Static and Dynamic Gains from Importing Intermediate Inputs: Theory and Evidence

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1 Static and Dynamic Gains from Importing Intermediate Inputs: Theory and Evidence Hongsong Zhang Department of Economics, Penn State University Gains from Importing" Hongsong Zhang, Penn State University 1

2 Motivation: Importing and Productivity 18.87% of plants; 28.42% of inputs used in production was imported. The imported inputs directly enter the production process => have an direct impact on production and productivity Gains from Importing" Hongsong Zhang, Penn State University 2

3 Motivation: Importing and Productivity Table 4: Mean of Value Added Per Worker: Importers and Non importers (1,000 Colombia Peso) Industry Name Non importers Importers Basic Ind Chemicals Pharmaceuticals Plastics Leather Shoes Printing&Publishing Clothing All six Industries I Consistent with: Amit and Konings (2007), Kugler and Verhoogen (2012), Vogel and Wagner (2010), etc. Gains from Importing" Hongsong Zhang, Penn State University 3

4 Possible Explanations 1. Self selection 2. Importing may have a positive e ect on productivity. Gains from Importing" Hongsong Zhang, Penn State University 4

5 Possible Explanations 1. Self selection 2. Importing may have a positive e ect on productivity. (1) Higher quality per dollar (2) More variety (3) Dynamic productivity e ect - Channels: exposure to foreign technology, technical support from foreign suppliers, more open-minded management. Gains from Importing" Hongsong Zhang, Penn State University 5

6 Literature Literature studying the gains from importing - Coe and Helpman (1995), Amit and Konings (2007), Kasahara and Rodrigue (2008), Goldberg, Khandelwal and etc. (2009, 2010), Vogel and Wagner (2010), Kasahara and Lapham (2012), Kugler and Verhoogen (2012), Smeets and Warzynski (2013). Contribution of my work 1. Incorporate dynamic productivity e ect of importing; decompose the total gains from importing: static + dynamic 2. Control for self selection of rms into importing by endogenizing rms dynamic importing decision. Gains from Importing" Hongsong Zhang, Penn State University 6

7 Preview of Main Results I construct a dynamic model to charaterize rms decision on whether to import intermediate inputs. In the model: - Importing decision is endogenous: productivity, along with other factors, determines rms importing decision. - Productivity is endogenous: the importing decision, in turn, a ects rms future productivity dynamically. Estimate this dynamic model structurally using micro data I nd: 1. Obvious selection: larger rms and more productive rms are more likely to import. 2. Gains from importing are large (1%-22% increase of rm value). 3. Dynamic productivity e ect is the major source of gains from importing. Gains from Importing" Hongsong Zhang, Penn State University 7

8 Plan Data Model Estimation Procedure Estimation Results Selection Gains from Importing Conclusion Gains from Importing" Hongsong Zhang, Penn State University 8

9 Data Plant-level data from Colombia during : basic industrial chemicals, pharmaceuticals, plastics, clothing, leather shoes, printing&publishing Panel data. Cover all plants with 10 or more employees. Variables: value of output, domestic input, imported input, labor, capital, investment, and some other rm characteristics. Gains from Importing" Hongsong Zhang, Penn State University 9

10 Turnover and Persistence of Importing Status Turnover: 10% of the importers are new; 12.6% quit importing Persistence: Table 3: Transition Probability of Importing Status Probability Date t+1 Import Not Import Date t Import Not Import Gains from Importing" Hongsong Zhang, Penn State University 10

11 The Model Single- rm model, in nite periods. Single di erentiated output. Monopolistic competition (output). Fixed input prices. Production: h Q jt = exp(ω jt ) L α l with M jt = jt Mα m jt i K α k jt M θ θ 1 θ 1 jdt + AM θ jft θ θ 1 Demand: Q D jt = Φ tp η jt Gains from Importing" Hongsong Zhang, Penn State University 11

12 Timing 1. At the beginning of each date, each rm observes its own state s jt = K jt, ω jt, d jt. 2. Choose static input (L jt, M jtd, M jtf ) and output price (P jt ) to maximize its static pro t for this period; 3. Observe two new import cost shocks (Cs jt, Cf jt ), i.i.d across j and t. 4. Choose importing status for next period (d jt+1 ) and investment (i jt ). Evolution of state variables K jt+1 = (1 δ k )K jt +i jt ω jt+1 = g 0 + g ω ω jt + g d d jt + ε jt+1, ε jt+1 N(0, σ 2 ε ) d jt+1 = 1, if pay the sunk/ xed cost (Cs jt, Cf jt ) Gains from Importing" Hongsong Zhang, Penn State University 12

13 Static Decision: Input and output price The rm chooses L jt, M jtd, M jtf, and P jt to maximize period pro t. ln R jt = γ τ D t + r k ln K jt + r ω ω jt + r d d jt (1) τ where r k, r d, and r w are functions of demand parameters and production parameters. Total variable cost C jt = 1 + η η (α l + α m ) R jt (2) Gains from Importing" Hongsong Zhang, Penn State University 13

