Measuring the Gains from Trade: They are Large!

Transcription

1 Measuring the Gains from Trade: They are Large! Andrés Rodríguez-Clare (UC Berkeley and NBER) May 12, 2012

2 Ultimate Goal Quantify effects of trade policy changes

3 Instrumental Question How large are GT? For Canada, GT = 1% or 10%?

4 Main Points Exciting "micro" features come up short

5 Main Points Exciting "micro" features come up short Krugman

6 Main Points Exciting "micro" features come up short Krugman Eaton-Kortum or Melitz

7 Main Points Exciting "micro" features come up short Krugman Eaton-Kortum or Melitz Variable markups

8 Main Points Exciting "micro" features come up short

9 Main Points Exciting "micro" features come up short Boring "macro" features matter a lot

10 Main Points Exciting "micro" features come up short Boring "macro" features matter a lot For Canada: 1.8% 5.2% 15%

11 Main Points Exciting "micro" features come up short Boring "macro" features matter a lot For Canada: 1.8% 5.2% 15% Elasticities cannot be taken lightly

12 Main Points Exciting "micro" features come up short Boring "macro" features matter a lot For Canada: 1.8% 5.2% 15% Elasticities cannot be taken lightly Micro (gravity, foreign vs foreign) vs macro (home vs foreign)

13 Main Points Exciting "micro" features come up short Boring "macro" features matter a lot For Canada: 1.8% 5.2% 15% Elasticities cannot be taken lightly Micro (gravity, foreign vs foreign) vs macro (home vs foreign) Aggregate vs sector-specific elasticities

14 Background Papers "New Trade Theories, Same Old Gains?" (AER, 2012, with Arkolakis and Costinot) "The Elusive Pro-Competitive Effects of Trade" (2012, with Arkolakis, Costinot and Donaldson) "Trade Theory with Numbers: Quantifying the Consequences of Globalization" (Handbook, in progress, with Costinot)

15 Things left out (in progress) Distributional implications Validation of model

16 Road Map Armington model, GT, elasticities Adding "micro" features while keeping gravity Adding "macro" features: multiple sectors and traded intermediates

17 The Armington Model Dixit-Stiglitz price index and "gravity" P 1 σ j X ij = with trade elasticity (i = l) ε ln = n i=1 (w i τ ij ) 1 σ (w i τ ij ) 1 σ i (w i τ i j ) 1 σ }{{} λ ij ( λij λ lj w j L j }{{} Y j )/ ln τ ij = σ 1

18 The Armington Model Let P ij w i τ ij. Then can write the gravity equation X ij = P1 σ ij i P 1 σ i j Y j Effect of a foreign shock (L j = L j, τ jj = τ jj ) on W j Y j /P j We are interesed in deriving d ln W j = d ln Y j d ln P j

19 The Armington Model: Basic Welfare Result Step 1: change in W j depends on changes in real GDP and ToT d ln W j = d ln Y j d ln P jj }{{} n i=1 λ ij (d ln P ij d ln P jj ). }{{} change in real GDP in j change in ToT for j

20 The Armington Model: Basic Welfare Result Step 1: change in W j depends on changes in real GDP and ToT d ln W j = d ln Y j d ln P jj }{{} n i=1 λ ij (d ln P ij d ln P jj ). }{{} change in real GDP in j change in ToT for j Letting P M j ( ) 1 σ Pij 1 σ, i =j then ) d ln W j = d ln Y j d ln P jj (1 λ jj ) (d ln Pj M d ln P jj. }{{}}{{} change in real GDP in j change in ToT for j

21 The Armington Model: Basic Welfare Result Step 1: changes in real income depend on changes in real GDP and ToT, ) d ln W j = d ln Y j d ln P jj (1 λ jj ) (d ln Pj M d ln P jj.

22 The Armington Model: Basic Welfare Result Step 1: changes in real income depend on changes in real GDP and ToT, ) d ln W j = d ln Y j d ln P jj (1 λ jj ) (d ln Pj M d ln P jj. Step 2: changes in relative imports depend on changes in ToT ) d ln (1 λ jj ) d ln λ jj = (1 σ) (d ln Pj M d ln P jj.

