Sample selection models are important for correcting for the effects of nonrandom sampling in microeconomic data. This note is about semiparametric estimation using a series approximation to the selection correction term. Regression spline and power series approximations are considered. Consistency and asymptotic normality are shown, as well as consistency of an asymptotic variance estimator.
We consider the estimation of sample selection (type II Tobit) models that exhibit spatial error dependence or spatial autoregressive errors (SAE). The method considered is motivated by a two-step strategy analogous to the popular heckit model. The first step of estimation is based on a spatial probit model following a methodology proposed by Pinkse and Slade (1998) that yields consistent estimates. The consistent estimates of the selection equation are used to estimate the inverse Mills ratio (IMR) to be included as a regressor in the estimation of the outcome equation (second step). Since the appropriate IMR turns out to depend on a parameter from the second step under SAE we propose to estimate the two steps jointly within a generalized method of moments (GMM) framework. We explore the finate sample properties of the proposed estimator using a Monte Carlo experiment; discuss the importance of the spatial sample selection model in applied work, and illustrate the application of our method by estimating the spatial production within a fishery with data that is censored for reasons of confidentiality.
Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Many relationships in economics, and also in other fields, are both dynamic and nonlinear. A major advance in econometrics over the last fifteen years has been the development of a theory of estimation and inference for dy namic nonlinear models. This advance was accompanied by improvements in computer technology that facilitate the practical implementation of such estimation methods. In two articles in Econometric Reviews, i.e., Pötscher and Prucha {1991a,b), we provided -an expository discussion of the basic structure of the asymptotic theory of M-estimators in dynamic nonlinear models and a review of the literature up to the beginning of this decade. Among others, the class of M-estimators contains least mean distance estimators (includ ing maximum likelihood estimators) and generalized method of moment estimators. The present book expands and revises the discussion in those articles. It is geared towards the professional econometrician or statistician. Besides reviewing the literature we also presented in the above men tioned articles a number of then new results. One example is a consis tency result for the case where the identifiable uniqueness condition fails.
