 
Summary: NONCOMPLIANCE BIAS CORRECTION BASED ON COVARIATES
IN RANDOMIZED EXPERIMENTS
YVES ATCHADE
AND LEONARD WANTCHEKON
November 1, 2005
Abstract
We propose some practical solutions for causal effects estimation when compliance to as
signments is only partial and some of the standard assumptions do not hold. We follow the
potential outcome approach but in contrast to Imbens and Rubin (1997), we require no prior
classification of the compliance behaviour. When noncompliance is not ignorable, it is known
that adjusting for arbitrary covariates can actually increase the estimation bias. We propose
an approach where a covariate is adjusted for only when the estimate of the selection bias of
the experiment as provided by that covariate is consistent with the data and prior information
on the study. Next, we investigate cases when the overlap assumption does not hold and, on
the basis of their covariates, some units are excluded from the experiment or equivalently, never
comply with their assignments. In that context, we show that a consistent estimation of the
causal effect of the treatment is possible based on a regression model estimation of the con
ditional expectation of the outcome given the covariates. We illustrate the methodology with
several examples such as the access to influenza vaccine experiment (McDonald et al (1992) and
the PROGRESA experiment (Shultz (2004)).