23 The Armington Model: Basic Welfare Result Step 1: changes in real income depend on changes in real GDP and ToT, ) d ln W j = d ln Y j d ln P jj (1 λ jj ) (d ln Pj M d ln P jj. Step 2: changes in relative imports depend on changes in ToT ) d ln (1 λ jj ) d ln λ jj = (1 σ) (d ln Pj M d ln P jj. Step 3: these two equations yield d ln W j = d ln Y j d ln P jj d ln λ jj σ 1.

24 The Armington Model: Basic Welfare Result Step 1: changes in real income depend on changes in real GDP and ToT, ) d ln W j = d ln Y j d ln P jj (1 λ jj ) (d ln Pj M d ln P jj. Step 2: changes in relative imports depend on changes in ToT ) d ln (1 λ jj ) d ln λ jj = (1 σ) (d ln Pj M d ln P jj. Step 3: these two equations yield d ln W j = d ln Y j d ln P jj d ln λ jj σ 1. Step 4: setting w j, and using ε = σ 1, d ln W j = d ln λ jj ε.

25 The Armington Model: Basic Welfare Result Step 1: changes in real income depend on changes in real GDP and ToT, ) d ln W j = d ln Y j d ln P jj (1 λ jj ) (d ln Pj M d ln P jj. Step 2: changes in relative imports depend on changes in ToT ) d ln (1 λ jj ) d ln λ jj = (1 σ) (d ln Pj M d ln P jj. Step 3: these two equations yield d ln W j = d ln Y j d ln P jj d ln λ jj σ 1. Step 4: setting w j, and using ε = σ 1, d ln W j = d ln λ jj. ε Step 5: integration yields (ˆx = x /x) Ŵ j = λ 1/ε jj

26 Counterfactuals Result Ŵ j = λ 1/ε jj is ready for ex-post analysis

27 Counterfactuals Result Ŵ j = λ 1/ε jj is ready for ex-post analysis For ex-ante analysis, need to predict ˆλ jj

28 Counterfactuals Result Ŵ j = λ 1/ε jj is ready for ex-post analysis For ex-ante analysis, need to predict ˆλ jj Gravity and "exact hat algebra" to get ˆλ jj from {λ ij, Y j } and ε and { ˆτ ij }

29 Counterfactuals Result Ŵ j = λ 1/ε jj is ready for ex-post analysis For ex-ante analysis, need to predict ˆλ jj Gravity and "exact hat algebra" to get ˆλ jj from {λ ij, Y j } and ε and { ˆτ ij } If counterfactual is autarky, then λ jj = 1, hence ˆλ jj = 1/λ jj, so W A j /W j = λ 1/ε jj.

30 Gains from Trade Define gains from trade as GT j 1 W A j /W j Previous result implies that GT j = 1 λ 1/ε jj.

31 Gains from Trade Need to implement GT j = 1 λ 1/ε jj

32 Gains from Trade Need to implement GT j = 1 λ 1/ε jj Gravity based estimate of ε

33 Gains from Trade Need to implement GT j = 1 λ 1/ε jj Gravity based estimate of ε Anderson and van Wincoop (2004) say ε [5, 10] (survey)

34 Gains from Trade Need to implement GT j = 1 λ 1/ε jj Gravity based estimate of ε Anderson and van Wincoop (2004) say ε [5, 10] (survey) ARRY get ε = 4.3 with τ as average tariffs

35 Gains from Trade Need to implement GT j = 1 λ 1/ε jj Gravity based estimate of ε Anderson and van Wincoop (2004) say ε [5, 10] (survey) ARRY get ε = 4.3 with τ as average tariffs SW get ε = 4 with τ from price gaps

36 Gains from Trade Need to implement GT j = 1 λ 1/ε jj Gravity based estimate of ε Anderson and van Wincoop (2004) say ε [5, 10] (survey) ARRY get ε = 4.3 with τ as average tariffs SW get ε = 4 with τ from price gaps Use ε = 5

