Firm-to-Firm Trade: Imports, Exports, and the Labor Market

Transcription

1 Firm-to-Firm Trade: Imports, Exports, and the Labor Market Jonathan Eaton, Samuel Kortum, Francis Kramarz Tokyo: March 2016

2 Objectives Model rms in a network both selling outputs and buying inputs Connect these interactions with rm employment Interpret the facts on rm-level exporting and importing Do it in a general-equilibrium setting At this point its still largely an untested theory...

3 A Peek at the Data Thanks to: Kramarz, Martin, Mejean (2014)

4 Table21:2Customers2per2French2Exporter Destination2Market Lithuania Denmark UK Germany Market2Size2($billions) Customers2per2Exporter: Mean Percentiles: 25th th th th th th Data2are2for22005.

5 French exporters, adjusted for market share Figure 2: French Exporters and Market Size MT LV CY EE LT LU SI SK NL FI AT IE DK GR PT SE PL CZ BE HU market size ($ billions) ES IT GB DE

6 Figure 3: Buyers per French Exporter, by Destination buyers per exporter MT LU CY LVEE LT SI SK BE PT NL GR IE AT SE DKFI PL HU CZ ES IT GB DE market size ($ billions)

7 Related Literature Firm-level imports: Biscourp and Kramarz (2007); Hummels, Jorgenson, Munch, and Xiang (2011); Blaum, Lelarge, and Peters (2014); Kramarz, Martin, and Mejean (2015); Antras, Fort, Tintelnot (2015). Networks: Chaney (2014); Eaton, Eslava, Jinkins, Krizan, and Tybout (2014); Bernard, Moxnes, and Ulltveit-Moe (2014) Theoretical elements: BEJK (2003); Melitz (2003); EKK (2011); EKS (2013); Garretto (2013); Ober eld (2014)

8 A Model of Firm-to-Firm Trade

9 Production Many countries i = 1; :::; N, trading subject to iceberg trade costs, d ni Firm j in country i produces CRS: Q i (j) = z i (j) KY k=1 m k;i (j) k Country i endowed with measure of rms with e ciency above z: z i (z) = T iz The task k input m k;i (j) is purchased at cost c k;i (j)

10 Simple Example Task 1 perfomed by labor, c 1;i (j) = w i Task 2 by intermediate good, c 2;i (j) = p i Implies that a measure n (c) of rms can supply n at a cost below c: n (c) = NX i=1 T i w 1 i p1 i d ni A c

11 Assessment With xed cost of selling and monopolistic competition, Melitz-Chaney which describes behavior of French exporters in EKK But fails to capture: granularity of demand (few customers per rm) network of rms supplying each other unique inputs rm-level importing and exporting

12 Back to the Model Drop xed cost of selling and monopolistic competition, but add idiosyncratic costs of carrying out tasks: ( ) wk;i c k;i (j) = min q k;i (j) ; pmin k;i (j)... where assume i.i.d.: Pr h q k;i (j) q i = F (q)... and derive: Pr h c k;i (j) c i = G k;i (c)

13 Matching: Buyers nding Suppliers A rm in i looking for low cost suppliers of intermediates to carry out task k is exposed to suppliers with cost c at intensity e k;i (c) = k;i i (c) Measure i (c) of rms can supply i at a cost below c, but rm is aware of a countable number, distributed Poisson with parameter: k;i (c) = Z c 0 e k;i(x)d i (x) = k;i 1 i(c) 1 Assume buyer has all the bargaining power so price equals cost

14 Key Result If: F (q) = e q = e q (1 ) Then: n (c) = n c with n = X i T i d ni KY k=1 k;i = i! + w k k;i

15 Discussion System of s is well behaved, given wages, if for each i, k;i = 0 for some k If all k;i s are zero, then back to our simple example, with = 1 and: w i = KY k=1 w k k;i Otherwise, every increasing in any T i or k;i

16 Implications: Distributions Price of low-cost intermediate for task k: Pr h p min k;i (j) pi = 1 e k;i(p) = 1 e k;i = i p Cost of carrying out task k: Pr h c k;i (j) c i = G k;i (c) = 1 e k;ic k... where k;i = k;i = i + w k;i

17 Implications: Shares Probability w k;i = k;i that a rm performs task k using its workers Aggregate labor share: L i = KX k=1 w k;i k k;i Measure of rms from i that can supply n at cost below c: ni (c) = i d ni KY k=1 k k;i 1 A c Trade share: ni = ni (c)= n (c)

18 Closing the Model

19 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: P C n = Q k k;n k =

20 Goods Market Clearing Total production in country i: Y i = NX n=1 ni h (1 L n )X C n + (1 L n)y n i... where L n is labor share in production and L n with k in place of k is de ned in parallel, Country i is endowed with L l i tasks k 2 l workers of type l who are able to perform Next, solve for equilibrium wages w l i, where w k;i = w l i for k 2 l

21 Labor Market Clearing Trade balance and income: X C i = Y L i = X l w l i Ll i Labor market equilibrium: w l i Ll i = l i Y L i + l i Y i Here l i (and likewise l i, with k in place of k ) are given by: l i = X k2 l k w k;i k;i

22 Numerical Exploration of Aggregates

23 Table 2: Baseline Parameter Settings for Simulation Parameter symbol value Pareto parameters: efficiency distribution theta 5 price distribution phi 2 Technology level per person T_i/L_i 3.6 World labor force L 1 Labor by type (fractions of labor force): L^l nonproduction (service) 0.6 production 0.4 Iceberg trade cost d 1.2 Tasks, by type: service tasks: number of tasks K 4 total share beta 0.4 production tasks: number of tasks K 12 total share beta 0.6 Task shares in consumption (same as for production) alpha Outsourcing parameters: lambda service 0 production 0.2

