Report

Modern trade theory for CGE modelling: the Armington, Krugman and Melitz models CoPS by Peter B. Dixon, Michael Jerie and Maureen T. Rimmer presentation by Peter B. Dixon CGE modelling workshop Victoria University August 11, 2014 The paper and zips of selected GEMPACK computations reported in the paper are at http://www.copsmodels.com/archivep/tpmj0140.zip The Open Economy lectures based on the paper were delivered by Peter Dixon at the Institute for Applied International Trade, Beijing, December 9, 2013 1 Dissatisfaction with Armington CoPS • Product differentiation (imperfect substitution) at the country level is an unattractive assumption • Armington models often imply that unilateral tariff cuts are welfare reducing: the terms of trade loss exceeds the efficiency gain • Starting in the 1980s with Krugman, trade theorists have been creating models with product differentiation at the firm level • Melitz introduces not only imperfect substitution at the firm level but also differences across firms in productivity: holds out hope for big welfare gains from unilateral tariff cuts 2 CoPS 1. Armington, Krugman and Melitz: special cases of an encompassing model 3 CoPS Special assumptions: Armington no fixed costs perceived elasticity is infinity, pure competition no difference in productivity across firms in industry j in country s number of firms (varieties) in j in country s is exogenous, assume 1 4 Special assumptions: Krugman fixed costs to produce in country s but no fixed costs to trade perceived elasticity is actual elasticity, monopolistic competition no difference in productivity across firms in country s number of firms is endogenous all firms trade in all countries 5 CoPS Special assumptions: Melitz CoPS fixed costs to produce in country s and fixed costs to trade on any link perceived elasticity is actual elasticity, monopolistic competition productivity differs across firms in country s number of firms is endogenous only high productivity firms can export 6 CoPS 2. Optimality Melitz: Monopolistic competition; increasing returns to scale; prices greater than marginal costs; high and low productivity firms. Do these features support arguments for government intervention? No, planner cost-minimizing problem 7 Implication of optimality Envelope theorems: global welfare effect of introducing a distorting tax/tariff into a previously optimal situation depends only on the tax/tariff rate and on the induced movement in absorption (consumption) of the taxed item -- welfare triangles 8 CoPS CoPS 3. Melitz sectors and Armington general equilibrium: a decomposition 9 CoPS Balistreri-Ruthford decomposition method for solving GE models with Melitz sectors B&R start by solving each Melitz sector based on initial guesses of wage rates and overall demand for sectoral product These Melitz computations generate estimates of sectoral productivity and other sectoral variables which are transferred into an Armington multisectoral general equilibrium model The Armington model is solved to generate estimates of wage rates and overall demand for sectoral product which are fed back into the Melitz sectoral computations. A solution of the GE model with Melitz sectors is obtained when wage rates and overall demand variables emerging from the Armington model coincide with those which were used in the Melitz sectoral computations 10 Implication of the BalistreriRutherford decomposition CoPS A solution to a Melitz general equilibrium model can be derived by solving an Armington model with extra shocks to productivity and preference variables. This suggests that Melitz results can be decomposed into the primary effect, the productivity effect, and the preference effect all calculated from an Armington model. 