Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Why has this not been done before? It would be nearly impossible to use e.g. Helpman, Melitz, and Yeaple (2004) off the shelf and put export platforms into it. Hard permutation problem at the firm-level Key idea for tractability: Each firm consists of a continuum of products In each country in which the firm has a plant, it receives product-location-specific productivity draws Analytic solution for the output at the plant-level (under convenient distributional assumption)
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Why has this not been done before? It would be nearly impossible to use e.g. Helpman, Melitz, and Yeaple (2004) off the shelf and put export platforms into it. Hard permutation problem at the firm-level Key idea for tractability: Each firm consists of a continuum of products In each country in which the firm has a plant, it receives product-location-specific productivity draws Analytic solution for the output at the plant-level (under convenient distributional assumption) Smooth substitutibility between the firm’s plants
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Preview of main quantitative results Fixed costs of foreign production are quantitatively important:
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Preview of main quantitative results Fixed costs of foreign production are quantitatively important: Without fixed costs multinationals would produce more than twice as much abroad.
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Preview of main quantitative results Fixed costs of foreign production are quantitatively important: Without fixed costs multinationals would produce more than twice as much abroad. Estimated model with fixed costs can match the export platform sales of US MNEs
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Preview of main quantitative results Fixed costs of foreign production are quantitatively important: Without fixed costs multinationals would produce more than twice as much abroad. Estimated model with fixed costs can match the export platform sales of US MNEs Effects of a foreign technology shock:
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Preview of main quantitative results Fixed costs of foreign production are quantitatively important: Without fixed costs multinationals would produce more than twice as much abroad. Estimated model with fixed costs can match the export platform sales of US MNEs Effects of a foreign technology shock: Welfare gains abroad from a US technology improvement are an order of magnitude larger than in a pure trade model
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Preview of main quantitative results Fixed costs of foreign production are quantitatively important: Without fixed costs multinationals would produce more than twice as much abroad. Estimated model with fixed costs can match the export platform sales of US MNEs Effects of a foreign technology shock: Welfare gains abroad from a US technology improvement are an order of magnitude larger than in a pure trade model Effects of regional trade and investment agreements:
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Preview of main quantitative results Fixed costs of foreign production are quantitatively important: Without fixed costs multinationals would produce more than twice as much abroad. Estimated model with fixed costs can match the export platform sales of US MNEs Effects of a foreign technology shock: Welfare gains abroad from a US technology improvement are an order of magnitude larger than in a pure trade model Effects of regional trade and investment agreements: CETA could divert around seven percent of European MNE’s production from US to Canada
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Related literature Quantitative models of trade Eaton and Kortum (2002), Anderson and van Wincoop (2003)
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Related literature Quantitative models of trade Eaton and Kortum (2002), Anderson and van Wincoop (2003) Proximity-concentration trade-off Horstmann and Markusen (1992), Brainard (1997), Helpman, Melitz, and Yeaple (2004), Irarrazabal, Moxnes, and Opromolla (2012)
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Related literature Quantitative models of trade Eaton and Kortum (2002), Anderson and van Wincoop (2003) Proximity-concentration trade-off Horstmann and Markusen (1992), Brainard (1997), Helpman, Melitz, and Yeaple (2004), Irarrazabal, Moxnes, and Opromolla (2012) Quantitative models of trade and multinational production Ramondo and Rodriguez-Clare (2012), Arkolakis, Ramondo, Rodriguez-Clare, and Yeaple (2012)
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Outline Model Estimation with firm-level data Calibration with aggregate data G.E. Counterfactuals
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Model
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Environment N countries
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Environment N countries Representative consumer: Measure of L j consumers / workers Dixit-Stiglitz preferences, elasticity of substitution σ > 1
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Environment N countries Representative consumer: Measure of L j consumers / workers Dixit-Stiglitz preferences, elasticity of substitution σ > 1 Firms: Measure of M i firms Country of origin i , core productivity level φ , fixed cost vector η , and plant productivity shifter ǫ
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Environment N countries Representative consumer: Measure of L j consumers / workers Dixit-Stiglitz preferences, elasticity of substitution σ > 1 Firms: Measure of M i firms Country of origin i , core productivity level φ , fixed cost vector η , and plant productivity shifter ǫ Trade costs τ lm to serve country m from country l Efficiency loss γ il for firms from country i in country l
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Production technology Each firm has a measure 1 of differentiated products.
