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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