UC Berkeley

The first chapter of this dissertation considers a new class of robust estimators in a linear instrumental variables (IV) model with many instruments. The estimators are generalized method of moments (GMM) estimators, and the class includes the limited maximum likelihood estimator (LIML) as a special case. Each estimator in the class is consistent and asymptotically normal under many instruments asymptotics, and this chapter provides consistent variance estimators that are of the ``sandwich'' type and can be used to conduct asymptotically correct inference. Furthermore, this chapter characterizes an optimal robust estimator among the members of the class. Compared to LIML, the optimal robust estimator is less influenced by outliers and more efficient under thick-tailed error distributions. In an empirical example (Angrist and Krueger, 1991), the optimal robust estimator is approximately 80 percent more efficient than LIML.

The second chapter of this dissertation provides a central limit theorem based on Stein's method (Stein, 1972) which is an integral component in the proof of the main theorem in the first chapter. It also appears to be general enough in its scope that it can be applied to a variety of other problems.