Granular Comparative Advantage

Granular Comparative Advantage Cecile Gaubert cecile.gaubert@berkeley.edu Oleg Itskhoki itskhoki@princeton.edu RASA IX International Conference Washington DC November 218 1 / 28

Exports are Granular Freund and Pierola (215): 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 / 28

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 (211), di Giovanni and Levchenko (212) 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 / 28

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, 212) 2 Literature on competition/markups (e.g., AB 28, EMX 214, AIK 214, Neary 215) 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 35 firms with the largest firm commanding a 2% market share 3 / 28

Granularity Our approach percentiles draws T(z) Productivity draws, ϕ 4 / 28

Granularity Our approach percentiles draws T(z) Productivity draws, ϕ Fundamental vs Granular 4 / 28

Granularity Our approach percentiles draws T(z) Productivity draws, ϕ Fundamental vs Granular: Why do we care? 4 / 28

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. Moments of firm-size distribution explain trade patterns 2 Granularity accounts for 2% of variation in export shares most export-intensive sectors tend to be granular 3 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 4 Policy in a granular economy: mergers and tariffs 5 / 28

Modeling Framework 6 / 28

Model Structure 1 Two countries: Home and Foreign inelastically-supplied labor L and L 2 Continuum of sectors z [, 1]: { 1 } Q = exp α z log Q z dz 3 Sectors vary in comparative advantage: T z /T z N (µ T, σ T ) 6 / 28

1 Two countries: Home and Foreign inelastically-supplied labor L and L Model Structure 2 Continuum of sectors z [, 1]: { 1 } Q = exp α z log Q z dz 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 / 28

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 / 28

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 and ΠK+1 K+1 < 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 [,1] Labor market clearing and trade balance (linear in X) Fast iterative algorithm 8 / 28

Estimation and Model Fit 9 / 28

Estimation procedure Data: French firm-level data (BRN) and Trade data Firm-level domestic sales and export sales Aggregate import data (Comtrade) 119 4-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. (215) 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 = 1 Stage 2: SMM procedure to estimate {σ, θ, τ, F, µ T, σ T }, while (Y, Y, L /L) are pinned down by GE 9 / 28

Estimated Parameters Parameter Estimate Std. error Auxiliary variables σ 5 κ = θ θ 4.37.246 σ 1 1.77 τ 1.341.61 w/w 1.13 F ( 1 5 ).946.252 L /L 1.724 µ T.137.193 Y /Y 1.526 σ T 1.422.232 Π/Y.211 1 / 28

Moment Fit Moments Data, ˆm Model, M( ˆΘ) Loss (%) 1. Log number of firms, mean log M 5.631 5.624.1 2. st. dev. z 1.451 1.222 7.9 3. Top-firm market share, mean.197.26 3.5 s 4. st. dev. z,1.178.149 3.8 5. Top-3 market share, mean 3 j=1 s.356.343 2. z,j 6. st. dev..241.175 11.5 7. Imports/dom. sales, mean Λ z.365.351 2.2 8. st. dev..24.268 14.8 9. Exports/dom. sales, mean Λ.328.35 6. 1. st. dev. z.286.346 6.5 Fraction of sectors with { } 11. P Xz > exports>dom. sales.185.92 37.9 Ỹz X z Regression coefficients 12. export share on top-firm share ˆb 1.215.243 2.6 (.156) (.14) 13. export share on top-3 share ˆb 3.254.232 1.1 (.18) (.9) 14. import share on top-firm share ˆb 1.16.2. (.97) (.79) 15. export share on top-3 share ˆb 3.2.5.1 (.74) (.69) show id 11 / 28

(a) Number of French firms (b) Top market share.3 Data Model 4.2 3 2.1 1 1 1 1 1 1.1.2.3.4.5 (c) Domestic import share (d) Pareto shape of sales.8 3.6 2.4.2 1.1.1.5 1.5 1 1.5 2 12 / 28