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Production technology Each firm has a measure 1 of differentiated products. Conditional on plant in l : Firm can produce product υ under CRS with productivity ν l ( υ ) in country l
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Production technology Each firm has a measure 1 of differentiated products. Conditional on plant in l : Firm can produce product υ under CRS with productivity ν l ( υ ) in country l Product-level productivities in county l ∈ Z are distributed Frechet: � − ( φǫ l ) θ ( γ il x ) − θ � Pr ( ν l ≤ x ) = exp
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Production technology Each firm has a measure 1 of differentiated products. Conditional on plant in l : Firm can produce product υ under CRS with productivity ν l ( υ ) in country l Product-level productivities in county l ∈ Z are distributed Frechet: � − ( φǫ l ) θ ( γ il x ) − θ � Pr ( ν l ≤ x ) = exp Technical restriction: θ > σ − 1
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Firm’s problem and timing The firm initially observes the following characteristics about itself: Country of origin i Core productivity, φ Fixed cost vector, η
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Firm’s problem and timing The firm initially observes the following characteristics about itself: Country of origin i Core productivity, φ Fixed cost vector, η The firm solves the following problem: Select a set of countries Z ∈ Z i in which to build a plant and pay 1 fixed costs: � k ∈ Z η k w k
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Firm’s problem and timing The firm initially observes the following characteristics about itself: Country of origin i Core productivity, φ Fixed cost vector, η The firm solves the following problem: Select a set of countries Z ∈ Z i in which to build a plant and pay 1 fixed costs: � k ∈ Z η k w k After plants are selected: 2
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Firm’s problem and timing The firm initially observes the following characteristics about itself: Country of origin i Core productivity, φ Fixed cost vector, η The firm solves the following problem: Select a set of countries Z ∈ Z i in which to build a plant and pay 1 fixed costs: � k ∈ Z η k w k After plants are selected: 2 Observe vector of plant-specific productivity shifters, ǫ , and receive product-location-specific productivity draws
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Firm’s problem and timing The firm initially observes the following characteristics about itself: Country of origin i Core productivity, φ Fixed cost vector, η The firm solves the following problem: Select a set of countries Z ∈ Z i in which to build a plant and pay 1 fixed costs: � k ∈ Z η k w k After plants are selected: 2 Observe vector of plant-specific productivity shifters, ǫ , and receive product-location-specific productivity draws Decide for each product which market to serve from where
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Firm’s problem and timing The firm initially observes the following characteristics about itself: Country of origin i Core productivity, φ Fixed cost vector, η The firm solves the following problem: Select a set of countries Z ∈ Z i in which to build a plant and pay 1 fixed costs: � k ∈ Z η k w k After plants are selected: 2 Observe vector of plant-specific productivity shifters, ǫ , and receive product-location-specific productivity draws Decide for each product which market to serve from where Set prices for each product i, φ, η Observe: ǫ , product-location-specific productivity draws Z ∈ Z i For each product and market: l ∈ Z , price Select:
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Plant-level output Given a set of countries Z in which the firm built a plant
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Plant-level output Given a set of countries Z in which the firm built a plant Firm selects for each product and market the plant with the minimum cost
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Plant-level output Given a set of countries Z in which the firm built a plant Firm selects for each product and market the plant with the minimum cost If l ∈ Z : ( γ il w l τ lm ) − θ ǫ θ � Y m σ − 1 l r l ( i, φ, Z, ǫ ) = κφ θ � � � ( θ +1 − σ P 1 − σ ) m θ ( γ ik w k τ km ) − θ ǫ θ m k k ∈ Z
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Location choice Expected variable profits from location set Z : � E ǫ ( π ( i, φ, Z, ǫ )) = 1 E ǫ ( r l ( i, φ, Z, ǫ )) σ l ∈ Z
