The Origins of Firm Heterogeneity: A Production Network Approach A. Bernard E. Dhyne G. Magerman K. Manova A. Moxnes Tuck@Dartmouth NBB ECARES Oxford Oslo CEPR, NBER UMons NBB CEPR CEPR Princeton, September 28, 2017 Preliminary 1 / 40
The Firm Size Distribution Density 0.1.2.3.4 10 4 10 3 10 2 10 1 10 0 10 1 10 2 10 3 10 4 Sales (demeaned) 2 / 40
The Firm Size Distribution Density 0.1.2.3.4 10 4 10 5 10 6 10 7 10 8 10 9 10 10 Turnover (euro) Primary and Extraction Utilities and Construction Non Market Services Manufacturing Market Services 3 / 40
Motivation Firm size distribution fundamental for Trade: who exports what & where, welfare gains. Macro: granularity, aggregate productivity, creative destruction. Labor: wages & income inequality (Autor et al, 2017). 4 / 40
Research Question Firms are part of production networks: buy inputs from other firms. sell to other firms and possibly to final consumers. production network is sparse & most goods lack centralized exchanges. What is the role of the production network in explaining the firm size distribution? Number of customers/suppliers. Characteristics of customers/suppliers. Match quality. 5 / 40
What We Do Model: Firms are both buyers and sellers own unit costs depend on suppliers unit costs. own sales depend on customers sales. Use model & production network data to identify firm-level fundamentals. Exact model-based decomposition of firm-level sales. Demand (# customers, capability of customers). Supply (production capability, # suppliers, capability of suppliers). Match. Use estimates + embed model in GE to perform counterfactuals. Links are pre-determined. 6 / 40
Related Literature Firm size distribution: Gibrat (1931), Sutton (1997). Firm size and productivity: Jovanovic (1982), Hopenhayn (1992), Melitz (2003), Luttmer (2007), Arkolakis (2016). Firm size and demand: Foster, Haltiwanger and Syverson (2015), Fitzgerald, Haller and Yedid-Levi (2016). Firm size variance decomposition: Hottman, Redding and Weinstein (2016). Firm-to-firm trade: Bernard et al (forthcoming), Eaton et al. (2016), Kramarz et al (2016), Lim (2016). Firm-employee matching: Abowd, Kramarz and Margolis (1999), Card et al. (2015). 7 / 40
Today Data. Model & Exact decomposition. Estimation. Results. GE. Sensitivity. Conclusions. 8 / 40
Data : Relationships Panel 2002-2014 with annual sales relationships between all VAT reporting firms in Belgium. Firm i selling to firm j for x euro in a given year within Belgium. Coverage (close to) universal, All sectors except financial services. All annual sales m ij > 250 included. 9 / 40
Data: Relationships 16.8 million B2B sales relationships in 2012. 812,543 firms (555,722 sellers and 797,595 buyers). Some firms only sell to final demand (buyers but not sellers). Top 10% relationships account for 92% of value. Relationship N Median Mean Top 100 Top 10 value ( ) 16,800,368 1,414 30,884 253 mill 1,310 mill Table: Distribution of bilateral relationships ( s) (2012). 10 / 40
Data : Balance sheet In main decomposition, we merge with balance sheet to get data on: Total sales Si, input purchases M i, labor cost share α j, 2-digit industry (NACE). We retain 87% of aggregate gross turnover. Industry N Mean Median All 111,581 7,361 788 Primary and Extraction 1,630 2,776 788 Manufacturing 11,052 21,400 1,276 Utilities 557 61,000 2,371 Market Services 93,449 5,610 775 Non-Market Services 4,893 4,553 419 Table: Sales ( 000s) (2012). 11 / 40
Heterogeneity in relationships Density 0.1.2.3.4 10 2 10 1 10 0 10 1 10 2 10 3 Number of suppliers (demeaned) Density 0.1.2.3.4.5 10 2 10 1 10 0 10 1 10 2 10 3 Number of customers (demeaned) Median/mean indegree (outdegree) 9/21 (2/21). Top 1% transact with more than 400 buyers and 177 sellers. 12 / 40
Relationships & Size 10 4 10 4 10 3 10 3 Turnover (euro), de meaned 10 2 10 1 10 0 10 1 10 2 Turnover (euro), de meaned 10 2 10 1 10 0 10 1 10 2 10 3 10 3 10 4 Linear slope: 0.68 (0.002) R squared: 0.35 10 2 10 1 10 0 10 1 10 2 10 3 10 4 Number of customers, de meaned 10 4 Linear slope: 1.21 (0.003) R squared: 0.52 10 2 10 1 10 0 10 1 10 2 Number of suppliers, de meaned Bigger firms have more buyers and suppliers (within industry). Average sales decreasing in # customers. 13 / 40