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:.94.18 (.8) (.8) Model:.64.25 (.7) (.6) Extensive margin of sales: log M z = c d + χ d Data:.563 (.82) Model:.861 (.11) log(ỹ z X z ) + ɛ d z 13 / 28

1.4 Equilibrium markups 1.35 1.3 1.25 Other Top 4 Top 3 Top 2 Top firm Oligopolistic (Bertrand) markups: averages (blue bars) and 1 9% range (red intervals) across industry σ Monopolistic competition markup: all oligopolistic markups σ 1 = 1.25 is lower bound for 14 / 28

Quantifying Granular Trade 15 / 28

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: 1 1 + (τω) θ Tz T z Γ z Λ z Φ z : E T {Γ z } = E T {Λ z Φ z } = Aggregate exports: X = Y 1 α z Λ z dz = ΦY, Φ 1 α z Φ z dz 15 / 28

Decomposition of Trade Flows 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.% 22.3% 26.% 28.4% 2.3% var(log Λ z ) var(log X z ) 57.2% 59.2% 62.5% 63.9% 59.% Pareto shape parameter κ z = θz σ 1 1.8 1. 1.2.96 1.15 Estimated Pareto shape ˆκ z 1.1 1.2 1.7 1.2 1.21 Top-firm market share s z,1.21.25.26.29.21 show fit 16 / 28

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.25.2 (a) Fraction of granular sectors 1/4 Granular 1/3 Granular 1/2 Granular (b) Granular contribution to trade.3 Export share Granular exports.15.2.1.1.5.2.4.7.1.15.21.29.4.58 1 Deciles of sectors, by export intensity Λ z -.5.2.4.7.1.15.21.29.4.58 1 Deciles of sectors, by export intensity Λ z 17 / 28

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 p5 p75 p9 p95 p99 1 p5 p75 p9 p95 p99.8.8.6.6.4.4.2.2.2.4.6.8 1.2.4.6.8 1 17 / 28

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,1.335.373.379.357.354 s z,1.254.268 log M z.8.12.16.11 log(α z Y ).5.13 Φ z.4.73 R 2.13.353.375.376.52.539 18 / 28

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 g( ), Φ z, Λ z, r z dφ z 19 / 28

Dynamics of Comparative Advantage 2 / 28

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 (, 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 2 / 28

Firm Dynamics and CA Empirical evidence in Hanson, Lind and Muendler (215): 1 Hyperspecialization of exports 2 High Turnover of export-intensive sectors Moment Data HLM France Model SR persistence std( s z,i,t+1 ).18.17 LR persistence corr( s z,i,t+1, s z,i,t ).86.83 Top-1% sectors export share 21% 17% 18% Top-3% sectors export share 43% 3% 33% Turnover I: remain in top-5% after 2 years 52% 71% Turnover II: remain in top-5% after 1 years 8% 79% Idiosyncratic firm productivity dynamics explains the majority of turnover of top exporting sectors over time show more 21 / 28

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.4.2 -.2 -.4 -.6 5 years 2 years Variation in export share, std( Λ z).6.5.4.3.2.1 -.8-1 -.38 -.24 -.14 -.7.4.13.24.42 1 Deciles of sectors, by granular Γ z -1 -.38 -.24 -.14 -.7.4.13.24.42 1 Deciles of sectors, by granular Γ z 22 / 28

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.4 Top firm share Loss in export share.3.2.1-1 -.8 -.4 -.1.1.3.6.9.13.21 1 Deciles of sectors, by granular Γ z show more 23 / 28

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 Figure: Total and Sectoral Labor Reallocation (fraction of total L) 24 / 28

Policy Counterfactuals 25 / 28

Policy counterfactuals 1 Misallocation and trade policy policies that hinder growth of granular firms why trade barriers often target individual foreign firm? 2 Merger analysis 25 / 28

