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Firm-to-Firm Trade: Imports, Exports, and the Labor Market Jonathan Eaton, Samuel Kortum, Francis Kramarz April 2015 Panel B: Normalized Entry 5000000 JAP entry normalized by French market share USA GER UNK AUL SWI CHN GEE BRA ITA TAI AUT SPA BUL FRA NZE SWE NET ARG FIN YUG NOR SOU CZE BEL ROM ISR DEN KOR MEX HOK GRE VIE VEN IND IRE HUN MAY SAU SIN CHICUB POR TUR COL ALG IRN EGY ECU SUD PER INO COTSYR PHI ZIM CAM PAN PAK TRIURU MOR ALB COS THA JOR KUW TAN DOMTUN SRI ETH ELS GUA BUK BOLPAR SEN IRQ HON ZAIOMA PAP BAN NIA MAS JAMANG TOG LIY SOM CHA MAL MAD NIC KEN UGA BEN NEP RWA NIG MOZ CEN BUR ZAM GHA MAU AFG LIB MAW 100000 10000 1000 USR CAN 1000000 SIE .1 1 10 100 market size ($ billions) 1000 10000 Introduction Micro data, Bernard and Jensen ... Treat exporting and exporting symmetrically Holmes vision vs. Melitz model Imports vs. labor within …rms Lucas, Ober…eld, Garetto A Peek at the Data Thanks to: Kramarz, Martin, Mejean (2014) 32000 Figure 1: French Exporters and Market Size BE number of French exporters 2000 4000 8000 16000 ES DE IT GB NL PT LU DK ATPL GR SE IE CZ FI HU LT SK CY LV EE 1000 MT SI 1 10 100 market size ($ billions) 1000 10000 French exporters, adjusted for market share 10000 100000 1000000 Figure 2: French Exporters and Market Size IT DE GB ES NL FI ATPL PT IE DK SE GR CZ BE SK HU LV LT CY LU EE SI MT 1 10 100 market size ($ billions) 1000 10000 32 Figure 3: Buyers per French Exporter, by Destination IT ES DE BE buyers per exporter 4 8 16 GB PT NL GR AT IE LU SE DKFI MT CY LVEE SI HU CZ SK 2 LT PL 1 10 100 market size ($ billions) 1000 10000 Table21:2Customers2per2French2Exporter Destination2Market Lithuania Denmark UK Market2Size2($billions) 18 94 882 Customers2per2Exporter: Mean 4.2 7.1 17.9 Percentiles: 25th 1 1 1 50th 2 2 3 75th 4 5 9 90th 9 12 25 95th 15 21 48 99th 40 77 224 Data2are2for22005. Germany 1480 24.9 2 4 12 35 70 329 Table21:2Customers2per2French2Exporter Destination2Market Lithuania Denmark UK Market2Size2($billions) 18 94 882 Customers2per2Exporter: Mean 4.2 7.1 17.9 Percentiles: 25th 1 1 1 50th 2 2 3 75th 4 5 9 90th 9 12 25 95th 15 21 48 99th 40 77 224 Data2are2for22005. Germany 1480 24.9 2 4 12 35 70 329 0 20 centile 40 60 80 100 Dist. of the Share of Production Labor 0 .2 .4 .6 share in total variable cost .8 1 0 20 centile 40 60 80 100 Dist. of the Share of Non-Skilled Production Labor 0 .2 .4 .6 share in total variable cost .8 1 Related Literature Firm-level imports: Biscourp and Kramarz (2007); Hummels, Jorgenson, Munch, and Xiang (2011); Blaum, Lelarge, and Peters (2014); Kramarz, Martin, and Mejean (2014); Eaton, Eslava, Jinkins, Krizan, and Tybout (2014); Antras, Tintelnot ... Networks: Chaney (2014); Eaton, Eslava, Jinkins, Krizan, and Tybout (2014), Bernard, Moxnes, and Saito (2014) Theoretical elements: BEJK (2003); Melitz (2003); EKK (2011); EKS (2013); Garretto (2013); Ober…eld (2014) A Model of Firm-to-Firm Trade Setting Many countries Iceberg trade costs, dni Continuum of …rms Firms supply intermediates to each other Each buyer encounters only a handful of suppliers Buyers have all the bargaining power Tasks Firm must carry out k = 1; :::; K tasks, using labor or an intermediate bought from another …rm: – Labor paid wk;i, random e¢ ciency Q – Intermediate available at random price P n o – Cost of carrying out task: C = min P; wk;i=Q Production Task outputs combine in constant-returns Cobb-Douglas production function Firm j ’s unit cost function: K Y 1 ck (j ) c(j ) = z (j ) k=1 bk k ! Firms di¤er in e¢ ciency z (j ) and task-speci…c realized costs ck (j ) Endowments Factors: country i endowed with Lli units of type l labor (skill types) – Type l labor is capable of performing tasks k 2 l – Equilibrium wage wil so that wk;i = wil for k 2 l Technology: country i endowed with measure ciency > z z (z ) i of …rms with e¢ - Distributions Measure