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Unformatted text preview: Economics 140A Identification in Simultaneous Equation Models Simultaneous Equation Models Our second extension of the classic regression model, to which we devote two lectures, is to a system (or model) of more than one equation. Together, the equations describe the simultaneous evolution of multiple endogenous variables and are termed simultaneous equation models. Up to this point, we have considered structures in which only one variable, the dependent variable, is endogenous. We often think of the regressors as causing the movements in the dependent variable in that the regressors can be condi- tioned upon when studying the dependent variable. In many cases of interest to economists the conditional structure of a single equation breaks down, as two or more quantities are jointly determined. Perhaps the simplest such structure is to consider price and quantity for a speci&c market (e.g. Vans tennis shoes in Santa Barbara). One might think of the following structure P t = & + & 1 Q t + U t ; where P t is the price of a pair of shoes in period- t and Q t is the quantity of shoes sold in the corresponding period. Without question, the price of shoes is a/ected by the quantity available. Surplus inventories are sold at discount and goods in short supply often sell at a premium. Yet, unless the Santa Barbara market forms only a tiny portion of total supply, the price at which the shoes are sold a/ects the quantity. Shoes sold at discount re¡ect excess inventories and indicate that production should fall, the converse holds for shoes sold at a premium. If the regressor is also a function of the dependent variable, it is clear that the regressor is correlated with the error and a classic assumption is violated. To overcome the bias (and inconsistency) of the OLS estimators, one could proceed with IV estimation. Yet not only is an adequate instrument rarely at hand, but often understanding of the economy requires that we more fully investigate the joint determination of the endogenous variables. To do so, it is helpful to distinguish between the theoretical quantities Q D t , which is the quantity of shoes demanded by consumers, and Q S t , which is the quantity of shoes supplied by producers. We think of Q D t as arising from a demand function Q D t = ¡ 1 + ¡ 2 P t + U 1 t ; where we expect & 2 < . We think of Q S t as arising from a supply function Q S t = ¡ 1 + ¡ 2 P t + U 2 t ; where we expect ¡ 2 > . The two quantities are theoretical because they are not separately observed, the equilibrium condition that Q D t = Q S t = Q t ensures that only Q t is observed. It is not possible to estimate the parameters of the demand and supply func- tions by the method of OLS. The reason is that the parameters are not identi&ed....
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This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08