Core Concept: Variables and Parameters (6 minute read)

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Learning Outcome:

At the end of this lesson, you will be able to define and explain variables, parameters, and the difference between them.

Key Points
Endogenous variable Its value is determined as the solution to a model equation, may be redefined as exogenous.
Exogenous variable Its value is fixed at its initial value, may be redefined as endogenous.
Parameter Its value is fixed at its initial value.

Endogenous and Exogenous Variables

CGE models have both variables and parameters...what is the difference between them?  In short, variables may vary, while parameters do not.

The value of an endogenous variable is determined as the solution to a model equation. For example, assume that a model equation defines the quantity of demand for peaches as a function of the price of peaches and income.  If income changes following an experiment, the quantity of peaches demanded will also change. The quantity of peaches is an endogenous variable.

The value of an exogenous variable is fixed at its initial level.  A tax rate, for example, is often an exogenous variable in CGE models. The tax rate remains fixed, even when prices or quantities of the taxed good change.

"Swapping" Endogenous and Exogenous Variables

Endogenous variables can be redefined to be exogenous and exogenous variables can be redefined to be endogenous. The modeler's decision about which variables are endogenous or exogenous is called "model closure."

Model closure decisions allow the modeler to adapt the model to provide realistic depictions of an economy.  For example, many CGE models include the assumption that a country's labor supply is fixed at its initial level - the supply is a fixed, exogenous variable. Wages are endogenous, and will adjust to equilibrate the labor supply and the demand for labor by production activities. But if a country has a pool of unemployed workers, its labor market may be represented more accurately by "swapping" an exogenous labor supply with the endogenous wage. This swap fixes the wage and allows the labor supply to expand if the demand for workers increases. (Conversely, the labor supply will contract if labor demand falls.)

Keeping the Model Square

Models must be "square."  This means they must have the same number of variables as equations.  When the modeler changes a closure they must be sure the model remains square. If they choose to make one or more exogenous variables endogenous they must now make the same number of endogenous variables exogenous.

Parameters

Parameters have fixed values that do not change when the model is shocked.  CGE models have two main types of parameters:

• elasticities of supply and demand
• shift and share coefficients used in the supply and demand equations.

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