Compliance-Effect Correlation Bias in Instrumental Variables Estimators

Instrumental variable estimators hold the promise of enabling researchers to estimate the effects of educational treatments that are not (or cannot be) randomly assigned but that may be affected by randomly assigned interventions. Examples of the use of instrumental variables in such cases are increasingly common in educational and social science research. The most commonly used instrumental variables estimator is two-stage least squares (2SLS). Many of the properties of the 2SLS estimator are well-understood, including its identifying assumptions and the issue of finite sample bias. Less well understood, however, is the behavior of the 2SLS estimator when individuals are heterogeneous in their compliance with the instrument (that is, heterogeneous in the extent to which the instrument affects their behavior). This paper investigates the effects of heterogeneous compliance on 2SLS estimates and the conditions under which such heterogeneous compliance results in bias. Findings reveal that the 2SLS estimator may be severely biased by correlations between instrument compliance and mediator effects, even if all the standard IV assumptions are met. This bias is in addition to finite sample bias, and is, in fact, exacerbated by weak instruments. Because there are many conditions that might yield compliance-effect correlations, this source of bias should be considered in designing and interpreting the results of studies that rely on instrumental variables estimation.