COMPUTABLE GENERAL EQUILIBRIUM MODELS (CGE): BASICS

COMPUTABLE GENERAL EQUILIBRIUM MODELS (CGE): BASICS

NOPOOR Project "Enhancing Knowledge for Renewed Policies against Poverty"

October 21st , 2013 UNIVERSIDAD AUTÓNOMA DE MADRID (UAM)

Saúl de Vicente Queijeiro

COMPUTABLE GENERAL EQUILIBRIUM MODELS (CGE)


IMPLEMENTATION OF A CGE MODEL

Data Source: structure of a SAM

Behavioral equations

Market-clearing conditions

SOLVING THE MODEL

Shock simulation

COMPUTABLE GENERAL EQUILIBRIUM MODELS (CGE)

DATA SOURCE: SOCIAL ACCOUNTING MATRIX (SAM)

THEORETICAL FRAMEWORK: SIMPLIFIED MODEL

SIMPLIFIED MODEL USING EXCEL

SIMPLIFIED MODEL USING GAMS

THEORETICAL FRAMEWORK: EXTENDED MODEL

EXTENDED MODEL USING GAMS: SIMULATION


IMPLEMENTATION OF A CGE MODEL: CGE framework

Income taxe s

Monetary fl ows

Phys ica l fl ows

Source: Liang and Wei (2012)

FACTOR MARKET

CAPITAL MARKET

COMMODITY MARKET

Foreign saving

TransferPayments

Profit distribution

Reve

nue

Expo

rts

Impo

rts

Expe

nditu

reTr

ansf

ers/

Tar

iffs

Expo

rts

reba

tes

Com

mod

ities Expe

nditu

reExpenditure

CommoditiesCommodities

Revenues

Investment

Indirect taxes

Transfers

Households saving

Firm

s sav

ing

Transfers/profit distribution

Production factors

Factors cost

Labour/ Capital

WagesReturn on

Capital

Transfers

Income taxes


IMPLEMENTATION OF A CGE MODEL: CGE framework-SAM Structure (source: Breisinger et al, 2009)


IMPLEMENTATION OF A CGE MODEL: CGE framework-SAM Structure

Activities Commodities Labor Capital Households Government Investment Rest of world Total

Activities 24,996 24,996

Commodities 12,029 12,142 1,805 4,680 5,151 35,807

Labor 9,717 9,717

Capital 3,250 3,250

Households 9,717 3,250 1,387 2,001 16,354

Government 2,372 940 739 4,052

Savings 3,272 860 548 4,680

Rest of world 8,439 8,439

Total 24,996 35,807 9,717 3,250 16,354 4,052 4,680 8,439


CGE THEORETICAL FRAMEWORK: SIMPLIFIED MODEL

•GOODS: BREAD AND WINE•FACTORS:

•CAPITAL•LABOUR

•INSTITUTIONS: HOUSEHOLDS

BRD WIN CAP LAB HOH TOTALBRD 15 15WIN 35 35CAP 5 20 25LAB 10 15 25HOH 25 25 50TOTAL 15 35 25 25 50


CGE THEORETICAL FRAMEWORK: SIMPLIFIED MODEL BEHAVIORAL EQUATIONS

HOUSEHOLDS

S.T.


CGE THEORETICAL FRAMEWORK: SIMPLIFIED MODEL BEHAVIORAL EQUATIONS

FIRMS Max


CGE THEORETICAL FRAMEWORK: SIMPLIFIED MODEL MARKET CLEARING CONDITIONS

Market Equilibrium


CGE MODEL USING GAMS/EXCEL: STEPS

DEFINITION OF TABLE NAME AND ITS SUFFICES LOADING DATA FROM SAMDECLARING AND FULLFILING PARAMETERS (EXOGENOUS AND INITIAL VALUES OF ENDOGENOUS)CALIBRATION: Declaring parameters (elasticities and technology state), obtained directly from the functional forms of the actors' behavior and the SAM. (EXOGENOUS)

MODEL SYSTEM DECLARATION:DECLARING VARIABLES (ENDOGENOUS)

DECLARING ECUATIONSCHOSING FUNCTIONAL FORMS OF BEHAVIOR EQUATIONS AND MARKET CLEARING CONDITIONS

OBJECTIVE FUNCTION

INITIALIZING VARIABLES AND SETTING LOWER BOUNDS

SOLVING THE MODELSIMULATIONDISPLAYING RESULTS AND BENCHMARKING


EXTENDED MODEL: WHAT IS NEW?

