Imperfect Competition and the Transmission of Shocks: The Network Matters

Transcription

1 Imperfect Competition and the Transmission of Shocks: The Network Matters Ayumu Ken Kikkawa 1 Glenn Magerman 2 Emmanuel Dhyne 3 1 University of Chicago 2 ECARES (ULB) 3 National Bank of Belgium February 2018 RIETI 0/28

2 Motivation Domestic firm-to-firm trade in Belgium 1.5 value added. High concentration in firms inputs. For the majority of Belgian firms, the number of suppliers is 28 or less. the largest supplier accounts for 27% or more of input purchases. What are the implications of oligopolistic competition and endogenous networks for the transmission of shocks in the aggregate? 1/28

3 This paper Presents two facts from Belgian firm-to-firm trade data. 1. Firm-level markups correlated with firms downstream sales shares within customer firms. 2/28

4 This paper Presents two facts from Belgian firm-to-firm trade data. 1. Firm-level markups correlated with firms downstream sales shares within customer firms. 2. Firms experience larger churn of suppliers when exposed to larger import supply shocks. 2/28

5 This paper Presents two facts from Belgian firm-to-firm trade data. 1. Firm-level markups correlated with firms downstream sales shares within customer firms. 2. Firms experience larger churn of suppliers when exposed to larger import supply shocks. Develops a model of firm-to-firm trade. 1. Oligopolistic competition (pairwise variable markups). 2/28

6 This paper Presents two facts from Belgian firm-to-firm trade data. 1. Firm-level markups correlated with firms downstream sales shares within customer firms. 2. Firms experience larger churn of suppliers when exposed to larger import supply shocks. Develops a model of firm-to-firm trade. 1. Oligopolistic competition (pairwise variable markups). 2. Endogenous networks with fixed costs. 2/28

7 This paper Presents two facts from Belgian firm-to-firm trade data. 1. Firm-level markups correlated with firms downstream sales shares within customer firms. 2. Firms experience larger churn of suppliers when exposed to larger import supply shocks. Develops a model of firm-to-firm trade. 1. Oligopolistic competition (pairwise variable markups). 2. Endogenous networks with fixed costs. In the benchmark case (without these two elements), firm-level variables are sufficient in calculating aggregate response to shocks. 2/28

8 This paper Presents two facts from Belgian firm-to-firm trade data. 1. Firm-level markups correlated with firms downstream sales shares within customer firms. 2. Firms experience larger churn of suppliers when exposed to larger import supply shocks. Develops a model of firm-to-firm trade. 1. Oligopolistic competition (pairwise variable markups). 2. Endogenous networks with fixed costs. In the benchmark case (without these two elements), firm-level variables are sufficient in calculating aggregate response to shocks. Analyzes the aggregate responses to a foreign price reduction. Oligopolistic competition with fixed networks (full data). Oligopolistic competition with endogenous networks (model simulation). 2/28

9 Networks and shock transmission Analyzes how consumer price index responds to a uniform foreign price reduction. A Foreign B i Home Oligopolistic competition Attenuate: µ Ai > 0. Amplify: µ Ai < 0. Endogenous networks Amplify: firms become importers. 3/28

10 Networks and shock transmission Analyzes how consumer price index responds to a uniform foreign price reduction. Foreign B A μ "# i Home Oligopolistic competition Attenuate: µ Ai > 0. Amplify: µ Ai < 0. Endogenous networks Amplify: firms become importers. 3/28

11 Networks and shock transmission Analyzes how consumer price index responds to a uniform foreign price reduction. Foreign B A μ "# i Home Oligopolistic competition Attenuate: µ Ai > 0. Amplify: µ Ai < 0. Endogenous networks Amplify: firms become importers. 3/28

12 Networks and shock transmission Analyzes how consumer price index responds to a uniform foreign price reduction. A Foreign B i Home Oligopolistic competition Attenuate: µ Ai > 0. Amplify: µ Ai < 0. Endogenous networks Amplify: firms become importers. 3/28

13 Networks and shock transmission Analyzes how consumer price index responds to a uniform foreign price reduction. A Foreign B i Home Oligopolistic competition Attenuate: µ Ai > 0. Amplify: µ Ai < 0. Endogenous networks Amplify: firms become importers. Full model predicts aggregate movements four times as large as those from the benchmark case. 3/28

14 Facts Model Structural analysis 3/28

15 Facts - Roadmap 1. Introduce dataset. 2. Firms competition within each customer s inputs. Concentration of suppliers. Firm s markup higher if firm has high input shares within customers. 3. Supplier-customer linkages over time. Large churn. Firms change suppliers in response to shocks. 4/28

16 National Bank of Belgium Business-to-Business Transaction Dataset Panel of VAT-id to VAT-id transactions among the universe of Belgian firms, over years (Dhyne, Magerman and Rubinova, 2015). Match VAT-ids with primary sector (NACE 4-digit), annual accounts and country-product (CN 8-digit) level international trade dataset. Aggregation VAT-ids into firms Sampling Industrial composition Descriptive B2B statistics 5/28

17 Facts - Roadmap 1. Introduce dataset. 2. Firms competition within each customer s inputs. Concentration of suppliers. Details Firm s markup higher if firm has high input shares within customers. 3. Supplier-customer linkages over time. Large churn. Firms experience larger churn of suppliers when exposed to larger import supply shocks. 5/28

