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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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P commodity prices (N) W mobile factor prices (F)

R sector-specific factor prices (N) Y dom. commodity supplies (N)

X mobile factor demands (N×F) D dom. final demands (N)

S ne t imports (N) V factor endowments (F)

U aggregate utility (1). φ Forei gn curr encye . xch rat e(1)

Variables in the basic model

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-- Suppose V and P are given, and let φ = 1 be the numérair eprice.

-- Aggregate revenue isgiven byG(P,V) = max{P⋅Y | V} . Fro m FONC:

Yj = Yj (P, V) (j = 1, ..., N), (5.1)

and t he prices of mobile andspecifi cfactors:

Wi = Wi(P, V) (i = 1, ..., F), (5.2)

Rj = Rj (P, V). (j = 1, ..., N), (5.3)

-- Each sector is a price-take r i nfactor markets. Therefor ,e the outpu t leve l that

maximizes revenue is also t he cost-minimizing level, andfrom FONC

of the sectora l cost minimizati on problem Cj (W, Yj) = min{W⋅X | Yj),

we obtai n demands for intersectorall ymobile factor :s

Xij = Xij (W, Yj) (i = 1, ..., F; j = 1, ..., N). , (5.4)

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Domestic final demands for each commodity are found from the

expenditure minimization problem E(P,U) = min{P⋅D | U}:

Dj = Dj (P, U) (j = 1, ..., N). , (5.5)

Ne t trade volumes are determined bymarke-t cleari ngcondition :s

Sj = Dj – Yj (j = 1, ..., N), , (5.6)

where Sj > (<) 0 indicates a ne t impo rt(expo )rt good. Import prices are set

i nworld markets, whil efor M exportables (M ≤ N), prices ar eset by

inverse foreign demand function :s

Pk = Pk (Sk) (k = 1, ..., M). (5.7)

Finall ,y t hemode l is closed byan aggregate budget constraint:

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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Data1. 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

Activities Factors InstitutionsRest of World

Total receipts

Firms Intermed. transactions

Dom. final demand

Exports Total sales

Factors Value- added

Value-added

Institutions Taxes & tariffs

Return on endowmts

Direct taxesHH & gov

income

Rest of world Imports Imports

Total expenditure Total costs

Factor payments

HH & gov. expenditure

Exports

Expenditures

Receipts

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Social accounting matrixAct-

ivities Capital LaborHouse-holds Gov’t

Capital account

Rest of world

Total income

Firms I-O accounts

Private cons. exp

Gov’t cons. exp

InvestmtNet

exportsTotal revenue

CapitalRentals

Total rentals

LaborWages

Total wages

House-holds

Capital income

Wage income

TransfersCapital inflow

H’hold income

Gov’t Indirect taxes

Direct taxes

Gov’t income

Capital

accountPrivate savings

Gov’t savings

Savings

Rest of world

ImportsReserve accum

Forex outflow

Total expend.

Total costs

Capital income

Labor income

H’hold exp.

Gov’t exp.

InvestmtForex 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 capitalAct-

ivities

‘Natural

capital’ Labor H’holds Gov’tCap. acc.

Rest of world

Total income

Firms I-O accounts

Private cons.

Gov’t cons

InvestmtNet

exportsTotal revenue

‘Natural

capital’Env.

servicesVal. env

damage

LaborWages

Total wages

H’holds 0 (open access)

Wage income

TransfersCapital inflow

H’hold income

Gov’t Indirect taxes

Direct taxes

Gov’t income

Cap. acc Private savings

Gov’t savings

Savings

Rest of world

ImportsReserve accum

Forex outflow

Total expend.

Costs w/o NC

0Labor

incomeH’hold expend.

Gov’t expend.

InvestmtForex 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.

2. In open access forests (non-commercial), opportunity cost of forest is set by ag. land values and clearing costs.

3. In commercial forestry, timber harvesting/replanting also depends on property rights.

• 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.