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8 Applied GE modeling of
economy & environment
1. Rationales
2. Basics of applied GE models
3. Incorporating environmental issues
4. An application
Main source: OEE Ch. 5.
Additional: Shoven & Whalley, JEL 1984; Ginsburgh & Keyzer,
Structure of applied general eq. models (MIT Press, 1997); Coxhead,
World Development 28(1), 2000.
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Pros and cons of AGE modeling
 Importance of economy-wide mechanisms and
implications
 Intractability of higher-dimension analytical models
 Opportunities for ‘structural sensitivity analysis’
X Limitations
– Time is usually not explicitly taken into account
– Micro details such as risk/uncertainty or credit market
imperfections usually ignored
– aggregations can mask important differences (e.g. intra-industry
variations)
– AGE approach is highly time and energy-intensive: benefits over
PE approach obtained at high cost.
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Overview of AGE models
• Describe Walrasian equilibria in fairly
detailed manner--sufficient to support
policy claims
– Too large to be solved analytically; must use
numerical solutions instead
– But structure and results depend on same
theoretical foundations
• Advantages and disadvantages of size.
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An N-good, F-factor economy
• General structure
• Equilibrium conditions
• Closure rules and decisions
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Variables in the basic model
P
commodit y p rices (N)
W
mobil e factor prices (F)
R
sector-specific f actor prices (N)
Y
dom. commodit y supplies (N)
X
mobil e factor demands (NF)
D
dom. final demand s (N)
S
net imports (N)
V
factor endow ments (F)
U
agg rega te utilit y (1).

Foreign cu rrency exch. r ate (1)
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-- Suppose V and P are giv en, and let  = 1 be the numéraire price.
-- Agg rega te revenue is given by G(P,V) = max{PY | V}. From F ONC:
Yj = Yj (P, V)
(j = 1, ..., N),
(5.1)
Wi = Wi(P, V)
(i = 1, ..., F),
(5.2)
Rj = Rj (P, V).
(j = 1, ..., N),
(5.3)
and the p rices of mobil e and specifi c factors:
-- Each sector is a price-taker in factor markets. Th erefore, the outpu t leve l that
maximi zes revenue is also the co st-mi nimi zing level, and from FONC
of the sectoral co st mi nim ization p roblem Cj (W, Yj) = mi n{WX | Yj),
we obtain de ma nds for intersectorall y mobil e factors:
Xij = Xij (W, Yj)
(i = 1, ..., F; j = 1, ..., N). ,
(5.4)
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Domestic fi nal dema nds for each commodit y are found from the
expend it ure minimi zation problem E(P,U) = mi n{PD | U}:
Dj = Dj (P, U)
(j = 1, ..., N). ,
(5.5)
Net trade vo lumes are determined by ma rket-clearing conditions:
Sj = Dj – Yj
(j = 1, ..., N), ,
(5.6)
whe re Sj > (<) 0 indicates a ne t impo rt (expo rt) good . Import prices are set
in world markets, whil e for M expo rtables (M Š N), prices are set by
inve rse foreign demand func tions:
Pk = Pk (Sk)
(k = 1, ..., M).
(5.7)
Finall y, the model i s closed by an agg rega te budge t cons traint:
E(P,U) = G(P,V)
(5.8)
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Closure
• No. of equations must match endog. vars.
– In (5.1)-(5.8): 4N + F + FN + M + 1 eqns.
– But we have 5N + 2F + FN + 2 variables.
– Must choose N - M + F + 1 exog. vars
• Declare V exog; (N - M) elements of P, and .
• Now (5.1)-(5.8) solves for Y, W, R, X, D, S and U as
endogenous variables.
– Endogenous: income, factor prices, quantities produced and
demanded, trade, and utility.
– Exogenous: factor endowments, traded goods’ prices and a
numeraire price.
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Closure rules and decisions
• Other closures are possible
– ‘Neoclassical’ closure has all domestic prices flexible
– Alternatives: e.g. fix wages, allow unemployment in
labor market.
• These choices reflect our beliefs or observations about the
real world.
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Other features
• Can add in:
– Intermediate inputs
– Products distinguished by source (domestic, imported)
– Different kinds of labor
– Many sources of final demand
– Trade and transport ‘margins’
– Tariffs, taxes, and other policies … etc.
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Solving the model: the
‘Johansen’ AGE structure
• First-order approximations to changes in variable values
• Models solved in proportional (percentage) changes of
variables, or ‘hat calculus’.
