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A Likelihood-Based Analysis for Relaxing the Exclusion Restriction in Randomized Experiments with Noncompliance
Article first published online: 3 MAY 2013
© 2013 Australian Statistical Publishing Association Inc. Published by Wiley Publishing Asia Pty Ltd.
Australian & New Zealand Journal of Statistics
Volume 55, Issue 2, pages 129–153, June 2013
How to Cite
Mercatanti, A. (2013), A Likelihood-Based Analysis for Relaxing the Exclusion Restriction in Randomized Experiments with Noncompliance. Australian & New Zealand Journal of Statistics, 55: 129–153. doi: 10.1111/anzs.12025
- Issue published online: 19 JUN 2013
- Article first published online: 3 MAY 2013
- exclusion restriction;
- mixture distributions;
- potential outcomes approach
The exclusion restriction is usually assumed for identifying causal effects in true or only natural randomized experiments with noncompliance. It requires that the assignment to treatment does not have a direct causal effect on the outcome. Despite its importance, the restriction can often be unrealistic, especially in situations of natural experiments. It is shown that, without the exclusion restriction, the parametric model is identified if the outcome distributions of various compliance statuses are in the same parametric class and that class is a linearly independent set over the field of real numbers. However, the relaxation of the exclusion restriction yields a parametric model that is characterized by the presence of mixtures of distributions. This scenario complicates the likelihood-based estimation procedures because it implies more than one maximum likelihood point. A two-step estimation procedure based on detecting the root that is closest to the method of moments estimate of the parameter vector is then proposed and analyzed in detail, under normally distributed outcomes. An economic example with real data concerning returns to schooling concludes the paper.