18 Markups and input shares Are firms markups higher when they have higher downstream sales shares? Markups at the firm level. µi: sum of firm s sales over sum of variable inputs. Robustness with markups via De Loecker and Warzynski (2012). Measure of how much share firm has within its customers goods inputs. s m i : firm i s weighted average input shares within its customers. Firm i s share within customer j s inputs: s m ij = s m i = j W i Sales ij InputPurchases j. InputPurchases j k W i InputPurchases k s m ij. Control for firm-level market shares within sectors. 6/28

19 Markups and input shares µ i,t = β SctrMktShare i,t + γ s m i,t + ϕ X i,t + δ t + ɛ i,t. Firm-level markups (1) (2) (3) SctrMktShare i,t (4-digit) ( ) ( ) (0.0129) Average input share s m i,t (0.0130) ( ) ( ) N Year FE Yes Yes Yes Sector FE (4-digit) Yes No No Firm FE No Yes Yes Controls Yes No Yes R Notes: The coefficients are X-standardized. p < 0.10, p < 0.05, p < Standard errors are clustered at the NACE 2-digit-year level. Controls include firms indegree, outdegree, employment, total assets, and age. Robustness 7/28

20 Facts - Roadmap 1. Introduce dataset. 2. Firms competition within each customer s inputs. Concentration of suppliers. Firm s markup higher if firm has high input shares within customers. 3. Supplier-customer linkages over time. Large churn. Details Firms experience larger churn of suppliers when exposed to larger import supply shocks. 7/28

21 Changes in linkages Do firms change their domestic suppliers in response to foreign price change? 8/28

22 Changes in linkages Do firms change their domestic suppliers in response to foreign price change? Y i = β CS i + γ X i,t0 + δ s(i) + ɛ i. Y i is the share of continuing/added domestic suppliers. t 0 : 5 suppliers. 8/28

23 Changes in linkages Do firms change their domestic suppliers in response to foreign price change? Y i = β CS i + γ X i,t0 + δ s(i) + ɛ i. Y i is the share of continuing/added domestic suppliers. t 1 : 7 suppliers. Dropped 2, added 4. Continuing suppliers: 3/5, added suppliers: 4/5. 8/28

24 Changes in linkages Do firms change their domestic suppliers in response to foreign price change? Y i = β CS i + γ X i,t0 + δ s(i) + ɛ i. Y i is the share of continuing/added domestic suppliers. CS i is the firm s change in Chinese sourcing. Why China? CS i = V China,i TotalInput i,t0. 8/28

25 Changes in linkages Do firms change their domestic suppliers in response to foreign price change? Y i = β CS i + γ X i,t0 + δ s(i) + ɛ i. Y i is the share of continuing/added domestic suppliers. CS i is the firm s change in Chinese sourcing. Why China? CS i = V China,i TotalInput i,t0. Instrument CS i with changes in Chinese exports to non-eu rich countries. IV i = k V ALL,i,k,t0 TotalInput i,t0 V China,Rich,k V W orld,rich,k. Identification assumption: Firms within sector variations of input compositions at t 0 are not correlated with unobservable characteristics that affect linkage forming decisions. 8/28

26 Larger churn of suppliers as larger CS Table: Shares of continuing and added (incumbent and new) suppliers (value) (1) (2) (3) (4) Continuing Added Added suppliers: Added suppliers: suppliers suppliers Incumbent firms New firms CS (0.0283) (0.0334) (0.0316) ( ) N st Fstat Controls Yes Yes Yes Yes Notes: Standard errors in parentheses. p < 0.10, p < 0.05, p < The coefficients of the second stage results are X-standardized. Controls include firm age and employment size in 2002 with sector fixed effects (NACE 2-digit) and geographic fixed effects (NUTS 3). The same controls are used in the first stage results. CS is the firm s average yearly increase of Chinese imports from 2002 to 2012 scaled by its total inputs in CS is instrumented by the weighted sum of the sectoral change in Chinese goods share in developed countries total imports from 2002 to Standard errors are clustered at the NACE 2-digit-NUTS 3 level. OLS first stage customers in numbers statistics of churn in linkages 9/28

27 Facts Model Model of a small open economy with two elements: Oligopolistic competition in firm-to-firm trade. Endogenous network formation. Firm-level variables sufficient in a benchmark case without the two. Structural analysis 9/28

28 Household Cobb-Douglas preference over heterogeneous goods and homogenous goods. CES across goods in heterogeneous goods sector. Assume σ > 1. Associated price indices ( U = β ih qih i σ 1 σ P = αp α p 1 α y ( P = Household s budget constraint where Π = i π i. i β σ ih p1 σ ih E = wl + Π, ) σ σ 1 α Y 1 α. ) 1 1 σ. 10/28

29 Technology Firms in the homogenous goods sector: y i = l Y i. Firms in the heterogeneous goods sector combine labor and goods bundle with CES. Goods bundle is another CES aggregate of suppliers and foreign goods. Assume η, ρ > 1. ( c i = φ 1 i p mi = ω η l w1 η + ω η m p1 η mi α ρ ji p1 ρ ji j Z i ) 1 1 η + I F i α ρ F i p1 ρ F 1 1 ρ. Z i is the set of i s suppliers and I F i is an indicator for importers. 11/28

30 Market structure Homogenous goods sector. Assume perfect competition and free trade. 12/28

31 Market structure Homogenous goods sector. Assume perfect competition and free trade. Heterogenous goods sector. Firms set monopolistic competitive prices in the final demand market. Exports p ih = σ σ 1 c i. 12/28

