Proximity vs Comparative Advantage: A Quantitative Theory of Trade and Multinational Production

Transcription

1 Proximity vs Comparative Advantage: A Quantitative Theory of Trade and Multinational Production Costas Arkolakis, Natalia Ramondo, Andres Rodriguez-Clare, Stephen Yeaple June 2011

2 Motivation WSJ (April 19) on U.S. multinationals during the 2000s: "declined employment in the U.S. by 2.9 million while increasing employment overseas by 2.4 million What are the implications of globalization on wages, profits, innovation? We need a quantitative model of trade and multinational production.

3 Background Melitz/Chaney with free entry: trade with no MP

4 Background Melitz/Chaney with free entry: trade with no MP Ramondo and McGrattan and Prescott: MP with no (gross) trade

5 Background Melitz/Chaney with free entry: trade with no MP Ramondo and McGrattan and Prescott: MP with no (gross) trade Helpman, Melitz and Yeaple: trade and MP but foreign affi liates cannot export BEA: U.S. foreign affi liates export 39% of their output

6 Background Melitz/Chaney with free entry: trade with no MP Ramondo and McGrattan and Prescott: MP with no (gross) trade Helpman, Melitz and Yeaple: trade and MP but foreign affi liates cannot export BEA: U.S. foreign affi liates export 39% of their output Ramondo and Rodriguez-Clare: trade and MP but no profits/innovation Net factor income flows (NFIA) were 20% of Irish GDP.

7 Model

8 Notation N countries. i: origin of idea, l: production location, n: destination market X iln : aggregate sales of firms from i, producing in l, selling to n Y l : total production by all firms in location l i,n X iln = Y l X n : total spending of country n i,l X iln = X n

9 Build on Melitz L i consumers/workers with Dixit-Stiglitz preferences, σ Monopolistic competition Exogenous entry, measure of firms M i Endogenous entry, entry cost w i f e i (innovation) Iceberg and marketing trade costs, τ ln and w n F n

10 To incorporate MP, we add Firms can produce anywhere, z = (z 1,..., z N )

11 To incorporate MP, we add Firms can produce anywhere, z = (z 1,..., z N ) MP costs, {γ il }

12 To incorporate MP, we add Firms can produce anywhere, z = (z 1,..., z N ) MP costs, {γ il } A firm with z from country i can serve market n from l at unit cost C iln = γ il w l τ ln z l

13 Firm Productivities Productivity (z 1,..., z N ) is drawn from a multivariate Pareto distribution G i (z 1,..., z N ) = 1 ( N l=1 [ T il z θ l ) ] 1 1 ρ 1 ρ, [ ] 1 ρ, with z l T 1/θ i, where T i l T 1/(1 ρ) il ρ [0, 1[, and θ > σ 1.

14 Firm Productivities Productivity (z 1,..., z N ) is drawn from a multivariate Pareto distribution G i (z 1,..., z N ) = 1 ( N l=1 [ T il z θ l ) ] 1 1 ρ 1 ρ, [ ] 1 ρ, with z l T 1/θ i, where T i l T 1/(1 ρ) il ρ [0, 1[, and θ > σ 1. Key parameters: θ, ρ.

15 Firm Productivities N = 2, high ρ

16 Firm Productivities N = 2, low ρ

17 Firm Productivities Multivariate Pareto distribution G i (z 1,..., z N ) = 1 ( N l=1 [ T il z θ l ) ] 1 1 ρ 1 ρ, [ ] 1 ρ, with z l T 1/θ i, where T i l T 1/(1 ρ) il ρ [0, 1[, and θ > σ 1.

18 Firm Productivities Multivariate Pareto distribution G i (z 1,..., z N ) = 1 ( N l=1 [ T il z θ l ) ] 1 1 ρ 1 ρ, [ ] 1 ρ, with z l T 1/θ i, where T i l T 1/(1 ρ) il ρ [0, 1[, and θ > σ 1. Assume that T il = T e i T p l.

19 Firm Productivities Multivariate Pareto distribution G i (z 1,..., z N ) = 1 ( N l=1 [ T il z θ l ) ] 1 1 ρ 1 ρ, [ ] 1 ρ, with z l T 1/θ i, where T i l T 1/(1 ρ) il ρ [0, 1[, and θ > σ 1. Assume that T il = T e i T p l. To simplify, assume T l = L 1 ρ l and f e i = f e.

20 Firm Productivities Multivariate Pareto distribution G i (z 1,..., z N ) = 1 ( N l=1 [ T il z θ l ) ] 1 1 ρ 1 ρ, [ ] 1 ρ, with z l T 1/θ i, where T i l T 1/(1 ρ) il ρ [0, 1[, and θ > σ 1. Assume that T il = T e i T p l. To simplify, assume T l = L 1 ρ l and f e i = f e. Looking ahead: country i has CA in innovation if T e i is relatively high.

