## AiU2t pUt wt 1927

Incidentally, note that the error terms vt and wt are linear combinations of the original error terms U1 and U2.

Equations (19.2.2) and (19.2.5) are reduced-form equations. Now our demand-and-supply model contains four structural coefficients a0, a1, Po, and p1, but there is no unique way of estimating them. Why? The answer lies in the two reduced-form coefficients given in (19.2.3) and (19.2.6). These reduced-form coefficients contain all four structural parameters, but there is no way in which the four structural unknowns can be estimated from only two reduced-form coefficients. Recall from high school algebra that to estimate four unknowns we must have four (independent) equations, and, in general, to estimate k unknowns we must have k (independent) equations. Incidentally, if we run the reduced-form regression (19.2.2) and (19.2.5), we will see that there are no explanatory variables, only the constants, and these constants will simply give the mean values of P and Q (why?).

What all this means is that, given time series data on P (price) and Q (quantity) and no other information, there is no way the researcher can guarantee whether he or she is estimating the demand function or the supply function. That is, a given Pt and Qt represent simply the point of intersection of the appropriate demand-and-supply curves because of the equilibrium condition that demand is equal to supply. To see this clearly, consider the scattergram shown in Figure 19.1.

Figure 19.1a gives a few scatterpoints relating Q to P. Each scatterpoint represents the intersection of a demand and a supply curve, as shown in Figure 19.1&. Now consider a single point, such as that shown in Figure 19.1c. There is no way we can be sure which demand-and-supply curve of a whole family of curves shown in that panel generated that point. Clearly, some additional information about the nature of the demand-and-supply curves is needed. For example, if the demand curve shifts over time because of change in income, tastes, etc., but the supply curve remains relatively stable, as in Figure 19.1d, the scatterpoints trace out a supply curve. In this situation, we say that the supply curve is identified. By the same token, if the supply curve shifts over time because of changes in weather conditions (in the case of agricultural commodities) or other extraneous factors but the demand curve remains relatively stable, as in Figure 19.1e the scatterpoints trace out a demand curve. In this case, we say that the demand curve is identified.

Gujarati: Basic I IV. Simultaneous-Equation I 19. The Identification I I © The McGraw-Hill

Econometrics, Fourth Models Problem Companies, 2004

Edition

CHAPTER NINETEEN: THE IDENTIFICATION PROBLEM 741

Quantity (a) 