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
Famous quotes containing the words structural, reduced, forms and/or variable:
“The reader uses his eyes as well as or instead of his ears and is in every way encouraged to take a more abstract view of the language he sees. The written or printed sentence lends itself to structural analysis as the spoken does not because the reader’s eye can play back and forth over the words, giving him time to divide the sentence into visually appreciated parts and to reflect on the grammatical function.”
—J. David Bolter (b. 1951)
“Narrowed-down by her early editors and anthologists, reduced to quaintness or spinsterish oddity by many of her commentators, sentimentalized, fallen-in-love with like some gnomic Garbo, still unread in the breadth and depth of her full range of work, she was, and is, a wonder to me when I try to imagine myself into that mind.”
—Adrienne Rich (b. 1929)
“I have always thought that one man of tolerable abilities may work great changes, and accomplish great affairs among mankind, if he first forms a good plan, and, cutting off all amusements or other employments that would divert his attention, make the execution of that same plan his sole study and business.”
—Benjamin Franklin (1706–1790)
“Walked forth to ease my pain
Along the shore of silver streaming Thames,
Whose rutty bank, the which his river hems,
Was painted all with variable flowers,”
—Edmund Spenser (1552?–1599)