Estimation of average treatment effect based on a semiparametric propensity score

Abstract

This paper considers the estimation of average treatment effect using propensity score method. We propose to use a semiparametric single-index model to estimate the propensity score. This avoids the curse of dimensionality problem with the nonparametric method based propensity score estimator. We establish the asymptotic distribution of the average treatment effect estimator. Monte Carlo simulation results show that the proposed method works well in finite samples and outperforms the conventional nonparametric kernel approach. We apply the proposed method to an empirical data examining the efficacy of right heart catheterization on medical outcomes.

Keywords:

• Average treatment effect
• propensity scores
• single-index method

JEL CLASSIFICATION:

• C13
• C14

Notes

1 Since in this paper we only focus on the case that the single-index function can be $\sqrt{n}$-consistently estimated, our regularity conditions are weaker than those given in Song (2014). We thank an anonymous referee for bringing Song (2014) to our attention.

2 Note that $E(v_i|x_i^{\prime }\gamma )=0$ by construction. It is easy to check that ${\widehat{t}}_i={\widehat{\mu }}_i+{\widehat{v}}_i.$ Also note that ${\widehat{t}}_i$ is a feasible estimator of ${\mu }_i=E(t_i|x_i^{\prime }\gamma ),$ while ${\widehat{\mu }}_i$ is an infeasible estimator of μ_i (as it involves ${\left\{{\mu }_j\right\}}_{j\ne i}^n$ which is unknown).

3 We are grateful to a referee for pointing this out to us.

4 For detailed definitions of the first 6 covariates, see Li et al. (2009).

5 We use the standard resampling bootstrap method.

6 We also tried $\alpha =1/15$ and 1/20, the results are similar and we omit them here to save space.