14 Dynamic choice of importing status Plant j s value before it observes the current-date xed cost/sunk cost ( ZZ V V (s jt ) = π(s jt )+ 1 (s max jt ) d jt C f ) jt 1 d jt C s jt, d jt+1 V 0 df s df f (s jt ) (3) where Z V 1 (s jt ) = δ max V (s jt+1, d jt+1 = 1)dF ω jt+1 jω jt, d jt (4) i jt Z V 0 (s jt ) = δ max i jt V (s jt+1, d jt+1 = 0)dF ω jt+1 jω jt, d jt (5) Gains from Importing" Hongsong Zhang, Penn State University 14

15 Idea for Identi cation Parameters to be estimated: α l, α m, α k, A, θ; η; g ω, g d, σ 2 ε ; F s, F f. α l, α m, α k, A, θ, η; g (, ), σ 2 ε identi ed from plants static decision - α l, α m, α k, η, g ω, σ 2 ε : non-importers static decision. - g d : comparison of productivity growth for importers and non-importers. - A, θ : relative usage of domestic and imported inputs for importers. F s, F f : identi ed from the conditional choice probability (CCP) of importing - Idea: sunk/ xed costs determines the turnover of importing status, so we can infer the distribution of sunk/ xed costs from the observed importing decisions. Gains from Importing" Hongsong Zhang, Penn State University 15

16 Estimation: Stage 1 Stage 1 estimates production parameters (α l, α m, α k, A, θ) and productivity evolution parameters (g ω, g d, σ 2 ε ); q jt = α l l jt +α m θ θ q jt = α l l jt +α m θ θ 1 ln 1 ln M θ θ 1 θ 1 jdt + AM θ jft d jt + α k k jt +ω jt {z } +ξ jt M θ θ 1 θ 1 jdt + AM θ jft d jt +φ(i jt, k jt, d jt+1 ) + ξ jt From φ(i jt, k jt, d jt+1 ) = α k k jt + ω jt, ω jt = g ω jt 1, d jt 1 + εjt bφ jt = α k k jt + g b φ jt 1 α k k jt 1, d jt 1 + ε jt + ξ jt Recover productivity: cω jt = bφ jt cα k k jt Gains from Importing" Hongsong Zhang, Penn State University 16

17 Stage 2: Demand Elasticity 2-1: given the estimates of α l and α m, estimate demand elasticity(η) from variable cost and revenue data. C jt = 1 + η η ( bα l + cα m ) R jt + ζ jt 2-2: construct the revenue functions from equation (1), and pro t function ln R jt = τ π jt = 1 γ τ D t + br k ln K jt + rb ω ω jt + rb d d jt + ζ jt 1 + bη bη ( bα l + cα m ) R jt Gains from Importing" Hongsong Zhang, Penn State University 17

18 Stage 3: Distribution of Costs Estimate F s, F f using MLE, based on conditional choice probability (CCP) of importing Assume: iid C s jt EXP(λ s ), C f jt EXP(λ f ) Probability to import: L 1 jt = Pr d jt+1 = 1 j s jt n = Pr d jt Cjt f + 1 d jt C s jt V 1 s jt V 0 s jt j sjt o Likelihood function: L = L j = j=1:n t=1:n where L jt = d jt+1 L 1 jt + (1 d jt+1)(1 L 1 jt ). L jt t=1:t Gains from Importing" Hongsong Zhang, Penn State University 18

19 Major di culty: V 1 s jt and V 0 s jt are unknown. They can be computed from equations (3) (5). (value function iteration) Gains from Importing" Hongsong Zhang, Penn State University 19

20 Computation Algorithm Discretize the state space S into S 0 with N grid points. 1. Pick a parameter λ 0 = λ 0 s, λ 0 f 2 Γ (parameter space). 2. Given λ 0, compute value function V (S 0 ) de ned in equation (1); 2.1 Pick an starting value function V 0 (S 0 ); 2.2 Compute the choice-speci c value function V 1 (S 0 ) and V 0 (S 0 ) from equations (2), and (3). 2.3 Use π (S 0 ), V 1 (S 0 ) and V 0 (S 0 ) to update the value function to V 1 (S 0 ); 2.4 Iterate until j V i+1 (S 0 ) V i (S 0 ) j small. 3. For given λ 0, compute the likelihood: L(λ 0 ) Pick λ = arg max λ2γ L(λ) (MLE). Gains from Importing" Hongsong Zhang, Penn State University 20