24 Table 3: Aggregate Results of Simulation Country Size L=0.001 L=0.009 L=0.09 L=0.2 L=0.3 L=0.4 Production value added: Share of GDP Share of gross production Fraction of production tasks outsourced: 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

25 Table 3: Aggregate Results of Simulation Country Size L=0.001 L=0.009 L=0.09 L=0.2 L=0.3 L=0.4 Production value added: Share of GDP Share of gross production Fraction of production tasks outsourced: Import share of production 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

26 Table 3: Aggregate Results of Simulation Country Size L=0.001 L=0.009 L=0.09 L=0.2 L=0.3 L=0.4 Production value added: Share of GDP Share of gross production Fraction of production tasks outsourced: Import share of production Wage: service production Skill premium (service/production) 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

27 Table 3: Aggregate Results of Simulation Country Size L=0.001 L=0.009 L=0.09 L=0.2 L=0.3 L=0.4 Production value added: Share of GDP Share of gross production Fraction of production tasks outsourced: Import share of production Wage: service production Skill premium (service/production) Real wage: service production Welfare (real per capita consumption) 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

28 Table 4: Aggregate Results with Different Trade Costs Trade Cost (small country, L=.009) Trade Cost (large country, L=0.3) Production value added: Share of GDP Share of gross production Fraction of prod. tasks outsourced: 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

29 Table 4: Aggregate Results with Different Trade Costs Trade Cost (small country, L=.009) Trade Cost (large country, L=0.3) Production value added: Share of GDP Share of gross production Fraction of prod. tasks outsourced: Import share of production 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

30 Table 4: Aggregate Results with Different Trade Costs Trade Cost (small country, L=.009) Trade Cost (large country, L=0.3) Production value added: Share of GDP Share of gross production Fraction of prod. tasks outsourced: Import share of production Wage: service production Skill premium (service/production) 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

31 Table 4: Aggregate Results with Different Trade Costs Trade Cost (small country, L=.009) Trade Cost (large country, L=0.3) Production value added: Share of GDP Share of gross production Fraction of prod. tasks outsourced: Import share of production Wage: service production Skill premium (service/production) Real wage: service production Welfare (real per capita cons.) 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

32 Firm-Level Implications

33 Matching: Suppliers nding Buyers Poisson number of potential customers in n (task k) for a rm delivering there at cost c: (L n + M n ) e k;n (c) Poisson number of actual customers in n (any task) for a rm delivering there at cost c: n (c) = (L n + M n ) X e k;n (c) h 1 G k;n (c) i k Probability of this rm having at least one customer in n: 1 e n(c)

34 Measure of Producers by Source Poisson number of customers anywhere for a rm from i with cost c in the home market: W i (c) = X n n (cd ni ) Measure of rms producing in i: Z 1 M i = 1 e W i (c) 0 d ii (c)

35 Firm Entry by Destination Market Measure of rms from i selling in n: N ni = Z e n (c) d ni (c) We can compute entry, and how it relates to market size... even though the model has no xed cost of selling in a market

36 Table 5: Firm- Level Results of Simulation Country Size L=0.001 L=0.009 L=0.09 L=0.2 L=0.3 L=0.4 Measures of firms: producing selling

37 Table 5: Firm- Level Results of Simulation Country Size L=0.001 L=0.009 L=0.09 L=0.2 L=0.3 L=0.4 Measures of firms: producing selling Measures normalized by Labor: producing selling

38 Table 5: Firm- Level Results of Simulation Country Size L=0.001 L=0.009 L=0.09 L=0.2 L=0.3 L=0.4 Measures of firms: producing selling Measures normalized by Labor: producing selling Fraction of firms selling domestically:

39 Table 5: Firm- Level Results of Simulation Country Size L=0.001 L=0.009 L=0.09 L=0.2 L=0.3 L=0.4 Measures of firms: producing selling Measures normalized by Labor: producing selling Fraction of firms selling domestically: Mean # customers per firm: Size distribution (percentiles): 25th th th th th th

40 Table 6: Firm- Level Results with Different Trade Costs Trade Cost (small country, L=.009) Trade Cost (large country, L=0.3) Measures of firms: producing selling

41 Table 6: Firm- Level Results with Different Trade Costs Trade Cost (small country, L=.009) Trade Cost (large country, L=0.3) Measures of firms: producing selling Measures normalized by Labor: producing selling

42 Table 6: Firm- Level Results with Different Trade Costs Trade Cost (small country, L=.009) Trade Cost (large country, L=0.3) Measures of firms: producing selling Measures normalized by Labor: producing selling Fraction of firms selling domestically:

43 Table 6: Firm- Level Results with Different Trade Costs Trade Cost (small country, L=.009) Trade Cost (large country, L=0.3) Measures of firms: producing selling Measures normalized by Labor: producing selling Fraction of firms selling domestically: Mean # customers per firm: Size distribution (percentiles): 25th th th th th th

44 French exporters, adjusted for market share Figure 2: French Exporters and Market Size MT LV CY EE LT LU SI SK NL FI AT IE DK GR PT SE PL CZ BE HU market size ($ billions) ES IT GB DE

45 Figure 3: Buyers per French Exporter, by Destination buyers per exporter MT LU CY LVEE LT SI SK BE PT NL GR IE AT SE DKFI PL HU CZ ES IT GB DE market size ($ billions)

46 country A suppliers, adjusted for market share a Figure 5: Suppliers and Market Size b market size c d e f

47 Figure 6: Buyers per Supplier, by Destination buyers per supplier a b c d e f market size