The Model Firms use labor and a CES bundle of inputs. Network is pre-determined. Heterogeneity in productivity/quality. Minimal set of assumptions. We impose a few more when solving the GE later on. 14 / 40
The Model Assumption The production function is y i = z i l α i v 1 α i σ/(σ 1) v i = (φ ki ν ki ) (σ 1)/σ. k Si Marginal costs and prices Firm-to-firm sales c i = κ w α P 1 α i and p ij = τ ij c i. z i m ij = ( φij p ij ) σ 1 P σ 1 j M j. 15 / 40
The Model Assumption Demand & supply (mark-up) shifters are φ ij = φ i φ ij τ ij = τ i τ ij. Rewrite firm-to-firm sales to m ij = ψ i θ j ω ij with ψ i ( φi τ i c i ) σ 1, θ j P σ 1 j M j, ω ij We discuss identification of Ψ = {ψ i, θ j, ω ij } soon. ( φij τ ij ) σ 1. 16 / 40
The Exact Decomposition Fraction of sales/purchases within the network: β c i and β s i. E.g., 1 β c i is exports. Total sales can be written: ln S i = ln ψ i + ln ξ i ln β c i ξ i j C i θ j ω ij Variance decomposition, using Ψ and data on βi c: Regress each component on ln S i. Each coefficient gives share of variation in sales explained by margin. All components demeaned at 2-digit industry level. 17 / 40
The Demand Side The demand parameter ξ i can be written: ln ξ i = ln ni c + ln θ i + ln Ω c i, θ i j Ci θ j 1/n c i Ω c i 1 n c i θ j ω ij θ j C i i Variance decomposition, using Ψ and data on n c i : Regress each component on ln ξi. 18 / 40
The Supply Side : The Reflection Problem Reflection problem: Seller effect ψ i embodies technology of suppliers. Given estimates Ψ and data on (M i, α), back out own production capability: z i ( ) φi z σ 1 ( ) 1 α i θi κτ i w α = ψ i M i Intuition: Cheap inputs θ i /M i = P σ 1 i low. To get zi, seller effect ψ i must be adjusted down. 19 / 40
The Supply Side The seller effect ψ i can be written ln ψ i = ln z i + (1 α) [ ln ni s + ln ψ i + ln Ω s i ln βi s ], ψ i 1/ni s Ω s i 1 n s i k S i ψ k ψ k ω ki ψ k S i i Variance decomposition, using Ψ and data on {M i, α, n s i, βs i }: Regress each component on ln ψi. 20 / 40
Estimation Step 1: Estimate Ψ. Step 2: Calculate variables for decomposition: ln ξ i, ln z i, ln θ i, ln ψ i, ln Ω s i and ln Ω c i. Step 3: Exact firm size decomposition. 21 / 40
Estimation : Step 1 The aim is to estimate ln m ij = ln ψ i + ln θ j + ln ω ij. ln ψ i average market share of i among her customers. ln θ j average market share of j among her suppliers. We get unbiased estimates when E [ln ψ i ln ω ij ] = E [ln θ j ln ω ij ] = 0. Conditional exogenous mobility: Assignment of suppliers to customers exogenous wrt ωij. 22 / 40
Estimation : Step 1 Identifying assumption holds if firms match based on.. ln ψi and ln θ j. Fixed costs (e.g., Lim, 2016, Bernard et al, forthcoming). Pair-wise shocks unrelated to ω ij (e.g., Eaton et al, 2015). Robustness 1: Asymmetry test a la Card et al (2015). Robustness 2: Include covariates for ω ij. 23 / 40
Estimation : Step 1 : Avalanching 2 customers seller effect ln ψ i. 2 suppliers buyer effect ln θ i. Avalanching: firm A dropped firm B too few links B dropped as well. Only main component used. 99% of links retained, 95% of value 75% of sellers retained, and 89% of buyers Initial Baseline, share # Links # Sellers # Buyers Links Value Sellers Buyers 16,800,368 555,722 797,595.99.95.75.89 Table: Avalanching (2012). 24 / 40
Estimation : Steps 2 & 3 Step 2: Use estimates Ψ with observables (ln Si, ln M i, ln βi c, ln βs i, ln nc i, ln ns i, C i and S i ) to get (ln ξ i, ln z i, ln ψ i, ln θ i, ln Ω s i and ln Ω c i ). Firms with missing S i and M i still part of 1st stage, but not main decomposition. α is total wage bill relative to production costs by 2-digit industry. Step 3: Demean variables by NACE 2-digit industry average. Regress each component on demeaned ln S i / ln ψ i / ln ξ i. 25 / 40
Results : 1st Stage Density 0.1.2.3.4 10 2 10 1 10 0 10 1 10 2 10 3 psi Density 0.5 1 10 2 10 1 10 0 10 1 10 2 10 3 theta R 2 =.43, sd (ln ψ i ) = 1.15, sd (ln θ i ) =.50, corr ( ln ψ i, ln θ i M i ) =.10 26 / 40
