ESTIMATING THE PRODUCTIVITY GAINS FROM IMPORTING

Transcription

1 1 ESTIMATING THE PRODUCTIVITY GAINS FROM IMPORTING Joaquin Blaum, Claire Lelarge, Michael Peters SCID IGC Conference, November 2014

2 INTRODUCTION Large fraction of world trade is accounted for by firms sourcing intermediate inputs from abroad Trade in inputs benefits domestic consumers: Better quality / new inputs reduce firms unit cost This lowers price of domestically produced goods Question: by how much? This paper: use theory and microdata to answer that question.

3 3 WHAT WE DO Study class of firm-based models of importing:

4 3 WHAT WE DO Study class of firm-based models of importing: Heterogeneous firms

5 3 WHAT WE DO Study class of firm-based models of importing: Heterogeneous firms CES between domestic and foreign inputs

6 3 WHAT WE DO Study class of firm-based models of importing: Heterogeneous firms CES between domestic and foreign inputs Many heterogeneous sourcing countries

7 3 WHAT WE DO Study class of firm-based models of importing: Heterogeneous firms CES between domestic and foreign inputs Many heterogeneous sourcing countries Love of variety + quality channel

8 3 WHAT WE DO Study class of firm-based models of importing: Heterogeneous firms CES between domestic and foreign inputs Many heterogeneous sourcing countries Love of variety + quality channel Sufficiency result: Simple formula for aggregate gains from trade Can be evaluated given the microdata on value added and firms domestic expenditure shares Quantitative exercise: Can a model calibrated to sales data predict the right gains? Welfare

9 RELATED LITERATURE Sufficient statistics to evaluate trade policy: Arkolakis, Costinot, Rodriguez-Clare (2012) Recent literature on measuring productivity gains from importing: Reduced-form analysis of trade reforms: Amiti, Konings (2007), Goldberg, Khandelwal, Pavcnik, Topalova (2010) Structural approach: Halpern, Koren, Szeidl (2012), Gopinath, Neiman (2013) GE model of importing: Antràs, Fort, Tintelnot (2014)

10 5 OUTLINE FOR TODAY 1. Firm Problem: Domestic spending and unit costs 2. Embed in Macro Model: Real Wage & Welfare 2.1 Sufficiency result 2.2 Bias compared to aggregative model 3. Application to French data: 3.1 Estimation of trade elasticity 3.2 Aggregate gains in France 3.3 Calibration exercise

11 6 A MODEL OF IMPORTING: SETUP Production structure where q c is country quality y = ϕk α l 1 α γ x γ ( x = x ε 1 ε D + x ε 1 ε I x D = η (q D,ϕ)z D ( x I = ) ε ε 1 (η (q c,ϕ)z c ) ρ 1 ρ dc c Σ η (q,ϕ) denotes the firm-specific quality flow Σ is the firms sourcing strategy ) ρ ρ 1 Output market: no restrictions for now // Ext margin: fixed costs to importing

12 7 HETEROGENEITY Country-level: quality (q c ), price (p c ) and fixed costs ( f c ) Firm-level: productivity (ϕ) and fixed cost ( f c ) This structure nests existing work (Koren, Halpern, Szeidl (2011), Gopinath Neiman (2013)) Details

13 8 IMPORTING AND UNIT COST Unit cost given by: UC = 1 ϕ Q(Σ,ϕ)γ r α w (1 α γ) where and Q(Σ,ϕ) = ((p D /η D ) 1 ε + A(Σ,ϕ) 1 ε) 1 ε 1 ( ) 1 A(Σ,ϕ) = (p c /η c (ϕ)) 1 ρ 1 ρ dc c Σ Firms problem

14 IMPORTING AND UNIT COST (CTD) Q(Σ,ϕ) depends on prices, qualities, sourcing strategy... Details 9

15 IMPORTING AND UNIT COST (CTD) Q(Σ,ϕ) depends on prices, qualities, sourcing strategy... But: Q(Σ,ϕ) = p D η D s D (Σ,ϕ) 1 ε 1 Details 9

