Productivity Dispersion, Import Competition, and Specialization in Multi-product Plants

Size: px

Start display at page:

Download "Productivity Dispersion, Import Competition, and Specialization in Multi-product Plants"

Brenda Harrell
5 years ago
Views:

1 Productivy Dispersion, Import Competion, and Specialization in Multi-product Plants Scott Orr Universy of Toronto October 2017

2 Introduction Enormous quanty of research into across-plant allocative gains from trade Growing lerature emphasizes whin-plant allocative gains Eckel and Neary (2010, Bernard et al. (2011, Mayer et al. (2014, 2016 Ltle to no empirical evidence documenting whether there is sufficient whin-plant heterogeney for these gains to matter. Why? Data Limations: Most data on multi-product plants only provide plant-level inputs (X

3 Introduction Enormous quanty of research into across-plant allocative gains from trade Growing lerature emphasizes whin-plant allocative gains Eckel and Neary (2010, Bernard et al. (2011, Mayer et al. (2014, 2016 Ltle to no empirical evidence documenting whether there is sufficient whin-plant heterogeney for these gains to matter. Why? Data Limations: Most data on multi-product plants only provide plant-level inputs (X y = f (X + ω (Standard Problem

4 Introduction Enormous quanty of research into across-plant allocative gains from trade Growing lerature emphasizes whin-plant allocative gains Eckel and Neary (2010, Bernard et al. (2011, Mayer et al. (2014, 2016 Ltle to no empirical evidence documenting whether there is sufficient whin-plant heterogeney for these gains to matter. Why? Data Limations: Most data on multi-product plants only provide plant-level inputs (X y = f (X + ω (Standard Problem y j = f (X j + ωj (New Problem

5 This Paper: Question #1 1 How to measure productivy in multiproduct plants if input allocations an unknown? I show that many workhorse IO models Function relating observable prices and quanties unobservable input allocations. Plants know their own productivy Information is incorporated into prices. Can use standard demand estimation tools to unpack this information. Answer: Use this function to estimate whin-firm input allocations y j = f (X j + ωj Under some restrictions that are used in most applied work: y j = f ( X j + ωj (Standard Problem

6 This Paper: Question #2 2 Do import shocks lead to whin-plant reallocations that increase productivy? Apply estimation methodology to Indian plants manufacturing machinery from Leverage Chinese Import Shock (Autor et al to examine import of Chinese imports on whin-plant reallocations. Answer: Chinese Import Shock IV Whin-plant reallocations that decrease productivy (QTFP

7 This Paper: Question #2 2 Do import shocks lead to whin-plant reallocations that increase productivy? Apply estimation methodology to Indian plants manufacturing machinery from Leverage Chinese Import Shock (Autor et al to examine import of Chinese imports on whin-plant reallocations. Answer: Chinese Import Shock IV Whin-plant reallocations that decrease productivy (QTFP...However, plants also reallocate inputs towards high qualy goods in response import shocks. High qualy large demand residual (Khandelwahl 2011 QTFP and qualy are negatively correlated Net effect of reallocations induced by doubling of Chinese imports on plant performance (RTFP 7% RTFP growth.

8 Contributions to related leratures 1 Whin-firm allocative gains from trade Eckel and Neary (2010, Goldberg et al. (2010, Bernard et al. (2011, Mayer et al. (2014, 2016, Medina (2017 My Contribution: Directly measure magnude of whin-plant heterogeney, as well as the effect of whin-plant reallocations on firm-performance Previous work relies on indirect evidence for allocative gains (product dropping, revenue skewness Qualy upgrading an important margin for RTFP growth Verhoogen (2008, Ami and Khandelwahl (2013, Medina (2017

9 Contributions to related leratures 2 Productivy estimation wh multi-product plants De Loecker (2011, Smeets and Warzynski (2013, Balat et al. (2016, De Loecker et al. (2016, Valmari (2016, Dhyne at al (2017 My Contribution: Provide general condions under which one can separately identify whin-firm input allocations from whin-firm TFP dispersion Whout some restrictions, TFP dispersion and input allocations not separately identified Pricing FOCs can provide these restrictions (Valmari (2016 I provide identification results for a broader class of models Model restrictions satisfied by most empirical work

10 Separately identifying QTFP and Input Allocations Suppose outputs, aggregate inputs, and production function for plant i known Y 1 = exp ( ω 1 F (L 1, K 1 Y 2 = exp ( ω 2 F (L 2, K 2 Y output in quanty uns, (L, K labour and capal. Two equations, six unknowns

