Computable general equilibrium
Computable general equilibrium (CGE) models are a class of economic models that use actual economic data to estimate how an economy might react to changes in policy, technology or other external factors. CGE models are also referred to as AGE (applied general equilibrium) models.
A CGE model consists of (a) equations describing model variables and (b) a database (usually very detailed) consistent with the model equations. The equations tend to be neo-classical in spirit, often assuming cost-minimizing behaviour by producers, average-cost pricing, and household demands based on optimizing behaviour. However, most CGE models conform only loosely to the theoretical general equilibrium paradigm. For example, they may allow for:
- non-market clearing, especially for labour (unemployment) or for commodities (inventories)
- imperfect competition (e.g., monopoly pricing)
- demands not influenced by price (e.g., government demands)
- a range of taxes
- externalities, such as pollution
A CGE model database consists of:
- tables of transaction values, showing, for example, the value of coal used by the iron industry. Usually the database is presented as an input-output table or as a social accounting matrix. In either case, it covers the whole economy of a country (or even the whole world), and distinguishes a number of sectors, commodities, primary factors and perhaps types of household.
- elasticities: dimensionless parameters that capture behavioural response. For example, export demand elasticities specify by how much export volumes might fall if export prices went up. Other elasticities may belong to the Constant Elasticity of Substitution class. Amongst these are Armington elasticities, which show whether products of different countries are close substitutes, and elasticities measuring how easily inputs to production may be substituted for one another. Expenditure elasticities show how household demands respond to income changes.
CGE models are descended from the input-output models pioneered by Wassily Leontief, but assign a more important role to prices. Thus, where Leontief assumed that, say, a fixed amount of labour was required to produce a ton of iron, a CGE model would normally allow wage levels to (negatively) affect labour demands.
CGE models derive too from the models for planning the economies of poorer countries constructed (usually by a foreign expert) from 1960 onwards. Compared to the Leontief model, development planning models focused more on constraints or shortages—of skilled labour, capital, or foreign exchange.
CGE modelling of richer economies descends from Leif Johansen's 1960 MSG model of Norway, and the static model developed by the Cambridge Growth Project in the UK. Both models were pragmatic in flavour, and traced variables through time. The Australian MONASH model is a modern representative of this class. Perhaps the first CGE model similar to those of today was that of Taylor and Black (1974). 
CGE models are useful whenever we wish to estimate the effect of changes in one part of the economy upon the rest. For example, a tax on flour might affect bread prices, the CPI, and hence perhaps wages and employment. They have been used widely to analyse trade policy. More recently, CGE has been a popular way to estimate the economic effects of measures to reduce greenhouse gas emissions.
CGE models always contain more variables than equations—so some variables must be set outside the model. These variables are termed exogenous; the remainder, determined by the model, are called endogenous. The choice of which variables are to be exogenous is called the model closure, and may give rise to controversy. For example, some modellers hold employment and the trade balance fixed; others allow these to vary. Variables defining technology, consumer tastes, and government instruments (such as tax rates) are usually exogenous.
CGE models are useful to model the economies of countries for which time series data are scarce or not relevant (perhaps because of disturbances such as regime changes). Here, strong, reasonable, assumptions embedded in the model must replace historical evidence. Thus developing economies are often analysed using CGE models, such as those based on the IFPRI template model.
Comparative-static and dynamic CGE models
Many CGE models are comparative-static: they model the reactions of the economy at only one point in time. For policy analysis, results from such a model are often interpreted as showing the reaction of the economy in some future period to one or a few external shocks or policy changes. That is, the results show the difference (usually reported in percent change form) between two alternative future states (with and without the policy shock). The process of adjustment to the new equilibrium is not explicitly represented in such a model, although details of the closure (for example, whether capital stocks are allowed to adjust) lead modellers to distinguish between short-run and long-run equilibria.
By contrast, dynamic CGE models explicitly trace each variable through time—often at annual intervals. These models are more realistic, but more challenging to construct and solve—they require for instance that future changes are predicted for all exogenous variables, not just those affected by a possible policy change. The dynamic elements may arise from partial adjustment processes or from stock/flow accumulation relations: between capital stocks and investment, and between foreign debt and trade deficits. However there is a potential consistency problem because the variables that change from one equilibrium solution to the next are not necessarily consistent with each other during the period of change.
Recursive-dynamic CGE models are those that can be solved sequentially (one period at a time). They assume that behaviour depends only on current and past states of the economy. Alternatively, if agents' expectations depend on the future state of the economy, it becomes necessary to solve for all periods simultaneously, leading to full multi-period dynamic CGE models. Within the latter group dynamic stochastic general equilibrium models explicitly incorporate uncertainty about the future.
Early CGE models were often solved by a program custom-written for that particular model. Models were expensive to construct, and sometimes appeared as a 'black box' to outsiders. Today most CGE models are formulated and solved using one of the GAMS or GEMPACK software systems. AMPL, Excel and MATLAB are also used. Use of such systems has lowered the cost of entry to CGE modelling; allowed model simulations to be independently replicated; and increased the transparency of the models.
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