16 IMPORTING AND UNIT COST (CTD) Q(Σ,ϕ) depends on prices, qualities, sourcing strategy... But: Hence: Q(Σ,ϕ) = p D η D s D (Σ,ϕ) 1 ε 1 UC = 1/ϕ (s }{{} D (Σ,ϕ)) γ ε 1 (p }{{} D /η D ) γ r α w (1 α γ) }{{} Exogenous PE Gains GE Details 9

17 IMPORTING AND UNIT COST (CTD) Q(Σ,ϕ) depends on prices, qualities, sourcing strategy... But: Hence: Q(Σ,ϕ) = p D η D s D (Σ,ϕ) 1 ε 1 UC = 1/ϕ (s }{{} D (Σ,ϕ)) γ ε 1 (p }{{} D /η D ) γ r α w (1 α γ) }{{} Exogenous PE Gains GE UC reduction relative to autarky (holding prices fixed) is observable Details 9

18 IMPORTING AND UNIT COST (CTD) Q(Σ,ϕ) depends on prices, qualities, sourcing strategy... But: Hence: Q(Σ,ϕ) = p D η D s D (Σ,ϕ) 1 ε 1 UC = 1/ϕ (s }{{} D (Σ,ϕ)) γ ε 1 (p }{{} D /η D ) γ r α w (1 α γ) }{{} Exogenous PE Gains GE UC reduction relative to autarky (holding prices fixed) is observable No assumptions about Heterogeneity: quality, prices, productivity Model for the extensive margin: fixed costs, search,... Output structure Never used CES-structure of the import bundle Homotheticity: η (ϕ, q) Details 9

19 10 AGGREGATION: FROM MICRO TO MACRO Up to now: firm level partial equilibrium unit costs To make statements about the aggregate price (real wage) Specify interaction on product markets ( pass through ) Structure of interlinkages across producers ( roundabout production ) For welfare: Need to take into account potential resource loss for extensive margin (e.g. fixed costs)

20 11 THE BASIC MACRO MODEL Measure of monopolistically competitive producers: y i = ϕ i l 1 γ i ( x i = x ε 1 ε Di x γ i + x ε 1 ε Ii Perfectly competitive final good producer: ) ε ε 1 ( ) σ σ 1 σ 1 Y = y i σ di Perfectly competitive domestic input producer: X D = Ml φ D Y 1 φ X

21 12 INTERNATIONAL TRADE Fixed costs in units of labor To close aggregate economy impose balanced trade exports in terms of the final good Assume exogenously given labor supply of L

22 13 REAL WAGES AND GAINS FROM TRADE The domestic price P and the gains from trade (rel. to autarky) are given by G PAut P 1 P = = ( 1 i=0 ( 1 i=0 1 [ ] ϕ i s γ σ 1 1 ε Di di) ( ϕi σ 1 1 i=0 ϕσ 1 i di ) 1 σ 1 1 (1 φ)γ γ(σ 1) 1 ε sdi di ) 1 1 σ 1 1 (1 φ)γ Details Equilibrium

23 13 REAL WAGES AND GAINS FROM TRADE The domestic price P and the gains from trade (rel. to autarky) are given by G PAut P 1 P = = ( 1 i=0 ( 1 i=0 1 [ ] ϕ i s γ σ 1 1 ε Di di) ( ϕi σ 1 1 i=0 ϕσ 1 i di ) 1 σ 1 1 (1 φ)γ γ(σ 1) 1 ε sdi di ) 1 1 σ 1 1 (1 φ)γ Require joint distribution of ϕ and s D Details Equilibrium

24 A SUFFICIENCY RESULT With micro-data on value added and domestic shares, we can identify innate productivity ϕ up to scale ( ) va = κ ϕs γ σ 1 1 ε D.

