# Semiparametric Estimation of Optimal Treatment Choices

Chapter
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 524)

## Abstract

In this chapter semiparametric estimation of the conditional expected potential outcomes E[Y r |X] is considered, which are the central ingredients to the derivation of optimal treatment choices, as discussed in Section 2.2. The previous chapter has shown that nonparametric regression, particularly SG matching, is suited for estimating average treatment effects in small samples or for small subpopulations. However the task of estimating treatment effects on an individual level is even more demanding, since the characteristics vector X usually must contain many covariates to identify the outcomes E[Y r |X] by the conditional independence assumption (2.4). Fully nonparametric estimation of E[Y r |X] might then be very imprecise. As an alternative, a semiparametric approach is developed in this chapter, which combines nonparametric SG matching on a subpopulation level with parametric specifications.

## Keywords

Parametric Estimator Vocational Rehabilitation Optimal Programme Medical Rehabilitation Lagrange Multiplier Test
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## Notes

1. 4.
Empirical Likelihood was introduced by Owen (1988) and Qin and Lawless (1994), empirical tilting by Imbens, Spady, and Johnson (1998). The approach used here follows Brown, Newey, and May (2001) and treats the coefficients θ as given and maximises with respect to πi.Google Scholar
2. 5.
In this case, refinements could be obtained by using bootstrap versions of these tests as discussed in Brown and Newey (2002) and Hall and Horowitz (1996).Google Scholar
3. 6.
The same variables are also used for the mean potential outcomes in Table 4.6. Some variables that were included in Frölich, Heshmati, and Lechner (2000b) are left out here since they caused a singularity problem in the bootstrap simulation described below. These are: widowed, county Halland, county Göteborg (county Värmland included instead), indications of alcohol abuse, disability pension recommended by case worker, rehabilitation prevented by other factors, physician and case worker recommended a wait&see strategy.Google Scholar