Parameter Identification

Abstract

A parameter is identified when it is uniquely determined by the joint distribution of the observable data given the model's assumptions. Identification is logically prior to estimation and asks a different question: not what the best guess from this sample is, but whether the entire population would pin the parameter down at all. Where it fails, no estimator, no larger sample of the same kind, and no model refinement repairs it. This entry develops identification through a restriction of the Pacifica dataset to the ten properties on one pattern, in a submarket where every excellent house (condition score 9.00) was remodeled and no good one (7.00) was. Within that subsample the recorded condition and the remodel indicator are an exact identity, the design matrix is rank deficient, and least squares must drop one column; the two possible drops are shown side by side, and what does not depend on the drop is the price difference between an excellent, remodeled house and a good one that was not remodeled, $100,000, which the sales determine to the dollar and cannot divide between the recorded condition and whatever the remodel brought that the other features do not record. GLA, lot, and view are recovered at their generating values throughout, showing that identification is parameter-by-parameter and that failure is invisible in the coefficients that succeed. Restoring the three average homes identifies the split only under a linearity assumption, resting on three sales --- the near case the entry calls dangerous; restoring the houses that separate the two columns directly identifies it from the sales alone. The entry separates bracketing's two questions, contrast and support, distinguishes a composite time adjustment --- an omitted-variable case in the sense of entry 008 (Omitted Variable Bias) --- from an unidentified one, reads USPAP's demand for supporting market data as making the identification question obligatory rather than restating it, and contrasts the case with entry 008: there the needed information was present and unused, here it is absent, and the remedy is design rather than computation.