25 14 A SUFFICIENCY RESULT With micro-data on value added and domestic shares, we can identify innate productivity ϕ up to scale Gains from trade ( ) va = κ ϕs γ σ 1 1 ε D. ( G = PAut P = va i vai di s γ Di 1 ε (1 σ) di ) 1 1 σ

26 A SUFFICIENCY RESULT With micro-data on value added and domestic shares, we can identify innate productivity ϕ up to scale Gains from trade ( ) va = κ ϕs γ σ 1 1 ε D. ( G = PAut P = va i vai di s γ Di 1 ε (1 σ) di ) 1 1 σ Fully determined from micro-data given parameters (ε,γ,σ)

27 A SUFFICIENCY RESULT With micro-data on value added and domestic shares, we can identify innate productivity ϕ up to scale Gains from trade ( ) va = κ ϕs γ σ 1 1 ε D. ( G = PAut P = va i vai di s γ Di 1 ε (1 σ) di ) 1 1 σ Fully determined from micro-data given parameters (ε,γ,σ) Any model in the above class will have the same gains G

28 A SUFFICIENCY RESULT With micro-data on value added and domestic shares, we can identify innate productivity ϕ up to scale Gains from trade ( ) va = κ ϕs γ σ 1 1 ε D. ( G = PAut P = va i vai di s γ Di 1 ε (1 σ) di ) 1 1 σ Fully determined from micro-data given parameters (ε,γ,σ) Any model in the above class will have the same gains G In particular: extensive margin does not matter (given the data!)

29 15 IMPORTANCE OF MICRO-DATA How important is the micro-heterogeneity?

30 15 IMPORTANCE OF MICRO-DATA How important is the micro-heterogeneity? Formula gives a simple answer: ) = ( P Aut ln P γ 1 ε ln( λ D) }{{} Aggregate Data + 1 ( 1 σ ln va ( i sdi ) γ vai di λ }{{ D } Bias ) 1 ε (1 σ) di.

31 15 IMPORTANCE OF MICRO-DATA How important is the micro-heterogeneity? Formula gives a simple answer: ) = ( P Aut ln P γ 1 ε ln( λ D) }{{} Aggregate Data + 1 ( 1 σ ln va ( i sdi ) γ vai di λ }{{ D } Bias ) 1 ε (1 σ) di. Can evaluate directly from micro-data

32 15 IMPORTANCE OF MICRO-DATA How important is the micro-heterogeneity? Formula gives a simple answer: ) = ( P Aut ln P γ 1 ε ln( λ D) }{{} Aggregate Data + 1 ( 1 σ ln va ( i sdi ) γ vai di λ }{{ D } Bias ) 1 ε (1 σ) di. Can evaluate directly from micro-data Crucial dimensions: cross-sectional dispersion of domestic shares correlation between domestic shares and firm-size

33 15 IMPORTANCE OF MICRO-DATA How important is the micro-heterogeneity? Formula gives a simple answer: ) = ( P Aut ln P γ 1 ε ln( λ D) }{{} Aggregate Data + 1 ( 1 σ ln va ( i sdi ) γ vai di λ }{{ D } Bias ) 1 ε (1 σ) di. Can evaluate directly from micro-data Crucial dimensions: cross-sectional dispersion of domestic shares correlation between domestic shares and firm-size Note: Bias can be positive or negative Bias > 0 σ > 1 + ε 1 γ

34 15 IMPORTANCE OF MICRO-DATA How important is the micro-heterogeneity? Formula gives a simple answer: ) = ( P Aut ln P γ 1 ε ln( λ D) }{{} Aggregate Data Can evaluate directly from micro-data Crucial dimensions: + 1 ( 1 σ ln va ( i sdi ) γ vai di λ }{{ D } Bias cross-sectional dispersion of domestic shares correlation between domestic shares and firm-size Note: Bias can be positive or negative Bias > 0 σ > 1 + ε 1 γ ) 1 ε (1 σ) di. Also: ε estimated from firm-level data is lower than aggregate trade elasticity

35 16 WELFARE Welfare is given by U = ( ( 1 γ + γφλ D ) ) 1 w σ 1 P (L L F) where L F is resource loss of of firms extensive margin Need to actually solve for firms sourcing strategies

36 17 EXTENSIVE MARGIN WITH FIXED COSTS OF SOURCING Optimal sourcing strategy solves { π (ϕ,[ f ]) = max Σ,y,l where Γ(Σ,y,ϕ,l) is cost function Problem: } py Γ(Σ,y,ϕ,l) wl w f c c Σ Complementarities introduce interdependence across markets ( export problem, e.g. EKK). If f c and q c both vary by country, need to compare all sourcing strategies.

