We can easily control for differences between the treatment and non-experimental comparison groups through the estimated propensity score, a single variable on the unit interval. Using propensity score methods, we are able to replicate the experimental treatment effect for a range of specifications and estimators.
The assumption underlying the method is that assignment to treatment depends only on observable pre-intervention variables (called the ignorable treatment assignment assumption or selection on observables; see Rubin 1974, 1977, 1978; Heckman and Robb 1985; or Holland 1986). Though this is a strong assumption, we demonstrate that propensity score methods are an informative starting point, because they quickly reveal the extent to which the treatment and comparison groups overlap in terms of pre-intervention variables.
The paper is organized as follows. Section 2 reviews Lalonde’s data and replicates his results. Section 3 identifies the treatment effect under the potential outcomes causal model, and discusses estimation strategies for the treatment effect. In Section 4, we apply our methods to Lalonde’s data set, and in Section 5, we discuss the sensitivity of the results to the methodology. Section 6 concludes the paper. debt