LOCAL ASYMPTOTIC SPECIFICATION ERROR ANALYSIS

摘要: An approximation to the inconsistency introduced by imposing an incorrect restriction on a parametric model is given. The can be applied estimators generated optimizing any objective function satisfying certain regularity conditions. Examples given include analysis of misspecification in discrete choice and time-series models estimated maximum likelihood, nonlinear regression model. SPECIFICATION ERROR ANALYSIS linear has been studied Theil [1], who gives formulas for, e.g., effect leaving out relevant variables expected values coefficients included variables. In this paper we suggest analogous for obtained subject restrictions. We have mind maximizing (1/n) x loglikelihood will usually use terminology. consider limit restricted estimator small violation case our formula coincides with that Theil. order keep results widely applicable avoid mass unnecessary detail make assumptions asymptotic behavior itself, rather than data-generating process per se. Many alternative sets data densities lead require functions. These not pursued here. interested reader referred to, White [12] independent observations Kohn [8] case. 1. GENERAL FORMULAS general approach take based likelihood at estimator. It sense local. For some local global specification error coincide; well known omitted regressors Essentially only cases involve linearity, although often there agreement regarding signs inconsistency. show below even fail coincide misspecified AR processes. Generally however, are unknown.2 Taylor expansions typically used together generating obtain distribution (Cramer [3]). concern ourselves distributions Vn -normed MLE's since these worked