• Advantages:
– Models are linear in variables
– Parameter values are intuitive and accessible (shares from SAM,
elasticities from other sources)
– Simulation results are additive in separate shocks
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Features of Johansen models
• Parameter values are shares and elasticities
• Quick checks:
– Homogeneity & ‘balance’ of underlying data base.
• Solution is by matrix inversion
– Entire model is a system of linear equations
• Examples of Johansen-style models:
– ORANI (Australian economy)
– GTAP (international agricultural trade)
– Models in OEE, Ch.6–8
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Data
1. Social accounting matrix: base year data
•
•
•
•
•
Input-output accounts of industries
Factor markets, household incomes &
expenditures
Trade and final demand
Taxes and G. expenditures
Micro and macro balance
2. Elasticities
•
Estimated (see www.aae.wisc.edu/coxhead/apex ),
or more commonly ‘guesstimated’.
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Schematic social accounts
Expenditures
Activities
Receipts
Firms
Factors
Institutions
Rest of
world
Total
expenditure
Factors
Intermed.
transactions
Institutions
Dom. final
demand
Rest of
World
Total
receipts
Exports
Total sales
Valueadded
Taxes &
tariffs
Valueadded
Return on
endowmts
HH & gov
income
Direct taxes
Imports
Total costs
Imports
Factor
payments
HH & gov.
expenditure
Exports
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Social accounting matrix
Activities
Firms
Capital
Labor
Labor
I-O
accounts
Private
cons. exp
Gov’t
Capital
account
Rest of
world
Total
income
Gov’t
cons. exp
Investmt
Net
exports
Total
revenue
Rentals
Total
rentals
Wages
Total
wages
Households
Gov’t
Capital
Households
Capital
income
Wage
income
Indirect
taxes
Private
savings
Imports
Total
expend.
Total
costs
Capital
income
Labor
income
H’hold
exp.
H’hold
income
Gov’t
income
Direct
taxes
Capital
account
Rest of
world
Capital
inflow
Transfers
Gov’t
savings
Savings
Reserve
accum
Forex
outflow
Gov’t
exp.
Investmt
Forex
inflow
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‘Standard’ national accounts
ignore environment
• Assumptions:
– Property rights on resources
– No externalities
– No non-marketed amenity values
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Open access to natural capital
Activities
‘Natural
capital’
Labor
H’holds
Gov’t
Cap.
acc.
Private
cons.
Gov’t
cons
Investmt
Rest of
world
Total
income
Net
exports
Total
revenue
Firms
I-O
accounts
‘Natural
capital’
Env.
services
Val. env
damage
Wages
Total
wages
Labor
H’holds
Gov’t
0 (open
access)
Wage
income
Indirect
taxes
Private
savings
Imports
Total
expend.
Costs
w/o NC
0
Labor
income
H’hold
expend.
H’hold
income
Gov’t
income
Direct
taxes
Cap. acc
Rest of
world
Capital
inflow
Transfers
Gov’t
savings
Savings
Reserve
accum
Forex
outflow
Gov’t
expend.
Investmt
Forex
inflow
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Addressing env. damages and
natural resource depletion
• Pigovian taxes (Bovenberg & Goulder, AER
1996)
• Private purchase of abatement services
• Public provision of abatement or clean-up
services
• Quotas or limits on resource use or
emissions (command & control)
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Environmental analysis in GE
• Most AGE models constructed for more
general analytical purposes: environmental
structure is added later
• Given uncertainty about env. variables and
valuations this may be appropriate!
• Industrial emissions: ‘side calculations’
• Natural resource degradation
• Questions about institutions.
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Deforestation & land degradation
• Commercial and non-comm’l deforestation:
does timber have market value?
– Non-comm’l deforestation is driven by search
for land, and responds to changes in the
marginal valuation of land in agricultural
production...
– … although institutional setting also matters
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Land degradation
• Hard to measure, and problems of
aggregation.
• Can use information on erosion rates by
crop, together with land use data, to build
‘baseline’ data set.
– Then erosion changes can be inferred from
changes in land use
• Production externalities: technical ‘regress’.
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Institutional issues
1.
Trees may be cut (or planted) to establish property rights
over land.
In open access forests (non-commercial), opportunity
cost of forest is set by ag. land values and clearing costs.
In commercial forestry, timber harvesting/replanting also
depends on property rights.
2.
3.
•
Will an increase in timber prices promote or retard tree-felling in
aggregate? Depends on property rights.
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‘Structural sensitivity analysis’
• Alter assumptions about market clearing
• Alter assumptions about property rights
• Alter assumptions about macroeconomic
closure
– e.g. Adjustment to equilibrium through
domestic tax system vs. adjustments through
accommodating international capital flows.
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