Granular Comparative Advantage

Transcription

1 Granular Comparative Advantage Cecile Gaubert Oleg Itskhoki Stanford University March / 26

2 Exports are Granular Freund and Pierola (2015): Export Superstars Across 32 developing countries, the largest exporting firm accounts on average for 17% of total manufacturing exports Our focus: French manufacturing Average export share of the largest firm Manufacturing 1 industry 7% 2-digit 23 sectors 18% 3-digit 117 sectors 26% 4-digit 316 sectors 37% 1 / 26

3 Firm-size distribution is: 1 fat-tailed (Zipf s law) 2 discrete } = Granularity Granularity Canonical example: power law (Pareto) with shape θ < 2 Intuitions from Gaussian world fail, even for very large N a single draw can shape N i=1 X illustration i average can differ from expectation (failure of LLN) 2 / 26

4 Firm-size distribution is: 1 fat-tailed (Zipf s law) 2 discrete } = Granularity Granularity Canonical example: power law (Pareto) with shape θ < 2 Intuitions from Gaussian world fail, even for very large N a single draw can shape N i=1 X illustration i average can differ from expectation (failure of LLN) Most common application: aggregate fluctuations Gabaix (2011), di Giovanni and Levchenko (2012) The role of granularity for comparative advantage of countries is a natural question, yet has not been explored Can a few firms shape country-sector specialization? 2 / 26

5 Trade Models Trade models acknowledge fat-tailed-ness but not discreteness emphasis on firms, but each firm is infinitesimal (LLN applies) hence, no role of individual firms in shaping sectoral aggregates Exceptions with discrete number of firms 1 One-sector model of Eaton, Kortum and Sotelo (EKS, 2012) 2 Literature on competition/markups (e.g., AB 2008, EMX 2014, AIK 2014, Neary 2015) 3 / 26

6 Trade Models Trade models acknowledge fat-tailed-ness but not discreteness emphasis on firms, but each firm is infinitesimal (LLN applies) hence, no role of individual firms in shaping sectoral aggregates Exceptions with discrete number of firms 1 One-sector model of Eaton, Kortum and Sotelo (EKS, 2012) 2 Literature on competition/markups (e.g., AB 2008, EMX 2014, AIK 2014, Neary 2015) Our focus: can granularity explain sectoral trade patterns? 1 sector-level comparative advantage (like DFS) 2 firm heterogeneity within sectors (like Melitz) 3 granularity within sectors (like EKS) relax the LLN assumption in a multi-sector Melitz model take seriously that a typical French sector has 350 firms with the largest firm commanding a 20% market share 3 / 26

7 Granularity Our approach percentiles draws 0 T(z) Productivity draws, ϕ 4 / 26

8 Granularity Our approach percentiles draws 0 T(z) Productivity draws, ϕ Fundamental vs Granular 4 / 26

9 Granularity Our approach percentiles draws 0 T(z) Productivity draws, ϕ Fundamental vs Granular: Why do we care? 4 / 26

10 Roadmap: This paper 1 Basic framework with granular comparative advantage 2 GE Estimation Procedure SMM using French firm-level data 3 Explore implications of the estimated granular model many continuous-world intuitions fail dynamic counterfactuals 5 / 26

11 Roadmap: This paper 1 Basic framework with granular comparative advantage 2 GE Estimation Procedure SMM using French firm-level data 3 Explore implications of the estimated granular model many continuous-world intuitions fail dynamic counterfactuals Highlights of the results from the estimated model: 1 A parsimonious granular model fits many empirical patterns 2 Granularity accounts for 20% of variation in export shares most export-intensive sectors tend to be granular 3 Moments of firm-size distribution explain trade patterns 4 Granularity can explain much of the mean reversion in CA more granular sectors are more volatile death of a single firm can alter considerably the CA 5 / 26

12 Modeling Framework 6 / 26

13 Model Structure 1 Two countries: Home and Foreign inelastically-supplied labor L and L 2 Continuum of sectors z [0, 1]: { 1 } Q = exp α z log Q z dz 0 3 Sectors vary in comparative advantage: T z /T z N (µ T, σ T ) 6 / 26

14 1 Two countries: Home and Foreign inelastically-supplied labor L and L Model Structure 2 Continuum of sectors z [0, 1]: { 1 } Q = exp α z log Q z dz 0 3 Sectors vary in comparative advantage: T z /T z N (µ T, σ T ) 4 Within a sector, a finite number of firms (varieties) K z : Q z = [ Kz i=1 q σ 1 σ z,i ] σ σ 1 5 Each sector has an EKS market structure 6 / 26

15 Productivity draws in a given sector z: Number of (shadow) entrants: Poisson ( M z ) Entrants productivity draws: Pareto ( θ; ϕ z ) EKS Sectors Denote N ϕ number of firms with productivity ϕ N ϕ Poisson ( T z ϕ θ), T z M z ϕ θ z with T z /T z shaping sector-level CA 7 / 26