Results : Main Decomposition N Final Demand Supply Demand lnβ c i lnψ i lnξ i lns i 95,529.00.15.85 Notes: Significance: * < 5%, ** < 1%, *** <0.1%. Table: Overall decomposition (2012). Variance in sales mostly explained by the demand component. Firms are not big because they have large market shares among their customers. 27 / 40
Results : Main Decomposition ln S i = ln ψ i + ln ξ i ln β c i 2 1 0 1 2 3 lnxi lnbeta lnpsi 4 2 0 2 4 lns 28 / 40
Results : Demand ln ξ i = ln n c i + ln θ i + ln Ω c i.69.14.17 2 0 2 4 lnn_c lntheta_bar lnomega_c 4 2 0 2 4 lnxi 29 / 40
Results : Supply ln ψ i = ln z i + (1 α) (ln n s i + ln ψ i + ln Ω s i ln β s i ).96.02.00.02.00 1 0 1 2 3 lnz lneta lnomega_s lnn_s lnpsi_bar 2 1 0 1 2 3 lnpsi 30 / 40
General Equilibrium Close the model and perform counterfactual analyses. CES final demand with same elasticity of substitution σ. Consumers supply labor inelastically. They are shareholders of the firms Income is X = wl + Π, where Π is aggregate profits. Constant (but potentially heterogeneous) mark-ups. Consequently, µi M i /S i = (1 α) /Markup i is constant. 31 / 40
Solution Method Solution method: 1 Use estimates of z i and ω ij in backward fixed point: with P j = P 1 σ j. P j = ( ) 1 σ pij = P 1 α i z i ω ij, φ ij i Si i S i 2 Use (i) estimates of z i and ω ij, (ii) data on µ i and (iii) solution for P j in forward fixed point: S i = z i P 1 α X P i + µ j S j ω ij, P j Ci j where P is the final demand price index. Next steps: Counterfactuals, e.g. shocks to z i, ω ij, network structure. 32 / 40
Extensions & Robustness Exogenous mobility test. Observables for ω ij : Distance. Firm growth. Across 2-digit industries. 33 / 40
Exogenous Mobility Test Empirical test in the spirit of Card et al (2015). Under exogenous mobility, we have E [ln m ij ln m ik ] = E [ln m ik ln m ij ] = ln θ j ln θ k. Under endogenous mobility, moves from big to small may not lead to (a large) decline if moves are driven by unobserved shocks. 34 / 40
Exogenous Mobility Test Procedure: Estimate Ψ for the 2005 cross-section (t = 0). Group firms into quartiles based on ln θ j, q k, k = 1, 2, 3, 4. Upgraders: Firms that have at least one q 1 buyer in t = 0 and add at least one q 4 buyer in t = 1. Calculate ln m ij(q4),t=1 ln m ij(q1),t=0, where j (q k ) denotes a customer in the q k th quartile. Form the average of all possible combinations: Up i. Take the average of Up i across all upgraders. Calculate Down i for downgraders. Prelim results: Down i > Up i. 35 / 40
Extensions : Growth Perform decomposition on growth rates. Estimate Ψ in 2002 (t = 0) and 2014 (t = 1). Calculate change in every variable, e.g. ln S i. Sample: Decomposition: Only survivors, with non-missing θ i and ψ i in both years. But adding/dropping of relationships OK, e.g. the terms ln ψi and ln ξ i change because of extensive margin. 36 / 40
Extensions : Growth Sales Demand Supply lns i lnξ i lnψ i Final Demand -lnβ c i.11 Supply lnψ i.04 Demand lnξ i.85 # customers n c i.57 Avg. customer capability θ i.08 Covariance Ω c i.35 Production capability z i 1.03 # suppliers n s i -.02 Avg. supplier capability ψ i.00 Covariance Ω c i.00 Outside network supply β s i -.01 Obs. 41,923 41,923 41,923 Notes: Significance: * < 5%, ** < 1%, *** <0.1%. Table: Growth decomposition (2012). 37 / 40
Extensions : Across Industries NACE Industry N Final Demand Supply Demand -lnβ i lnψ i lnξ i 01-09 Primary and Extraction 2,836 -.03.24.79 10-33 Manufacturing 16,886 -.01.26.75 35-39 Utilities 849.04.15.81 41-43 Construction 18,976 -.10.11.99 45-82 Market Services 52,908.05.18.77 84-96 Non-Market Services 1,134.02.13.85 Table: Across industries (2014). 38 / 40
Conclusions Exact decomposition framework yields new insights: Variance in sales mostly driven by customer component. The supply component mostly driven by own productivity. This begs the question: How do firms attract customers? 39 / 40
Appendix : Correlation Matrix lns i lnψ i lnξ i lnβ c i lns i.14.61.00 lnψ i -.22.47 lnξ i.49 lnβ c i Table: Correlation Matrix (2012). 40 / 40