Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments

The authors consider the problem of making asymptotically valid inference on structural parameters in instrumental variables regression with weak instruments. Using local-to-zero asymptotics, they derive the asymptotic distributions of likelihood ratio (LR) and Lagrange multiplier (LM) type statistics for testing simple hypotheses on structural parameters based on maximum likelihood and generalized methods of moments estimation methods. In contrast to the nonstandard limiting behavior of Wald statistics, the limiting distributions of certain LR and LM statistics are bounded by a chi-square distribution with degrees of freedom given by the number of instruments.