32 Market structure Homogenous goods sector. Assume perfect competition and free trade. Heterogenous goods sector. Firms set monopolistic competitive prices in the final demand market. Exports p ih = σ σ 1 c i. Firm i sets price pij to maximize profits from sales to j, taking as given {Z j, I F j, I jf }, prices of the other suppliers {p kj }, c j, and q j. p ij = ε ij ε ij 1 c i ε ij = ρ ( 1 s m ij ) + ηs m ij. Firms maximization problem Alternative specifications 12/28

33 Linkage formation Firm j pays labor fixed cost f Dj F D ( ) when sourcing from another firm, pays f F j F IM ( ) when importing, pays f jf F EX ( ) when exporting. Firm j chooses {Z j, I F j, I jf } to maximize net profits, taking as given other firms sourcing decisions. max πj var (Z j, I F j, I jf ) wf Dj I F j wf F j I jf wf jf. Z j,i F j,i jf i Z j 13/28

34 Equilibrium under fixed networks Taking as given the foreign demand shifter, foreign price and the network structure {Z i, I F i, I if }, the equilibrium under fixed networks is the set of variables { w, p y, P, E, c i, {µ ij }, {q ij }, q ih, q if, l } Y. They satisfy household s utility maximization problem. firms cost minimization problems. firms profit maximization problems. household s budget constraints and trade balance condition. Aggregation Take homogenous good s price as the numeraire, w = p y = 1. Firm 14/28

35 Equilibrium under endogenous networks In addition to the equilibrium under fixed networks, the network structure {Z i, I F i, I if } satisfy firms domestic sourcing and international trade participation problems. Focus on a pairwise stable equilibrium where firms sequentially make their sourcing decisions. The most productive firm makes its sourcing decision first. Then the second most productive firm makes its decision, and so on. Firm j decides {Z j, I F j, I jf } taking as given aggregate demand, its customers unit costs and total production, and other firms sourcing decisions. 15/28

36 Benchmark case Consider the global change in the domestic price index given an exogenous change in foreign price. In a special case of the model, firm-level variables become sufficient statistics. Lemma Assume (1) only composite final consumption goods are exported, (2) Cobb-Douglas both in preference and in technologies, (3) perfect competition (p i = c i ), and (4) exogenous and fixed network. Then the change in price index, ˆP, can be expressed solely by firm-level observables. ln ˆP = i p i q i αe + Exp s F i ln ˆp F. Intuition Network irrelevance with common CES parameter Network irrelevance in Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi (2012) 16/28

37 Facts Model Structural analysis 16/28

38 Structural analysis - Roadmap Estimate the model and analyze how aggregate price index P changes in response to a reduction in foreign price p F. 17/28

39 Structural analysis - Roadmap Estimate the model and analyze how aggregate price index P changes in response to a reduction in foreign price p F. 1 Estimate σ, η, and ρ. 2 Counterfactual analysis, under fixed networks. 1. Start with the benchmark case where firm-level info sufficient. 2. Constant markups with estimated σ, ρ, η > 1, fixed networks. 3. Variable markups with oligopolistic competition, fixed networks. 3 Estimate parameters for endogenous networks. Productivity distribution. Fixed cost parameters for FD ( ), F IM ( ) and F EX ( ). 4 Counterfactual analysis, under endogenous networks. 4. Full model, with variable markups and endogenous networks. 17/28

40 Structural analysis - Roadmap Estimate the model and analyze how aggregate price index P changes in response to a reduction in foreign price p F. 1 Estimate σ, η, and ρ. 2 Counterfactual analysis, under fixed networks. 1. Start with the benchmark case where firm-level info sufficient. 2. Constant markups with estimated σ, ρ, η > 1, fixed networks. 3. Variable markups with oligopolistic competition, fixed networks. 3 Estimate parameters for endogenous networks. Productivity distribution. Fixed cost parameters for FD ( ), F IM ( ) and F EX ( ). 4 Counterfactual analysis, under endogenous networks. 4. Full model, with variable markups and endogenous networks. 17/28

41 Estimating the CES parameters Markups are functions of CES parameters (η, ρ, σ) and observables s m ij. µ ih = µ if = σ σ 1 µ ij = ε ij ε ij 1 ε ij = ρ ( 1 s m ij ) + ηs m ij. Firm s total input costs equal sum of firm s sales divided by destination-specific markups. c i q i = j p ij q ij µ ij + p ihq ih µ ih + p if q if µ if + ξ i. ξ i : measurement errors in firms labor costs (component of c i q i ). 18/28

42 Estimates Estimate (η, ρ, σ) by solving: min c i q i η,ρ,σ i j 2 p ij q ij + p ihq ih + p if q if. µ ij µ ih µ if η ρ σ σ 1 Estimate s.e η (Labor and goods) ρ (Firms goods in production) σ (Firms goods in consumption) Implied value Assuming Cournot competition Accounting for capital 19/28

43 Structural analysis - Roadmap Estimate the model and analyze how aggregate price index P changes in response to a reduction in foreign price p F. 1 Estimate σ, η, and ρ. 2 Counterfactual analysis, under fixed networks. 1. Start with the benchmark case where firm-level info sufficient. 2. Constant markups with estimated σ, ρ, η > 1, fixed networks. 3. Variable markups with oligopolistic competition, fixed networks. 3 Estimate parameters for endogenous networks. Productivity distribution. Fixed cost parameters for FD ( ), F IM ( ) and F EX ( ). 4 Counterfactual analysis, under endogenous networks. 4. Full model, with variable markups and endogenous networks. 19/28

