A Likelihood‐Based Analysis for Relaxing the Exclusion Restriction in Randomized Experiments with Noncompliance

Abstract

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.

Evaluation of Language Training Programs in Luxembourg using Principal Stratification

“…This implies that the likelihood can show multiple ML points even if it is identified (in the sense that the parameter space is in an one-to-one relation with the space of the model). Mercatanti (2013) shows that the likelihood for a closely related but simpler normal mixture model with non-compliance is identified but it only locally satisfies the regularity likelihood conditions and, consequently, it can exhibit multiple modes. Among the several local ML points detected in our model, Table 4 reports the extreme cases, corresponding to the lower and upper values of the estimated treatment effect on wages for the always-employed, and to the lower and upper values of the effect on employment.…”

“…6) do not hold globally, but locally. Consequently, given that the ML estimator is not guaranteed to be the efficient likelihood estimator, the issue arises as to how to detect the local ML point that corresponds to this efficient estima-Those proposals, however, have been implemented in the context of considerably simpler mixture models with few parameters (e.g.,Mercatanti, 2013). The adoption of the above proposals in our model would considerably increase the computational burden.…”

Evaluation of Language Training Programs in Luxembourg Using Principal Stratification

“…in the context of considerably simpler mixture models with few parameters (e.g., Mercatanti, 2013). The adoption of the above proposals in our model would considerably increase the computational burden.…”

Evaluating the causal effect of university grants on student dropout: Evidence from a regression discontinuity design using principal stratification

“…But the average causal effects for always-applicants and compliant-applicants, τ AA,s 0 and τ CA,s 0 can be only non-parametrically partially identified (Mealli and Pacini, 2013). One can also use likelihood approaches to parametrically estimate causal effects (e.g., Frumento et al, 2012;Mercatanti, 2013). Randomization-based inference (Fisher, 1925), as in Cattaneo, Frandsen and Titiunik (2015), could also be adopted.…”