37 18 EXTENSIVE MARGIN: TRACTABILITY To make progress, impose more assumptions:

38 18 EXTENSIVE MARGIN: TRACTABILITY To make progress, impose more assumptions: 1. Fixed costs are constant across countries Σ reduces to cut-off q (or share of countries n)

39 18 EXTENSIVE MARGIN: TRACTABILITY To make progress, impose more assumptions: 1. Fixed costs are constant across countries Σ reduces to cut-off q (or share of countries n) 2. Other simplifying assumptions: Homothetic demand: η (q,ϕ) = q Distribution of qualities is Pareto: G(q) = 1 (q min /q) θ Prices are given by: p c = αq ν c

40 18 EXTENSIVE MARGIN: TRACTABILITY To make progress, impose more assumptions: 1. Fixed costs are constant across countries Σ reduces to cut-off q (or share of countries n) 2. Other simplifying assumptions: Homothetic demand: η (q,ϕ) = q Distribution of qualities is Pareto: G(q) = 1 (q min /q) θ Prices are given by: p c = αq ν c Implication: Firm-specific price index A(Σ,ϕ) 1 = zn η η and z depend on structural parameters (ρ,θ,qmin,ν) can directly be estimated from micro-data Details

41 19 EMPIRICAL APPLICATION Application to French micro data population of manufacturing firms customs data matched to fiscal data at firm-level Procedure Step 1: Estimate (ε,γ) from micro data Step 2: Use micro-data and sufficiency result to quantify gains and bias Step 3: Calibrate firm-based model requires extensive margin

42 20 ESTIMATING THE TRADE ELASTICITY ε Estimate in two stages y = ϕs γ 1 ε D lα k β X γ 1. Estimate productivity residual from ln(s) = αln(k) + βln(l) + γln(x) + ln(ϑ) 2. Decompose ln(ϑ) into trade and innate component Details ln(ϑ) = γ ε 1 ln( s D) + ln(ϕ) instrumenting s D with firm-specific supply shocks (Hummels, et. al. 2014) Z it = WES ckt s pre cki ck

43 21 ESTIMATING ε : RESULTS ln ( ) ˆϑ ist = δs + δ t ε γ sln ( s D ) ist + uist First Stage IV Estimate Baseline Importers in 2001 Balanced Panel WES *** (0.003) γ s ln(s D ) ** * ** (0.356) (0.324) (0.282) Implied ε (0.648) (1.087) (0.676) N 67,696 67,696 58,027 48,480 R

44 22 THE GAINS FROM TRADE IN FIRM-BASED MODELS OF IMPORTING Measure aggregate gains as where G = VA k G k k ( γ va ik G k = vaik di s k 1 ε (1 σ) Dik di ) 1 1 σ

45 22 THE GAINS FROM TRADE IN FIRM-BASED MODELS OF IMPORTING Measure aggregate gains as where Result G = VA k G k k ( γ va ik G k = vaik di s k 1 ε (1 σ) Dik di Micro Data = 13% Aggregate Data = 11.9% ) 1 1 σ

46 22 THE GAINS FROM TRADE IN FIRM-BASED MODELS OF IMPORTING Measure aggregate gains as where Result G = VA k G k k ( γ va ik G k = vaik di s k 1 ε (1 σ) Dik di ) 1 1 σ Bias Micro Data = 13% Aggregate Data = 11.9% Bias = 13% 11.9% 11.9% = 9%

47 22 THE GAINS FROM TRADE IN FIRM-BASED MODELS OF IMPORTING Measure aggregate gains as where Result G = VA k G k k ( γ va ik G k = vaik di s k 1 ε (1 σ) Dik di Micro Data = 13% Aggregate Data = 11.9% ) 1 1 σ Bias 13% 11.9% Bias = = 9% 11.9% Wide class of firm-based models of importing will arrive exactly at this number

