Parameter Identification

Abstract

A parameter is identified when it is uniquely determined by the distribution of 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, sample size, or 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 condition-3 was remodeled and no condition-2 was --- a common market pattern rather than a contrived one. Within that subsample the renovation coefficient is not merely imprecise but absent: the design matrix is rank deficient and least squares reports no value, while the condition coefficient returns exactly $100,000, the sum of the two effects and the only form in which the two effects are determined. Lot, GLA, 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. The entry recasts the bracketing requirement as an identification requirement, treats USPAP's demand for adequate supporting market data as a demand that adjustments be identified by the data relied upon, 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.