11 Separately identifying QTFP and Input Allocations Suppose outputs, aggregate inputs, and production function for plant i known Y 1 = exp ( ω 1 F (L 1, K 1 Y 2 = exp ( ω 2 F (L 2, K 2 Y output in quanty uns, (L, K labour and capal. Two equations, six unknowns Can restrict heterogeney to obtain identification (De Loecker et al : Suppose K j = Lj K 1+K 2 L 1 +L2 = S j, and ωj = ω for j = 1, 2 Implies S 1 + S 2 = 1 Three equations, and three unknowns ( S 1, S, 2 ω If ω 1 ω2, we need at least one more restriction I obtain that restriction using a pricing FOC combined wh cost-minimization

12 Baseline Restrictions Suppose: F (. is homogeneous of degree φ > 0 and constant whin firm Assumed in almost all empirical work Single industry firms Inputs perfectly transferable across uses whin a firm Firms minimize static input costs for desired output bundle, condional on dynamic inputs CM Problem FOCs for cost minimization imply: Derivation? X j X S j = MC j Y j k Y MC ky k for X = L, K, M

13 Baseline Restrictions Suppose: F (. is homogeneous of degree φ > 0 and constant whin firm Assumed in almost all empirical work Single industry firms Inputs perfectly transferable across uses whin a firm Firms minimize static input costs for desired output bundle, condional on dynamic inputs CM Problem FOCs for cost minimization imply: Derivation? X j X S j = MC j Y j k Y MC ky k for X = L, K, M Market structure restrictions P j Perfect Competion: P j = MC j related to MC j

14 Input share inversion: Further Examples S j = MC j Y j k Y MC k Y k Obtain revenue shares if P j = µ MC j, µ firm-level markup CES demand generates this property. If markups vary whin firm, input share inversion depends on demand parameters Log Bertand pricing: MC j = Pj 1 α(1 QS j α a demand parameter, QS j quanty share of firm product j in market output Multi-product plants wh cannibalization effects: MC = ( 1 Q + P matrix of demand derivatives, P, Q, and MC vectors of plant-level prices, quanties, and marginal costs. General Case

15 General Points Input shares can be recovered from demand side data as long as model generates a mapping between demand side information and marginal costs Extensions? Generated by a very large class of demand systems and pricing models (Berry and Haile 2014 The exact mapping depends on the structure of the demand system and the nature of competion Next Step: Use this property to identify whin-plant heterogeney Estimation Steps ( 1 Estimate demand Qualy ( 2 Impose market structure assumption Inputs Shares 3 Use estimated input( allocations to estimate production function QTFP ω j η j S j

16 Data Indian Annual Survey of Industries (ASI Panel of manufacturing plants Observables: Plant: Worker Hours, Capal Stock, Intermediate Inputs (price and quanty by 5-dig ASICC code. Product: Revenue, Quanty, Price (un values by 5-dig ASICC code. Product codes g Varieties j Λ g t Industry: Machinery, Equipment, and Parts Details Why?

17 Summary Statistics Table: Plant-product level data Variable ( Obs Mean Std. Dev. Min Max P50 Log Revenue r jg ( Log Quanty Sold ( q jg Log Prices p jg ( Log Quanty Produced y jg Multi-Product Multi-product Single Industry Table: Plant level data Variable Obs Mean Std. Dev. Min Max P50 Log labour hours (l Log capal stock (rupees (k Log materials (Cobb-Douglas aggregator (m Number of Varieties

18 Demand I use a version of the continuous/discrete choice demand system described in Björnerstedt and Verboven (2013 Details Nested log model wh continuous quanty choice Choice sets, or sub-markets, indexed by h (3-dig ASICC codes Codes? Nests (products indexed by g (5-dig ASICC codes Varieties indexed by j (D g t, IM g t (Plant-products

19 Nesting Structure For Demand Variety example?

20 Demand Estimation Estimating equation, based on Berry (1994 inversion, for j Λ g t : ( ( RS jgh R jg ln RSt 0h =(1 σ ln ( α ln P jg (k,g D g t + η jg R kg + (k,g IM g t R kg R jg RS jg and P jg revenues and price of variety j revenue share of variety j in market h, RS 0h t share of outside option. revenue

21 Demand Estimation ln ( RS jgh RS 0h t =(1 σ ln ( α ln ( P jg (k,g D g t + η jg R kg R jg + (k,g IM g t R kg σ governs magnude of across-product code substution α governs whin-product code substution Can allow (α, σ to vary across product codes Have tried this, not statistically different at 2-dig level.

