MsM LECTURE SERIESComputable General Equilibrium (CGE) Modelling for Management Decisions
Lecture outline• How can CGE contribute to decision making?• Why general equilibrium?• Why computable general equilibrium?• What does CGE modelling involve? Isn't it difficult?• Tell me more about those data requirements?• How do you solve one of these models?• Aren't these models just black boxes?• OK, what about model validation?• Could you give me that bottom line, again?
HOW CAN CGE CONTRIBUTE TO DECISION MAKING?
Is (CGE) modelling useful?
Part & parcel of a bigger picture
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Macro Environment
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Your Company (Manager)
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(CGE) Modelling for decision support
• All (CGE) models should ultimately be seen as pedagogical devices, their calculations a means to the end of helping managers/decision-makers think through their decisions.
• For this, the (CGE) model used should be:• Transparent: e.g. understand its structure, trace the flow of
expenditures through its equations, etc.;• Easy to tinker with: flexible (yet realistic/real-world and
logical) assumptions; and• It should be clear what is governing its results.
(CGE) Modelling for decision support
• Companies and customers operate in a dynamic environment….• Need to better understand:
• the implications of changes to the operating environment of customers
• in turn implications to operations and revenue implications for your company
• Identified need for a strategic information framework to:• provide a logical, standardised and consistent approach to
inform key questions• provide context around your customers within the internal
company as well as the broader national/macro context• provide enhanced strategic decision making information.
(CGE) Modelling for decision support
• Companies and customers operate in a dynamic environment….• The idea is to understand how the economy links together
(to capture feedback effects) and how these inter-linkages contribute to gains and losses (mainly on an aggregated level) in the broader economy.
• Thus, for a manager, CGE can help you to:• understand the broader economy/environment within which
your company operates; and• understand other aspects of your customers’ business
environments (e.g. impact of changes in the international markets and commodity prices, etc.)
WHY GENERAL EQUILIBRIUM?
General Equilibrium theory• Economic models fall into two broad genres:
• Macroeconomic models: belong mostly in central banks• They capture the economy's ups and downs, providing a
compass for the folks with their hands on the monetary tiller.• CGE models: largely ignore the vagaries of the business
cycle• They concentrate on the underlying structure of production,
shedding light on the long-term repercussions of such things as…• the Doha trade round• a big tax reform• a global financial crisis (recession)• economic integration• issues of North-South or South-South trade• climate change• or energy and environmental policies.
General Equilibrium theory• Both kinds of models share a debt to Leon Walras.• Walras was adamant that one could not explain anything in an economy until one had explained everything.
• Each market—for goods, labour and capital—was connected to every other, however remotely.• This interdependence is apparent whenever faster car
sales in Texas result in an increase in grocery shopping in Detroit, the home of America's “big three” carmakers.
• Or when steep prices for oil lead, curiously enough, to lower US interest rates, because the money the Saudi Arabians and the Russians make from crude is spent on US Treasury bonds.
General Equilibrium theory• This fundamental insight moved one economist to quote the poetry of Francis Thompson:• “Thou canst not stir a flower/Without troubling of a star.”
• Such thinking comes naturally to economists, but escapes many politicians, who blindly uproot flowers, ignorant of the celestial commotion that may ensue.• They slap tariffs on steel imports, for example, to save jobs
in one area, only to find this costs more jobs in the domestic industries that use the metal.
• GE models can help decision-makers think twice about the knock-on effects of their decisions.
General Equilibrium theory• Wassily Leontief was one of the first to do more than just theorise about this web of interdependence.
• In 1941 he published his book “The Structure of American Economy”.• It contained an input-output model showing the flow of
commodities and services back and forth among America's households, trading partners and 41 national industries.
• In Leontief's blueprint, each industry is represented by an equation.• The inputs to the industry are entered on one side of the
equation, and the industry's output appears on the other.• Since the output of one industry (e.g. steel) serves as an input
for another (construction), one cannot solve any equation without solving them all simultaneously.
Why general equilibrium?• GE refers to a state where the needs of all participants in an economy are satisfied.• This implies that there exists no excess of demand for, or
supply of, any goods or services traded in this economy.
• GE models provide a comprehensive and detailed description of an economy…• that is based on microeconomic foundations; and• is consistent with key macroeconomic balances and
principles.
WHY COMPUTABLE GENERAL EQUILIBRIUM?
Why CGE?• Two reasons why using CGE models makes sense:
• First, while qualitative results are nice, we typically want to know whether a particular change/shock mattered a lot or a little.