48 22 THE GAINS FROM TRADE IN FIRM-BASED MODELS OF IMPORTING Measure aggregate gains as where Result G = VA k G k k ( γ va ik G k = vaik di s k 1 ε (1 σ) Dik di Micro Data = 13% Aggregate Data = 11.9% ) 1 1 σ Bias 13% 11.9% Bias = = 9% 11.9% Wide class of firm-based models of importing will arrive exactly at this number... if successfully calibrated to the micro-data Micro Gains

49 23 THE SIZE OF THE BIAS FIGURE: Bootstrap Distribution of the Bias Confident that bias is between 8% and 9.5%

50 CALIBRATING THE MACRO MODEL Strategy: 1. Use estimated parameters (γ,ε,η) from above Estimate η 2. Calibrate heterogeneity in productivity and fixed costs ( ) (( ) ( ln(ϕ) µϕ σ 2 N, ϕ ρσ ϕ σ f ln( f ) µ f ρσ ϕ σ f σ 2 f )) 3. Comparison: 3.1 Matching features of joint distribution of s D and sales 3.2 Calibrate to sales data only

51 T HE J OINT D ISTRIBUTION OF F IRM S IZE AND I MPORT I NTENSITY Importers, 2004 (domshare/agg. domshare) (γ/(1 ε) *(σ 1)) 300 Non importers, e e Size (share of total value added) Graphs by D_imp F IGURE : Micro gains and firm size 25

52 26 CALIBRATION: RESULTS Target Moments French Data Model Parameter Aggregate Domestic Share µ f = 9.05 Share of Importers f I = Dispersion in Domestic Shares (Importers) σ f = 3.26 Dispersion in log Sales (Importers) σ ϕ = 1.01 Correlation log Sales - Dom Shares (Importers) ρ = 0.41 Parameters

53 27 THE IMPORTANCE OF DOMESTIC SHARES Baseline No s D Data Model Parameter Model Parameter Aggregate Domestic Share 0.71 µ f = µ f = 5.19 Dispersion in log Sales 1.62 σ ϕ = σ ϕ = 1.72 Share of Importers 0.32 f I = f I = 8.8e 05 Dispersion in Domestic Shares 0.26 σ f = σ f = 0 Correlation log Sales - Dom Shares ρ = ρ = 0 Real Wage Gains % 12.94% Welfare Gains 16.46% 13.73% Ignoring micro data on domestic shares lowers predicted gains from trade by 16.3% (Real Wage) and 16.6% (Welfare) For comparison: ACR-type gains: 0.71 γ/(1 ε) = 12.5%

54 28 SOURCE OF BIAS Different models may lead to different magnitude of the gains from trade, because they predict different counterfactual autarky equilibria (CRC, 2014)

55 28 SOURCE OF BIAS Different models may lead to different magnitude of the gains from trade, because they predict different counterfactual autarky equilibria (CRC, 2014) Here: predict productivity ϕ from sales and s D ( var (ln(sales)) = σϕ 2 γ + ε 1 Two types of biases: ) 2 σ 2 SD }{{} Dispersion Bias 2 γ ε 1 cov(log(ϕ),log(s D)) }{{} Correlation Bias 1. Too little dispersion in domestic shares Too much variance in ϕ Gains are downward biased 2. Too strong a negative correlation between ϕ and s D Too little variance in ϕ Gains are upward biased

56 28 SOURCE OF BIAS Different models may lead to different magnitude of the gains from trade, because they predict different counterfactual autarky equilibria (CRC, 2014) Here: predict productivity ϕ from sales and s D ( var (ln(sales)) = σϕ 2 γ + ε 1 Two types of biases: ) 2 σ 2 SD }{{} Dispersion Bias 2 γ ε 1 cov(log(ϕ),log(s D)) }{{} Correlation Bias 1. Too little dispersion in domestic shares Too much variance in ϕ Gains are downward biased 2. Too strong a negative correlation between ϕ and s D Too little variance in ϕ Gains are upward biased In our case: dispersion effect dominates σ Full ϕ = 1.01 < 1.72 = σ NSD ϕ