•HOUSEHOLDS (DISPOSABLE RENT)

•FIRMS (INTERMEDIATE INPUTS)

•GOVERNMENT (TAXES)

•INVESTMENT (SAVING)

•INTERNATIONAL TRADE•SMALL COUNTRY ASSUMPTION•ARMINGTON ASSUMPTION

•MARKET CLEARING CONDITIONS


EXTENDED MODEL: GENERAL STRUCTURE


CGE THEORETICAL FRAMEWORK: EXTENDED MODEL

•GOODS: BREAD AND WINE•FACTORS:

•CAPITAL•LABOUR

•INSTITUTIONS: HOUSEHOLDS, GOVERNMENT(WITH TARIFFS AND INDIRECT TAXES), INVESTMENT AND REST OF THE WORLD

BRD WIN CAP LAB HOH GOV INV IDT TRF EXT TOTALBRD 21 8 20 19 16 8 92WIN 17 9 30 14 15 4 89CAP 20 30 50LAB 15 25 40HOH 50 40 90GOV 23 9 3 35INV 17 2 12 31IDT 5 4 9TRF 1 2 3EXT 13 11 24

TOTAL 92 89 50 40 90 35 31 9 3 24


THEORETICAL FRAMEWORK: EXTENDED MODEL. BEHAVIORAL EQUATIONS

HOUSEHOLDSNew income constraint:



FIRMS: INTERMEDIATE INPUTS

-The bottom stage:

𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝜋𝑗𝑦 = 𝑝𝑗𝑦𝑦𝑗 − 𝑟ℎℎ 𝐹ℎ𝑗

Subject to;

-The top stage:

𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒𝑍𝑗,𝑌𝑗,𝑋𝑖𝑗 𝜋𝑗 = 𝑝𝑗𝑠𝑍𝑗 −൭𝑝𝑗𝑦 𝑌𝑗 + 𝑝𝑖𝑞 𝑋𝑖𝑗𝑖 ൱

Subject to:

𝑍𝑗 = min൬𝑋𝐵𝑟𝑒𝑎𝑑 𝑗𝑎𝑥𝐵𝑟𝑒𝑎𝑑 𝑗 , 𝑋𝑊𝑖𝑛𝑒 𝑗𝑎𝑥𝑊𝑖𝑛𝑒 𝑗 , 𝑌𝑗𝑎𝑦𝑖൰



INTERMEDIATE INPUTS𝜋𝑗:𝑃𝑟𝑜𝑓𝑖𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑗− 𝑡ℎ 𝑓𝑖𝑟𝑚 𝑎𝑡 𝑡ℎ𝑒 𝑡𝑜𝑝 𝑠𝑡𝑎𝑔𝑒

𝜋𝑗𝑦:𝑃𝑟𝑜𝑓𝑖𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑗− 𝑡ℎ 𝑓𝑖𝑟𝑚 𝑎𝑡 𝑡ℎ𝑒 𝑏𝑜𝑡𝑡𝑜𝑚 𝑠𝑡𝑎𝑔𝑒

𝑧𝑗:𝑔𝑟𝑜𝑠𝑠 𝑜𝑢𝑡𝑝𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑗− 𝑡ℎ 𝑔𝑜𝑜𝑑

𝑥𝑖𝑗:𝑖𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 𝑖𝑛𝑝𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑔𝑜𝑜𝑑 𝑢𝑠𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑗− 𝑡ℎ 𝑓𝑖𝑟𝑚

𝑌𝑗:𝑣𝑎𝑙𝑢𝑒 𝑎𝑑𝑑𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑓𝑖𝑟𝑚

𝑎𝑥𝑖𝑗:𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑒𝑛𝑡 𝑓𝑜𝑟 𝑚𝑖𝑛𝑛𝑢𝑚 𝑟𝑒𝑞𝑢𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑖− 𝑡ℎ 𝑖𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 𝑖𝑛𝑝𝑢𝑡 𝑓𝑜𝑟 𝑜𝑛𝑒 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑔𝑟𝑜𝑠𝑠 𝑜𝑢𝑡𝑝𝑢𝑡 𝑎𝑥𝑖𝑗= 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑓𝑜𝑟 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑟𝑒𝑞𝑢𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑠 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒 𝑎𝑑𝑑𝑒𝑑 𝑓𝑜𝑟 𝑜𝑛𝑒 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑔𝑟𝑜𝑠𝑠 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑗𝑠 = 𝑠𝑢𝑝𝑝𝑙𝑦 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑗− 𝑡ℎ 𝑔𝑜𝑜𝑑

𝑝𝑖𝑞 = 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑖𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑎𝑡𝑒 𝑔𝑜𝑜𝑑,𝑎𝑛𝑑

𝑝𝑗𝑦 = 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑎𝑑𝑑𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑗− 𝑡ℎ 𝑓𝑖𝑟𝑚



