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 useful whenever we wish to estimate the effect of changes in one part of the economy upon the rest.
More recently, CGE has been a popular way to estimate the economic effects of measures to reduce greenhouse gas emissions.
However, most CGE models conform only loosely to the theoretical general equilibrium paradigm.
These variables are termed exogenous; the remainder, determined by the model, is 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 modelers 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.
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.
[7] 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.
More recently, CGE has been a popular way to estimate the economic effects of measures to reduce greenhouse gas emissions.
Here, strong, reasonable, assumptions embedded in the model must replace historical evidence.
[9] CGE models can specify consumer and producer behaviour and ‘simulate’ effects of climate policy on various economic outcomes.
By optimising the prices paid for various outputs the direct burdens are shifted from one taxpayer to another.
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, in particular the reallocation of labor and capital across sectors, usually is not explicitly represented in such a model.
[11] The alternative approach involves explicit modeling of dynamic adjustment paths.
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.
The modeling of the path of adjustment may involve forward-looking expectations,[12] where agents' expectations depend on the future state of the economy and it is necessary to solve for all periods simultaneously, leading to full multi-period dynamic CGE models.
Recursive dynamic models where a single period is solved for, comparative steady-state analysis, is a special case of recursive dynamic modeling over what can be multiple periods.
This not only makes the formulas more concise and clear but also facilitates the use of analytical tools from linear algebra and matrix theory.
The above eigenequations for the square matrix can be extended to the von Neumann general equilibrium model:[13][14]
The structural equilibrium model can be solved using the GE package in R. Below, we illustrate the above structural equilibrium model through a linear programming example,[16] with the following assumptions: (1) There are 3 types of primary factors, with quantities given by
The quantities of the 3 factors required by each of the 3 firms for one day of production are shown in the columns of the following input coefficient matrix:
。 We need to find the optimal numbers of production days for the three firms, which maximize total output.
By solving the above linear programming problem, the optimal numbers of production days for the three firms are found to be 2, 0, and 8, respectively; and the corresponding total output is 280.
Next, we transform this linear programming problem into a general equilibrium problem, with the following assumptions: (1) There are 4 types of goods in the economy (i.e., the product and 3 primary factors) and 4 economic agents (i.e., 3 firms and 1 consumer).
The results obtained by solving this structural equilibrium model are the same as those from the optimization approach:
Now, most CGE models are formulated and solved using one of the GAMS or GEMPACK software systems.