Measuring the Gains from Trade: They are Large!

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

Ultimate Goal Quantify effects of trade policy changes

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

Main Points Exciting "micro" features come up short

Main Points Exciting "micro" features come up short Krugman

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

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

Main Points Exciting "micro" features come up short

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

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

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

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)

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)

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

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

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

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

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

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.

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.

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

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

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.

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.

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

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

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)

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

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

Gains from Trade λ jj % GT j Canada 0.91 1.8 Denmark 0.94 1.2 France 0.93 1.4 Portugal 0.88 2.4 U.S. 0.97 0.7

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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.

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)

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

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 )

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

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

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

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

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

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)

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)

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

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

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

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

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

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%.

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

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

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

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

GT and macro elasticity for Canada Recall gains for Canada of 1.8 Now gains can be much higher: ρ 1 2 4 8 % GT MS 5.2 4 2.7 1.7 ε M 3.1 3.7 4.8 7.1 Key: interaction between ε s and λ jj,s

GT and macro elasticity for Denmark

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

Tradable intermediates, GT % GT j % GT MS j % GT IO j Canada 1.8 5.2 14.7 Denmark 1.2 4.6 7.1 France 1.4 2.7 6.8 Portugal 2.4 8.5 22.2 U.S. 0.7 1.2 2.4

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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.