22 Demand Estimation ln ( RS jgh RS 0h t =(1 σ ln ( α ln ( P jg (k,g D g t + η jg R kg R jg + (k,g IM g t R kg η jg the demand-residual (Qualy Prices and whin-product code market shares will be correlated wh η jg I use input price instruments based on average price paid by firms who do not sell machinery and parts Details Z jg Z jg = Z g t average input price for g in other markets average input price for other other products produced whin the same plant

23 Demand Estimation: Results ( ln ( ln P jg RS j g (1 (2 OLS IV *** ** ( ( *** 0.845*** ( (0.214 Observations 60,098 60,098 Standard errors clustered by plant and product code *p<0.1; **p<0.05; ***p<0.01 Controls: Dummies for year, state, census status, ownership type, number of products, age First-Stage

24 Production Function Estimation Given demand estimates and assuming Nash-Bertrand pricing, can determine marginal costs and input allocations Details Estimate: y jg = β L l jg Assuming ω jg = ρ g 0 + ρωjg above to obtain : y jg + β K k jg i,t 1 + ξjg Why not proxy variable? =ρ g jg 0 (1 ρ + ρyi,t 1 + β L ( + β K k jg ρkjg i,t 1 + β Mm jg + ωjg, can ρ-difference the ( l jg ρl jg ( + β M i,t 1 m jg ρmjg i,t 1 + ξ jg Estimate by nonlinear GMM Instruments: Lagged labour, output and materials, current and lagged capal, as well as input price instruments.

25 Production Function Estimation: Results Table: Production Function Estimates OLS GMM β L 0.526*** 0.358** (0.062 (0.141 β K 0.247*** (0.038 (0.078 β M 0.262*** 0.783*** (0.021 (0.127 β L + β K + β M 1.037*** 1.209*** (0.036 (0.090 Observations Block bootstrapped standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

26 Results Having estimated the demand and production function I now know: Qualy ( Next up: η jg ( Input Shares ( QTFP ω jg S jg 1 Variety level correlations 2 Magnudes of whin-plant heterogeney 3 Import shocks and whin-plant reallocations

27 Product Level Heterogeney Correlations Table: Variety-Level Correlations Variables ( Qualy QTFP Price Markup Qualy η jg ( QTFP ( ω jg ( *** Price ln P jg ( 0.877*** *** Markups 0.027*** P jg MC jg All variables demeaned whin product-code/year

28 Product Level Heterogeney Correlations Table: Variety-Level Correlations Variables ( Qualy QTFP Price Markup Qualy η jg ( QTFP ( ω jg ( *** Price ln P jg ( 0.877*** *** Markups 0.027*** P jg MC jg All variables demeaned whin product-code/year

29 TFP versus Qualy (Product Level Single Product Only? Whin Plant?

30 Across versus Whin Plant Heterogeney Table: Multi-product Plant Variance Decomposions Across Firm Whin Firm Total Qualy Variance Percentage 60 % 40 % 100 % QTFP Variance Percentage 64 % 36 % 100 % Observations 11,187 11,187 11,187 All variables demeaned whin product-code/year

31 Across versus Whin Plant Heterogeney Table: Multi-product Plant Variance Decomposions Across Plant Whin Plant Total Qualy Variance Percentage 60 % 40% 100 % QTFP Variance Percentage 64 % 36% 100 % Observations 11,187 11,187 11,187 All variables demeaned whin product-code/year

32 Import Competion Trade, Whin-Plant Reallocations, and Productivy Eckel and Neary (2010, Bernard et al. (2011, Mayer et al (2014, 2017: Trade Liberalization Whin-firm reallocations towards high performing products Tested indirectly by eher looking at product dropping or changes in revenue skewness These reallocations can lead to plant-level productivy improvements. Since I have direct measures of productivy, can determine magnude of changes directly from data...but do we want productivy improvements if QTFP and qualy are negatively correlated?

33 Import Competion Plant Performance Wh Two-Dimensional Heterogeney Examine Revenue-TFP (RTFP, which will incorporate both qualy and QTFP Can use structure of demand system to determine revenue production function (Klette and Griliches 1996,De Loecker 2011: κ = ( ln(r jg = κ β L l jg + β K k jg α σ 1+ α, ω jg σ = κω jg, and ηjg + β Mm jg + ω jg is a demand shifter, + ηjg }{{} RTFP (h jg incorporating qualy, demand shocks, and product-space congestion effects Formula?

34 Import Competion Plant Performance Wh Two-Dimensional Heterogeney h (j,g Y S jg hjg : Plant level RTFP Can decompose into average and allocative efficiency terms as in Olley and Pakes (1996: h = ( h }{{} + OP S, h }{{} Average Performance Allocative Efficiency S and h vector of plant-variety level input shares and RTFP measures ( OP S, h ( OP Covariance quantifies the contribution of whin-plant reallocations to plant level RTFP.

