modern trade theory for cge modelling: the armington , krugman and melitz models
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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CoPSModern 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 workshopVictoria 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
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CoPSDissatisfaction 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
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1. Armington, Krugman and Melitz: special cases of an encompassing model
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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
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CoPSSpecial 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
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CoPSSpecial assumptions: Melitz
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
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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
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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
Implication of optimality
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3. Melitz sectors and Armington general equilibrium: a decomposition
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CoPSBalistreri-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
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CoPSImplication 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, andthe preference effect
all calculated from an Armington model.
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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
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CoPSMelitzGE 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 ta12=32.56
Endogenous variables Country
1 Country
2 Country
1 Country
2 Country
1 Country
2
Welfare decomposition
Welfare -0.824 0.593 -1.436 0.726 -2.908 -0.046
made up of contributions from changes in:
Tax-carrying flows (welfare triangle) 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
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CoPSTariff increase by country 2:Melitz & Armington, substitution elasticity of
3.8
Melitz Armington
Shock ta12=7.18 country 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
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CoPSTariff increase by country 2:Melitz & Armington, substitution elasticity of
3.8
Melitz Armington
Shock ta12=13.33 country 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
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CoPSTariff increase by country 2:Melitz & Armington, substitution elasticity of
3.8
Melitz Armington
Shock ta12=33.56 country 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
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CoPSTariff increase by country 2:Melitz & Armington, substitution elasticity of
3.8
Melitz Armington Melitz Armington Melitz Armington
Shock ta12=7.18 ta12=13.33 ta12=33.56
Welfare (%) 0.6 0.8 0.7 1.4 -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
Welfare for country 2
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CoPSIs Melitz simply Armington with a high substitution elasticity?
Melitz with =3.8
Armington with = 8.45
Shock ta12=7.18
Endogenous variables 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
Welfare decomposition
Welfare -0.824 0.593 -0.830 0.655
made up of contributions from changes in:
Tax-carrying flows (welfare triangle) 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
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CoPSMelitz substitution elasticities and equivalent Armington elasticities in the simulation of a
7.18% tariff imposed by country 2
0
1
2
3
4
5
6
7
8
9
10
2.5 3 3.5 4 4.5 5
in Armington
in Melitz
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Computational times for solving MelitzGE in GEMPACK (seconds)
No. of countries
No. of Commodities 2 10 100
2 1 1 34
10 1 2 198
57 1 8 5887
100 1 15 24312
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CoPS5. 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 modelwith extra shocks to productivity and preferences.
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CoPSConcluding remarks
Melitz welfare results can be decomposed into primary effectproductivity effectpreference 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
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CoPSAn envelope result
Choose 1X and 2X To minimize Cost = 1 1 2 2W X W X
Subject to 1 2 0g X , X
First order conditions:
1 1W g
2 2W g
1 2 0g X , X
i i i i
i i
Cost W * X W * X
But 0 i i i ii i
W * X * g * X
Therefore i ii
Cost W * X
Conclusion Cost does not depend on changes in X’s