44 Four cases: ˆP (Using full data) 1. Start with the benchmark case where firm-level info sufficient. σ = ρ = η = 1, pi = c i, fixed network. ln ˆP = i p i q i αe+exp s F i ln ˆp F /28

45 Four cases: ˆP (Using full data) 2. Constant markups. System Estimated values of σ, ρ, η. Increased substitutability across inputs /28

46 Four cases: ˆP (Using full data) 3. Variable markups. System Decomposition (first order apprx.) Attenuation effect: incomplete price pass through. Pro-competitive effect: markup affected by price changes of other suppliers /28

47 Attenuation and pro-competitive effects dµ ji dc j dp ji = Γ ji + Γ ji. µ ji c j p ji }{{}}{{} attenuation effect pro-competitive effect Maximum magnitudes display hump shape w.r.t. input share s m ji. Exposures to shock ( dcj c j, dp ji p ji ) determine the magnitudes within same s m ji. Analytical characterizations Γ ji : elas. of µ ji w.r.t. ĉ j Variation in atten. Variation in pro-comp. 21/28

48 The net effects Average change in markups for firm i: j Z i s m ji (ˆµ ji 1). Correlated with measure of indirect exposure to shock: s T F otal i s F i. Total foreign input share : s T F otal i = s F i + k s kis T F otal k. Shock to one firm Aggregation 22/28

49 Structural analysis - Roadmap Estimate the model and analyze how aggregate price index P changes in response to a reduction in foreign price p F. 1 Estimate σ, η, and ρ. 2 Counterfactual analysis, under fixed networks. 1. Start with the benchmark case where firm-level info sufficient. 2. Constant markups with estimated σ, ρ, η > 1, fixed networks. 3. Variable markups with oligopolistic competition, fixed networks. 3 Estimate parameters for endogenous networks. Other parameters Productivity distribution. Details Fixed cost parameters for FD ( ), F IM ( ) and F EX ( ). 4 Counterfactual analysis, under endogenous networks. 4. Full model, with variable markups and endogenous networks. 23/28

50 Estimating F D ( ), F IM ( ) and F EX ( ) Assume log normal distributions for F D ( ), F IM ( ) and F EX ( ). Estimate scale parameters Φ scale D, Φscale IM dispersion parameter Φ disp. and Φscale EX Estimation via Simulated Methods of Moments., and a common Moments: Fraction of firms with at least one domestic suppliers, to pin down Φ scale D. Fraction of importers, to pin down Φ scale IM. Fraction of exporters, to pin down Φ scale EX. Correlation between number of suppliers and customers, to pin down Φ disp. Simulate economy with N = 30. One sector model 24/28

51 Estimates and model fit Estimates. Local identification Φ scale D Φ scale IM Φ scale EX Φ disp Estimate s.e Targeted moments. Data Model Fraction of firms sourcing from domestic firms Fraction of importers Fraction of exporters Corr(#supplier, #customer) /28

52 Estimates and model fit Non-targeted moments. Data Model Corr(Sales, #supplier) Corr(Sales, #customer) Corr(Sales i, Sales j ) Median s m ij 0.18% 0.34% 26/28

53 Structural analysis - Roadmap Estimate the model and analyze how aggregate price index P changes in response to a reduction in foreign price p F. 1 Estimate σ, η, and ρ. 2 Counterfactual analysis, under fixed networks. 1. Start with the benchmark case where firm-level info sufficient. 2. Constant markups with estimated σ, ρ, η > 1, fixed networks. 3. Variable markups with oligopolistic competition, fixed networks. 3 Estimate parameters for endogenous networks. Productivity distribution. Fixed cost parameters for FD ( ), F IM ( ) and F EX ( ). 4 Counterfactual analysis, under endogenous networks. 4. Full model, with variable markups and endogenous networks. 26/28

54 Four cases: ˆP (Model simulation) 4. Full model, with endogenous network. Common CES parameter /28

55 Conclusion Main contributions: Established empirical facts suggesting that firms compete with each other within each customer s inputs. firms change linkages in response to shocks. Built a model with Oligopolistic competition: attenuation and pro-competitive effect. Endogenous networks: firms become importers. Demonstrated their relevance for counterfactual predictions. 28/28

56 Thank you! 28/28

57 APPENDIX 1/47

58 Aggregating vats to firms We group all VAT-id into firms that are either linked with more than 50% of ownership (ownership filings). owned by a common foreign firm (FDI filings). In 2012, 896K VAT-ids collapsed to 860K firms. Of those firms, 842K firms consisted of single VAT-ids. The number of VAT-ids for multiple VAT-id firms are as below. Mean 10% 25% 50% 75% 90% max Num. VAT-id The 18K firms with multiple VAT-ids account for 60% of the total output. Back 2/47

59 Sample of analysis Following De Loecker, Fuss and Van Biesebroeck (2014), we restrict the sample of analysis according to the criteria below: Belgian firms with positive labor cost in industries other than government and finance. File positive employment, tangible assets of more than 100 euro, positive total assets for at least one year throughout the period. Year Private, non-financial Selected sample M X GDP Output Count V.A. Sales M X , , , Notes: All numbers except for Count are denominated in billion Euro in current prices. Belgian GDP and output are for all sectors excluding public and financial sector. Data for Belgian GDP, output, imports and exports are from Eurostat. Back 3/47

