Modern trade theory for CGE modelling: the
Armington, Krugman and Melitz models
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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
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Dissatisfaction with Armington
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• 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
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
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Special assumptions: Melitz
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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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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
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3. Melitz sectors and Armington general
equilibrium: a decomposition
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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
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Implication of the BalistreriRutherford decomposition
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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.
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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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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
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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)
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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
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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
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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
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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
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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)
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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
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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
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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.
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Concluding remarks
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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
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GEMPACK is effective in computing Melitz solutions
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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
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Conclusion Cost does not depend on changes in X’s
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