Instrumental Variables Analysis of Randomized Experiments with One-Sided Noncompliance

TLDR: In this article, the authors discuss a second approach to analyzing causal effects when unconfoundedness of the treatment of interest is questionable, in which they consider alternative assumptions regarding causal effects.

Abstract: INTRODUCTION In this chapter we discuss a second approach to analyzing causal effects when unconfoundedness of the treatment of interest is questionable. In Chapter 22 we also relaxed the unconfoundedness assumption, but there we did not make any additional assumptions. The resulting sensitivity and bounds analyses led to a range of estimated values for treatment effects, all of which were consistent with the observed data. Instead, in this chapter we consider alternatives to the standard unconfoundedness assumption that still allow us to obtain essentially unbiased point estimates of some treatment effects of interest, although typically not the overall average effect. In the settings we consider, there is, on substantive grounds, reason to believe that units receiving and units not receiving the treatment of interest are systematically different in characteristics associated with the potential outcomes. Such cases may arise if receipt of treatment is partly the result of deliberate choices by units, choices that take into account perceptions or expectations of the causal effects of the treatment based on information that the analyst may not observe. In order to allow for such violations of unconfoundedness, we rely on the presence of additional information and consider alternative assumptions regarding causal effects. More specifically, a key feature of the Instrumental Variables (IV) approach, the topic of the current chapter and the next two, is the presence of a secondary treatment, in the current setting the assignment to treatment instead of the receipt of treatment, where by “secondary” we do not mean temporily but secondary in terms of scientific interest. This secondary treatment is assumed to be unconfounded. In fact, in the randomized experiment setting of the current chapter, the assignment to treatment is unconfounded by design. This implies we can, using the methods from Part II of the book, unbiasedly estimate causal effects of the assignment to treatment. The problem is that these causal effects are not the causal effects of primary interest, which are the effects of the receipt of treatment. Assumptions that allow researchers to link these causal effects are at the core of the instrumental variables approach.