37 Gains from Trade Need to implement GT j = 1 λ 1/ε jj Gravity based estimate of ε Anderson and van Wincoop (2004) say ε [5, 10] (survey) ARRY get ε = 4.3 with τ as average tariffs SW get ε = 4 with τ from price gaps Use ε = 5 λ jj is share of gross expenditure devoted to home purchases, computed from OECD-STAN as gross production - exports gross expenditure

38 Gains from Trade λ jj % GT j Canada Denmark France Portugal U.S

39 Armington, Micro vs Macro Elasticities Consider two-tier CES preferences: domestic vs foreign, foreign vs foreign

40 Armington, Micro vs Macro Elasticities Consider two-tier CES preferences: domestic vs foreign, foreign vs foreign σ is EoS bw domestic and foreign, σ is EoS among foreign countries

41 Armington, Micro vs Macro Elasticities Consider two-tier CES preferences: domestic vs foreign, foreign vs foreign σ is EoS bw domestic and foreign, σ is EoS among foreign countries Macro trade elasticity ( 1 1 σ λjj = ln λ jj )/ ln τ

42 Armington, Micro vs Macro Elasticities Consider two-tier CES preferences: domestic vs foreign, foreign vs foreign σ is EoS bw domestic and foreign, σ is EoS among foreign countries Macro trade elasticity ( 1 1 σ λjj = ln λ jj )/ ln τ Micro trade elasticity (i = l, i = j, l = j) ( )/ λij 1 σ = ln ln τ ij λ lj

43 Armington, Micro vs Macro Elasticities Gravity regression picks up 1 σ, while now d ln (1 λ jj ) d ln λ jj = ( 1 σ ) ( d ln P M j d ln P jj ) so GT = 1 λ 1/(σ 1) jj

44 Armington, Micro vs Macro Elasticities Gravity regression picks up 1 σ, while now d ln (1 λ jj ) d ln λ jj = ( 1 σ ) ( d ln P M j d ln P jj ) so GT = 1 λ 1/(σ 1) jj Assumption σ = σ seems natural, but see Feenstra Obstfeld and Russ

45 Armington, Micro vs Macro Elasticities Gravity regression picks up 1 σ, while now d ln (1 λ jj ) d ln λ jj = ( 1 σ ) ( d ln P M j d ln P jj ) so GT = 1 λ 1/(σ 1) jj Assumption σ = σ seems natural, but see Feenstra Obstfeld and Russ If σ < σ then GT larger

46 Armington, Micro vs Macro Elasticities Gravity regression picks up 1 σ, while now d ln (1 λ jj ) d ln λ jj = ( 1 σ ) ( d ln P M j d ln P jj ) so GT = 1 λ 1/(σ 1) jj Assumption σ = σ seems natural, but see Feenstra Obstfeld and Russ If σ < σ then GT larger They find σ = 1!?!?

47 The exciting "micro" stuff: variety, selection, markups Krugman adds variety effects

48 The exciting "micro" stuff: variety, selection, markups Krugman adds variety effects Melitz adds selection/reallocation effects

49 The exciting "micro" stuff: variety, selection, markups Krugman adds variety effects Melitz adds selection/reallocation effects Melitz-Ottaviano add pro-competitive effects

50 The exciting "micro" stuff: variety, selection, markups Krugman adds variety effects Melitz adds selection/reallocation effects Melitz-Ottaviano add pro-competitive effects How are gains from trade affected?

51 Variety effects... where did they go? Krugman s model with CES, L.O.V. elasticity is 1/ (σ 1)

52 Variety effects... where did they go? Krugman s model with CES, L.O.V. elasticity is 1/ (σ 1) But entry is proportional to L and all goods traded

53 Variety effects... where did they go? Krugman s model with CES, L.O.V. elasticity is 1/ (σ 1) But entry is proportional to L and all goods traded Hence trade does not affected variety

54 Variety effects... where did they go? Krugman s model with CES, L.O.V. elasticity is 1/ (σ 1) But entry is proportional to L and all goods traded Hence trade does not affected variety Gravity and gains as in the Armington model

55 Selection/reallocation effects... new gains? EK, BEJK, Melitz-Chaney-EKK

56 Selection/reallocation effects... new gains? EK, BEJK, Melitz-Chaney-EKK CES + continuum of goods, P ij is price index of goods from i in j

57 Selection/reallocation effects... new gains? EK, BEJK, Melitz-Chaney-EKK CES + continuum of goods, P ij is price index of goods from i in j In Armington had P ij = τ ij P ii and P ii = w i, now P ij = τ ij P ii (τ ij P i /P j ) η ρ ij and P ii = w i (w i /P i ) η ζ i.

