Econometrica: Sep 2017, Volume 85, Issue 5
On Completeness and Consistency in Nonparametric Instrumental Variable Models
Joachim FreybergerThis paper provides positive testability results for the identification condition in a nonparametric instrumental variable model, known as completeness, and it links the outcome of the test to properties of an estimator of the structural function. In particular, I show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator. This is the case for a large class of complete distributions as well as certain incomplete distributions. As a byproduct, the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself.
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Supplement to "On Completeness and Consistency in Nonparametric Instrumental Variable Models"
This supplement contains additional material to accompany the main text. First, I show that the results in Theorem 1 also hold as ε → 0 and I informally outline a bootstrap procedure to select the critical value. I then provide additional explanations for the main assumptions as well as extensions of the main results.