60 Industrial composition (2012) Industry Count V.A. Sales Imports Exports Agriculture 3, Construction 26, Manufacturing 20, Wholesale and Retail 42, Other Services 43, Other 2, Total 139, Notes: All numbers except for Count are denominated in billion Euro in current prices. Back 4/47

61 Descriptive statistics (2012) Mean Percentiles 10% 25% 50% 75% 90% s m ij = Sales ij/inputpurchases j 1.62% 0.00% 0.00% 0.18% 0.82% 3.15% Num. suppliers Num. customers Back 5/47

62 Concentration of suppliers Majority of Belgian firms have 28 suppliers or less. For the majority of Belgian firms, the largest supplier accounts for 27% or more of input purchases. HHI 1.5e+04 Frequency 1.0e maxi (sijm ) Notes: s m ij is defined as firm i s goods share among firm j s input purchases from other Belgian firms and abroad. ( The above histogram shows the distribution of max i s m ) ij, which is the maximum value of s m ij for each customer firm j in 2012 that has more than 10 suppliers. Back 6/47

63 HHI of input shares For the majority of Belgian firms, the HHI of input shares across suppliers are 0.15 or higher.. 2.0e e+04 Frequency 1.0e HHI j Notes: s m ij is defined as firm i s goods share among firm j s input purchases from other Belgian firms and abroad. The above histogram shows the HHI of s m ij for all customer firms j in 2012 that have more than 10 suppliers. The median value is The two vertical lines indicates HHI being 0.15 and Back 7/47

64 Robustness Positive correlation between µ i and s m i robust when Alternative measures of µ i. Estimated firm level markups via De Loecker and Warzynski (2012). Go Alternative measures of s m i. Simple average or median of input shares across customers. Computing input shares within customer s total inputs. Computing input shares within customer s inputs that are classified as same goods. Back 8/47

65 Markups via De Loecker and Warzynski (2012) (1) (2) (3) SctrMktShare i,t (4-digit) ( ) ( ) ( ) Average input share s m i,t ( ) ( ) ( ) N Year FE Yes Yes Yes Sector FE (4-digit) Yes No No Firm FE No Yes Yes Controls Yes No Yes R Notes: Standard errors in parentheses. p < 0.10, p < 0.05, p < We use firm-level markups recovered using methods from De Loecker and Warzynski (2012) as the LHS variables. The coefficients are X-standardized. Standard errors are clustered at NACE 2-digit-year level. Back 9/47

66 Yearly churn of suppliers and customers Median share (yearly, in terms of value) Dropped suppliers Added suppliers Dropped customers Added customers Back In terms of numbers 10/47

67 Yearly churn of suppliers and customers Median share (yearly, in terms of number) Dropped suppliers Added suppliers Dropped customers Added customers Back 11/47

68 Chinese imports Imports over GDP (2002 value normalized at 1) Imports over GDP (percent) Year CHN FRA GBR DEU NLD USA Year BRA CHN COL IRN IRQ MEX MYS PER THA TUR ZAF Back 12/47

69 OLS results Table: Shares of continuing and added (incumbent and new) suppliers (value) (1) (2) (3) (4) Continuing Added Added suppliers: Added suppliers: suppliers suppliers Incumbent firms New firms CS ( ) ( ) ( ) ( ) N R Controls Yes Yes Yes Yes Notes: Standard errors in parentheses. p < 0.10, p < 0.05, p < The coefficients are X-standardized. Controls include firm age and employment size in 2002, with sector fixed effects (NACE 2-digit) and geographic fixed effects (NUTS 3). CS is the firm s average yearly increase of Chinese imports from 2002 to 2012 scaled by its total inputs in Standard errors are clustered at the NACE 2-digit-NUTS 3 level. Back 13/47

70 First stage results (1) (2) (3) (4) Supplier, value Customer, value Supplier, number Customer, number IV ( ) ( ) ( ) ( ) N R F Stat Controls Yes Yes Yes Yes Standard errors in parentheses p < 0.10, p < 0.05, p < 0.01 Notes: This table shows the first stage results when CS is regressed on IV. Controls include firm age and employment size in 2002, with sector fixed effects (NACE 2-digit) and geographic fixed effects (NUTS 3). Standard errors are clustered at the NACE 2-digit-NUTS 3 level. Back 14/47

71 Table: Shares of continuing and added (incumbent and new) customers (value) (1) (2) (3) (4) Continuing Added Added customers: Added customers: customers customers Incumbent firms New firms CS (0.0686) (0.0890) (0.0815) ( ) N st Fstat Controls Yes Yes Yes Yes Notes: Standard errors in parentheses. p < 0.10, p < 0.05, p < The coefficients of the second stage results are X-standardized. Controls include firm age and employment size in 2002 with sector fixed effects (NACE 2-digit) and geographic fixed effects (NUTS 3). The same controls are used in the first stage results. CS is the firm s average yearly increase of Chinese imports from 2002 to 2012 scaled by its total inputs in CS is instrumented by the weighted sum of the sectoral change in Chinese goods share in developed countries total imports from 2002 to Standard errors are clustered at the NACE 2-digit-NUTS 3 level. Back 15/47

