Modern trade theory for CGE modelling: the Armington , Krugman and Melitz models

1. Modern trade theory for CGE modelling: the Armington, Krugman and Melitz models • 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

2. Dissatisfaction with Armington • 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

3. 1. Armington, Krugman and Melitz: special cases of an encompassing model

4. Special assumptions: Armington

5. Special assumptions: Krugman

6. Special assumptions: Melitz

7. 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

8. 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

9. 3. Melitz sectors and Armington general equilibrium: a decomposition

10. 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 multi-sectoral 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

11. Implication of the Balistreri-Rutherford decomposition 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.

12. 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

13. MelitzGE results for the effects of tariffs imposed by country 2 with =3.8: extra Melitz effects cancel out

14. Tariff increase by country 2:Melitz & Armington, substitution elasticity of 3.8 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

15. Tariff increase by country 2:Melitz & Armington, substitution elasticity of 3.8 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

16. Tariff increase by country 2:Melitz & Armington, substitution elasticity of 3.8 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

17. Tariff increase by country 2:Melitz & Armington, substitution elasticity of 3.8 Welfare for country 2 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

18. Is Melitz simply Armington with a high substitution elasticity?

19. Melitz substitution elasticities and equivalent Armingtonelasticities in the simulation of a 7.18% tariff imposed by country 2

20. Computational times for solving MelitzGE in GEMPACK (seconds)

21. 5. Concluding remarks 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.

22. Concluding remarks 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 GEMPACK is effective in computing Melitz solutions

24. An envelope result