• Second, solid microfoundations enhance managers' ability to understand the behaviour of consumers, producers and the government in an economy.
• The aim of CGE modelling is to convert the abstract representation of an economy into realistic, solvable models of actual economies.
Strengths of CGE approach• Theoretical consistency.
• Comparative statics and counterfactual simulations.
• Accounting consistency.• Closed system with no leak.
• Capture both direct and indirect inter-sectoral, inter-regional, and inter-temporal effects.
• Clear microeconomic structure with links between micro and macro aspect.
• It can provide managers with a base for dialogue.
• Distributional aspects• ‘everything depends on
everything else’• Ability to disaggregate
sectors of interest.• Facility to evaluating second
best situations.• Improving confidence in
simulation results.• Sensitivity analyses: within
and across models.• Ex-post verifications.• Use also focused models.
• Simplicity of functional forms• Parameterisation and calibration• Equilibrium is a strong assumption• Possibility of multiple equilibria• Confidence intervals cannot easily be derived• Results can often be a black box to non-specialists• Very intensive in terms of time and data• Not strong on analysing monetary phenomena• Micro behaviour limited
Weaknesses of CGE approach
WHAT DOES CGE MODELLING INVOLVE? ISN'T IT DIFFICULT?
What does CGE modelling involve?
• A lot of people seem to think that CGE modelling is difficult: nonsense.
• Take a very simple partial equilibrium question:• How will consumption change when prices rise?
• To answer this question, we need four things.• First, some theory, such as a demand curve.• Second, calibration: the original point on this demand
curve.• Third, an estimate of the size of the shock; and• Fourth, the elasticity of demand.
What does CGE modelling involve?
• These same four elements are all you need to perform a CGE exercise:• The theory can be whatever you want; but Walrasian
theory can be easily summarised…• for every sector, price equals cost; for every commodity,
demand equals supply; for every household, income equals expenditure.
• Calibration involves putting a number on every input, output, consumer demand, trade flow, and factor endowment and all these flows have to be compatible with each other.
• Next is measuring the exogenous shocks.• Finally, picking elasticities of substitution in the production
and utility functions.
Steps in CGE modelling
Comparative Static analysis• CGE models are used mainly
for comparative static analysis (SCA).
• This form of analysis involves comparing equilibrium positions as opposed to examining the path that the market follows when moving from the old to the new equilibrium.
• Results of comparative-static CGE’s all refer implicitly to the economy at some future time period.
Employment
0 T
Change
A
years
B
C
Dynamic modelling• The example can be viewed as
analogous to CSA example with the exception that the path through time is included.
• The advantages of this technique is:• Although, the net effect is still
positive, (higher growth than in the base case) the growth remains negative. This cannot be deduced from the CSA;
• The adjustment that is required is not positive relative to the base case in all the years under review. Another position that cannot be deduced from the CSA.
1996 1997 1998 1999 2000 2001 2002
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Change
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Employment
The concept of equilibrium• An individual market is in equilibrium when the quantity demanded is equal to the quantity supplied.
• But that is static, partial equilibrium analysis.• General equilibrium analysis deals with the inter-relationships between different markets and different sectors in the economy.
• The simplest model of the economy can be represented as the circular flow of economic activity.
The circular flow model
If there are m commodity markets and n factor markets there will be altogether m+n markets and m+n equilibrium prices to be determined.
Setting up a model• What are models?• The equations of a model are statements of the functional relationships between economic variables.
• Generally: QD = QD(P) dQ/dP < 0QS = QS(P) dQ/dP > 0QD = QS
• There are two behavioural equations on describing the equilibrium condition for the market.
• Adding constant terms...• Endogenous and exogenous variables…
A two sector model• Assume:
• Two goods,• Each produced by one of two firms,• Using two factors of production, capital and labour,• And the factor endowments are fixed,• And the factors are owned by one representative
household.
• A general equilibrium model of this economy should specify:• Demand and supply relations.• The equilibrium condition for each market.• A specification of the income constraint of each of the
economic agents in the economy.
The demand relations• The consumer is assumed to maximise utility subject to a budget constraint.Maximise U = U(C1,C2)
subject to P1C1 + P2C2 = Y
• From the solution it is possible to derive the demand relations: C1 = C1(P1,P2,Y)
C2 = C2(P1,P2,Y)
C1
C2
U3
The supply relations• The derivation of the supply relations takes place in two steps:• Determining the cost-minimising quantities of the factors
of production required to produce a given level of output.• Determining the profit-maximising level of output.