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Location choice Expected variable profits from location set Z : � E ǫ ( π ( i, φ, Z, ǫ )) = 1 E ǫ ( r l ( i, φ, Z, ǫ )) σ l ∈ Z Expected total profits from location set Z : � E ǫ (Π( i, φ, Z, ǫ, η )) = E ǫ ( π ( i, φ, Z, ǫ )) − η k w k k ∈ Z,k � = i
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Location choice Expected variable profits from location set Z : � E ǫ ( π ( i, φ, Z, ǫ )) = 1 E ǫ ( r l ( i, φ, Z, ǫ )) σ l ∈ Z Expected total profits from location set Z : � E ǫ (Π( i, φ, Z, ǫ, η )) = E ǫ ( π ( i, φ, Z, ǫ )) − η k w k k ∈ Z,k � = i Each firm chooses the set of locations that maximizes its expected profits. Z ( i, φ, η ) ∈ arg max Z ∈Z i E ǫ (Π( i, φ, Z, ǫ, η ))
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Motivation to build foreign plants Proximity to markets Comparative advantage Benefits get reduced by efficiency losses of foreign production, γ il Trade-off between these benefits and fixed costs
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Aggregation and Equilibrium Aggregate over the choices of firms ( φ, η, ǫ ) from all countries ( i ). Profits are distributed to consumers in countries in which the firms originated Equilibrium definition is standard (monopolistic competition): Consumers / Firms optimize Markets clear Fixed point for price indices and income in every country.
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Equilibrium computation Y l Consumers and firms need to know A l = and w l , l = 1 , .., N P 1 − σ l in order to make their decisions. Given parameter vector β , the equilibrium can be computed as a solution for A and w of: A l ( β, w, A ) = A l ∀ l = 1 , .., N L d ∀ l = 1 , .., N − 1 l ( β, w, A ) = L l
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Remarks Special case: Anderson and van Wincoop (2003) Model is suitable to address both firm level and aggregate data Continuum of products and product-location-specific productivity shocks make it feasible to solve and estimate the model
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Estimation
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Overview of estimation Data on all German multinationals in 12 Western European and North American countries
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Overview of estimation Data on all German multinationals in 12 Western European and North American countries Observe for each firm Set of locations Total output of each affiliate and of the parent company
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Overview of estimation Data on all German multinationals in 12 Western European and North American countries Observe for each firm Set of locations Total output of each affiliate and of the parent company Additional data on aggregate manufacturing expenditures, and proxies for bilateral trade costs and price indices
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Overview of estimation Data on all German multinationals in 12 Western European and North American countries Observe for each firm Set of locations Total output of each affiliate and of the parent company Additional data on aggregate manufacturing expenditures, and proxies for bilateral trade costs and price indices Estimate distribution of fixed costs, ˜ η t,k ∼ log N ( µ ˜ η ), unit η , σ ˜ input costs, ˜ w k = w k γ ik , and other distributional parameters via Maximum Likelihood
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Overview of estimation Data on all German multinationals in 12 Western European and North American countries Observe for each firm Set of locations Total output of each affiliate and of the parent company Additional data on aggregate manufacturing expenditures, and proxies for bilateral trade costs and price indices Estimate distribution of fixed costs, ˜ η t,k ∼ log N ( µ ˜ η ), unit η , σ ˜ input costs, ˜ w k = w k γ ik , and other distributional parameters via Maximum Likelihood Fix σ = 6, θ = 7 Estimation of θ
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Intuition for identification The intensive margin – how much do firms produce in a country relative to home – identifies the unit input cost in that country.
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Intuition for identification The intensive margin – how much do firms produce in a country relative to home – identifies the unit input cost in that country. The extensive margin – in which sets of countries do the firms establish plants – identifies the fixed cost parameters.
