Structural and Reduced Forms With An Exogenous Variable
Exogenous variables are variables which are not determined by the system. If we assume that demand is influenced not only by price, but also by an exogenous variable, Z. The structural form becomes:
- supply:
- demand:
In the above set of equations, the choice of the endogenous variables can not be derived from the equations themselves; the modeller might alternatively have chosen for instance Q and Z as endogenous variables, which would make P the exogenous variable.
This structural model can be rewritten in the reduced form:
As before, the four reduced form coefficients can be derived from the five structural form coefficients. Note that both endogenous variables depend on the exogenous variable Z.
By combining the two reduced form equations to eliminate Z, the structural coefficients of the supply side model ( and ) can be derived from the four reduced form coefficients (, and ):
Note however, that this still does not allow us to identify the structural parameters of the demand-side model. For that, we would need an exogenous variable which is included in the supply-side of the structural model, but not on the demand-side.
Read more about this topic: Reduced Form
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