11 CoPS 4. Illustrative computations with a Melitz CGE model r initially identical countries n commodities produced in each country No tariffs or other distortions in the initial situation Fixed costs calibrated so that each country initially exports 25.4% of its GDP; fixed setup costs are 16% of GDP; and fixed trade costs are 10% of the value of exports 12 MelitzGE results for the effects of tariffs imposed by country 2 with =3.8: extra Melitz effects cancel out Shocks ta12=7.18 ta12=13.33 CoPS ta12=32.56 Country 1 Country 2 Country 1 Country 2 Country 1 Country 2 -0.824 0.593 -1.436 0.726 -2.908 -0.046 0.000 -0.164 0.000 -0.497 0.000 -1.994 Terms of trade -0.818 0.802 -1.425 1.375 -2.832 2.617 Production technology or productivity -3.332 -2.795 -5.890 -5.021 -12.229 -10.835 Conversion technology or preferences 3.327 2.750 5.879 4.869 12.152 10.165 Endogenous variables Welfare decomposition Welfare made up of contributions from changes in: Tax-carrying flows (welfare triangle) 13 CoPS Tariff increase by country 2: Melitz & Armington, substitution elasticity of 3.8 Melitz ta12=7.18 Shock country Armington 1 2 1 2 Exports -18.8 -21.6 -7.8 -11.2 Imports -21.6 -18.8 -11.2 -7.7 Welfare -0.8 0.6 -0.9 0.8 It looks as though: Armington underestimates how much tariffs hurt trade but perhaps we shouldn’t use the same substitution elasticity when we compare Armington and Melitz 14 CoPS Tariff increase by country 2: Melitz & Armington, substitution elasticity of 3.8 Melitz ta12=13.33 Shock country Armington 1 2 1 2 Exports -32.0 -36.4 -13.8 -19.5 Imports -36.4 -32.0 -19.5 -13.8 Welfare -1.4 0.7 -1.6 1.4 It looks as though: Armington underestimates how much tariffs hurt trade but perhaps we shouldn’t use the same substitution elasticity when we compare Armington and Melitz 15 CoPS Tariff increase by country 2: Melitz & Armington, substitution elasticity of 3.8 Melitz ta12=33.56 Shock country Armington 1 2 1 2 Exports -60.4 -66.4 -29.2 -39.6 Imports -66.4 -60.4 -39.6 -29.3 Welfare -2.9 -0.0 -3.3 2.1 It looks as though: Armington underestimates how much tariffs hurt trade but perhaps we shouldn’t use the same substitution elasticity when we compare Armington and Melitz 16 CoPS Tariff increase by country 2: Melitz & Armington, substitution elasticity of 3.8 Welfare for country 2 Melitz Shock Welfare (%) Armington Melitz ta12=7.18 0.6 0.8 Armington Melitz ta12=13.33 0.7 1.4 Armington ta12=33.56 -0.0 2.1 It looks as though: Armington overestimates the optimal tariff for country 2 but perhaps we shouldn’t use the same substitution elasticity when we compare Armington and Melitz 17 Is Melitz simply Armington with a high substitution elasticity? Melitz with =3.8 Armington with = 8.45 ta12=7.18 Shock Country 1 Country 2 Country 1 Country 2 Real consumption -0.824 0.593 -0.830 0.655 Volume of exports -18.811 -21.622 -18.789 -21.682 Volume of imports -21.622 -18.811 -21.682 -18.789 -0.824 0.593 -0.830 0.655 0.000 -0.164 0.000 -0.161 Terms of trade -0.818 0.802 -0.830 0.816 Production technology or productivity -3.332 -2.795 0.0 0.0 Conversion technology or preferences 3.327 2.750 0.0 0.0 Endogenous variables Welfare decomposition Welfare made up of contributions from changes in: Tax-carrying flows (welfare triangle) 18 CoPS Melitz substitution elasticities and equivalent CoPS Armington elasticities in the simulation of a 7.18% tariff imposed by country 2 10 in Armington 9 8 7 6 5 4 3 2 1 in Melitz 0 19 2.5 3 3.5 4 4.5 5 CoPS Computational times for solving MelitzGE in GEMPACK (seconds) No. of countries No. of Commodities 20 2 10 100 2 1 1 34 10 1 2 198 57 1 8 5887 100 1 15 24312 5. Concluding remarks CoPS We have shown that Armington is a special case of Krugman Krugman is a special case of Melitz, and Melitz is a special cases of a more general model Despite increasing returns to scale, imperfect competition, separate variety for each firm, and different productivity levels across firms, the Melitz model produces an optimal market outcome. -- envelope theorems work Melitz solutions can be calculated in an Armington model with extra shocks to productivity and preferences. 21 Concluding remarks CoPS Melitz welfare results can be decomposed into primary effect productivity effect preference effect all calculated in an Armington model. Productivity and preference effects offset - envelope theorem Melitz results can be reproduced in an Armington model with a high Armington elasticity Melitz is a micro foundation story, supporting Armington, not a reason to reject Armington 22 GEMPACK is effective in computing Melitz solutions CoPS 23 An envelope result Choose X1 and X 2 To minimize Cost = W1X1 W2 X 2 g X1 , X 2 0 Subject to First order conditions: W1 g1 W2 g 2 g X1 , X 2 0 Cost Wi * X i Wi * X i i But W * X i i i * g i * X i 0 i i Therefore Cost Wi * X i i 24 Conclusion Cost does not depend on changes in X’s CoPS