of …rms in i with e¢ ciency > z ( > 0): z (z ) i = Tiz Probability workers perform a task at e¢ ciency below q (0 < F (q ) = e q ): Matching Buyer encounters individual supplier with intensity (0 < 1): ek;n(c) = k;n n(c) Here n(c) is the measure of …rms that supply n at a cost below c Number of suppliers a buyer encounters at cost below c is distributed Poisson with parameter: k;n(c) = Z c 0 ek;n(x)d n(x) = k;n 1 1 n (c) Conjecture Assume: = (1 ) Then: n (c) = nc Implications for Intermediates Prices Price distribution of low-cost intermediate: Pr [P pk ] = 1 k;n (pk ) e Expected price: pk;n = (1 + 1= ) k;n = n 1= 1= = ' k;n n 1= Implications for Task-Speci…c Costs Distribution of the cost of performing task k: h n o Gk;n(ck ) = Pr min P; wk;i=Q where: k;n = i ck = 1 ' pk;n + wk;n e k;n ck ; Implications for Labor’s Share Probability that task k is performed by workers: k;n = wk;n k;n Share of type l labor: l n = X k k;n K X k k;n k2 l Aggregate labor share: L n = k=1 Completing the Circle I Unit cost of …rm j from i delivering to n (given cost of performing tasks): K dni Y c(j ) = ck k =bk zi(j ) k=1 Measure of such …rms that can supply n at a cost below c: ni (c) = Z 1 0 ::: Z 1 0 1 K Y z @ dni ck k =bk A dG1;i(c1):::dGK;i(cK ) i c k=1 0 Completing the Circle II Note that: ni (c) = Tidni c K Y bk k=1 Z 1 0 ck k dG k;i(ck ) Simpli…es (by prudent choice of bk ’s): ni (c) = Q k k;i k ! Tidni c Completing the Circle III Summing across sources veri…es our conjecture: n (c) = N X ni (c) = nc i=1 With n satisfying: n = X i Tidni K Y k=1 = k;i i + wk;i ! k ; a contraction mapping if at least 1 task can’t be outsourced ( k;i = 0 for some k) Partial Equilibrium Aggregate Representation Consider a representative …rms taking wages wk;i and intermediate prices pk;i as given Its production function is CES nested within Cobb-Douglas: Yi = K Y ' ~ Lk;i =( +1) + (1 ' ~ ) Mk;i =( +1) k=1 with elasticity of substitution 1 + ' ~= and share parameter 1 + ' =(1+ ) 1 k( +1)= Aggregate Representation II Firm will choose: wk;iLk;i pk;iIk;i = ' wk;i pk;i ! Implies share of type l same as that generated by …rm-to-…rm trade: l i = X k2 l wk;i k k;i Households and the Cost of Living Utility function is like the production function but with k in place of k Households choose …nal goods like …rms choosing intermediates Exact price index for households: PnC = Q k= k k;n Bilateral Trade Shares Probability that a …rm (that can supply an intermediate good to n at a cost below c) is from i: ni (c) = = ni n (c) Tidni Q = k k;i i + wk;i n Since household choices mimic those of …rms, this probability becomes the bilateral trade share: Xni = ni Xn General Equilibrium General Equilibrium I Total production in country i: Yi = N X n=1 ni h (1 L )X C n n L )Y n n + (1 i where the aggregate labor share in production is L n = K X k=1 and for households L n wk;n k k;n is de…ned in parallel, with k in place of k General Equilibrium II Trade balance and income: XiC = YiL = X wil Lli l = X wk;iLk;i k Labor market equilibrium: wil Lli = liYiL + liYi where li (and likewise l, i with l i = k in place of k ) are given by: X k2 l wk;i k k;i Numerical Exploration of Aggregates Table 2: Baseline Parameter Settings for Simulation Parameter Pareto parameters: efficiency distribution price distribution Technology level per person World labor force Labor by type (fractions of labor force): nonproduction (service) production Iceberg trade cost Tasks, by type: service tasks: number of tasks total share production tasks: number of tasks total share Task shares in consumption (same as for production) Outsourcing parameters: service production symbol value theta phi T_i/L_i L L^l d K beta 5 2 3.6 1 0.6 0.4 1.2 4 0.4 K beta alpha lambda 12 0.6 0 0.2 Table 3: Aggregate Results of Simulation L=0.001 L=0.009 Country Size L=0.09 L=0.2 Production value added: Share of GDP 0.126 0.126 0.128 Share of gross production 