Efficient Semiparametric Estimation of Duration Models With Unobserved Heterogeneity

Abstract

This paper develops a new semiparametric approach for the estimation of hazard functions in the presence of unobserved heterogeneity+ The hazard function is specified parametrically, whereas the distribution of the unobserved heterogeneity is indirectly estimated using the method of kernels+ The semiparametric efficiency bounds are derived+ The estimator obtains these bounds in large samples+ The authors thank

Smoothed Maximum Score Estimation of Discrete Duration Models

“…We note first that semiparametric estimation of continuous-time models has been the focus of substantial research in the discipline. Numerous authors have developed distribution theory for semiparametric estimation of various continuous-time duration models including Horowitz (1999), Nielsen et al (1998), Van der Vaart (1996) and Bearse et al (2007). While these and other semiparametric estimators allow for the relaxation of some parametric assumptions associated with continuous-time duration models, they are not generally appropriate when the duration random variable has a discrete distribution.…”

Higher order bias reduction of kernel density and density derivative estimation at boundary points

“…However the usual kernel density estimator of f (1) (y) is biased in the same manner that f is. In fact the second order bias of f (1) depends on f, f (1) and f (2) . More generally, it can be shown that the bias of, say, f (j) , j ≤ s depends on f, f (1) , .…”

“…Also, in some semiparametric problems, the kernel estimator of the nonparametric component of a model is assumed to have the higher order bias removed. For example, this is the case in Klein and Spady (1993) and Bearse, Canals and Rilstone (2007). In many instances, such as with duration models, boundary problems are the norm rather than the exception.…”

“…where K has support [−1, 1]. Let g (s) denote the s-order derivative of a function g. Put g |m| = (g, g (1) , g (2) , . .…”

Semiparametric competing risks analysis

“…In addition, because of non‐linearities and censoring, a misspecification of the distribution of the unobserved heterogeneity leads to inconsistent estimates (Flinn and Heckman 1982a; Heckman and Singer 1984; Gallant and Nychka 1987). These considerations have led to the development of estimation methods that do not require parametric specification of the distribution of unobserved heterogeneity (Heckman and Singer 1984; Bearse, Canals and Rilstone 2007). Horowitz (1996) and Chen (2002) consider more general semi‐parametric methods.…”