58 Selection/reallocation effects... new gains? EK, BEJK, Melitz-Chaney-EKK CES + continuum of goods, P ij is price index of goods from i in j In Armington had P ij = τ ij P ii and P ii = w i, now P ij = τ ij P ii (τ ij P i /P j ) η ρ ij and P ii = w i (w i /P i ) η ζ i. Armington η = 0, but in EK, BEJK and Melitz-Chaney-EKK η = θ σ 1 1 > 0

59 Selection/reallocation effects... new gains? Gravity equation is now X ij = χ ij (w i τ ij ) ε n l=1 χ lj (w l τ lj ) ε Y j with trade elasticity ε = (1 + η) (σ 1)

60 Selection/reallocation effects... new gains? Gravity equation is now X ij = χ ij (w i τ ij ) ε n l=1 χ lj (w l τ lj ) ε Y j with trade elasticity ε = (1 + η) (σ 1) EK, BEJK and EKK = ε = θ

61 Selection/reallocation effects... new gains? As before, have d ln λ jj d ln W j = d ln Y j d ln P jj }{{}} σ {{ 1 } change in real GDP in j change in ToT in j but we no longer have d ln Y j d ln P jj = 0 because of selection effects.

62 Selection/reallocation effects... new gains? As before, have d ln λ jj d ln W j = d ln Y j d ln P jj }{{}} σ {{ 1 } change in real GDP in j change in ToT in j but we no longer have d ln Y j d ln P jj = 0 because of selection effects. Selection implies a negative effect on real GDP, d ln Y j d ln P jj = θ ( σ 1 σ 1 θ ) 1 (d ln P jj d ln P j )

63 Selection/reallocation effects... new gains? As before, have d ln λ jj d ln W j = d ln Y j d ln P jj }{{}} σ {{ 1 } change in real GDP in j change in ToT in j but we no longer have d ln Y j d ln P jj = 0 because of selection effects. Selection implies a negative effect on real GDP, d ln Y j d ln P jj = θ ( σ 1 σ 1 θ Together with CES, λ jj = (P jj /P j ) 1 σ, then d ln W j = ) 1 (d ln P jj d ln P j ) ( 1 σ 1 1 ) d ln λ jj d ln λ jj θ σ 1 = d ln λ jj θ = d ln λ jj ε

64 Selection/reallocation effects... new gains? Key assumption is that η is the same across countries This allows for a single "trade elasticity" that 1. can be recovered from gravity and 2. is the elasticity that matters for welfare

65 Variable markups: pro-competitive effects? Two ways to go: drop MC or drop CES

66 Variable markups: pro-competitive effects? Two ways to go: drop MC or drop CES Demand with choke price that encompasses

67 Variable markups: pro-competitive effects? Two ways to go: drop MC or drop CES Demand with choke price that encompasses Krugman (1979)

68 Variable markups: pro-competitive effects? Two ways to go: drop MC or drop CES Demand with choke price that encompasses Krugman (1979) Melitz-Ottaviano

69 Variable markups: pro-competitive effects? Two ways to go: drop MC or drop CES Demand with choke price that encompasses Krugman (1979) Melitz-Ottaviano Translog (Feenstra)

70 Variable markups: pro-competitive effects? Two ways to go: drop MC or drop CES Demand with choke price that encompasses Krugman (1979) Melitz-Ottaviano Translog (Feenstra) Keep Pareto (to get gravity)

71 Variable markups: pro-competitive effects? Two ways to go: drop MC or drop CES Demand with choke price that encompasses Krugman (1979) Melitz-Ottaviano Translog (Feenstra) Keep Pareto (to get gravity) No fixed (marketing) costs (marginal varieties don t affect welfare)