0.31 0.31 0.30 Fraction of production tasks outsourced: 0.48 0.48 0.50 Import share of production 1.00 0.97 0.79 Wage: service 0.87 0.87 0.91 production 1.02 1.02 1.03 Skill premium (service/production) 0.85 0.86 0.88 Real wage: service 1.45 1.46 1.50 production 1.71 1.71 1.70 Welfare (real per capita consumption) 1.55 1.56 1.58 1. Production value added does not include service tasks (i.e. purchased services) 2. Wage is normalized so that labor income of the World is 1 L=0.3 L=0.4 0.130 0.29 0.51 0.61 0.131 0.28 0.53 0.49 0.132 0.28 0.54 0.39 0.94 1.03 0.91 0.98 1.04 0.94 1.00 1.05 0.96 1.55 1.69 1.61 1.58 1.69 1.63 1.62 1.69 1.64 Table 4: Aggregate Results with Different Trade Costs Trade Cost (small country, L=.009) 10.00 1.80 1.20 1.05 1.00 Production value added: Share of GDP 0.06 0.09 0.13 0.13 0.13 Share of gross production 0.49 0.43 0.31 0.27 0.26 Fraction of prod. tasks outsourced: 0.19 0.29 0.48 0.55 0.57 Import share of production 0.00 0.76 0.97 0.99 0.99 Wage: service 0.73 0.62 0.87 0.98 1.02 production 1.34 1.00 1.02 0.99 0.97 Skill premium (service/production) 0.55 0.62 0.86 0.99 1.04 Real wage: service 0.98 1.10 1.46 1.66 1.74 production 1.78 1.76 1.71 1.68 1.67 Welfare (real per capita cons.) 1.30 1.36 1.56 1.67 1.71 1. Production value added does not include service tasks (i.e. purchased services) 2. Wage is normalized so that labor income of the World is 1 Trade Cost (large country, L=0.3) 10.00 1.80 1.20 1.05 1.00 0.12 0.32 0.47 0.00 0.13 0.31 0.48 0.11 0.13 0.28 0.53 0.49 0.13 0.26 0.56 0.65 0.13 0.26 0.57 0.70 0.93 1.11 0.83 0.94 1.11 0.85 0.98 1.04 0.94 1.00 0.99 1.01 1.02 0.97 1.04 1.42 1.71 1.54 1.45 1.71 1.55 1.58 1.69 1.63 1.69 1.68 1.69 1.74 1.67 1.71 Firm-Level Implications Buyers Poisson number of customers in n for a …rm delivering there at cost c: n (c) = (Ln + Mn) X h ek;n(c) 1 k i Gk;n(c) Poisson number of customers anywhere for a …rm from i with cost c (at home): W (c) i = X n n (cdni ) Probability of …rm in i with cost c exporting to n: 1 e n (cdni ) Firm Entry Measure of …rm producing in i: Mi = Z 1 0 1 e W (c) i d ii(c) Measure of …rms from i selling in n: Nni = Z 1 0 1 e n (c) d ni(c) From these expressions we can compute entry and how it relates to market size (even though no …xed cost) Table 5: Firm-‐Level Results of Simulation Measures of firms: producing selling Measures normalized by Labor: producing selling Fraction of firms selling domestically: Mean # customers per firm: Size distribution (percentiles): 25th 50th 75th 90th 95th 99th Country Size L=0.09 L=0.2 L=0.001 L=0.009 L=0.3 L=0.4 0.02 0.08 0.14 0.61 1.60 3.93 3.95 7.38 6.32 10.15 8.80 12.67 15.7 84.9 0.02 1.13 15.9 67.6 0.11 1.44 17.8 43.7 0.53 2.56 19.8 36.9 0.74 3.47 21.1 33.8 0.83 4.12 22.0 31.7 0.88 4.68 1 1 1 1 2 3 1 1 1 2 3 8 1 1 2 4 7 22 1 1 2 5 10 34 1 1 3 6 12 43 1 1 3 7 14 51 Table 6: Firm-‐Level Results with Different Trade Costs Measures of firms: producing selling Measures normalized by Labor: producing selling Fraction of firms selling domestically: Mean # customers per firm: Size distribution (percentiles): 25th 50th 75th 90th 95th 99th Trade Cost (small country, L=.009) 10.00 1.80 1.20 1.05 1.00 0.29 0.29 0.09 0.21 0.14 0.61 0.22 1.07 11.4 11.4 9.6 10.8 6.3 10.1 6.8 11.7 7.3 12.7 31.9 31.9 1.00 2.33 9.5 23.7 0.60 1.52 15.9 21.6 24.4 67.6 101.6 118.5 0.11 0.06 0.04 1.44 1.47 1.48 37.9 37.9 1.00 5.73 32.0 36.1 1.00 5.23 21.1 33.8 0.83 4.12 22.6 38.9 0.61 4.08 24.4 42.4 0.52 4.14 1 1 2 4 6 19 1 1 1 2 3 9 1 1 3 9 17 66 1 1 3 8 16 59 1 1 3 6 12 43 1 1 3 6 12 43 1 1 3 6 12 44 1 1 1 2 3 8 0.19 0.91 Trade Cost (large country, L=0.3) 10.00 1.80 1.20 1.05 1.00 1 1 1 2 3 8 1 1 1 2 3 8 Figure 5: Suppliers and Market Size country A suppliers, adjusted for market share .1 1 10 f d c b a .001 .01 .0001 e .01 market size .1 1 8 Figure 6: Buyers per Supplier, by Destination f buyers per supplier 2 4 e d c b 1 a .0001 .001 .01 market size .1 1