• Cost-minimising production:• Certain combinations of capital (K) and labour (L) are
required to produce a given level of output.• The relationship between inputs and outputs is given by
the production function Xi = Xi(Ki,Li)
• The cost of production is determined by the price of capital (r) and the price of labour (l).
The supply relations• Cost-minimising production:
• The least-cost combination of factors is the solution to the cost-minimisation problem:Minimise TCi = rKi + wLi
subject to Xio = Xio(Ki,Li)
• Where TCi represents the total costs of firm i,
• And Xio is the desired level of output.
XioKi
Li
The supply relations• Profit-maximising output:
• Each firm is assumed to maximise profits – the difference between total revenue and total cost.
• Xio is the profit-maximising level of output determined for firm i by the price at which it sells its product Pi and by the costs of production.
• The general form of the supply functions is described by the equations X1 = X1(P1,w,r)
X2 = X2(P2,w,r)
Equilibrium• Equilibrium in the product markets:
• The demand relations C1 = C1(P1,P2,Y)
C2 = C2(P1,P2,Y)
• The supply relations X1 = X1(P1,w,r)
X2 = X2(P2,w,r)• The market clearing equations C1 = X1
C2 = X2
• Equilibrium in the factor markets:• The functions that relate the demand for factors by each
firm to the chosen level of output Xi, and the factor prices r and w, are:K1 = K1(X1,w,r) L1 = L1(X1,w,r)
K2 = K2(X2,w,r) L2 = L2(X2,w,r)
Equilibrium• Equilibrium in the factor markets:
• The functions that relate the demand for factors by each firm to the chosen level of output Xi, and the factor prices r and w, are:K1 = K1(X1,w,r) L1 = L1(X1,w,r)
K2 = K2(X2,w,r) L2 = L2(X2,w,r)
• In the simple model it is assumed that the total quantities of capital and labour are fixed exogenously at K* and L*.
• Thus, the factor market clearing equations take the form:K1 + K2 = K* L1 + L2 = L*
• Finally there are the income equations of the firms and households.
Equilibrium• The income equations of the firms and households:
• Each firm makes profits equal to the difference between its total revenue from the sale of its products and its expenditure on factor inputs:Π1 = P1X1 – wL1 – rK1 Π2 = P2X2 – wL2 – rK2
• The household supplies the factor services and also receives the profits of the two firms:
Y = w(L1 + L2) + r(K1 + K2) + Π1 + Π2
• Thus, the general equilibrium system is complete with 15 endogenous variables and 2 exogenous variables.
The need for a numeraire• Example of ‘homogeneity of degree zero’…• In the model it is not possible to determine the absolute price level, but only relative prices.
• To find the equilibrium prices the answer is to set one price equal to one and then solve the system for all other (relative) prices.
• The good with price set equal to unity is known as the numeraire commodity.
• Choosing the numeraire is known as the ‘normalisation’ procedure.
Walras’ Law• Walras’s Law states that for a given set of prices, the sum of the excess demand over all markets must be equal to zero.
• Thus,• if all markets but one are in equilibrium, • then the last market is in equilibrium as well.
Complicating it• The basic two-sector model can be solved numerically.
• To the basic structure one can add:• More sectors.• More factors.• More households.• Macro relations.
• The functions were kept general but one has to consider functional forms of for example the demand functions: Cobb-Douglas, LES, CES…
• Parameters have to be estimated…• Choice of exogenous and endogenous variables…
Closing the model• In the end, CGE models typically have more variables than equations:• Endogenous variables are explained by the model.• Exogenous variables have to be set by the user.
• The closure is about the choice of exogenous variables.
• The choice of closure affects the length of run, T. In the short-run it is assumed that:• T is long enough for price changes to be transmitted throughout
the economy, and for price-induced substitution to take place.• T is not long enough for investment decisions to greatly affect the
useful size of sectoral capital stocks.• This T might be 2 years.
Closing the model
Private Consumption
InvestmentGovernment Consumption
Real Wage
Capital StocksTech Change
Rate of return on
capital
Trade balance
Employment
GDP= +++
EndogenousExogenous
SHOCK
• Causation in short-run closure
Closing the model• A possible long-run closure would:
• Let capital stocks adjust to maintain fixed rates of return.• While aggregate employment is fixed and the real wage
adjusts.
• Note:• Many closures might be used for different purposes.• There is no unique natural or correct closure.• There must be at least one exogenous variable measured
in local currency units.• Normally just one price is called the numeraire – often it is
the exchange rate.• Some quantity variables must also be exogenous, such as
primary factor endowments and final aggregate demands.
