Robust Confidence Sets in the Presence of Weak Instruments

This paper considers instrumental variable regression with a single endogenous variable and the potential presence of weak instruments. I construct confidence sets for the coefficient on the single endogenous regressor by inverting tests robust to weak instruments. I suggest a numerically simple algorithm for finding the Conditional Likelihood Ratio (CLR) confidence sets. The full descriptions of possible forms of the CLR, AndersonRubin (AR) and Lagrange Multiplier (LM) confidence sets are given. I show that the CLR confidence sets has nearly shortest expected arc length among similar symmetric invariant confidence sets in a circular model. I also prove that the CLR confidence set is asymptotically valid in a model with non-normal errors. Digitized by the Internet Archive in 2011 with funding from MIT Libraries http://www.archive.org/details/robustconfidence0727miku