yes Importer-Exporter-Industry FE yes yes yes yes Year FE no yes yes yes Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. The errors clustered by importer-exporter and 4-digit industry. Robustness checks Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

59 Appendix Results using Poisson PML: Fixed costs and aggregate trade ows Table: Zeros and trade: Esimations with PPML Dependent variable S nij (1) (2) (3) (4) ln Dist ni *** *** *** *** (0.109) (0.117) (0.0427) (0.0500) ln Dist ni R&D j Intensity ** ** (0.0297) (0.0292) ln Dist ni *GM Index (0.193) ln Dist ni ln ladder j * (0.0341) ln Dist ni ladder j ** (0.0163) Constant yes yes yes yes Industry SITC 3-digit xed e ects yes yes no no Industry SITC 2-digit xed e ects no no yes yes Importer xed e ects yes yes yes yes Exporter xed e ects yes yes yes yes Observations 243, , , ,829 Notes: * signi cant at 10%; ** signi cant at 5%; *** signi cant at 1%. Robustness checks Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

60 Appendix Welfare e ects of trade liberalization E ect of xed trade costs on welfare: d ln W = 1 1 d ln f ni ξ j σ j θ! j α j λ nij (14) Trade share of goods from industry j and country i to country n: λ nij = S nij S ij = α j (σ j 1)(1 θ ξj j) fni α j(σ j 1) f nn f ni τ ξ j ni α j (σ j 1)(1 θ ξj j) fni α j(σ j 1) n f nn f ni τ ξ j ni (15) Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

61 Appendix Welfare e ects of trade liberalization E ect of xed trade costs on welfare: d ln W = 1 1 d ln f ni ξ j σ j θ! j α j λ nij (14) Trade share of goods from industry j and country i to country n: λ nij = S nij S ij = α j (σ j 1)(1 θ ξj j) fni α j(σ j 1) f nn f ni τ ξ j ni α j (σ j 1)(1 θ ξj j) fni α j(σ j 1) n f nn f ni τ ξ j ni (15) Result: Welfare gains from trade liberalization are lower in industries with a high scope for vertical di erentiation. Welfare Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

62 Appendix Welfare e ects by industry Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26

63 Appendix Relative welfare e ects compared to benchmark Flach & Unger (LMU Munich) Quality and Gravity (University of Munich 14. Juni University 2016 of26 Munich) / 26