742 PART FOUR: SIMULTANEOUS-EQUATION MODELS
The "bogus," or "mongrel," equation (19.2.10) is observationally indistinguishable from either (18.2.1) or (18.2.2) because they involve the regression of Q and P. Therefore, if we have time series data on P and Q only, any of (18.2.1), (18.2.2), or (19.2.10) may be compatible with the same data. In other words, the same data may be compatible with the "hypothesis" (18.2.1), (18.2.2), or (19.2.10), and there is no way we can tell which one of these hypotheses we are testing.
For an equation to be identified, that is, for its parameters to be estimated, it must be shown that the given set of data will not produce a structural equation that looks similar in appearance to the one in which we are interested. If we set out to estimate the demand function, we must show that the given data are not consistent with the supply function or some mongrel equation.
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