72 Variable markups: pro-competitive effects? Two ways to go: drop MC or drop CES Demand with choke price that encompasses Krugman (1979) Melitz-Ottaviano Translog (Feenstra) Keep Pareto (to get gravity) No fixed (marketing) costs (marginal varieties don t affect welfare) Free entry (not important)

73 Variable markups: pro-competitive effects? Mark-up distribution and profit share invariant to trade costs

74 Variable markups: pro-competitive effects? Mark-up distribution and profit share invariant to trade costs Extensive margin and Pareto are key here

75 Variable markups: pro-competitive effects? Mark-up distribution and profit share invariant to trade costs Extensive margin and Pareto are key here Model yields gravity, so same response to trade liberalization

76 Variable markups: pro-competitive effects? Mark-up distribution and profit share invariant to trade costs Extensive margin and Pareto are key here Model yields gravity, so same response to trade liberalization But welfare implications are different

77 Variable markups: pro-competitive effects? We show that d ln W j = i λ ij d ln(w i τ ij ) }{{} Change in marginal costs + ( ρ) i λ ij d ln(w i τ ij ) }{{} Direct markup effect where ρ is a sales weighted average of the markup elasticities + ρd ln p j }{{} GE markup effect

78 Variable markups: pro-competitive effects? Proposition: The compensating variation associated with a small trade cost shock in j is d ln W j = (1 η) d ln λ jj θ If markups with productivity then ρ > 0 so with "known demand systems" get η 0

79 Variable markups: pro-competitive effects? Proposition: The compensating variation associated with a small trade cost shock in j is d ln W j = (1 η) d ln λ jj θ If markups with productivity then ρ > 0 so with "known demand systems" get η 0 Conditional on d ln λ jj, welfare gains are weakly lower than with CES

80 Variable markups: pro-competitive effects? Proposition: The compensating variation associated with a small trade cost shock in j is d ln W j = (1 η) d ln λ jj θ If markups with productivity then ρ > 0 so with "known demand systems" get η 0 Conditional on d ln λ jj, welfare gains are weakly lower than with CES Since model at the macro level is like EKK, then d ln λ jj, is the same as with CES

81 Variable markups: pro-competitive effects? Proposition: The compensating variation associated with a small trade cost shock in j is d ln W j = (1 η) d ln λ jj θ If markups with productivity then ρ > 0 so with "known demand systems" get η 0 Conditional on d ln λ jj, welfare gains are weakly lower than with CES Since model at the macro level is like EKK, then d ln λ jj, is the same as with CES Gains from trade liberalization are weakly lower than in gravity models with constant markups

82 Putting Numbers on the New Welfare Formula Recall that d ln W j = (1 η) d ln λ jj θ Under separable preferences, using θ = 5 then η (0, 1/6) Downward adjustment to GT liberalization can be at most 17%.

83 Now for some boring "macro" features Back to Armington 1. Add multiple sectors 2. Add traded intermediates

84 Multiple sectors, GT Upper level EoS ρ and lower level EoS ε s, GT MS j ( ) 1/(ρ 1) = 1 e j,s λ (ρ 1)/ε s jj,s. s If ε s = ε = ρ 1 then GT MS j ( ) 1/ε = 1 e j,s λ jj,s = 1 λ 1/ε jj s

85 Multiple Sectors, Macro Trade Elasticity The macro trade elasticity is ( 1 λjj = ln ε M j λ jj )/ ln τ j where τ ij,s = τ j τ ij,s and τ ji,s = τ j τ ji,s for all i = j and s

86 Multiple Sectors, Macro Trade Elasticity The macro trade elasticity is ( 1 λjj = ln ε M j λ jj )/ ln τ j where τ ij,s = τ j τ ij,s and τ ji,s = τ j τ ji,s for all i = j and s If no inter industry trade (λ jj,s = λ jj all s) then ε M j = S s=1 ε s e j,s

87 Multiple Sectors, Macro Trade Elasticity The macro trade elasticity is ( 1 λjj = ln ε M j λ jj )/ ln τ j where τ ij,s = τ j τ ij,s and τ ji,s = τ j τ ji,s for all i = j and s If no inter industry trade (λ jj,s = λ jj all s) then ε M j = S s=1 ε s e j,s If no intra industry trade (λ jj,s = 0 or 1 all s) then ε M j = ρ 1