Closing the model• The closure leads to three macro “don’t knows”:
• Absolute price level: Numeraire choice determines whether changes in the real exchange rate appear as changes in domestic prices, or as changes in the exchange rate. Real variables unaffected.
• Labour supply: Closure determines whether labour market changes appear as changes in either wage or employment.
• Size and composition of domestic absorption: Either exogenous or else adjusting to accommodate a fixed trade balance. Closure determines how changes in national income appear.
TELL ME MORE ABOUT THOSE DATA REQUIREMENTS?
Data requirements• Data requirements for CGE modelling are enormous.
• True, but think of the alternatives.• If you are prepared to calibrate a model, rather than
estimate it econometrically, then all you need is lots of data for one benchmark period: a census year, for example.
• Calibrating theoretical equations to data for one year can be a lot easier than gathering lots of time series data, and estimating structural or reduced form equations.• For example, you avoid the econometric problems
associated with time series data;• not to mention changes in the way statistics were collected
over time.
Data requirements• The main source of data for a CGE model is a social accounting matrix (SAM).
• Since a SAM represents the circular flow of income in an economy, it is considered to be a natural candidate for a CGE to be based upon.
• A SAM, coupled with a conceptual framework that contains the behavioural and technical relationships among variables within and among sets of accounts, can be used for the evaluation of the economy-wide effects of exogenous changes.• The conceptual framework is supplied in the form of a CGE
model.
Broad overview of a CGE modelMac
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theo
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Micro Econom
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theory
Exte
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Behavioural & technical relationships
Prices (e.g. inflation, exchange rate
wage rates etc.)
Marke
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Basic
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Demand
Income
Production
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Core Input-Output framework
Industry
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Social accounting matrix (SAM)
Households
Income by income groups
Employment Supply of labour
Other
Other
Exp
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GovernmentImportsExports etc.
HOW DO YOU SOLVE ONE OF THESE MODELS?
How do you solve CGE models?• A CGE model is just a system of simultaneous equations.
• Specifying those equations is straightforward, at least if you stick to Walrasian (or almost Walrasian) models.
• Now you have to solve them.• Simultaneous non-linear equation solvers like GAMS, GEMPACK and GAUSS can handle any size shocks.
• To solve a model, you just need to specify it, and come up with the numbers.• This leaves the modeller free to focus on data issues, and
economic intuition.
Two approaches to CGE modelling
Aus./ORANI-style GEMPACK
• Uses percentage change equations
• Has a big, detailed database • Has industry-specific fixed factors
of production • Has a short-run focus (2 years) • Contains many prices • Shows the winners and losers of
economic shocks or policy interventions
• Has more exogenous variables – missing macro relations
• Has a variety of different “closures”
• Uses an input-output database augmented to a SAM
US/GAMS-style
• Uses levels equations• Uses less detailed data • Has mobile capital and labour• Has a medium- to long-run focus
(7-20 years) • Has few prices • Shows the national welfare
implications of economic shocks or policy interventions
• Is a closed model with labour supply, income-expenditure links
• Has one main closure • Uses a SAM database
AREN'T THESE MODELS JUST BLACK BOXES?
Aren't these models just black boxes?
• Not if they're constructed and presented properly.• Remember, the (CGE) model used should be:
• Transparent: e.g. understand its structure, trace the flow of expenditures through its behavioural equations, etc.;
• Easy to tinker with: flexible (yet realistic/real-world and logical) assumptions; and
• It should be clear what is governing its results.
• This will ensure that your reasoning and results are clear and concise.
• CGE's are "theory with numbers" – thus strong theoretical underpinning.
OK, WHAT ABOUT MODEL VALIDATION?
What about model validation?• Does the model explain anything we observe today or in the recent past (VALIDATION)?
• Clearly finding better and more systematic ways of subjecting your results to sensitivity analysis is a major challenge for CGE modellers.
• Equally important is finding a way to present the results of such analyses concisely.
• One important contribution of CGE modelling can be to bring out clearly the contingent nature of a lot of our knowledge.
• Solidly grounded uncertainty can be preferable to ignorant certainty.
COULD YOU GIVE ME THAT BOTTOM LINE, AGAIN?
A final word…• All (CGE) models are ultimately pedagogical devices...
• They can't provide all of the answers, but they do provide a good start…• Managers can understand the broader economic
environment in which they (and their customers) operate;• Management is still in a position to inform decisions based
on broad assumptions;• As key parameters change “fresh” analysis is possible at
much reduced effort and time requirements;• “Scenario” analysis can be conducted to inform
management decisions; and• A logical, standardised and consistent (and repeatable)
approach to inform relevant key questions is provided.
Q & A