72 Table: Shares of continuing and added (incumbent and new) suppliers (number) (1) (2) (3) (4) Continuing Added Added suppliers: Added suppliers: suppliers suppliers Incumbent firms New firms CS (0.0275) (0.0236) (0.0238) ( ) N st Fstat Controls Yes Yes Yes Yes Notes: Standard errors in parentheses. p < 0.10, p < 0.05, p < The coefficients of the second stage results are X-standardized. Controls include firm age and employment size in 2002 with sector fixed effects (NACE 2-digit) and geographic fixed effects (NUTS 3). The same controls are used in the first stage results. CS is the firm s average yearly increase of Chinese imports from 2002 to 2012 scaled by its total inputs in CS is instrumented by the weighted sum of the sectoral change in Chinese goods share in developed countries total imports from 2002 to Standard errors are clustered at the NACE 2-digit-NUTS 3 level. Back 16/47

73 Table: Shares of continuing and added (incumbent and new) customers (number) (1) (2) (3) (4) Cont Added Incumbent New CS (0.0839) (0.112) (0.105) ( ) N st Fstat Controls Yes Yes Yes Yes Standard errors in parentheses p < 0.10, p < 0.05, p < 0.01 Notes: The coefficients are X-standardized. Controls include firm age and employment size in 2002, with sector fixed effects (NACE 2-digit) and geographic fixed effects (NUTS 3). deltacs is the firm s average yearly increase of Chinese imports from 2002 to 2012 scaled by its total inputs in deltacs is instrumented by the weighted sum of the sectoral change in Chinese goods share in developed countries total imports from 2002 to Standard errors are clustered at the NACE 2-digit-NUTS 3 level. Back 17/47

74 Changes in suppliers and customers Yearly avg. (02-12) 10 year (02-12) Median Cont. Share Added Share Cont. Share Added Share Sup. Number Sup. Value Cus. Number Cus. Value Back 18/47

75 International markets If I F i = 1, i imports quantity q F i at an exogenous price p F. If I if = 1, i charges the same price for exports as it does for final demand, p if = p ih. Foreign has the same preference of the firms goods as the representative household, with demand elasticity σ and demand shifter D. D may include trade costs and tariffs, V if = τ 1 σ ( βih ) σ p 1 σ ih (P ) 1 σ E = p 1 σ ih D. Back 19/47

76 Firm i s problem Embed Atkeson and Burstein (2008) in firm-to-firm trade. Firm i sets p ij to maximize profits from sales to j. Takes as given prices of the other suppliers {pkj }, c j, and q j. Takes into account the effect pij has on m j and p mj. max (p ij c i ) q ij p ij s.t. p ij q ij = α ρ ij p1 ρ ij p ρ mj m j p mj m j = ω η m p1 η mj φη 1 j c η j q j. Back 20/47

77 Alternative specifications Current setup: Firm i sets price p ij taking as given c j and q j. p ij = ε ij ε ij 1 c i ε ij = ρ ( 1 s m ij ) + ηs m ij. Alternatively, take into account the effect on c j and q j. Take as given demand shifters that j faces from final demand and from other firms. Go Assume a constant demand elasticity that j faces. Go Back Sector layer 21/47

78 Firm as tuple Firm i is a tuple consisting of core productivity φi. three draws of fixed costs fdi, f F i and f if. saliency parameters βih, {α ji} and α F i. Back 22/47

79 Both c j p ij 0 and q j p ij 0 Firm i takes into account the effect of p ij on c j and q j. But i takes as given the demand shifters of j s goods, D jh and D jb as given: q j = c σ j D jh + c ρ j D jb. Then price p ij becomes p ij = ε ij ε ij 1 c i ε ij = ρ ( 1 s m ij ) + ηs m ij + (σs q jh + ρsq jb η ) s m ij s mj. s q jh is the quantity output share of firm j s goods sold to final demand. is the quantity output share of firm j s goods sold to other firms. s q jb Back 23/47

80 Both c j p ij 0 and q j p ij 0 Firm i takes into account the effect of p ij on c j and q j. But i assumes that j faces demand elasticity of ν and takes demand shifter D j as given: q j = c ν j D j. Then price p ij becomes p ij = ε ij ε ij 1 c i If ν = η, then same as current setup. ε ij = ρ ( 1 s m ij ) + ((1 smj ) η + s mj ν)s m ij. Back 24/47

81 Sector layer Consider an additional sector layer s (i), in which firm i takes into account the effect of p ij on c j and q j. Let δ be the substitutability across sectors. p ij = ε ij ε ij 1 c i ( ) ( ) ε ij = ρ 1 s s(i) ij + δs s(i) ij 1 s m s(i)j + ηs s(i) ij s m s(i)j, is the share of i s goods among j s sector s (i) inputs, and s m s(i)j share of sector s (i) inputs among j s intermediate inputs. s s(i) ij is the Back 25/47

82 Aggregation Household s budget constraint: E = wl + i Ω π i. Trade balance and labor market clearing conditions: [TB] :0 = I if p 1 σ ih D I F i s F i c iq i + wl Y (1 α) E }{{} i Ω i Ω }{{}}{{} Net exports of homog. Hetero. exports Hetero. imports [LMC] :wl = s li c iq i + wf Di + I F i wf F i + I if wf if + wl Y i Ω i Ω j Z i Back 26/47