21 Equilibrium Current Account balance Labor market clearing Zero profit condition (if endogenous entry)

22 The no-mp benchmark Let r i L e i /L i. We can show that r i = X i /Y i 1 + η X i /Y i

23 The no-mp benchmark Let r i L e i /L i. We can show that r i = X i /Y i 1 + η X i /Y i With no MP, X i /Y i = 1 and hence r i = η

24 The no-mp benchmark Let r i L e i /L i. We can show that r i = X i /Y i 1 + η X i /Y i With no MP, X i /Y i = 1 and hence r i = η With no MP, r i, M i independent of trade (as in EK 2001)

25 A frictionless world: the role of Comparative Advantage With frictionless trade and MP, then (T e r i = 1 (1 η) ( j δ j i ) 1 θ/(1 ρ) ) 1 θ/(1 ρ) Tj e where δ j L j Tj e / L k Tk e k

26 A two country world: the role of Home Market Effects Consider two identical countries except L 1 > L 2. Assume that τ 12 = τ 21 = τ, γ 12 = γ 21 = γ.

27 A two country world: the role of Home Market Effects Consider two identical countries except L 1 > L 2. Assume that τ 12 = τ 21 = τ, γ 12 = γ 21 = γ. If τ = γ = 1 or either τ = or γ = then r 1 = r 2 = η.

28 A two country world: the role of Home Market Effects Consider two identical countries except L 1 > L 2. Assume that τ 12 = τ 21 = τ, γ 12 = γ 21 = γ. If τ = γ = 1 or either τ = or γ = then r 1 = r 2 = η. With frictionless MP, the large country specializes in production (r 1 < η < r 2 )

29 A two country world: the role of Home Market Effects Consider two identical countries except L 1 > L 2. Assume that τ 12 = τ 21 = τ, γ 12 = γ 21 = γ. If τ = γ = 1 or either τ = or γ = then r 1 = r 2 = η. With frictionless MP, the large country specializes in production (r 1 < η < r 2 ) With frictionless trade, the large country specializes in innovation (r 2 < η < r 1 )

30 Gain from opennes The gains from openness are GO n X n/p n X A n /P A n

31 Gain from opennes The gains from openness are GO n X n/p n X A n /P A n GO n can be computed from flows as GO n = ( Xnnn X n ) 1 ρ θ ( l X nln X n ) ρ θ }{{} Direct Effect ) 1+ θ (σ 1) θ(σ 1) ( ( ) Xn η 1 + Xn /Y 1/θ n χ + (1 χ) Y n ηx n /Y n } {{ } Indirect Effect on Profits or Innovation

32 Can US workers be worse off because of MP? Under exogenous entry, the answer is yes.

33 Can US workers be worse off because of MP? Under exogenous entry, the answer is yes. Workers in a country with a high M/L can be made worse off by falling barriers to outward MP.

34 Can US workers be worse off because of MP? Under exogenous entry, the answer is yes. Workers in a country with a high M/L can be made worse off by falling barriers to outward MP. Depends on parameters: ρ and σ.

35 Can US workers be worse off because of MP? Under exogenous entry, the answer is yes. Workers in a country with a high M/L can be made worse off by falling barriers to outward MP. Depends on parameters: ρ and σ. Under endogenous entry, the answer is no.

36 Can US workers be worse off because of MP? Under exogenous entry, the answer is yes. Workers in a country with a high M/L can be made worse off by falling barriers to outward MP. Depends on parameters: ρ and σ. Under endogenous entry, the answer is no. Provided we remain away from corners (0 < r < 1).

37 Calibration

38 The Gravity Equation An OLS regresion of ln ( i X iln ) on ln τ with exporter and importer fixed effects does not recover θ

39 The Gravity Equation An OLS regresion of ln ( i X iln ) on ln τ with exporter and importer fixed effects does not recover θ The same regression but restricted to ln X iln gives us θ/ (1 ρ)

40 The Gravity Equation An OLS regresion of ln ( i X iln ) on ln τ with exporter and importer fixed effects does not recover θ The same regression but restricted to ln X iln gives us θ/ (1 ρ) We use tariff data and BEA data for X iln for i = US and selected l, n pairs Unrestricted Restricted Trade Elasticity ( 2.1) ( 3.08) Obs R sq

41 Parameters Use the endogenous entry model for the calibration.

42 Parameters Use the endogenous entry model for the calibration. Need to choose σ, θ, and ρ. Targets:

43 Parameters Use the endogenous entry model for the calibration. Need to choose σ, θ, and ρ. Targets: θ/ (1 ρ) = 10.8

44 Parameters Use the endogenous entry model for the calibration. Need to choose σ, θ, and ρ. Targets: θ/ (1 ρ) = 10.8 Share of intangible capital in income, 15% (Corrado et. al.) η 0.15

