Firm-to-Firm Trade: Imports, Exports, and the Labor Market. IEA: Mexico City. Jonathan Eaton, Samuel Kortum, Francis Kramarz.

Transcription

1 Firm-to-Firm Trade: Imports, Exports, and the Labor Market Jonathan Eaton, Samuel Kortum, Francis Kramarz IEA: Mexico City June 2017

2 Overview Develop granular theory of rms, jobs, and international trade Individual rms may export goods and import intermediates Guidance from French Customs data on transactions:... French exporters and their customers in 24 EU countries Today: toward estimation

3 Fundamental Features As in Chaney (2014, 2017): international trade via rms establishing a network of buyers... with trade frictions becoming information frictions Central feature is a xed point à la Lucas (2009) and Ober eld (2013):... distribution of costs governs suppliers you meet... which shapes distribution of costs Search frictions have implications similar to xed costs of entry... and bilateral information frictions inhibit trade

4 Other 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: Eaton, Eslava, Jinkins, Krizan, and Tybout (2014); Bernard, Moxnes, and Ulltveit-Moe (2014); Lim (2017) Theoretical elements: BEJK (2003); Melitz (2003); EKK (2011); EKS (2013); Garretto (2013); Armenter and Koren (2014)

5 A Peek at the Data From Kramarz, Martin, and Mejean (2015):... customers of individual French manufacturing exporters, in each EU country Similar stylized facts emerge from Bernard, Moxnes and Ulltveit-Moe (2017):... customers of Norwegian exporters, in every country

6 France Germany Firm 1 Firm 2 Lithuania Firm 3

7 Identities French exports to destination n: X nf = X n nf Relationships between French exporters and buyers in n: R nf = N nf B nf

8 Regressions Number of French exporters (ignore constant): ln N nf = 0:50 (0:04) ln X n + 0:68 (0:11) ln nf Number of relationships (ignore constant): ln R nf = 0:83 (0:06) ln X n + 1:04 (0:16) ln nf Mean number of buyers per French exporter (ignore constant): ln B nf = 0:33 (0:03) ln X n + 0:36 (0:08) ln nf

9 Figure 3: French Relationships and Market Size IT DE French relationships, adjusted for market share MT CY LV EE LU LT SI SK BENL PT AT GR IE DKFI SE PL HU CZ ESGB market size ($ billions)

10 Customers in DE of French Exporters average customers per firm EE MT LV CY LT SI SK HU FI IE CZ AT GR SE DK PL LU PT NL ITES GB BE DE number exporting to Germany and elsewhere

11 Model of Firm-to-Firm Trade

12 Setting Many countries (n destination, i source) n; i = 1; :::; N Separated by iceberg trade costs d ni and search frictions ni Endowed with workers of various skills and a continuum of potential producers

13 Production Measure of potential rms in i with e ciency above z: z i (z) = T iz Each rm has Cobb-Douglas production function over K tasks A task is performed by labor or by purchasing an input from another rm

14 Matching Chance meetings between buyers (manufacturers looking for inputs M n or others B n )... and suppliers with cost below c (looking for customers) governed by a matching function: where m n (c) = K 1 (M n + B n ) L ' n n (c) 1 n (c) = X i ni ni (c) and ni (c) is measure of rms from i that supply n at a cost below c

15 Firm 3 Firm 2 Cost Firm 1

16 Distributional Results Buyer encounters suppliers (with cost below c), distributed Poisson: n (c) = 1 L ' n n (c) 1 Chooses low cost supplier or employs labor, with random e ciency Resulting distribution for cost of rm j in country n performing a task: Pr [c n (j) c] = G n (c) = 1 e (1 ) 1;nc 1;n = 1 L n ' 1 n + w (1 ) n

17 Main Result Measure of rms from i that supply n at a cost below c: ni (c) = d ni T i i c where i = 0 1 L ' i X i 0 ii 0d ii 0 T i 0 i 0 11 A + w i 1 (1 ) C A And, measure relevant to buyers in n: n (c) = X i ni ni (c) = n c

18 Key Macro Implications Bilateral trade shares (n s purchases devoted to imports from i): ni = nid ni T i i n Labor shares in production: L i = (1 0 ) w (1 ) i 1;i