83 Intuition ˆP is a weighted sum of ĉ i, ln ˆP = i s ih ln ĉ i. 27/47

84 Intuition ˆP is a weighted sum of ĉ i, ln ˆP = i s ih ln ĉ i. Change in firm s unit cost reflects its exposure to the change in foreign price, its suppliers exposures, and so on. ln ĉ i = k s ki ln ĉ k + s F i ln ˆp F. 27/47

85 Intuition ˆP is a weighted sum of ĉ i, ln ˆP = i s ih ln ĉ i. Change in firm s unit cost reflects its exposure to the change in foreign price, its suppliers exposures, and so on. ( ln ĉ = I S ) 1 sf ln ˆp F. 27/47

86 Intuition ˆP is a weighted sum of ĉ i, ln ˆP = i s ih ln ĉ i. Change in firm s unit cost reflects its exposure to the change in foreign price, its suppliers exposures, and so on. ( ln ĉ = I S ) 1 sf ln ˆp F. Firm s sales reflects its sales to final demand, its customers sales to final demand, and so on. p i q i = s ih (αe + Exp) + j s ij p j q j. 26/47

87 Intuition ˆP is a weighted sum of ĉ i, ln ˆP = i s ih ln ĉ i. Change in firm s unit cost reflects its exposure to the change in foreign price, its suppliers exposures, and so on. ( ln ĉ = I S ) 1 sf ln ˆp F. Firm s sales reflects its sales to final demand, its customers sales to final demand, and so on. p q αe + Exp = (I S) 1 s H. 26/47

88 Intuition ˆP is a weighted sum of ĉ i, ln ˆP = i s ih ln ĉ i. Change in firm s unit cost reflects its exposure to the change in foreign price, its suppliers exposures, and so on. ( ln ĉ = I S ) 1 sf ln ˆp F. Firm s sales reflects its sales to final demand, its customers sales to final demand, and so on. p q αe + Exp = (I S) 1 s H. The measures of firms importance as suppliers of goods, and as consumers of goods coincide. ln ˆP = i p i q i αe + Exp s F i ln ˆp F. Back 25/47

89 Assuming common CES parameter One can relax the Cobb-Douglas assumption and assume common CES parameter σ. Proposition Assume (1) only composite final consumption goods are exported, (2) CES structure with common σ in preference and in technologies, (3) perfect competition (p i = c i ), and (4) exogenous and fixed network. Then the change in price index, ˆP, can be expressed as ˆP 1 σ = i p i q i αe + Exports ( s li + s F i ˆp 1 σ F ). Back 26/47

90 Acemoglu et.al. (2012) Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi (2012) focus on the variance of changes in aggregate variables, under closed economy, Cobb-Douglas both in preference and in technologies, competitive prices, exogenous and fixed network. Firm-level information sufficient when focusing on the changes in aggregate variables. Back 27/47

91 (η, ρ, σ) under Cournot competition When assuming Cournot competition, we have Estimates: p ij = ε ij ε ij 1 c i ( ) 1 ( ) ε ij = 1 s m 1 1 ρ ij + η sm ij. 1 η 1 ρ σ σ 1 Estimate s.e η (Labor and goods) ρ (Firms in production) σ (Firms in consumption) Implied value Markups under Bertrand and Cournot Back 28/47

92 Markups under Bertrand and Cournot Bertrand (Baseline) Cournot with Bertrand parameters Cournot with Cournot parameters Back 29/47

93 Accounting for capital In the model, total input, c i q i, is an aggregate of labor costs and goods purchases. Here we account for capital inputs by interpreting labor as composite input of labor and capital. 1 Uniformly scale up labor cost, by assuming common labor share. 2 Assume user cost of capital being the depreciation rate and the interest rate, and compute firm level capital rental costs. Back 30/47

94 Accounting for capital Common labor share. η ρ σ σ 1 Estimate s.e η (Labor and goods) ρ (Firms goods in production) σ (Firms goods in consumption) Implied value Back 31/47

95 Accounting for capital Firm level capital costs. η ρ σ σ 1 Estimate s.e η (Labor and goods) ρ (Firms goods in production) σ (Firms goods in consumption) Implied value Back 32/47

96 System of price changes (constant markups) Solve for firm level changes in unit costs ĉ i : ĉ 1 η i ˆp 1 ρ mi = s li + s mi ˆp 1 η mi = s m jiĉ1 ρ j j Z i + s m F i ˆp1 ρ F. Back The change in aggregate price index: ( ˆP = i s ih ĉ 1 σ i ) 1 1 σ. 33/47

97 System of price changes (variable markups) Solve for firm level changes in unit costs ĉ i, and pair level changes in markups ˆµ ji : ĉ 1 η i ˆp 1 ρ mi = s li + s mi ˆp 1 η mi = s m ji ˆµ1 ρ ji ĉ 1 ρ j j Z i ˆµ ji = ˆε ji ε ji 1 ˆε ji ε ji 1 + s m F i ˆp1 ρ F ε ij = ρ ( 1 s m ) ij + ηs m ij ˆε ji = 1 ( ( ρ 1 s m ε ji ŝ m ) ji + ηs m ji ŝ m ji) ji ŝ m ji = ˆµ1 ρ ji ĉ 1 ρ j ˆp ρ 1 mi. The change in aggregate price index: ( ˆP = i s ih ĉ 1 σ i ) 1 1 σ. Back 34/47