35 Import Competion Plant Performance Wh Two-Dimensional Heterogeney h (j,g Y S jg hjg : Plant level RTFP Can decompose h into average and allocative efficiency terms as in Olley and Pakes (1996: h = ( h }{{} + OP S, h }{{} Average Performance Allocative Efficiency S and h vector of plant-variety level input shares and RTFP measures ( OP S, h ( OP Covariance quantifies the contribution of whin-plant reallocations to plant level RTFP. I will focus on this margin s contribution to RTFP growth

36 Import Competion Further Decomposing Whin-Firm Allocative Gains Can break variety-level RTFP down into whin and across product code demand shifters and productivy shifters h jg = ωg t + η g t }{{} Across Code + ω j g + η j g }{{} Whin Code Can apply ( OP decomposions four times, decomposing OP S, h into four terms: ( OP S, ( ( h = OP S, ω g t + OP S, η g t }{{}}{{} Cheap product codes High demand product codes ( ( OP S, ω j g t + OP S, η j g t }{{} Comparative advantage varieties }{{} Relatively high qualy varieties

37 Import Competion Further Decomposing Whin-Firm Allocative Gains Can break variety-level RTFP down into whin and across product code demand shifters and productivy shifters h jg = ωg t + η g t }{{} Across Code + ω j g + η j g }{{} Whin Code Can apply ( OP decomposions four times, decomposing OP S, h into four terms: ( OP S, ( ( h = OP S, ω g t + OP S, η g t }{{}}{{} Cheap product codes ( OP S, ω j g t }{{} Comparative advantage varieties High demand product codes + OP ( S, η j g t }{{} Relatively high qualy varieties

38 Import Competion Trends in Whin-Firm Allocative Efficiency Levels?

39 Import Competion Import Shocks?

40 Import Competion Qualy Specialization and Chinese Import Competion Specialization = β ln g Λ IM g China,t + α t + γ i + ɛ Imports endogenous Low performing product codes Larger increase in imports Leverage China Shock as in Autor et al. (2013 or Bloom et al. (2016 to obtain estimates of the effect of import competion Instrument total exposure to Chinese imports at the firm-level wh total imports from china in other low-to-middle income countries excluding India Z China = ln g Λ k C No India IM g k,t

41 Import Competion Import Competion and Qualy Specialization ln ( g Λ IMg China,t (OLS (OLS (OLS (OLS (OLS High Qualy Comparative Advantage High RTFP Theil Theil Specialization Specialization Specialization Revenue Inputs *** * *** *** ( ( ( ( ( Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 ln ( g Λ IMg China,t (IV (IV (IV (IV (IV High Qualy Comparative Advantage High RTFP Theil Theil Specialization Specialization Specialization Revenue Inputs ** *** * *** *** ( ( ( ( ( Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 First-Stage

42 Import Competion Import Competion and Qualy Specialization ln ( g Λ IMg China,t (OLS (OLS (OLS (OLS (OLS High Qualy Comparative Advantage High RTFP Theil Theil Specialization Specialization Specialization Revenue Inputs *** * *** *** ( ( ( ( ( Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 ln ( g Λ IMg China,t (IV (IV (IV (IV (IV High Qualy Comparative Advantage High RTFP Theil Theil Specialization Specialization Specialization Revenue Inputs ** *** * *** *** ( ( ( ( ( Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 First-Stage

43 Import Competion Import Competion and Qualy Specialization ln ( g Λ IMg China,t (OLS (OLS (OLS (OLS (OLS High Qualy Comparative Advantage High RTFP Theil Theil Specialization Specialization Specialization Revenue Inputs *** * *** *** ( ( ( ( ( Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 ln ( g Λ IMg China,t (IV (IV (IV (IV (IV High Qualy Comparative Advantage High RTFP Theil Theil Specialization Specialization Specialization Revenue Inputs ** *** * *** *** ( ( ( ( ( Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 First-Stage

44 Import Competion Interpreting Magnudes Net effect of relative qualy specialization, relative TFP specialization Double Chinese imports 10% decrease in plant RTFP due to reallocations towards relatively high qualy products Qualy margin only: 15% increase in plant RTFP These numbers ignore the effect of across product code reallocations.