19 Closing the Model (for another day!)

20 Firm-Level Results

21 Suppliers nding Buyers Recall the matching function, m n (c) Number of buyers in n for rm in i (with cost c in i) is Poisson: ni (cd ni ) = ni f n (cd ni ) where, letting = (1 ): f n (x) = (1 ) m n(x) n (x) [1 = (M n + B n ) L n ' n G n(x)] (x) Ke 1;n(x)

22 Computations Use Poisson parameter ni (cd ni ) to solve for rm-level observables by integrating over the density of producers with cost c in the source country: d ii (c) = T i i c 1 dc Calculate measure of active producers by country, and bilaterally... exporters and relationships

23 Measure of Active Firms Number of buyers around the world for a rm from i (cost c) is Poisson: W i (c) = X n ni (cd ni ) Measure of active rms in i: M i = Z e W i (c) d ii (c)

24 Firm Entry by Destination Measure of rms from i selling in n: N ni = Z e ni (cd ni ) d ii (c) Changing the variable of integration: N ni = d ni Z e ni f n (c) d ii (c)

25 Entry and Market Size The search friction acts like a xed cost,... entry margin varying with M n + B n, ni, and d ni For xed ni and n, get N ni rising in proportion to i s market share in n ( ni )... as in EKK I If ni rises with ni, then N ni rises less than in proportion, as ni hits diminishing returns... as having just one customer in n is all it takes to be an exporter to n

26 Relationships The measure of relationships between sellers in i and buyers in n: R ni = Z 1 0 ni (cd ni )d ii (c) = ni (M n + B n ) K 1 L n ' 1 n 1;n Note it s proportional to ni, hence to ni d ni (as in the data) Here, and in what follows, consider only other manufacturers as customers

27 Distribution of Buyers per Exporter Fraction of exporters (from i to n) with s buyers: N ni (s) N ni = 1 N ni Z 1 0 e ni(cd ni ) ni (cd ni ) s d ii (c) s!

28 Toward Estimation

29 Simpli cations Service works perform task 0, manufacturing workers all other tasks Task-speci c contact rates: 0 = 0 and k = Task shares: 0 (purchased services) and k = (1 0 )=K Other buyers behave in parallel to manufacturers

30 Strategy I Partial equilibrium: condition on ni, labor shares in manufacturing 1;L n, and relationships of French rms... t key macro implications perfectly! Set bilateral information frictions: ni =! ni ii Iceberg costs absorb all the rest to t bilateral trade shares.

31 Strategy II Labor shares satis es: n = (1 0 ) w 1;n 1;L 1;n From results of previous slide, back out the 1;n from: 1;n = ;L L n ' = n n

32 Strategy III Relationships of French rms: R nf = nf (M n + B n ) K 1 L n ' = n 1;n = nf (M n + B n ) K 1 0 1;L n 1 0 Invert, to obtain the number of customers: M n + B n = R nf nf K ;L n

33 Data Data we condition on comes from WIOD, 2005:... Timmer, Dietzenbacher, Los, Stehrer, and de Vries (2015) Lihua Xiao and Lixing Liang constructed, for manufacturing industries: and ni = X ni X n 1;L n = V n Y n For congestion, L n is population

34 Parameters Set two parameters: 0 = 0:3, K = 20 Fit 5 others: = 3:1, = 2:1, ' = 0:25, = 0:53, = 0:45 Everything we need to calculate model implications

35 Results Buyers per French Exporter Lithuania Denmark U.K. Germany Mean Median th th

36 Regressions on Simulated Data Number of French exporters: ln N nf = 0:61 ln X n + 0:71 ln nf Number of relationships (same as data): ln R nf = 0:82 ln X n + 1:05 ln nf Mean number of buyers per French exporter: ln B nf = 0:21 ln X n + 0:34 ln nf

37 Buyers per Firm in Germany Conditional on Entry Regression corresponding to Figure (ignore constant): ln B DF j n = 0:38 (0:02) ln N nf jd Regression on simulated data : ln B DF j n = 0:55 ln N nf jd

38 Conclusion Theory captures some striking patterns in the micro data Yet easy to work with at the aggregate level Amenable to estimation in partial equilibrium Then, many issues to explore with GE counterfactuals