Semiparametric least squares (SLS) and weighted SLS estimation of single-index models

Abstract

For the class of single-index models, I construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1/ v'n-consistency and asymptotic normality. This class of models includes censored and truncated Tobit models, binary choice models, and duration models with unobserved individual heterogeneity and random censoring. I also investigate a weighting scheme that achieves the semi parametric efficiency bound. •1 thank Professors Daniel McFadden and James Powell fovadvice and Professor Charles Manski for encouragement. I have benefited from many comments I received from Professors Jonathan Feinstein, Robert Gertner, Peter Hall, Lung-Fei Lee, Daniel McFadden, and Kazumitsu Nawata. The points lowe to them are indicated in the paper. I also received extensive editorial suggestions from Dr. Steven Herzenberg on a very early version and professional editorial help from Patricia Haswell on this version. I am grateful to all of these individuals. This paper supersedes three earlier papers, "Single Index Models and their Consistent Semi parametric Estimation" (October 1985), "Estimation of Single Index Models" (September 1987) (Ph.D. thesis), and "Semi parametric Least Squares Estimation of Single Index Models" (August 1988).

Counterfactual distributions with sample selection adjustments: Econometric theory and an application to the Netherlands

“…As we do not know the form of this conditional probability, we estimate G(·) using kernel regression. This semi-parametric least squares procedure, as described in Ichimura (1993), gives a consistent estimate of γ. Again, we are following the approach taken in Buchinsky (1998a).…”

Binary response correlated random coefficient panel data models

“…One way to identify the model is transferring the model to a single-index model, which can be estimated nonparametrically. However, the single-index model only admits limited heterogeneity, see Powell, Stock, and Stoker (1989), Ichimura (1993), Klein and Spady (1993), Härdle and Horowitz (1996), Newey and Ruud (2005). Another way of identification is based on the conditional quantile restrictions.…”

Estimation in semiparametric models with missing data

“…See Powell, Stock and Stoker (1989), Ichimura and Lee (1991), Ichimura (1993), Härdle, Hall and Ichimura (1993), among many others for important results on the estimation and inference for this model when all the data are completely observed. We assume here that the response Y is missing at random.…”