INTERMEDIATE INPUTS

𝑋𝑖𝑗 = 𝑎𝑥𝑖𝑗𝑍𝑗,∀𝑖 𝑌𝑗 = 𝑎𝑦𝑗𝑍𝑗,∀𝑗

𝐹ℎ𝑗 = 𝛽ℎ𝑗𝑝𝑗𝑦𝑟ℎ 𝑌𝑗,∀ℎ



INTERMEDIATE INPUTS

zero-profit condition:

𝜋= 𝑝𝑗𝑠𝑍𝑗 −൭𝑝𝑗𝑦𝑌𝑗 + 𝑝𝑖𝑞𝑋𝑖𝑗𝑖 ൱

= 𝑝𝑗𝑠𝑍𝑗 −൭𝑎𝑦𝑗𝑝𝑗𝑦𝑍𝑗 + 𝑎𝑥𝑖𝑗𝑝𝑖𝑞𝑍𝑗𝑖 ൱= 0,∀𝑗

𝑝𝑗𝑠 = 𝑎𝑦𝑗𝑝𝑗𝑦 + 𝑎𝑥𝑖𝑗𝑝𝑖𝑞. ∀𝑗𝑖



GOVERNMENT

𝑋𝑖𝑔:𝑝𝑢𝑏𝑙𝑖𝑐 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑐𝑜𝑚𝑜𝑑𝑖𝑡𝑦 𝑇𝑗:𝑡𝑎𝑥 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 𝑓𝑟𝑜𝑚 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑗− 𝑡ℎ 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦 𝜏𝑗:𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝑜𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑗− 𝑡ℎ 𝑐𝑜𝑚𝑜𝑑𝑖𝑡𝑦 𝑖𝑛 𝑡𝑒𝑟𝑚 𝑜𝑓 𝑙𝑜𝑐𝑎𝑙 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡. 𝑆𝑔:𝑝𝑢𝑏𝑙𝑖𝑐 𝑠𝑎𝑣𝑖𝑛𝑔,𝑎𝑛𝑑 𝜇𝑖:𝑠ℎ𝑎𝑟𝑒 𝑜𝑓 𝑒𝑥𝑝𝑒𝑑𝑖𝑡𝑢𝑟𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑖− 𝑡ℎ 𝑐𝑜𝑚𝑜𝑑𝑖𝑡𝑦 ൬0 ≤ 𝜇𝑖 ≤ 1, 𝜇𝑖 = 1𝑖 ൰



INVESTMENT

𝑋𝑖𝑣 = 𝜆𝑖𝑝𝑖𝑞 ൫𝑆+ 𝑆𝑔 + 𝜀𝑆𝑓൯.∀𝑖 S: private saving

Sf:foreign saving ሺor current account deficit in balance of paymentሻin foreign currency Xiv:investment demand for the i − th comodity ε:exchange rate (local currency per foreign currency)

λ i:share of expediture for the i − th commodity (0 ≤ λ i≤ 1, λ i = 1i



•INTERNATIONAL TRADE: SMALL COUNTRY ASSUMPTION𝑝𝑖𝑒 = 𝜀𝑝𝑖𝑊𝑒,∀𝑖 𝑝𝑖𝑚 = 𝜀𝑝𝑖𝑊𝑚,∀𝑖 σ 𝑝𝑖𝑤𝑒𝐸𝑖 + 𝑆𝑓 = σ 𝑝𝑖𝑤𝑚𝑀𝑖𝑖𝑖 Balance of payments condition

𝑝𝑖𝑤𝑒:𝑒𝑥𝑝𝑜𝑟𝑡𝑠 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦 𝑖𝑛 𝑓𝑜𝑟𝑒𝑖𝑔𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑡𝑒𝑟𝑚𝑠 (𝑒𝑥𝑜𝑔𝑒𝑛𝑜𝑢𝑠)

𝑝𝑖𝑒 = 𝑒𝑥𝑝𝑜𝑟𝑡 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦 𝑖𝑛 𝑙𝑜𝑐𝑎𝑙 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑡𝑒𝑟𝑚𝑠, 𝐸𝑖 = 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑒𝑥𝑝𝑜𝑟𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦

𝑝𝑖𝑤𝑚 = 𝑖𝑚𝑝𝑜𝑟𝑡 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦 𝑖𝑛 𝑓𝑜𝑟𝑒𝑖𝑔𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑡𝑒𝑟𝑚𝑠 (𝑒𝑥𝑜𝑔𝑒𝑛𝑜𝑢𝑠)

𝑝𝑖𝑚 = 𝑖𝑚𝑝𝑜𝑟𝑡 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦 𝑖𝑛 𝑙𝑜𝑐𝑎𝑙 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑡𝑒𝑟𝑚𝑠,𝑎𝑛𝑑

𝑀𝑖 = 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑖𝑚𝑝𝑜𝑟𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑖 − 𝑡ℎ 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦



