lecture 2 overview of cge modeling
TRANSCRIPT
Lecture 2Overview of CGE Modeling
David Roland-Holst and Sam Heft-Neal, UC BerkeleyFaculty of EconomicsChiang Mai University
13 July 2010
Roland-Holst 2Chiang Mai University Faculty of Economics13 July 2010
GE Modeling Applications
1. SAM to CGE – A Very Basic Model2. The Thai_Mini Model3. Excel Implementation4. Scenario Examples
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SAM Review
ACT COM VA HH GOV INV ROW TOTALS
ACT Gross Output
Receipts
COM Int. Use Household Consmption
GovernmentExpenditure
GrossInvestment
Exports Demand
VA GDP at Factor Cost
Factor Income
HH GDP at Factor Cost
ROW Trans. to HH
Household Income
GOV Net IndirectTaxes
Household Taxes
Government Borrowing
Government Revenue
INV Household Saving
Government Saving
Current account balance
Savings
ROW Imports ROW
TOTALS Payments Supply Factor Allocation
Household Expenditure
Government Expenditure
Investment ROW
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SAM to CGE
• The SAM provides a snapshot of the economy at equilibrium (columns equal rows), but it is a static equilibrium with fixed prices, no substitution, and typically average behavior.
• On the contrary, in many cases what we are interested in examining is how economic actors respond to changes in relative prices.
• CGE allows for flexible prices, substitution, and marginal behavior, at the same time meeting the accounting constraints enforced by SAM structure.
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SAM to CGE
• To put this another way, CGE models overcome the shortcomings of a SAM by specifying a functional form for every cell in the SAM.
• Each cell in the SAM can be represented by a price and quantity, so the model must be able to determine both prices and quantities.
• Let’s start with a VERY simple CGE model, then work our way to something a bit more complicated.
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Very Basic CGE
• To see how we go from a SAM to a CGE model, let’s begin with a 2-sector, 2-factor really really simple SAM (RRSS):
Producers Factors Institutions ROWSUM
AG OTH L K HH
AG 150 150
OTH 500 500
L 100 200 150
K 50 300 150
HH 300 350 650
COLSUM 150 500 300 350 650
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Our Simple Economy
• Note that the government is not an economic actor, the economy is closed, factor costs are the only input to production, and households spend all their income.
• In this case, we have three economic actors Producers (2; AG and OTH) Factors (2; L and K) Households (1)
• Let’s further assume that labor and capital are fully mobile across sectors (1 wage and rental rate).
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Side Note
• (Let’s maintain our convention of having i be rows and j be columns; this means that i will reflect the income side of the economy and j will reflect the expenditure side of the economy).
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Supply
• On the supply side, at a minimum we need to specify how producers behave (e.g., minimize costs), how they choose inputs (factor demands), and how their decisions determine aggregate supply. Using a Cobb-Douglas form, we can describe production within our economy as:
Total Supply
Labor Demand
Capital Demand
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Demand
• On the demand side, we need to specify the level of household income, and how households decide to spend that income. Household income is the sum of factor incomes:
(Remember that we are decomposing SAM transactions into prices and, in this case, volumes.)
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Demand
• Household consumption is modeled with a constant elasticity of substitution (CES) utility function:
Maximizing U s.t. a budget constraint gives us the two reduced form consumption functions:
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Equilibrium
• Lastly, we need to define some sort of equilibrium conditions for the economy, which in our case we can represent by supply = demand in product and factor markets.
Commodity Market
Labor Market
Capital Market
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Endogenous Variables
• In 13 equations we have built a simple general equilibrium model.