16 Productivity draws in a given sector z: Number of (shadow) entrants: Poisson ( M z ) Entrants productivity draws: Pareto ( θ; ϕ z ) EKS Sectors Denote N ϕ number of firms with productivity ϕ N ϕ Poisson ( T z ϕ θ), T z M z ϕ θ z with T z /T z shaping sector-level CA Marginal cost: c = w/ϕ at home and τw/ϕ abroad Fixed cost of production and exports: F in local labor 7 / 26

17 Productivity draws in a given sector z: Number of (shadow) entrants: Poisson ( M z ) Entrants productivity draws: Pareto ( θ; ϕ z ) EKS Sectors Denote N ϕ number of firms with productivity ϕ N ϕ Poisson ( T z ϕ θ), T z M z ϕ θ z with T z /T z shaping sector-level CA Marginal cost: c = w/ϕ at home and τw/ϕ abroad Fixed cost of production and exports: F in local labor Oligopolistic (Bertrand) competition and variable markups Atkeson-Burstein (2008): {c i } {s i, µ i, p i } Kz i=1 show 7 / 26

18 Market Entry and GE Assumption: sequential entry in increasing order of unit cost [ w/ϕ c 1 < c 2 <... < c K <..., where c i = i, if Home, τw /ϕ i, if Foreign unique equilibrium Profits: Π i = s i ε(s i ) α zy wf 8 / 26

19 Market Entry and GE Assumption: sequential entry in increasing order of unit cost [ w/ϕ c 1 < c 2 <... < c K <..., where c i = i, if Home, τw /ϕ i, if Foreign unique equilibrium Profits: Π i = s i ε(s i ) α zy wf Entry: Π K K 0 and ΠK+1 K+1 < 0 determines K z 8 / 26

20 Market Entry and GE Assumption: sequential entry in increasing order of unit cost [ w/ϕ c 1 < c 2 <... < c K <..., where c i = i, if Home, τw /ϕ i, if Foreign unique equilibrium Profits: Π i = s i ε(s i ) α zy wf Entry: Π K K 0 and ΠK+1 K+1 < 0 determines K z General equilibrium: GE vector X = (Y, Y, w, w ) Within-sector allocations Z = { } K z, {s z,i } Kz i=1 z [0,1] Labor market clearing and trade balance (linear in X) Fast iterative algorithm 8 / 26

21 Foreign share: Properties of the Granular Model Λ z X z α z Y = K z i=1 (1 ι z,i)s z,i Expected foreign share: { } T Φ z = E Λ z z T = z Granular residual: (τω) θ Tz T z Γ z Λ z Φ z : E T {Γ z } = E T {Λ z Φ z } = 0 Aggregate exports: X = Y 1 0 α z Λ z dz = ΦY, Φ 1 0 α z Φ z dz 9 / 26

22 Estimation and Model Fit 10 / 26

23 Estimation procedure Data: French firm-level data (BRN) and Trade data Firm-level domestic sales and export sales Aggregate import data (Comtrade) digit manufacturing sectors Parametrize sector-level comparative advantage: T (z)/t (z) log N (µ T, σ T ) Based on empirical distribution shown in Hanson et al. (2015) Stage 1: calibrate Cobb-Douglas shares {α z } and w/w CD shares read from domestic sales + imports, by sector w/w = 1.13, trade-weighted wage of France s trade partners Normalizations: w = 1 and L = 100 Stage 2: SMM procedure to estimate {σ, θ, τ, F, µ T, σ T }, while (Y, Y, L /L) are pinned down by GE 10 / 26

24 Estimated Parameters Parameter Estimate Std. error Auxiliary variables σ 5 κ = θ θ σ τ w/w F ( 10 5 ) L /L µ T Y /Y σ T Π/Y / 26

25 Moment Fit Moments Data, ˆm Model, M( ˆΘ) Loss (%) 1. Log number of firms, mean log M st. dev. z Top-firm market share, mean s 4. st. dev. z, Top-3 market share, mean 3 j=1 s z,j 6. st. dev Imports/dom. sales, mean Λ z st. dev Exports/dom. sales, mean Λ st. dev. z Fraction of sectors with { } 11. P Xz > exports>dom. sales Ỹz X z Regression coefficients 12. export share on top-firm share ˆb (0.156) (0.104) 13. export share on top-3 share ˆb (0.108) (0.090) 14. import share on top-firm share ˆb (0.097) (0.079) 15. export share on top-3 share ˆb (0.074) (0.069) 12 / 26

26 (a) Number of French firms (b) Top market share 0.3 Data Model (c) Domestic import share (d) Pareto shape of sales / 26

27 Non-targeted Moments Correlation between top market share and number of firms: s z,1 = const + γ M log M z + γ Y log Ỹ z + ɛ s z Data: (0.008) (0.008) Model: (0.007) (0.006) Extensive margin of sales: log M z = c d + χ d Data: (0.082) Model: (0.011) log(ỹ z X z ) + ɛ d z 14 / 26