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Intuition for identification The intensive margin – how much do firms produce in a country relative to home – identifies the unit input cost in that country. The extensive margin – in which sets of countries do the firms establish plants – identifies the fixed cost parameters. The size distribution of firms identifies the core productivity level distribution parameters and the noise in the output of the firm the dispersion parameter of the plant-wide productivity shifters.
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Likelihood function Parameters: Θ = { ˜ η , µ φ , σ φ } w, σ ǫ , µ ˜ η , σ ˜ Likelihood function: L (Θ; { Z t , r t } T t =1 ) � T � Pr ∗ ( Z = Z t | φ ; ˜ = w, σ ǫ , µ ˜ η , σ ˜ η ) g ( r t | Z t , φ ; ˜ w ) dG ( φ | µ φ , σ φ ) φ t =1
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Likelihood function Parameters: Θ = { ˜ η , µ φ , σ φ } w, σ ǫ , µ ˜ η , σ ˜ Likelihood function: L (Θ; { Z t , r t } T t =1 ) � T � Pr ∗ ( Z = Z t | φ ; ˜ = w, σ ǫ , µ ˜ η , σ ˜ η ) g ( r t | Z t , φ ; ˜ w ) dG ( φ | µ φ , σ φ ) φ t =1 Control for unobserved heterogeneity in core productivity levels
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Constrained maximum Likelihood estimation Estimation problem Θ ,ψ log L (Θ; { Z t , ψ t } T max t =1 ) � w l τ lm ) − θ ψ θ ( ˜ Y m t,l s.t. r t,l ( ˜ w, Z t , ψ t ) = κ � � ( θ +1 − σ P 1 − σ ) m θ � m w k τ km ) − θ ψ θ ( ˜ t,k k ∈ Z t ∀ t ∈ { 1 , ...T } , l ∈ { 1 , ...N } such that l ∈ Z t .
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Parameter estimates Unit input costs Fixed costs w ˜ µ ˜ η Austria 1.076 4.659 (0.021) (0.423) Belgium 1.144 5.609 (0.038) (0.500) S.d. log fixed cost, σ ˜ 2.1902 η 1.324 5.067 Canada (0.320) (0.080) (0.571) Scale parameter productivity, µ φ 1.1329 Switzerland 1.264 4.468 (0.017) (0.055) (0.472) Shape parameter productivity, σ φ 5.1026 Spain 1.223 3.912 (0.620) (0.018) (0.335) S.d. log productivity shock, σ ǫ 0.1844 France 1.229 3.683 (0.009) (0.023) (0.243) United Kingdom 1.341 3.906 Log-Likelihood -1.21E+004 (0.021) (0.321) Number of firms, T 665 1.127 6.149 Ireland (0.052) (0.671) Fixed costs in Euro Italy 1.334 3.978 (0.039) (0.309) Data summary by country Netherlands 1.194 5.303 (0.029) (0.513) 1.420 3.847 United States (0.016) (0.250)
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Decomposing the sources of home bias in production Average share of foreign production in the output of German MNEs across counterfactual production costs Data Model No fixed Same unit No fixed costs input costs as costs and same in Germany unit input costs as in Germany 0.288 0.317 0.716 0.676 0.883 (0.013) (0.009) (0.021) (0.001)
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Calibration
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Calibration of the general equilibrium Data: Bilateral manufacturing trade flows from OECD Bilateral MP from Ramondo, Rodriguez-Clare, and Tintelnot (in process) Size of labor force and skill level from Barro and Lee (2010) Gravity variables from CEPII Estimates of German MNEs’ production costs in various destination countries
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Calibration targets Targets: Trade shares: 1 ξ lm = X lm Y m MP-shares: � 2 X ilm m � κ il = . X lm m Variable production costs for German firms in country l relative to 3 w j = w l γ jl w l ˜ costs at home ( j ): ˜ w j
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Restrictions on parameters Variable iceberg trade and MP costs const ( dist lm ) β τ β τ dist ( β τ contig ) contig lm ( β τ lang ) language lm τ lm = for l � = m const ( dist il ) β γ β γ dist ( β γ contig ) contig il ( β γ lang ) language il = for i � = l γ il Fixed MP costs: η l ∼ log N (ln f il , β f σ ) const ( dist il ) β f β f dist ( β f contig ) contig il ( β f lang ) language il = for i � = l f il Fixed endowments: L i , M i Fixed parameters: σ = 6, θ = 7 σ ǫ = 0 φ ∼ Pareto with shape parameter 5.5
