Bootstrap Confidence Sets with Weak Instruments

We study several methods of constructing confidence sets for the coefficient of the single right-hand-side endogenous variable in a linear equation with weak instruments. Two of these are based on conditional likelihood ratio (CLR) tests, and the others are based on inverting <italic>t</italic> statistics or the bootstrap <italic>P</italic> values associated with them. We propose a new method for constructing bootstrap confidence sets based on <italic>t</italic> statistics. In large samples, the procedures that generally work best are CLR confidence sets using asymptotic critical values and bootstrap confidence sets based on limited-information maximum likelihood (LIML) estimates.