INTRODUCTION

Part IV of this text focused on estimation and inference under regular assignment mechanisms, that is, ones that are individualistic with probabilistic assignment, as well as unconfounded. In Part V we study methods that confront the unconfoundedness assumption. In Chapter 21 we discussed methods to assess the plausibility of this assumption by combining it with additional assumptions. In the current chapter we relax the unconfoundedness assumption without replacing it with additional assumptions, and so do not focus on obtaining point estimates of the causal estimands of interest. Instead we end up with ranges of plausible values for these estimands, with the width of these ranges corresponding to the extent to which we allow the unconfoundedness assumption to be violated.

We consider two approaches that have much in common. The first, developed by Manski in a series of studies (e.g., Manski, 1990, 1996, 2003, 2013), allows for arbitrarily large violations of the unconfoundedness assumption. This bounds or partial identification approach, as it is called, leads to sharp results, but at the same time will be seen to limit severely the types of inferences about causal effects that can be drawn from observational data. The second approach, following work in this area by Rosenbaum and Rubin (1983) and Rosenbaum (1995), with important antecedents in the work by Cornfield et al. (1959), works from the other extreme in the sense that unconfoundedness is the starting point, and only limited violations from it need to be considered. If we allow for large violations in the Rosenbaum-Rubin approach, it will often lead to essentially the same results as the Manski bounds approach, but with limited violations of the unconfoundedness assumption, the sensitivity approach results in narrower ranges for the estimands than the partial identification approach.

The key to any sensitivity analysis will be how to assess the magnitude of violations from unconfoundedness. The setup in the current chapter assumes that unconfoundedness is satisfied conditional on an additional, unobserved covariate. If, conditional on the other, observed, covariates, this unobserved covariate is independent of the potential outcomes, or if, again conditional on the observed covariates, it is independent of treatment assignment, unconfoundedness holds even without conditioning on this additional covariate.