57 MARGINAL DISTRIBUTIONS Domestic share, importers ln(sales), importers Fraction of firms (in 100 bins of equal length) French data Baseline No domestic share data Zoom Note: the distributions of ln(sales) have been normalized to have a mean of 1 29

58 30 CONCLUSIONS Wide class of models: domestic spending shares fully capture UC reductions through sourcing Micro-data on value added and domestic shares fully determine the macro gains from trade in non-aggregative environment robust across models aggregate statistic gives biased answer of 9% Source of bias: domestic shares are required to identify physical productivity physical productivity is required to predict counterfactual allocations in autarky Puts discipline on quantitative models of importing and useful for applied work

59 Appendix 31

60 32 RELATION TO EXISTING PAPERS This framework encompasses most of the existing papers, e.g. 1. Koren, Halpern, Szeidl (2011) Homothetic demand: η (q,ϕ) = q Single outside country: ρ and G k (q) degenerate No quality/price differences between products: q k /p k = A equal fixed costs (plus firm-specific noise): fck = f u where u is firm-specific 2. Gopinath Neiman (2013) Homothetic demand: η (q,ϕ) = q No distinction between products and countries All countries are alike: G k (q) degenerate Constant fixed costs across firms ( f n λ ) We show direct evidence on substantial dispersion in quality: G(q) not degenerate importance of complementarities: ρ < back

61 33 OPTIMAL IMPORT DEMAND Back Useful to solve the firms problem in 2 steps: { ( π (ϕ,f) max py Γ(Σ,y,ϕ,k,l) wl rk w Σ,y,l,k c Σ { } p c z c dc s.t. ϕk α l 1 α γ x γ y c Σ Γ(Σ,y,ϕ,k,l) min z where (2) intensive margin (1) extensive margin Note: (1) is hard and requires strong assumptions (2) can be characterized without additional assumptions Key: (2) is all we need to measure effect of trade on unit cost )} f c dc + f I I(Σ) (1) (2)

62 34 INTENSIVE MARGIN OF TRADE Given Σ, solve for optimal import demand 1. Letting m be import spending: ( ) 1 x I /m = A(Σ,ϕ) = (η (q c,ϕ)/p c ) ρ 1 ρ 1 dc c Σ 2. Letting X be total intermediary spending: x = ( (η ( q D,ϕ ) /p D ) ε 1 + A(Σ,ϕ) ε 1 ) 1 ε 1 X Q(Σ, ϕ)x Note: Σ affects A and Q ϕ only matters through η (.,ϕ)

63 INTENSIVE MARGIN (CTD) We showed: x = A(Σ,ϕ)m Domestic vs foreign trade-off: And: s D = p Dz D X = (η (q D,ϕ)/p D ) ε 1 (η (q D,ϕ)/p D ) ε 1 + A(Σ,ϕ) ε 1 x = ( x ε 1 ε D ) ε + x ε 1 ε 1 ε I = Q(Σ,ϕ)X where Hence: Q(Σ,ϕ) ((η (q D,ϕ)/p D ) ε 1 + A(Σ,ϕ) ε 1) ε 1 1 X Q(Σ,ϕ) = η ( q D,ϕ ) ε 1 s 1 D p D back 35

64 IMPORT QUALITY FUNCTION PROPOSITION Let n the mass of varieties imported. Then, import price index is given by where z = η = A(n,ϕ) 1 = A(n) 1 = zn η [ ( )( θ 1 E [q] θ 1 ρ 1 1 ν θ θ θ (1 ν)(ρ 1) ) 1 ] 1 ν (1 ν)(ρ 1) Details back 36