88 GT and macro elasticity for Canada Recall gains for Canada of 1.8 Now gains can be much higher: ρ % GT MS ε M Key: interaction between ε s and λ jj,s

89 GT and macro elasticity for Denmark

90 Tradable intermediates, GT Set ρ = 1, add tradable intermediates with Input-Output structure Labor shares are 1 α j,s and input shares are α j,ks ( k α j,ks = α j,s ) Gains from trade are now G IO j = 1 S k,s=1 (λ jj,k ) e C j,s β j,ks /ε k

91 Tradable intermediates, GT % GT j % GT MS j % GT IO j Canada Denmark France Portugal U.S

92 Combination of micro and macro features In Krugman, free entry leads to scale effects absent in Armington

93 Combination of micro and macro features In Krugman, free entry leads to scale effects absent in Armington In Melitz, both scale effects and selection effects

94 Combination of micro and macro features In Krugman, free entry leads to scale effects absent in Armington In Melitz, both scale effects and selection effects In both models, trade may affect entry and fixed costs

95 Combination of micro and macro features In Krugman, free entry leads to scale effects absent in Armington In Melitz, both scale effects and selection effects In both models, trade may affect entry and fixed costs All these effects do not play a role in the one sector model

96 Combination of micro and macro features In Krugman, free entry leads to scale effects absent in Armington In Melitz, both scale effects and selection effects In both models, trade may affect entry and fixed costs All these effects do not play a role in the one sector model With multiple sectors and traded intermediates, these effects come back

97 Combination of micro and macro features In Krugman, free entry leads to scale effects absent in Armington In Melitz, both scale effects and selection effects In both models, trade may affect entry and fixed costs All these effects do not play a role in the one sector model With multiple sectors and traded intermediates, these effects come back Effects on GT? (in progress)

98 Quantify gains from trade policy 1. Consider { ˆτ ij,s }, modeled as change in tariffs

99 Quantify gains from trade policy 1. Consider { ˆτ ij,s }, modeled as change in tariffs 2. Use "exact hat algebra" to get { ˆλ ij,s } and change in tariff revenues

100 Quantify gains from trade policy 1. Consider { ˆτ ij,s }, modeled as change in tariffs 2. Use "exact hat algebra" to get { ˆλ ij,s } and change in tariff revenues 3. Use formulas above to get welfare implications

101 Quantify gains from trade policy This is what CGE exercises (e.g., Michigan, GTAP) do

102 Quantify gains from trade policy This is what CGE exercises (e.g., Michigan, GTAP) do Contribution here:

103 Quantify gains from trade policy This is what CGE exercises (e.g., Michigan, GTAP) do Contribution here: Link to theory

104 Quantify gains from trade policy This is what CGE exercises (e.g., Michigan, GTAP) do Contribution here: Link to theory Issues on calibration

105 Quantify gains from trade policy This is what CGE exercises (e.g., Michigan, GTAP) do Contribution here: Link to theory Issues on calibration Quantify mechanisms

106 Final Thoughts Complementarities between trade and MP/diffusion can increase GT

107 Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger

108 Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger How can small countries be rich?

109 Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger How can small countries be rich? Gains from openness + domestic frictions

110 Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger How can small countries be rich? Gains from openness + domestic frictions Scale economies = y DNK /y US = 1/3.

111 Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger How can small countries be rich? Gains from openness + domestic frictions Scale economies = y DNK /y US = 1/3. Domestic frictions bring this to 2/3

112 Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger How can small countries be rich? Gains from openness + domestic frictions Scale economies = y DNK /y US = 1/3. Domestic frictions bring this to 2/3 Relative GO are then 3/2

113 Final Thoughts Complementarities between trade and MP/diffusion can increase GT Gains from openness (including MP, diffusion) can be much larger How can small countries be rich? Gains from openness + domestic frictions Scale economies = y DNK /y US = 1/3. Domestic frictions bring this to 2/3 Relative GO are then 3/2 If GO US = 5% (twice GT) then GO DNK = 45%