45 Import Competion Net Effects ln ( g Λ IMg China,t (1 (2 (3 (4 (5 High Qualy Comparative Advantage High Demand Cheap Products RTFP Specialization Specialization Specialization Specialization Specialization ** *** ** ( ( ( ( ( Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 Double Chinese Imports 7 % RTFP growth

46 Import Competion Extensions and Robustness Robustness Alternative Estimation Approaches Go Input Price Dispersion Go Swchers? Go Tariff Regressions Go Welfare? Go

47 Import Competion Conclusion This paper: Develops a general methodology to deal wh multi-product firms in productivy estimation Useful for future research, and multi-product datasets becoming more common Applies approach to machinery, equipment, and parts industry in India, and find: Chinese Import competion led plants to specialize in qualy, not productivy Trade-off: Better goods, but more costly

48 Import Competion Conclusion Thank you!

49 Firm s Pricing Problem V t (S = ( ( Max P j P, I, K Qj Pt C K, ( Q Pt, ω, W j Y K K d K (K i,t 1, K, I K + βe{v t+1 (S i,t+1 S } subject to: K i,t+1 = l K (K, I K, I K i,t+1 K K Taking the first-order condion for any p j yields: Q j + Qk k Y P j ( P k MC k = 0 Back

50 Firm s Pricing Problem: MC Inversion All firm-product FOCs in matrix notation. Q t + t ( Pt MC t = 0 Where t = O t t General marginal cost inversion: MC t = 1 t Q t + P t 1 t must be invertible: Invertible if demand system exhibs connected substutes in price (Berry and Haile 2014 Can allow for different competion structures via different O t (Nevo 1998 Back

51 Optimal Share Formula Let ν X = w X if X M, and ν X = µx if X K FOC for any input X j : Back ν X λ j exp (ωj j F (SX ( = 0 ν X = λ j X exp (ωj Divide the above by Y j (ω = exp j and rearrange, yielding: Key Observation: F ( X X S j S j φ 1 F ( X X F (S j ( ( φ X = exp ω j S j F ( X, = F ( X λ j Y j X F ( X ν X 1 F ( X ν X does not depend on j. This generates an input allocation rule that will not depend on production function parameters, except through realized condional marginal costs

52 Machinery and Parts ASICC 74: MISC. MANUFACTURE OF BASE METALS E.g. Cylinders, Wheels, Rims ASICC 75: NON-ELECTRICAL MACHINE TOOLS & GENERAL PURPOSE MACHINERIES AND COMPONENTS AND PARTS THEREOF E.g. Gears, Ball Bearings, Valves ASICC 76: NON-ELECTRICAL INDUSTRY SPECIFIC EQUIPMENT/MACHINERIES INCL PARTS THEREOF E.g. Agriculture Implements, Textile Machinery, Drilling Machines ASICC 77: ELECTRICAL & ELECTRONIC MACHINERY & EQUIPMENT INCL PARTS E.g. Transformers, Control Equipment, Batteries ASICC 78: ELECTRONICS EQUIPMENT E.g. Printed Circu Plate, T.V. Set, Personal Computer Back

53 Preferences and Demand Utily Function for consumer c ( ( U ct (j, Qct, j ɛ j ct = Qct j ηt j + ɛ j ct exp α βi (Q c0 1 β I (Rescaled Indirect Utily Function condional on j Ω t Ṽ ct (j, ɛ cjgt, Y ct = c ct + α ( ln (Y ct α ln Pt j + ηt j + ɛ j ct β I Consumers choose one variety j Ω t that gives largest indirect utily. Leads to overall demand: ( ( ( δ j σ k Λ g exp δ k σ 1 mt t σ Q j = E exp t P j G l=0 ( ( k Λ l exp δ k mt t σ σ if j Λ g t Back

54 Economies of Scope and Common Inputs Suppose X j = X C + X Pj, X C = θx and j Y X Pj = (1 θx If firm choose allocation of private inputs, X Pj, condional on X, effective inputs, X j, will inputs satisfy: Back X j = mc j Y j k Y mc k Y k X Pj = j Y mc j Y j k Y mc ky k (1 θx Effective inputs are scaled up by 1 1 θ Wh Cobb-Douglas, this will simply show up as an increase in TFP. θ may vary wh number of products include number of product fixed effects in estimation

55 Input Price Instruments For each 5-dig output product code g, let I g denote the set of 5-dig products codes observed being used as inputs for single product firms that produce code g. If machinery parts producers are > 30% of observed observations buying input k, drop k from I g Let F kg t denote the set of firms observed in the ASI at time t who purchase an input wh product code k I g, who do not sell any outputs in the Machinery, Equipment, and Parts Industry. ( Z jg = Z g t = γ kg i F ln kg W k k I T g γkg i F ln kg Wiτ k τ F kg τ t k I g F kg t T τ=1 Back Where γ kg is the overall cost share of input k I g. Also include Z jg = ( k Y Z kl J 1 Z jg

56 Relaxing Functional Form Restrictions General inversion rule a solution to the following system of equations: ( ( θ j X j g j Qt, P t, t, O t Y j X j = ( k Y θ k X k g k ( Qt, P t, t, O t X Y k Depends on production function parameters through input ( elasticies θ j X j F j ( X j X j X j = X F j ( X j Fixed point will always exists for Cobb-Douglas ( β j X g j Qt, P t, t, O t Y j k Y β k X g k ( Qt, P t, t, O t X Y k Back

57 Economies of Scope and Common Inputs Suppose X j = X C + X Pj, X C = θx and j Y X Pj = (1 θx If firm choose allocation of private inputs, X Pj, condional on X, effective inputs, X j, will inputs satisfy (Wh Cobb-Douglas: Back X j = g j (. Y j k Y g k (. Y k X j = j Y g j (.Y j k Y g k (.Y k ( 1 + (J 1 κ X X Effective inputs are scaled up by 1 + (J 1 κ X This will simply show up as an increase in TFP. Can control for size of public input effects wh number of product dummies.