65 IMPORT QUALITY FUNCTION PROPOSITION Let n the mass of varieties imported. Then, import price index is given by where z = η = A(n,ϕ) 1 = A(n) 1 = zn η [ ( )( θ 1 E [q] θ 1 ρ 1 1 ν θ θ θ (1 ν)(ρ 1) ) 1 ] 1 ν (1 ν)(ρ 1) Production function for import quality TFP z depends on diversity (θ), mean quality (E [q]), complementarity (ρ) returns to scale η depends on diversity (θ), complementarity (ρ) Details back 36

66 IMPORT QUALITY FUNCTION PROPOSITION Let n the mass of varieties imported. Then, import price index is given by where z = η = A(n,ϕ) 1 = A(n) 1 = zn η [ ( )( θ 1 E [q] θ 1 ρ 1 1 ν θ θ θ (1 ν)(ρ 1) ) 1 ] 1 ν (1 ν)(ρ 1) Production function for import quality TFP z depends on diversity (θ), mean quality (E [q]), complementarity (ρ) returns to scale η depends on diversity (θ), complementarity (ρ) Only need (z,η) for firms problem and hence the macro-exercise Details back 36

67 THE GAINS FROM DIVERSITY RESULT Consider import quality A(n) = zn η. 1. Diversity increases import productivity z, as z(e [q],θ,ρ) > E [q] 1 ν = lim θ z(e [q],θ,ρ) z(e[q],θ,ρ) θ < 0 2. Substitutability increases import productivity z, as z(e[q],θ,ρ) ρ > 0 3. Diversity and substitutability are complements, as 2 z(e[q],θ,ρ) θ ρ < 0 Intuition: import productivity A satisfies A ρ 1 = q q (1 ν)(ρ 1) dg(q). As (ρ 1)(1 ν) > 1, firms are risk loving and value diversity If ρ is high, firms can leverage quality differences Similar to input-output linkages in Jones (2011) back 37

68 38 PRICES AND MARGINAL COSTS Competitive domestic input & final good sectors: p D = φ 1 M wφ P 1 φ P = ( ) 1 p 1 σ 1 σ i di Monopolistic competition between producer and FG firm: p i = σ σ 1 MC i where MC i = 1 ( ) γ s D (Σ,ϕ) γ pd ε 1 w 1 γ h ϕ i η D back

69 39 EQUILIBRIUM An equilibrium is a set of prices (w,[p(i)] i, p D ), labor allocations ([l (i)] i,[l F (i)] i,l D ), differentiated product supplies ([y(i)] i ), input demands ([z D (i)] i,[z c (i)] ci ), quantities of the final good (Y C,Y X,Y ROW ), supply of domestic intermediates X D and sourcing strategies ([Σ(i)] i ) such that Variety producers maximize profits Final good producers maximize profits Domestic input producers maximize profits Trade is balanced Markets clear back

70 40 ESTIMATING THE TRADE ELASTICITY ε (CTD) Back Step 1. Estimate production function in each two-digit industry following DeLoecker and Warzynski (2012) Obtain industry-specific ˆγ and Step 2. Estimate: instrumenting s D,it with: ˆ ln(ϑ) for every firm. Results ln(ϑ it ) = β 0 + β 1 γ s ln(s D,it ) + u it z it = WES ckt s pre cki ck where WES ckt is the change in total exports for product k of country c at year t to the world (excl. France) and s pre cki are firm i s import share on (k,c) prior to our sample

71 41 PF ESTIMATION: EQUATION Observe revenue, not physical output Hence estimate: where γ = σ 1 σ And: ln(s) = δ + αln(k) + βln(l) + γln(x) + ln(ω) γ, α = σ 1 σ α and β = σ 1 σ (1 α γ) ln(ω) = σ 1 σ ln(ϑ) = 1 1 ε γln(s D) + σ 1 σ ln(ϕ) back

72 42 FIRST STAGE IN ESTIMATION OF ε back Levels Differences γ s ln(s D ) γ s ln(s D ) WES *** (0.000) WES *** (0.003) N 103,333 67,696 R

73 43 DISTRIBUTION OF PRODUCTIVITY GAINS IN FRANCE Back Gains FIGURE: The distribution of productivity gains (s D,i ) γ 1 ε Average gains: 12%, Median gains 5% Details Correlates