• Our 13 endogenous variables include: Pi – prices for AG and OTH goods r – rate of return on capital w – wage rate LDj – labor demand for AG and OTH producers KDj – capital demand for AG and OTH producers XSj – aggregate supply Ci – household consumption of AG and OTH goods Y – household income
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Exogenous Variables
• We have left 2 variables exogenous: LS – Aggregate labor supply KS – Aggregate capital supply
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Initializing Prices
• Prices are going to be endogenous in our simple CGE model, but we are going to represent prices in a price index rather than as absolute values. Prices can be initialized to any level, but 1 is generally the most obvious choice. PAG = 1 POTH = 1
• We select PAG as the numeraire, which fixes our economy-wide relative price as P = POTH / PAG
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Initializing Prices
• We represent factor prices in the same way (as an index). w = 1 r = 1
(i.e., capital is more expensive in relative terms than labor)
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Initializing Endogenous Variables
• We can assign values to endogenous variables based our SAM: LDAG0 = 100 LDOTH0 = 200 KDAG0 = 50 KDOTH0 = 300 XSAG0 = 150 XSOTH0 = 500 CAG0 = 150 COTH0 = 150 Y0 = 650
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SAM Check
Producers Factors Institutions ROWSUM
AG OTH L K HH
AG 150 150
OTH 500 500
L 100 200 150
K 50 300 150
HH 300 350 650
COLSUM 150 500 300 350 650
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Initializing Endogenous Variables
• LD, KD, XS, and C are volumes, so we need to convert them to volumes by dividing by the appropriate initialized price LDAG0/w0 = 100/1 =100 LDOTH0/w0 = 200/1 = 200 KDAG0/r0 = 50/1 = 50 KDOTH0/r0 = 300/1 = 300 XSAG0/pAG0 = 150/1 = 150 XSOTH0/pOTH0 = 500/1 =
500 CAG0/pAG0 = 150/1 = 150 COTH0/pOTH0 = 500/1
= 500
• We can also initialize LS and KS volumes LS0 = LDAG0+ LDOTH0 KS0 = KDAG0+ KDOTH0
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Model Calibration
• We can use SAM data to determine the baseline values of some of our parameters; in this case: Cobb-Douglas scaling factors (Aj) Cobb-Douglas share parameters (αj) CES utility function share parameters (δ)
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Model Calibration
• From our aggregate output equation
• We can calculate the Cobb-Douglas scaling factors as
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Model Calibration
• Similarly, from labor demand
we can calculate the Cobb-Douglas share parameters as
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Model Calibration
• The CES share parameters are derived from
with a less than tidy result of
Roland-Holst 24Chiang Mai University Faculty of Economics13 July 2010
Model Calibration
• Alternatively, the CES utility function’s substitution elasticity (σ) cannot be determined with SAM data.
• We can either specify σ heuristically (e.g., a 0 if we determine that the goods are perfect complements, or a high value if they are perfect substitutes) or through econometrics.
• In this case, let’s arbitrarily assign σ with a value of 0.3.
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Model Simulation
• Let’s walk through what happens when we perturb one of the exogenous variables in the model. Say we have an exogenous increase in labor supply (LS). From
we know this exogenous increase in LS will be accompanied by an increase in aggregate LD.
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Model Simulation
• But it isn’t clear how this change will affect our other variables:
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To a New Equilibrium
• We need a way to move from our initial equilibrium, in which all of our model equations held (i.e., our markets cleared), to a new equilibrium, in which all of our equations hold again. This shift from an old equilibrium to a new equilibrium is what is usually meant by “adjustment.”
• To find our new equilibrium solution, our endogenous variables will have to adjust so that both our equations hold, and our exogenous shock is accounted for.
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Model Solutions and Consistency
• CGE models require numerical solutions, which means that you will need to use some sort of solver package to generate a solution.
• To ensure that the model is consistent and you have not made errors in coding, in general your first step after building a CGE model is to make sure that you can reproduce the base solution (i.e., with no exogenous shock).
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A Quick Thought on Model Building
• Before we get into more complex models, a bit of advice. It is always useful to start any research project with a quick theoretical model that maps relationships among the variables that you wish to examine.
• By doing this kind of exercise, you can get a good sense of where you can make simplifications, where you should be more detailed, and how much you can leave out of your model, and what your data requirements will be.
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Toward more Complex Models
Our next model — THAI_MINI — is significantly more complex, but still simple as far as CGE models go.