58 Full Firm Problem V t (S = subject to: ( Max P j I,X, X Qj Pt j Y K K W M M j M M j Y d K (K i,t 1, K, I K + βe{v t+1 (S i,t+1 S } exp(ω j F ( X j Y j X j = X X K j Y = Qj ( Pt K i,t+1 = l K (K, I K, I K i,t+1 K K j Y Back

59 Summary Statistics: Plant Level Single-Product Firms Obs Mean Std. Dev. Min Max Median Log Revenue (r Log Mandays (l Log Net Closing Value (k Log Cobb-Douglas Materials (m Average Import Competion Average Tariff Rate Multi-Product Firms Log Revenue (r Log Mandays (l Log Net Closing Value (k Log Cobb-Douglas Materials (m Number of Products (J Y Average Import Competion Average Tariff Rate Multi-Product Firms (No Vertical Integration Log Revenue (r Log Mandays(l Log Net Closing Value (k Log Cobb-Douglas Materials (m Number of Products (J Y Average Import Competion Average Tariff Rate Back

60 Summary Statistics:Product-Plant Level Single-Product Firms Obs Mean Std. Dev. Min Max Median Log Revenue (r j Log Un Value (p j Log Quanty Sold (q j Log Quanty Produced (y j Import Competion Tariff Rate Multi-Product Firms Log Revenue (r j Log Un Value (p j Log Quanty Sold (q j Log Quanty Produced (y j Import Competion Tariff Rate Multi-Product Firms (No Vertical Integration Log Revenue (r j Log Un Value (p j Log Quanty Sold (q j Log Quanty Produced (y j Import Competion Tariff Rate Back

61 First-Stage Demand Estimates ( (1 ( (2 ln ln P jg RS j g Zt g 0.331*** 0.156*** (0.110 ( Z jg *** (0.267 (0.145 Observations 60,098 60,098 F-Stat Standard errors clustered by plant and product code *p<0.1; **p<0.05; ***p<0.01 Back

62 Why Not Use A Proxy-Variable Approach? Olley and Pakes (1996 and Levinsohn and Petrin (2003 suffer from some internal consistency issues (Ackerberg et al Could potentially use estimator in Ackerberg et al (2015 [ACF]. However... Dimensionaly problems in ACF: Entire vector of unobserved TFP terms are state variables Control function estimation would suffer from a dimensionaly problem, as the set product codes are state variables On the other hand, ACF moment condions are almost identical to the rho-differenced moment condions (y j i,t 1 replaces ˆΦ j Back

63 ACF versus Rho-Differencing Key advantage of rho-differencing: Does not require scalar unobservabily E.g. Consistent even if capal and labour adjustment costs differ across firms. Key cost: Must restrict evolution of productivy Eher forced to assume productivy process is linear (i.e. AR(1, or abstract from ex-post shocks. For output choices to reveal input shares, I already need to assume the latter. Existence of productivy shocks that are unobserved by the firm when they make their input decisions will generate measurement error in my input shares Back

64 Input Shares Whin Multiproduct plants versus Qualy Firm-level MC inversion: MC = ( 1 Q + p = g(, P, Q matrix of firm-level own and cross-price derivatives. Q j P j = Qj P j ( 1 + α σ (1 σ αrsj g σ αrs j if j Λ g t Q j P k = Q j P k ( (1 σαrs j g σ Q j αrs k P k + αrs j if (j, k Λ g t if j Λ gt, k Λ l t, l g Input shares: X j = ( g j P, Q, RS, RS g, α, σ Y j ( P, Q, RS, RS g, α, σ k Y g k X Y k Back

65 Skewness Measures I use the Theil index to measure skewness, as in Mayer et al. (2014, 2016 ( Theil(S = 1 j S S j ln J j Y 1 J j Y S j 1 J j Y S j Varies from 0 (equal shares to ln(j (all inputs in one good Back