•INTERNATIONAL TRADE: ARMINGTON ASSUMPTION𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒𝑄𝑖,𝑀𝑖,𝐷𝑖 𝜋𝑖𝑞 = 𝑝𝑖𝑞𝑄𝑖 −൫𝑝𝑖𝑚𝑀𝑖 + 𝑝𝑖𝑑𝐷𝑖൯

S. T:

𝑄𝑖 = 𝛾𝑖൫𝛿𝑚𝑖𝑀𝑖𝜂𝑖 + 𝛿𝑑𝑖𝐷𝑖𝜂𝑖൯1𝜂𝑖

𝑀𝑖 = ቆ𝛾𝑖𝜂𝑖𝛿𝑚𝑖𝑝𝑖𝑞𝑝𝑖𝑚 ቇ

11−𝜂𝑖 𝑄𝑖,∀𝑖 𝐷𝑖 = ቆ

𝛾𝑖𝜂𝑖𝛿𝑑𝑖𝑝𝑖𝑞𝑝𝑖𝑑 ቇ

11−𝜂𝑖 𝑄𝑖,∀𝑖



•INTERNATIONAL TRADE: ARMINGTON ASSUMPTION: 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒𝑍,𝐵,𝐷 𝜋𝑖𝑧 = ൫𝑝𝑖𝑒𝐸𝑖 + 𝑝𝑖𝑑𝐷𝑖൯−ሺ𝜏𝑖 + 𝑝𝑖𝑠ሻ𝑍𝑖, S.T:

𝑍𝑖 = 𝜃𝑖 ቀ𝛿𝑒𝑖𝐸𝑖∅𝑖 + 𝛿𝑑𝑖 𝐷𝑖∅𝑖ቁ1∅𝑖

𝐸𝑖 = ቆ𝜃𝑖∅𝑖 𝛿𝑒𝑖(𝜏𝑖 + 𝑝𝑖𝑠)𝑝𝑖𝑒 ቇ

11−∅𝑖 𝑧𝑖,∀𝑖

𝐷𝑖 = ቆ𝜃𝑖∅𝑖 𝛿𝑑𝑖ሺ𝜏𝑖 + 𝑝𝑖𝑠ሻ𝑝𝑖𝑑 ቇ

11−∅𝑖 𝑧𝑖,∀𝑖


THEORETICAL FRAMEWORK: EXTENDED MODEL

•MARKET CLEARING CONDITIONS

𝑄𝑖 = 𝑋𝑖𝑝 + 𝑋𝑖𝑔 + 𝑋𝑖𝑣 + 𝑋𝑖𝑗,𝑗 ∀𝑖

𝐹ℎ𝑗 = 𝐹𝐹ℎ ∀ℎ 𝑗


EXTENDED MODEL USING GAMS

•DEFINITION OF TABLE NAME AND ITS SUFFICES

•LOADING DATA FROM SAM:

• 5 COLUMUNS (+) •IMPORTING DATA FROM A TXT. FILE

• DECLARING AND FULLFILING PARAMETERS (EXOGENOUS AND INITIAL VALUES OF ENDOGENOUS )

•VALUE ADDED AND INTERMEDIATE INPUTS• GOVERNMENT (TAXES)• S-I• REST OF THE WORLD•COMPOSITE GOODS (ARMINGTON)



•CALIBRATION: DECLARING AND CALCULATING PARAMETERS (EXOGENOUS)

•SUBSTITUTION ELASTICITIY PARAMETER•TRANSFORMATION ELASTICITY PARAMETER•SHARE PARAMETERS (LEONTIEF, CES, CET)•AVERAGE PROPENSITY FOR SAVING•TAX RATE



•DEFINING MODEL SYSTEM

•VARIABLES (ENDOGENOUS)•EQUATIONS

•HOUSEHOLD CONSUMPTION•DOMESTIC PRODUCTION: VA, INTERMEDIATE DEMANDCOST FUNCTION•GOVERNMENT•INVESTMENT•INTERNATIONAL TRADE:

•PRICES•ARMINGTON AND TRANSFORMATION FUNCTIONS

•MARKET CLEARING CONDITIONS•SAVINGS: (NUMBER OF VARIABLES=NUMBER OF EQUATIONS)•OBJECTIVE FUNCTION

•INITIALIZING VARIABLES AND SETTING LOWER BOUNDS



•SIMULATION

•DIFFERENCES BETWEEN INITIAL EQUILIBRIUM AND COUNTER-FACTUAL SOLUTION


THANK YOU


Saúl de Vicente Queijeiro

October 21st , 2013 UNIVERSIDAD AUTÓNOMA DE MADRID (UAM)

Documents

COMPUTABLE GENERAL EQUILIBRIUM MODELS (CGE): BASICS