THAIMINI will address several of the oversimplifications of our previous model: Producers typically have non-factor intermediate
inputs and non-uniform substitution elasticities Households are more complex than CES utility
describes Most economies have an active government and
capital markets Most economies have ROW interactions
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Production - CES Stratification
= 0
m k
v
p XP
ND VA
L KF
K F
XAp
XM XDd
XP - OutputND - Aggregate intermediate demandVA - Value added bundleL - Demand for laborKF - Capital/sector specific capital bundleK - Demand for capitalF - Demand for sector specific factorXAp - Input/output matrixXDd - Domestic demand for domestic goodsXM - Demand for importssp -Top level substitution elasticity (ND and VA)sv -Substitution elasticity between L and KFsk -Substitution elasticity between K and Fsm - Armington elasticity
Roland-Holst 32Chiang Mai University Faculty of Economics13 July 2010
Production - CES Stratification
= 0
m k
v
p XP
ND VA
L KF
K F
XAp
XM XDd
XP - OutputND - Aggregate intermediate demandVA - Value added bundleL - Demand for laborKF - Capital/sector specific capital bundleK - Demand for capitalF - Demand for sector specific factorXAp – Aggregate (Dom+Imp) IntermediateXDd - Domestic demand for domestic goodsXM - Demand for importsp - Top level substitution elasticity(ND and VA) v - Substitution elasticity between L and KF k - Substitution elasticity between K and F m - Armington elasticity
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Unit Costs and Prices(1)
(2)
(1) ii
indii XP
PNDPXND
pi
(2) ii
ivaii XP
PVAPXVA
pi
(3) pip
ipi
ivaii
ndii PVAPNDPX
1/111
(4) ipii PVAPP 1
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Factor Demand I
(5) iil
ili
di VA
WPVAL
viv
i
1
(6) ii
ikfii VA
PKFPXKF
vi
(7)
vi
vi
vi
ikfil
i
lii PKFWPVA
1/1
11
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Factor Demand II
(8) ii
iki
ki
di KF
RPKFK
ki
ki
1
(9) ii
ifi
fi
di KF
PFPKFF
ki
ki
1
(10)
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ifik
i
ikii
PFRPKF
1/111
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Leontief Intermediate Technology
(11) jijij NDaXAp
(12) i
iitpijijj PAaPND 1
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Household Income and Final Demand
(13) gh
i
dii
dii
di TRPFPFKRWLYH .
(14) DeprYYHYD 1
(15) iitci
iii PA
YXAc
1
*
(16) j
jjitcj PAYDY 1*
(17) i
iiitci
h XAcPAYDS 1
(18) 0.DeprYPDeprY
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Government
(19) 0XGXG
(20) XGPA
PGXAgg
iitgi
gii
1
(21) g
g
ii
itgi
gi PAPG
1/1
11
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Investment
(22) DeprYSERSSXIPI fgh ..
(23) XIPA
PIXAii
iitii
iii
1
(24) i
i
ii
itii
ii PAPI
1/1
11
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Trade: Demand
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(26) ii
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di XA
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mi
(27) ii
imii XA
PMPAXM
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imii
dii PMPDPA
1/111
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Trade: Supply
(29)
xiii
xii
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idi
si
PPPD
XPPPPDXD
xi
if
if
(30)
xiii
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ieii
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XPPPPEES
xi
if
if
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Production Possibilities for Domestic and Export Supply
(31)
xii
sii
xii
eii
dii
ESXDXP
PEPDPPxix
ixi
if
if1/111
(32)
iii
ii
ieii
WPEWPE
WPEWPEED
i
if
if
*
*
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Trade Prices
(33) imii WPMERPM 1
(34) eiii WPEERPE 1/.
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Goods Equilibrium
(35) si
di XDXD
(36) ii ESED
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Factor Equilibrium
(37) l
PWL ls
(38) i
di
s LL
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Capital Market Equilibrium
(39) ss TKTK 0
(40)
ki
ksiki
si
TRR
TKTRRK
k
if
if
(41)
k
i
di
s
k
ii
ki
KTK
RTRk
k
if
if1/1
1
(42) si
di KK
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Other Resource Equilibrium
(43) f
i
PPFF if
is
i
(44) si
di FF
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Macro Closure I: Fiscal
(45)
ii
itiii
itgii
itci
jij
itpiji XAiXAgXAcXApPAITaxY
(46) i
iiei
iii
mi ESPEXMWPMERTradeY
(47) YHXPPXTradeYITaxYGRevi
iipi .
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Macro Closure II: Financial
(48) hg
g TRPXGPGGRevS ..