66 Condional Cost Minimization Lagrangian for cost minimization condional on dynamic inputs: Full Firm Problem? L = W M M j + λ j M M j Y j Y + µ K K K K j Y K j ( Y j (ω exp j F ( X j By envelope theorem: λ j = C ( K, Y, ω, W Y j MC j Back

67 Interpreting Welfare Changes Consumers of machinery, equipment, and parts are likely downstream producers Utily = Effective uns of an input chosen for a task Welfare changes = Changes in the expected price per effective un Details Total cost savings due to decreased price per effective un, holding quanties fixed: c P CF M Data c ( P P Data Mc Data CF = P Data 1 P Data Mc Data c Back

68 Welfare impact of whin-plant reallocations? ( Double Chinese Imports AE η jg gt = If all reallocations occur between the top and bottom qualy product whin each plant: ( ( S Top, η jg gt AE i,t 1 Ŝ Top i,t 1, gt ηjg S Top Ŝ Top i,t 1 = AE = gt η Top gt η Top gt η Bottom gt η Bottom Back

69 Interpreting Welfare Details Downstream producer c choose j Ω t to minimize costs condional of some desired level of effective input M ct where: ( M ct = Q j η j ct exp + ɛj c α Expected minimum price per effective un: ( P t = E (Min j Ωht (P j exp η j ɛj c α ( = Γ α G g=0 1 ( ( g j Λ exp t η j t α ln(pj t σ σ 1 α Back

70 Demand Shifters η j = ηj α + σ α σ (1 σ 1 + α ln σ α σ l Ω h t ( ln Et h ( δ k exp σ k Λ g t ln k Λ l t ( δ k exp σ σ Back

71 Levels: Whin-Plant Comparative Advantage Specialization Back

72 Levels: Whin-Plant Qualy Specialization Back

73 Tariff Cuts and Specialization (1 (2 (3 High Qualy Comparative Advantage High RTFP Specialization Specialization Specialization Tariffs * * ( ( ( Observations 1,753 1,753 1,753 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 Back

74 First-Stage: Chinese Import Regressions ln ( g Λ IMg China,t Z China 0.857*** ( Observations 1,753 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 F-Stat = Back

75 Whin-Plant Price Dispersion If static inputs have different prices across production lines: M j = j λ Y j W jm M λ k Y k Y k W km If qualy input price, this could be generating negative correlation between TFP and qualy whin-plants. Similar to De Loecker et al. (2016, control for unobserved price variation using data on output qualy Estimate the following for set of single-product plants: ln(w M = β 0 η j + β 1 ( η j 2 + β3 ( η j 3 + θg + α t + γ s + ɛ Out-of-sample prediction to estimate input price dispersion whin multi-product plants Back

76 Whin-Plant Price Dispersion Table: QTFP and Qualy Correlations wh Whin-Plant Price Dispersion (1 (2 (3 (4 (5 (6 QTFP QTFP QTFP QTFP QTFP QTFP Qualy *** *** *** *** *** *** (0.141 ( (0.143 ( (0.142 ( Observations 11,187 11,187 11,187 11,187 11,187 11,187 Plant FE NO YES NO YES NO YES Materials Price Adjustment NO NO YES YES YES YES Wage Adjustment NO NO NO NO YES YES Standard errors clustered separately by plant and product code *p<0.1; **p<0.05; ***p<0.01 Back

77 Alternatives for Production Function Estimation 1 Accounting for endogenous productivy as in De Loecker (2013 ω jg = ρ g 0 +ρωjg i,t 1 +β 0tariff g t 1 +β 1 ln g Λ IM g China,t 1 +ξ jg 2 Blundell and Bond (2000 y jg ( =ρ y jg i,t 1 + β L l jg ρ l jg ( + β M m jg ρ mjg i,t 1 i,t 1 + ξ jg + β K ( k jg jg ρ k i,t 1 Back

78 Alternatives for Production Function Estimation Table: Core Results: Alternative Methods ln ( g Λ IMg China,t (1 (2 Comparative Advantage Comparative Advantage Specialization Specialization *** *** ( ( Observations 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 Back

79 TFP versus Qualy Back

80 TFP versus Qualy Back

81 Fix IV Product Set at Intial Bundle Table: Core Results: China instrument constant at inial bundle ln ( g Λ IMg China,t (IV (IV (IV (IV (IV High Qualy Comparative Advantage High RTFP Theil Theil Specialization Specialization Specialization Revenue Inputs Shares Shares Shares ( ( (0.153 (0.150 (0.116 Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 First Stage F-stat = 6.92 Back

82 Fix IV Product Set at Panel-Level Bundle Table: Core Results: China instrument constant at panel-level bundle ln ( g Λ IMg China,t (IV (IV (IV (IV (IV High Qualy Comparative Advantage High RTFP Theil Theil Specialization Specialization Specialization Revenue Inputs Shares Shares Shares ( ( (0.218 (0.209 (0.140 Observations 1,718 1,718 1,718 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01 First Stage F-stat = 3.86 Back

