Choosing Exogeneity Assumptions in Potential Outcome Models

TL;DR

This paper analyzes how to choose exogeneity assumptions in potential outcome models by linking them to the nature of treatment selection on unobservables, offering methods to assess their plausibility and implications for identification.

Contribution

It introduces a framework connecting exogeneity assumptions to treatment selection patterns, and proposes a weaker quantile independence assumption allowing for monotonic selection.

Findings

Both quantile and mean independence imply non-monotonic treatment selection.

A new weaker quantile independence condition permits monotonic treatment selection.

Implications for identification depend on the chosen exogeneity assumption.

Abstract

There are many kinds of exogeneity assumptions. How should researchers choose among them? When exogeneity is imposed on an unobservable like a potential outcome, we argue that the form of exogeneity should be chosen based on the kind of selection on unobservables it allows. Consequently, researchers can assess the plausibility of any exogeneity assumption by studying the distributions of treatment given the unobservables that are consistent with that assumption. We use this approach to study two common exogeneity assumptions: quantile and mean independence. We show that both assumptions require a kind of non-monotonic relationship between treatment and the potential outcomes. We discuss how to assess the plausibility of this kind of treatment selection. We also show how to define a new and weaker version of quantile independence that allows for monotonic treatment selection. We then show the implications of the choice of exogeneity assumption for identification. We apply these results in an empirical illustration of the effect of child soldiering on wages.