The general form of an adjustment factor for nonparametric estimates is derived and analyzed. The usefulness of the formula is illustrated by deriving propositions on invariance of the limiting distribution with respect to the nonparametric estimator, conditions for nonparametric estimation to have no effect on the asymptotic distribution, and the form of a correction term for the presence of nonparametric projection and density estimators. Examples discussed are quasi-maximum likelihood estimation of index models, panel probit with semiparametric individual effects, average derivatives, and inverse density weighted least squares. The paper also develops a set of regularity conditions for the validity of the asymptotic variance formula. Specific examples are polynomial estimators of average derivative and semiparametric panel probit models.
Efficiency bounds for some semiparametric selection models.
Journal Of Econometrics. In this paper, we calculate semiparametric efficiency bounds for the regression coefficients in an 'outcome' equation subject to censoring under weak conditions on the form of the selectivity bias. It is assumed that the regression function for the binary selection variable which governs the censoring mechanism is nonparametric, as is the form of the selection correction term in the outcome equation. John Wiley and Sons Ltd. 1991. To explore the application of data envelopment analysis to assessing economic performance.