83 3-Dig ASICC Codes Table: 3-Dig ASICC Codes ASICC code Description 740 MISC. MANUFACTURE OF BASE METALS, N.E.C NON-ELECTRICAL MACHINE TOOLS & GENERAL PURPOSE MACHINERIES AND 751 COMPONENTS AND PARTS THEREOF 761 AGRICULTURAL & FORESTRY MACHINERIES/PARTS THEREOF 762 FOOD, BEVERAGES & TOBACCO PROCESSING MACHINERIES & PARTS 763 MININGS, QUARRYING & METALLURGICAL MACHINERIES/PARTS 764 CONSTRUCTION/CEMENT MACHINERIES & PARTS TEXTILE, LEATHER & RUBBER PROCESSING, PAPER PRINTING MACHINERIES 765 & PARTS THEREOF 766 NON-ELECTRICAL DOMESTIC/OFFICE APPLIANCES & PARTS 767 CHEMICAL/PLASTIC/GLASS/WEAPON/AMMUNITION MACHINERIES AND PARTS THEREOF 768 LIFT AND LIFTING EQUIPMENT, FIXED OR MOBILE & PARTS THEREOF 769 MISC NON-ELECTRICAL MACHINERIES AND PARTS THEREOF, N.E.C 771 ELECTRICAL MACHINERY/EQUIPMENT ELECTRICAL MOTORS, GENERATORS, TRANSFORMER, POWER PACK [THIS INCL PUMP 772 SET FITTED WITH ELECTRIC MOTOR] SWITCH, SWITCH-GEAR, CONTROL PANEL, CIRCUIT BREAKERS ETC AND PARTS 773 THEREOF 774 LAMP, FILAMENT, ELECTRODES/ANODES/CONNECTORS, FITTINGS & PARTS 775 MEASURING/CONTROLLING/REGULATING INSTRUMENTS 776 BATTERY, ACCUMULATORS, CELLS AND PARTS THEREOF 777 DOMESTIC AND OFFICE ELECTRICAL EQUIPMENT 778 ELECTRO MAGNET, FANS, ARMATURE, COILS & ELECTRO-MAGNETIC EQUIPMENT 779 ELECTRICAL EQUIPMENT, PARTS AND ACCESSORIES, N.E.C 781 TELEPHONE/TELECOMMUNICATION/TRANSMISSION EQUIPMENT 782 AUDIO/VIDEO/SOUND APPARATUS & PARTS 783 COMPUTER & COMPUTING EQUIPMENT & PERIPHERALS & PARTS 784 ELECTRONIC VALVES/TUBES & COMPONENTS ELECTRONIC CARDS & ITS 785 COMPONENTS 789 OTHER ELECTRONIC COMPONENTS & PARTS Back

84 Import Competion and Allocative Efficiency ln ( g Λ IMg China,t (OLS (IV AE RTFP ** ( ( Observations 1,718 1,718 Standard errors clustered by plant *p<0.1; **p<0.05; ***p<0.01

85 Welfare impact of whin-plant reallocations? Did qualy reallocations increase welfare? Tradeoff: Cheaper goods versus better goods. Use demand model to quantify consumer gains implied by point estimates Suppose Chinese imports doubled, but whin-firm reallocations induced by the shock did not occur. How worse off are consumers whout the whin-plant adjustments?

86 Welfare Gains from Whin-Plant Reallocations

87 Welfare Gains from Whin-Plant Reallocations

88 Welfare Gains from Whin Plant Reallocations

89 Welfare Gains from Whin-Plant Reallocations Estimate size of S j t from trade shock using point estimates of specialization regressions Details Key assumption: Reallocations only occur from lowest qualy to highest qualy

90 Welfare Changes

91 Equivalent Variation Measures Total Gains = 19 million 2006 USD (0.07 % of market size Details Small? Back-of-the-envelope gains from trade implied by same shock using Arkolakis et al. (2012 formula: 1.14 %

92 Some Extensions F j (. rather than F (., and non-homogeneous technologies Go Public Inputs Go Back

93 Why Machinery? Figure: Chinese Imports in India: Machinery vs. Other Industries Back

94 What s a Variety? Back

Productivity Dispersion, Import Competition, and Specialization in Multi-product Plants

Productivity Dispersion, Import Competition, and Specialization in Multi-product Plants Productivy Dispersion, Import Competion, and Specialization in Multi-product Plants Scott Orr Sauder School of Business Universy of Brish Columbia January 11, 2019 Abstract Import competion can increase