(49) PSRS gg /
(50) gg RSRS 0
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Macro Closure III: Trade
(51) i
iif
i
dii XMWPMSEWPE
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Macro Closure IV: Numeraire
(52) i
dii
dii
di FPFKRWLGDPFC
(53) i
di
fii
di
kii
di
li FPFKRLWRGDP 0,0,0
(54) RGDPGDPFCP /
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Excel Implementation for Thailand
Download the Excel spreadsheet Thai_Mini_CGE.xlsThis is a heuristic, 2 sector CGE model in six spreadsheets:1. AggMat – A matrix of zeros and ones to aggregate a
standard GTAP SAM to fit the two sector framework2. BaseSAM – The initial input SAM, taken from GTAP 5.3. SAM – The aggregated initial SAM and a counterfactual
SAM for comparative static assessment4. Model – The primary data and equation spreadsheet5. Parameters – A registry of structural parameter values6. Dictionary – complete definitions of variables and
parameters
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Model Spreadsheet
This is the primary functional component of the Mini_CGE, containing all
1. Endogenous variables, 87 (suffixes _a and _o for agriculture and other)
2. Equations 86 (one is redundant because of WalrasLaw)
3. Exogenous variables, 27 and 4. A few examples of counterfactual experiments.
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Parameters: Supply and Demand
Productionp sigmap - Substitution elasticity between total
intermediate demand, ND, and value added, VA. v sigmav - Substitution elasticity between labor, and the
capital-sector specific factor bundle, KF. k sigmak - Substitution elasticity between capital and
the sector specific factor.
Final demand eta - Income elasticity g sigmag - Government expenditure substitution
elasticity i sigmai - Investment expenditure substitution elasticity
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Parameters – Trade and Factors
Trade elasticitiesm sigmam - Armington import elasticity x sigmax - CET transformation elasticity (between
domestic and export supply). epse - Export demand elasticity.
Supply elasticities l omegal - Aggregate labor supply elasticity k omegak - Capital mobility elasticity. 0 emulates sector-
specific capital. Use a high value to approximate perfectly mobile capital.
f sigmak - Sector-specific supply elasticities.
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Install or Initialize the Solver
Look under Tools/Solver or the Office Button/Excel Options
The Solver solution algorithm is invoked by clicking on the Solve button. The status bar at the bottom of the Excel screen displays (minimal) information on
each iteration, including iteration count and value of the objective function.
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Simulation Results
If successful, the solver will display the following dialog box:
To have the Solver overwrite the values of the endogenous variables, simply click on the OK button. Users can experiment with the other options.
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Convergence and Consistency
If solution convergence was achieved, the model should have re-produced the base data set (within the limits of the convergence tolerance). All equations should evaluate to 0. The expression of Walras’ Law should evaluate to 0. All deviations from initial values should evaluate to 0. A final test is to check the consistency of the resulting SAM.
The SAM spreadsheet, contains the solution SAM. The solution SAM is expressed in terms of the model solution. For example, the labor remuneration cell (in agriculture) contains the formula:=wage*ld_a/scale
If the SAM is not consistent, either the solution is inconsistent, the model has been mis-specified, or the formulas in the SAM have been mis-specified. The formula is adjusted by the scale variable to make the solution SAM comparable with the initial SAM.
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Homogeneity Test
If this is a new model, it is recommended to check model homogeneity. This involves a perturbation of the model numéraire. If the model is homogeneous in prices, perturbation of the model numéraire should leave all volumes constant, and adjust all prices and value variables by the same percentage amount as the percentage change in the numéraire(i.e. all relative prices remain constant). To check homogeneity, multiply the initial value of the numéraire by some constant, e.g. in cell L23, for the exchange rate substitute=er0*1.1
Initially, the only equations which will be affected by this change are the domestic investment equation, the domestic trade prices, and the tariff revenue equation because these are the only equations where the numéraire (the exchange rate) appears. Invoke Solver to find a new solution to the model. If the homogeneity test fails (other than due to the lack of convergence), at least one of the equations has been mis-specified, or there could be a built-in nominal rigidity, such as a fixed nominal wage. If both tests succeed, the model should be re-initialized, and the next step is to run one or more shocks to the model.
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Installed Scenarios
1. Tariff Abolition2. Full Trade Reform3. Agricultural Export Tax4. Agricultural Export Price Changes5. Other Export Price Changes