21 Estimation Results Table 5: Parameters in Production Function Industry B.I.Chemicals Pharmaceuticals Plastics L.Shoes Print&Pub Clothing L share (α l ) (0.0024) (0.0026) (0.0013) (0.0012) (0.0006) (0.0003) M share (α m ) (0.0011) (0.0019) (0.0006) (0.0006) (0.0003) (0.0001) K share (α k ) (0.0096) (0.0036) (0.0014) (0.0020) (0.0002) (0.0014) Quality (A) (0.4611) (0.0828) (0.0233) (0.5430) (0.0359) (0.1013) Elasticity (θ) (0.1287) (0.0897) (0.0577) (0.3821) (0.0479) (0.5232) Notes: (1) The standard errors are in the parentheses. (2) I also control for age and ownership dummy in this regression. Gains from Importing" Hongsong Zhang, Penn State University 21

22 Productivity Evolution Table 6: Productivity Evolution Process Industry Chemicals Pharmaceuticals Plastics L.Shoes Print&Pub Clothing g (0.9385) (0.9876) (0.5828) (0.9686) (0.0320) (0.3650) g ω (0.1169) (0.5460) (0.2666) (0.2548) (0.0128) (0.1111) g d (0.0072) (0.0128) (0.0035) (0.0157) (0.0012) (0.0070) σ ω Notes: (1) Standard errors in parentheses. (2) I control for export in the regression. ω jt = g 0 + g ω ω jt 1 +g d d jt 1 +ε jt Robustness check. Gains from Importing" Hongsong Zhang, Penn State University 22

23 Distribution of Fixed and Sunk Costs Table 8: Distribution of Sunk and Fixed Cost (MLE) Industry B.I.Chemicals Pharmaceu. Plastics L.Shoes Print&Pub Clothing logλ s (0.2410) (0.2619) (0.1917) (0.3880) (0.1455) (0.1956) logλ f (0.0599) (0.0596) (0.0324) (0.0628) (0.0237) (0.1022) Notes: Standard deviation in parentheses. Gains from Importing" Hongsong Zhang, Penn State University 23

24 Self Selection: New Importer Begin importing if: C s jt V 1 (s jt j d jt = 0) V 0 (s jt j d jt = 0) More productive/larger rms tend to start importing. Figure: Thresholds for new importing: Fixed Costs, Productivity, and Firm Size. Gains from Importing" Hongsong Zhang, Penn State University 24

25 Self Selection: Old Importer Stop importing if: C f jt V 1 (s jt j d jt = 1) V 0 (s jt j d jt = 1) More productive/larger rms tend to continue importing. Figure: Thresholds for Continuing Importing: Fixed Costs, Productivity, and Firm Size. Gains from Importing" Hongsong Zhang, Penn State University 25

26 Importing Probability: New Importer VS Old Importer Gains from Importing" Hongsong Zhang, Penn State University 26

27 Gains from Importing Total Gain: Total Gain = V (s jt0 ) V aut (ω jt, K jt ) (6) where s jt0 = (ω jt, K jt, d jt = 0). Decomposition: Dynamic E ect = V (s jt0 ) V (s jt0 j g d = 0) (7) Static E ect = V (s jt0 j g d = 0) V aut (ω jt, K jt ) (8) Gains from Importing" Hongsong Zhang, Penn State University 27

28 Total Gains Table 9: Total Gains From Importing Industry Name Pctg. Gain Basic Ind Chemicals 14.47% Pharmaceuticals 22.28% Plastics 16.25% Leather Shoes 6.17% Printing&Publishing 4.50% Clothing 0.87% Notes: "Pctg. Gain" refers to the percentage gain of firm value from importing. It is defined as (total gain)/v(s jt0 ). Gains from Importing" Hongsong Zhang, Penn State University 28

29 Sources of the Gains: Dynamic & Static E ects Table 10: Dynamic and Static Effects from Importing Industry Name Dynamic Effect Static Effect Total E. Basic Ind Chemicals 13.94% 0.53% 14.47% Pharmaceuticals 21.82% 0.47% 22.28% Plastics 15.76% 0.49% 16.25% Leather Shoes 5.35% 0.82% 6.17% Printing&Publishing 4.46% 0.03% 4.50% Clothing 0.75% 0.12% 0.87% Gains from Importing" Hongsong Zhang, Penn State University 29

30 Conclusion and Future Work 1. Incorporate dynamic productivity e ect of importing into consideration; decompose the total gains from importing: static e ect + dynamic e ect (1) Total gains from importing are large. (Increase rm value by 0.87%-22%) (2) Dynamic productivity e ect is the major source of gains from importing. (85% total gain; 1.5% annual productivity) 2. Control for self selection of rms into importing by endogenizing rms dynamic importing decision. Based on a dynamic structural model which is estimated using micro data. (3) Self selection: more productive/larger plants are more likely to import intermediate materials. Gains from Importing" Hongsong Zhang, Penn State University 30

31 Extensions 1. Location Choice: origin country of import a ects the size/sources of gains (work in progress) 2. Import & Export: understand the dynamics of import and export (work in progress) 3. R&D and importing Gains from Importing" Hongsong Zhang, Penn State University 31