Estimating Heterogeneous Treatment Effects with Observational Data

Heterogeneous treatment effects are widely recognized but seldom studied empirically in quantitative sociological research. We suspect that lack of accessible statistical methods is one reason why heterogeneous treatment effects are not routinely assessed and reported. In this paper, we discuss a practical approach to studying heterogeneous treatment effects, under the same assumption commonly underlying regression analysis: ignorability. We specifically describe two methods. For the first method (SM-HTE), we begin by estimating propensity scores for the probability of treatment given a set of observed covariates for each unit and construct balanced propensity score strata; we then estimate propensity score stratum-specific average treatment effects and evaluate a trend across the strata-specific treatment effects. For the second method (MS-HTE), we match control units to treated units based on the propensity score and transform the data into treatment-control comparisons at the most elementary level at which such comparisons can be constructed; we then estimate treatment effects as a function of the propensity score by fitting a non-parametric model as a smoothing device. We illustrate the application of the two methods with a concrete empirical example.