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Introduction to Computable General Equilibrium Model

(CGE)

Dhazn Gillig&

Bruce A. McCarl

Department of Agricultural EconomicsTexas A&M University

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Course Outline

Overview of CGE

An Introduction to the Structure of CGE

An Introduction to GAMS

Casting CGE models into GAMS

Data for CGE Models & Calibration

Incorporating a trade & a basic CGE application

Evaluating impacts of policy changes and casting nested functions & a trade in GAMS

Mixed Complementary Problems (MCP)

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This Week’s Road Map

Incorporating a simple trade relationship in a

CGE model

SAM in GAMS

Calibration in GAMS

Basic CGE application (Shoven & Whalley)

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Incorporating Trade – modifications to a basic CGE model

Basic relationships for a simple CGE model1. Supply–Demand2. Zero profit condition3. Factor demand by producers4. Product demand by households5. Income balance constraint for households6. Government balance7. Trade Balance

assumption:- Small open-economy- Only goods are tradable.- Goods are homogenous across countries

(ignore the CET and ARMINGTON approaches for now)

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1. The commodity market balance

jjjjj1

jjh

jh PRsQQaX /11, +−+∑∑

Incorporating Trade – modifications to a basic CGE model

jP≤0 ⊥

2. The factor market balance => no change (assuming no trade on factors)

3. The profit condition=> no change

4. The household income equation=> no change

jj QImpQExp −+ j

∀≤ 0

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5. The government tax revenue balance

∑∑ −+−≤h

hhKhLhj

jjj FKWLWtQPtR )(

( ) ∑ ++j

jKkjjLlj KWtLWt

R≤0 ⊥

∑∑∈∈

++imj

jjjexj

jjj PQImptImpPQExptExp

Incorporating Trade – modifications to a basic CGE model

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6. The domestic (US) trade price equations

Exports:

exjTransCostExchangePWExpPExp jj ∈∀−×≤ )(

jPWExp≤0 ⊥

jPWImp≤0 ⊥

imjTransCostExchangePWImpPImp jj ∈∀+×≤ )(

Imports:

Incorporating Trade – modifications to a basic CGE model

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7. The domestic (US) trade quantity equations

Exports:

exjPWExpfQExp jj ∈∀≤ ),( ε

jQExp≤0 ⊥

jQImp≤0 ⊥

Imports:

imjPWImpfQImp jj ∈∀≤ ),( µ

where ε and µ are price elasticities

-INF < ε < 0 and 0 < µ < INF

Note: Shoven and Whalley showed that ε < -1 so that the export-demand curve slopes downward and the import-supply slopes upward.

Incorporating Trade – modifications to a basic CGE model

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Incorporating Trade – modifications to a basic CGE model

8. The domestic & trade price relationshipExport tax => price received by domestic producers from

exports NOT = from domestic goodsImport tax => price paid by domestic consumers for imports

NOT = for domestic goods

jPExp≤0 ⊥

jPImp≤0 ⊥Imports:

exjPtExpPExp jjj ∈∀−= )1(

imjPtImpPImp jjj ∈∀+= )1(

Exports:

9. The zero trade balance : The exchange rate is used to clear a market where values of

imports are equal to values of exports.

Exchange≤0 ⊥ ∑∑∈∈

≤exj

jjimj

jj QExpPWExpQImpPWImp

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SAM

Recall: SAM Table used in the class example last week

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SAM in GAMS

STEPS entering SAM Table in GAMS

1. Define SETS and elements of SETS

2. Create SUBSETS from SETS

3. Enter data using a TABLE statement

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SAM in GAMS

STEP 1: Define SETS and elements of SETS

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SAM in GAMSSTEP 2: Create SUBSETS from SETS

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SAM in GAMSSTEP 3: . Enter data using a TABLE statement

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Calibration in GAMS

Using GAMS to check if SAM accounts are balanced before

starting a calibration

=> a column sum = a row sum

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Calibration in GAMS

Output from GAMS

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Creating a parameter to flag on accounts that are not balanced

Calibration in GAMS

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Calibration in GAMS

STEPS used in a calibration:

(1). Define parameters used in a calibration

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Calibration in GAMS

(2). Decide on units for goods and factors so that prices and quantities are separately obtained.

Normalizing prices to unity

Modifying SAM TABLE so that units are in quantities

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Calibration in GAMSRecall: The numerical example for the Cobb Douglas

production function used last week αα −= 1FFFF LKAQ

25.0120013001

=××

==FF

FFF QP

Krα

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Calibration in GAMS

75.1900300

120075.025.01 === −αα

FF

FF LK

QA

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Calibration in GAMSReplication check after a calibration

120090030075.1 75.025.0

1

=××== −

ααFFFF LKAQ

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Calibration in GAMS

300175.0125.0

75.11200

)1(75.0

1

=

××

=

−

=−α

αα

rw

AQKF

FF

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Wrap Up

Incorporating the trade relationship in the CGE model SAM in GAMSCalibration in GAMS

Next:MCPEvaluating results from the CGE modelIncorporating nested functions and a trade in GAMSManne A. S. and R. G. Richels. “An alternative approach to establishing trade-offs among greenhouse gases.” Nature410, 675-677 (2001).

Reference:Shoven, J. B. and J. Whalley. “Applying general equilibrium.” Surveys of

Economic Literature, Chapter 7, 1998.