Confidence Sets Based on Inverting Anderson-Rubin Tests

Economists are often interested in the coefficient of a single endogenous explanatory variable in a linear simultaneous equations model. One way to obtain a confidence set for this coefficient is to invert the Anderson-Rubin test. The “AR confidence sets” that result have correct coverage under classical assumptions. In this paper, however, we show that AR confidence sets also have many undesirable properties. Their coverage conditional on quantities that the investigator can observe, notably the Sargan statistic, can be far from correct. It is well known that they can be unbounded when the instruments are weak. Even when they are bounded, their length may be very misleading. We argue that, at least when the instruments are not so weak that inference is hopeless, it is much better to obtain confidence intervals by bootstrapping either the IV or LIML t statistic on the coefficient of interest in a particular way that we propose. This research was supported, in part, by grants from the Social Sciences and Humanities Research Council of Canada, the Canada Research Chairs program (Chair in Economics, McGill University), and the Fonds Québécois de Recherche sur la Société et la Culture.