45 Parameters Use the endogenous entry model for the calibration. Need to choose σ, θ, and ρ. Targets: θ/ (1 ρ) = 10.8 Share of intangible capital in income, 15% (Corrado et. al.) η 0.15 Mark-up between 15% and 25% (Martins et. al.) σ/ (σ 1) 1.2

46 Parameters Use the endogenous entry model for the calibration. Need to choose σ, θ, and ρ. Targets: θ/ (1 ρ) = 10.8 Share of intangible capital in income, 15% (Corrado et. al.) η 0.15 Mark-up between 15% and 25% (Martins et. al.) σ/ (σ 1) 1.2 Trade elasticity (unrestricted) around 4.

47 Parameters Use the endogenous entry model for the calibration. Need to choose σ, θ, and ρ. Targets: θ/ (1 ρ) = 10.8 Share of intangible capital in income, 15% (Corrado et. al.) η 0.15 Mark-up between 15% and 25% (Martins et. al.) σ/ (σ 1) 1.2 Trade elasticity (unrestricted) around 4. Compromise:

48 Parameters Use the endogenous entry model for the calibration. Need to choose σ, θ, and ρ. Targets: θ/ (1 ρ) = 10.8 Share of intangible capital in income, 15% (Corrado et. al.) η 0.15 Mark-up between 15% and 25% (Martins et. al.) σ/ (σ 1) 1.2 Trade elasticity (unrestricted) around 4. Compromise: σ = 4, θ = 4.3 and ρ = 0.6.

49 Parameters Use the endogenous entry model for the calibration. Need to choose σ, θ, and ρ. Targets: θ/ (1 ρ) = 10.8 Share of intangible capital in income, 15% (Corrado et. al.) η 0.15 Mark-up between 15% and 25% (Martins et. al.) σ/ (σ 1) 1.2 Trade elasticity (unrestricted) around 4. Compromise: σ = 4, θ = 4.3 and ρ = 0.6. Imply θ/ (1 ρ) = 10.8, η = 17.4, σ/ (σ 1) = 1.33, and (after calibration) a trade elasticity of 4.9.

50 L i = equipped labor from data. Parameters

51 Parameters L i = equipped labor from data. Compute output from expenditure as Y l = X iln i,n

52 Parameters L i = equipped labor from data. Compute output from expenditure as Y l = X iln i,n Allow for current account imbalances, j = X j w j L j

53 Parameters L i = equipped labor from data. Compute output from expenditure as Y l = X iln i,n Allow for current account imbalances, j = X j w j L j Compute w j L j from w j L j = (1 η) Y j + η X jln l,n

54 Parameters L i = equipped labor from data. Compute output from expenditure as Y l = X iln i,n Allow for current account imbalances, j = X j w j L j Compute w j L j from w j L j = (1 η) Y j + η X jln l,n Compute r j from data as implied by the model with η = 17.4 r j = w jl j /Y j 1 + η w j L j /Y j

55 Parameters L i = equipped labor from data. Compute output from expenditure as Y l = X iln i,n Allow for current account imbalances, j = X j w j L j Compute w j L j from w j L j = (1 η) Y j + η X jln l,n Compute r j from data as implied by the model with η = 17.4 r j = w jl j /Y j 1 + η w j L j /Y j {τ ln }, {γ il } and {T e i } from trade and MP data and r i (with τ ln, γ il 1).

56 Results

57 Implied r vs R&D labor share

58 Bridge MP Is the calibrated model consistent with observed X iln? Let bmp il n =l X iln / n X iln. BEA data for i = US.

59 Comparative Advantage and HMEs (Ti e ) 1/θ Calibrated Ti e = 1 (own) Ti e = 1 (all) Belgium Canada Finland Germany Japan Netherlands Norway New Zealand Portugal United States r i

60 Gains from Openness

61 The Effects of "China" End. Entry, γ US,CH = 1 Ex. Entry, γ US,CH = 1 r r % (w/p) % (w/p) % (X /P) Belgium 15.9% 0.4% -1% 0% 1% Canada 1.2% 0.1% 15% 0% 0% Finland 17.9% 19.5% 2% 0% 0% Germany 4.6% 16.0% 0% 0% 0% Japan 17.8% 16.4% 2% 1% 1% Netherlands 27.9% 1.5% 4% 0% 1% Norway 18.6% 19.5% 1% 0% 0% China 18.9% 0.1% 30% 16% 6% Portugal 11.1% 12.4% 5% 1% 1% United States 17.8% 55.6% 33% 4% 30%