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Calibration procedure Fit of targets ξ ( β, w, A ) − ξ κ ( β, w, A ) − κ d ( β, w, A ) = w ( β,w,A ) ˜ w ˜ − w j w j ˜ Calibration problem β,w,A d ( β, w, A ) ′ d ( β, w, A ) min subject to: ∀ l = 1 , .., N A l ( β, w, A ) = A l L d ∀ l = 1 , .., N − 1 l ( β, w, A ) = L l
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Trade and MP costs estimates Pure trade Global production model model Trade cost constant 0.722 0.789 distance 0.139 0.121 language 0.922 0.929 contiguity 0.934 0.925 Variable MP cost constant 1.259 distance 0.006 language 0.962 contiguity 0.963 Fixed MP cost constant 0.089 distance 0.073 language 1.025 contiguity 1.105 dispersion 0.299 Norm trade fit 0.258 0.262 Norm MP fit 0.158
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Share of exports in production of US affiliates: Data and Model 1 0.9 IRL 0.8 0.7 CHE BEL NLD 0.6 AUT data 0.5 DEU ESP 0.4 CAN FRA GBR ITA 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 model Figure: Export platform shares for US multinationals - data and model
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP G.E. Counterfactuals
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP The benefits of foreign technology How does a technology shock in one country affect production and welfare outcomes in all countries?
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP The benefits of foreign technology How does a technology shock in one country affect production and welfare outcomes in all countries? Suppose all US firms improve their productivity by 20 percent.
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP The benefits of foreign technology How does a technology shock in one country affect production and welfare outcomes in all countries? Suppose all US firms improve their productivity by 20 percent. With and without multinational production, US welfare improves by around 20 percent.
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Benefits from US technology improvement Pure trade Global production model model Austria 0.45 14.52 Belgium 0.26 9.34 Canada 3.53 28.69 Switzerland 0.37 9.26 Germany 0.15 7.07 Spain 0.26 14.11 France 0.17 7.76 United Kingdom 0.32 13.60 Ireland 1.12 20.93 Italy 0.18 10.92 Netherlands 0.32 13.03 United States 100.00 100.00 Results without increasing returns
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Effects from CETA Comprehensive Economic and Trade Agreement (Canada and EU)
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Effects from CETA Comprehensive Economic and Trade Agreement (Canada and EU) What are the effects on signatory countries and the United States?
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Effects from CETA Comprehensive Economic and Trade Agreement (Canada and EU) What are the effects on signatory countries and the United States? My model is particularly suitable to address this question:
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Effects from CETA Comprehensive Economic and Trade Agreement (Canada and EU) What are the effects on signatory countries and the United States? My model is particularly suitable to address this question: Trade costs between US and Canada are low
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Effects from CETA Comprehensive Economic and Trade Agreement (Canada and EU) What are the effects on signatory countries and the United States? My model is particularly suitable to address this question: Trade costs between US and Canada are low Some European firms want to have only one plant in North America
Model Estimation Calibration G.E. Counterfactuals Conclusion BACK-UP Effects from CETA Comprehensive Economic and Trade Agreement (Canada and EU) What are the effects on signatory countries and the United States? My model is particularly suitable to address this question: Trade costs between US and Canada are low Some European firms want to have only one plant in North America Re-optimization by multinational firms induces a third-country effect additional to the terms of trade effect.
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