28 Equilibrium markups Other Top 4 Top 3 Top 2 Top firm 15 / 26

29 Quantifying Granular Trade 16 / 26

30 Decomposition of Trade Fflows Variance decomposition of X z = Λ zα z Y with Λ z = Φ z + Γ z: var(λ z) = var(φ z) + var(γ z), var(log X z ) var(log α z ) + var(log Λ z) Table: Variance decomposition of trade flows Granular contribution Export share contribution Common θ Sector-specific θ z (1) (2) (3) (4) (5) var(γ z ) var(λ z ) 17.0% 22.3% 26.0% 28.4% 20.3% var(log Λ z ) var(log X z ) 57.2% 59.2% 62.5% 63.9% 59.0% Pareto shape parameter κ z = θz σ Estimated Pareto shape ˆκ z Top-firm market share s z, / 26

31 Export Intensity and Granularity Granularity does not create additional trade on average Yet, granularity creates skewness across sectors in exports most export-intensive sectors are likely of granular origin (a) Fraction of granular sectors 1/4 Granular 1/3 Granular 1/2 Granular (b) Granular contribution to trade 0.3 Export share Granular exports Deciles of sectors, by export intensity Λ z Deciles of sectors, by export intensity Λ z 17 / 26

32 Export Intensity and Granularity Granularity does not create additional trade on average Yet, granularity creates skewness across sectors in exports most export-intensive sectors are likely of granular origin (a) Distribution of Λ z Φ z (b) Distribution of Φ z Λ z 1 p50 p75 p90 p95 p99 1 p50 p75 p90 p95 p / 26

33 Properties of Granular Exports Γ z = Λ z Φ z are orthogonal with Φ z, log(α z Y ) and log M z Best predictor of Γ z is s z,1, the relative size of the largest firm Table: Projections of granular exports Γ z (1) (2) (3) (4) (5) (6) s z, s z, log M z log(α z Y ) Φ z R / 26

34 Identifying Granular Sectors Which sectors are granular? Neither Φ z, nor Γ z are observable P{Γ z ϑλ z Λ Λ z, r z } = z Φ ϑλ g( Φ z, Λ ) z, r z dφ z z 1 0 g( ), Φ z, Λ z, r z dφ z Top home-firm market share, s z,(1) Export share, Λ (z) 0 19 / 26

35 Dynamics of Comparative Advantage 20 / 26

36 Dynamic Model Use the granular model with firm dynamics to study the implied time-series properties of aggregate trade Shadow pull of firms in each sector with productivities {ϕ it } Productivity of the firms follows a random growth process: log ϕ it = µ + log ϕ i,t 1 + νε it, ε it iidn (0, 1) with reflection from the lower bound ϕ and µ= θν 2 /2 Each period: static entry game and price setting equilibrium Calibrate idiosyncratic firm dynamics (volatility of shocks ν) using the dynamic properties of market shares No aggregate shocks 20 / 26

37 Firm Dynamics and CA Empirical evidence in Hanson, Lind and Muendler (2015): 1 Hyperspecialization of exports 2 High Turnover of export-intensive sectors Moment Data HLM France Model SR persistence std( s z,i,t+1 ) LR persistence corr( s z,i,t+10, s z,i,t ) Top-1% sectors export share 21% 17% 18% Top-3% sectors export share 43% 30% 33% Turnover: remain in top-5% after 20 years 52% 71% Idiosyncratic firm productivity dynamics explains the majority of turnover of top exporting sectors over time 21 / 26

38 Mean Reversion in CA Idiosyncratic firm dynamics in a granular model predicts mean reversion in comparative advantage In addition, granular sectors are more volatile (a) Mean reversion in Λ z (b) Volatility of Λ z Expected change in export share, Λ z years 20 years Variation in export share, std( Λ z) Deciles of sectors, by granular Γ z Deciles of sectors, by granular Γ z 22 / 26

39 Death of a Large Firm Death (sequence of negative productivity shocks) of a single firm can substantially affect sectoral comparative advantage In the most granular sectors, death of a single firm can push the sector from top-5% of CA into comparative disadvantage / 26

40 Granularity and reallocation Sectoral labor allocation: L z L α z + θ NX z σκ 1 Y Interaction between trade openness and granularity results in sectoral reallocation and aggregate volatility 24 / 26

41 Policy Counterfactuals 25 / 26

42 1 Merger analysis Policy counterfactuals 2 Misallocation and trade policy policies that hinder growth of granular firms why trade barriers often target individual foreign firm? 25 / 26

43 1 Merger analysis Policy counterfactuals 2 Misallocation and trade policy policies that hinder growth of granular firms why trade barriers often target individual foreign firm? Figure: Welfare effects of Merger / 26

44 Conclusion 26 / 26

45 Conclusion The world is granular! (at least, at the sectoral level) We better develop tools and intuitions to deal with it Applications: 1 Innovation, growth and development 2 Misallocation 3 Industrial policy 4 Cities and agglomeration 26 / 26

46 APPENDIX 27 / 26

47 Granularity Illustration The role of top draw, as the number of draws N increases ( corr max i X i, ) X i i max i X i i X i Number of draws Number of draws back to slides 28 / 26

48 Sectoral equilibrium Sectoral equilibrium system: p i = µ i c i, µ i = ε i ε i 1 where ε i = σ(1 s i ) + s i, s i = ( pi ) ( 1 σ K ) 1/(1 σ) where P = P i=1 p1 σ i. back to slides 29 / 26