98 Attenuation and pro-competitive effects Change in P Change in pf Constant Mkup Margin, Fixed Network (First order apprx.) Atten. Effect Margin (First order apprx.) Pro comp. Effect Margin (First order apprx.) Back 35/47

99 Attenuation and pro-competitive effects Back System of first order approximated price changes. Under constant markups: Under variable markups: dc i c i dc i c i = = dc j s ji c j Z j i j Z i s ji + s F i dp F p F. ( dµji + dc ) j dp F + s F i, µ ji c j p F dµ ji dc j dp ji = Γ ji + Γ ji. µ ji c j p ji }{{}}{{} attenuation effect pro-competitive effect Γji: elasticity of markup µ ji with respect to the supplier s cost c j. dp ji p ji : average price changes of suppliers other than j: dp ji p ji = ( ) dµki k Z i,k j sm ki µ ki + dc k c k + s m F i dp F p F. 1 s m ji 36/47

100 Elasticity Γ ji Γ ji represents the elasticity of markup µ ji with respect to the supplier s cost c j : ) Γ ji = µ ji c Υ j ji (1 s m ji = c j µ ji 1 Υ ji s m ji Υ ji = (ρ ε ji ) (ρ 1) (ε ji 1) ε ji + (ρ ε ji ) (ρ 1) Back 37/47

101 Attenuation effect: Γ ji dc j c j Variation within the same s m ji comes from the supplier s cost change. Firm s cost change correlated with total foreign input share, s T F otal j : s T otal F j = s F j + k s kj s T otal F k. One-to-one mapping between s T otal F j and ĉ j in benchmark case. Back 38/47

102 Pro-competitive effect: Γ ji dˆp ji ˆp ji Variation within the same s m ji comes from average cost changes of other suppliers. Compute average total foreign input shares for other suppliers. Back 39/47

103 Shock to one firm Shock a single importer I, with import price reduction ˆp F. Stronger correlation between j Z i s m ji (ˆµ ji 1) and s T otal Ii. s T otal Ii = s ki s T otal Ik k Z i if i I s T otal Ii = 1 if i = I. Back 40/47

104 The aggregate effects First order approximated change of aggregate price index. Under constant markups: dp P = i s ih dc j s ji c j Z j i + s F i dp F p F, where s ih is i s share in final goods consumption. Under variable markups: dp P = i + i s ih dc j s ji c j Z j i + s F i dp F p F s ih s mi s m dµ ji ji. µ j Z ji i }{{} avg. change in markups Back 41/47

105 Other parameters Set β ih = α ij = α F i = 1. Calibrate ωl = 0.3 and ω m = 0.7 to match the average labor share (0.34). α = 0.55 to match the aggregate share of private and non-financial sectors. D = to match the average export share for exporting firms (0.2). pf = 5 to match the average import share for importing firms (0.31). Back 42/47

106 Recovering productivity distribution From the model, we obtain the following equation to recover productivity distribution up to a scale: ln φ i = 1 σ 1 ln p ihq ih + 1 ( σ η ) η 1 ln s li + ln σ 1 ω η 1 l P 1 α 1 σ 1 E 1 σ 1. Variations in p ih q ih reflects the variations in firms unit costs, which reflect firms productivities and firms sourcing capabilities. Since wage is common, sourcing capabilities are inversely related to s li. Back 43/47

107 One sector partial equilibrium model Production technology: ( c i = φ 1 i p mi = ω η l w1 η + ω η mp 1 η mi α ρ ji p1 ρ ji j Z i + α ρ oi p1 ρ o ) 1 1 η + I F i α ρ F i p1 ρ F 1 1 ρ. Monopolistic competition when selling to outside sector: p io = ρ ρ 1 c i. Estimate fixed costs distributions using data on 2-digit manufacturing sector (3481 firms), where the largest 30 firms account for 99% of output. sales among the largest 30 firms account for 99% of firm-to-firm sales. Back 44/47

108 Local identification Fraction of firms sourcing from domestic firms Corr(Indeg, Outdeg) Fraction of importers Fraction of exporters Notes: These figures illustrate local identification of the four fixed cost parameters. In each figure, on the x-axis we plot the parameter to identify, which we vary while fixing all other parameters to their estimated values. On the y-axes we plot the moments we use to identify the parameters. The horizontal lines indicate the observed value of the moment in the data. Back 45/47

109 Common CES parameter Network irrelevance result given a common CES parameter σ: ˆP = i Ω p i q ( i αe + Exports s li + s F i ˆp 1 σ F ) 1 1 σ Common CES = 1.27 Common CES = 2.78 Common CES = 4.99 Common CES = 10 Back 46/47

110 Acemoglu, Daron, Vasco M. Carvalho, Asuman Ozdaglar, and Alireza Tahbaz-Salehi, The Network Origins of Aggregate Fluctuations, Econometrica, 2012, 80 (5), Atkeson, Andrew and Ariel Burstein, Trade Costs, Pricing to Market, and International Relative Prices, American Economic Review, 2008, 98 (5), De Loecker, Jan and Frederic Warzynski, Markups and Firm-Level Export Status, American Economic Review, 2012, 102 (6), , Catherine Fuss, and Johannes Van Biesebroeck, International competition and firm performance : Evidence from Belgium, NBB Working Paper Series, 2014, (269). Dhyne, Emmanuel, Glenn Magerman, and Stela Rubinova, The Belgian production network , National Bank of Belgium Working Paper Series, 2015, /47