Policy counterfactuals 1 Misallocation and trade policy policies that hinder growth of granular firms why trade barriers often target individual foreign firm? 2 Merger analysis Welfare analysis of a policy: Ŵ d log Y P = wl dtr d log w + Y Y + 1 and across sectors Ŵ = 1 α zŵzdz In partial equilibrium: Ŵ z = α z dπ z α z Y dz dtrz +dπz α z Y 1 d log P z α z d log P z dz In general equilibrium: spillovers to other sectors via (w, Y ) 25 / 28

Merger Merger is more beneficial: 1 The larger is the productivity spillover ϱ ϕ z,2 = ϱϕ z,1 + (1 ϱ)ϕ z,2. Baseline ϱ =.5. For low ϱ =.1 2 The more open is the economy τ 3 The more granular is the sector Γ z click (a) Welfare effect of a merger, Ŵ Z (b) Decomposition of Ŵ Z, τ =1.34 2.5% 2% 1.5% 1%.5% Baseline τ =1.34 Low τ =1 High τ =2.68 3% Baseline ŴZ Profits d Π/Y Price dlog P 2% 1% % % -1% -.5% 1 2 3 4 5 Quintiles of sectors by granular Γ z -2% 1 2 3 4 5 Quintiles of sectors by granular Γ z 26 / 28

Import Tariff Tariff on the top importer ς z,1 vs a uniform import tariff ς z yielding the same tariff revenue ς z,1 ς z, particularly in the foreign granular industries (Γ z ) (a) Uniform tariff (b) Granular tariff.6%.4% Overall welfare Tariff revenue Producer surplus Consumer surplus.6%.4% Overall welfare Tariff revenue Producer surplus Consumer surplus.2%.2% % % -.2% -.2% 1 2 3 4 5 Quintiles of sectors by import granularity Γz 1 2 3 4 5 Quintiles of sectors by import granularity Γz 27 / 28

Conclusion 28 / 28

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 28 / 28

APPENDIX 29 / 28

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 1 1.8.8.6.6.4.4.2.2 1 2 1 1 1 1 Number of draws 1 2 1 1 1 1 Number of draws back to slides 3 / 28

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 31 / 28

6.5 (a) Number of French firms F θ τ µt σt.3 (b) Top French firm share F θ τ µt σt 6.25 5.5.2 5-1 -.5.5 1.15-1 -.5.5 1.5 (c) Domestic import share F θ τ µt σt (d) Export projection coefficient.5 F θ τ µt σt.4.4.3.3.2.1.2-1 -.5.5 1-1 -.5.5 1 32 / 28

(a) Pareto shape, κ z = θz σ 1 (b) Estimated Pareto, ˆκ z 1.5 1 κ 1.2 H1 H2 H3 1.5 Data H1 H2 H3 1.5.5.5 1 1.5 2.5 1 1.5 2 (c) Top-firm sales share, s z,1 (d) Number of firms, M z.4 4.3 3 2.2 1.1.1.2.3.4.5 1 1 1 1 1 back 33 / 28

Probability a sector remains among top-5% of export-intensive sectors 1.9.8.7.6.5 T = 1 2 3 4 5 T, years back 34 / 28

Trade effects of individual firm exit (a) All sectors, deciles of Γ z (b) All sectors, deciles of Λ z.3.25 Top firm share Loss in export share.25.2 Top firm share Loss in export share.2.15.15.1.1.5.5-1 -.8 -.5 -.3 -.2 -.1 -.1.4.1 1 Deciles of sectors, by granular Γ z.2.4.7.1.15.21.29.41.58 1 Deciles of sectors, by export share Λ z back 35 / 28

Merger Low spillover ϱ =.1.5% % Welfare effect of a merger, Ŵ Z Baseline τ =1.34 Low τ =1 High τ =2.68 4% 3% 2% Decomposition of Ŵ Z, τ = 1.34 Baseline ŴZ Profits d Π/Y Price dlog P 1% % -.5% -1% -2% -1% 1 2 3 4 5 Quintiles of sectors by granular Γ z -3% 1 2 3 4 5 Quintiles of sectors by granular Γ z back 36 / 28