INTRODUCTION

Many of the procedures for estimating and assessing causal effects under unconfoundedness involve the propensity score. In practice it is rare that we know the propensity score a priori in settings other than those involving randomized experiments. Such practical settings could have complex designs where the unit-level probabilities differ in known ways. An example is the allocation of admissions to students applying for medical school in The Netherlands in the 1980s and 1990s. Based on high school grades, applicants would be assigned a priority score that determined their probability of getting admitted to medical school. The actual admission to medical school was then based on a (random) lottery. Such settings are rare, however, and a more common situation is where, given the pre-treatment variables available, a researcher views unconfoundedness as a reasonable approximation to the actual assignment mechanism, with only vague a priori information about the form of the dependence of the propensity score on the observed pre-treatment variables. For example, in many medical settings, decisions are based on a set of clinically relevant patient characteristics observed by doctors and entered in patients’ medical records. However, there is typically no explicit rule that requires physicians to choose a specific treatment based on particular values of the pre-treatment variables. In light of this degree of physician discretion, there is no explicitly known form for the propensity score. In such cases, for at least some of the methods for estimating and assessing treatment effects discussed in this part of the book, the researcher needs to estimate the propensity score. In this chapter we discuss some specific methods for doing so.

It is important to note that the various methods that will be discussed in the chapters following this one, specifically Chapters 14–17, use the propensity score in different ways. Some of these methods rely more heavily than others on an accurate approximation of the true propensity score by the estimated propensity score.