74 44 DISTRIBUTIONS OF GAINS: MOMENTS Mean Median p25 p75 N ,723 ε 1 Notes: The Table reports moments of the empirical distribution of sd,i. γ back

75 45 CORRELATES OF THE GAINS Dep. Variable: Gains from Importing ( γ 1 ε ln(s D)) ln(va) 0.005*** *** *** (0.000) (0.000) (0.000) ln(l) 0.002*** (0.000) Exporter 0.023*** 0.013*** (0.001) (0.001) Foreign Group 0.079*** 0.063*** (0.002) (0.002) Num of varieties 0.083*** 0.092*** (0.001) (0.001) N 111, , , , ,975 R TABLE: Variation in the gains from trade back

76 46 ESTIMATING THE RETURNS TO VARIETY η back Theory implies that (q D /p D ) ε 1 s D = (q D /p D ) ε 1 + (zn η ) ε 1 Estimate η from 1 ε 1 ln ( 1 sd s D ) = const + ηln(n) more results graph

77 47 THE ln(s D ) ln(n) SCHEDULE back lv_i lv_i Fitted values lowess logit_domshare lv_i Fitted values lowess logit_domshare lv_i FIGURE: log( 1 sd s D ) = m(ln(n)) in the data

78 48 ESTIMATING RETURNS TO VARIETY η(ctd) back 1 ε 1 ln ( 1 sd,ist s D,ist ) = δ s + δ t + δ nk + ηln(n ist ) + u ist Mutiple Varieties Full Sample Num of varieties 0.253*** 0.389*** 0.405*** (0.011) (0.005) (0.005) Exporter *** *** (0.016) (0.008) Foreign Group 0.126*** 0.097*** (0.011) (0.009) ln(k/l) *** (0.003) N 34, , ,723 R graph

79 49 EXTENSIVE MARGIN AND η back Extensive margin foc where n (ϕ, f ) = max n { D MC 1 ϕ ( ) 1 σ 1 n f w I(n > 0) f w} I MC(n) ((q D /p D ) ε 1 + (zn η ) ε 1) γ ε 1 Then n (ϕ, f ) s D (ϕ, f ) Important parameter: η

80 CALIBRATION: PARAMETERS Set Exogenously Symbol Value Demand Elasticity σ 3 Strength of Linkages φ (0,1) Estimated Elasticity of Substitution ε 2.83 Returns to Scale of Importing η 0.3 Material Share γ 0.63 Calibrated Dispersion in Productivity Average Fixed Cost Dispersion in Fixed Costs Correlation Fixed Costs - Productivity Fixed Cost of Being Importer σϕ 2 µ f σ 2 f ρ f I Back 50

81 51 CALIBRATION: GAINS FROM TRADE φ = 0 φ = 0.25 φ = 0.5 φ = 0.75 φ = 1 Real Wage Gains (in %) Welfare Gains (in %) % of Labor in Fixed Cost Production VA-weigthed Avg Gains (in %)

82 52 CALIBRATION: NON-TARGETED MOMENTS Non-Targeted Moments French Data Baseline No Micro Data Agg Domestic Share (Importers) Avg Domestic Share (Importers) Dispersion log Sales (Population) Share of Sales by Importers

83 53 VARIANCE OF SALES Back In terms of obversables: cov(ln(sales),ln(s D )) = (σ 1)cov(ln(ϕ),ln(s D )) So that γ (σ 1) ε 1 σ s 2 D ( γ σϕ 2 = var(ln(sales)) + ) 2 σ 2 s D ε 1 + 2γ 1 ε 1 σ 1 corr(ln(sales),ln(s D))σ Sales σ sd

84 MARGINAL DISTRIBUTIONS: ZOOM IN Domestic share, importers ln(sales), importers Fraction of firms (in 100 bins of equal length) Back French data Baseline No domestic share data Note: the distributions of ln(sales) have been normalized to have a mean of 1 54

85 55 CORRELATION STRUCTURE Average Domestic Share Sales Quintile French Data Baseline NSD