Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments
研究弱工具变量下结构参数的渐近有效推断，推导了LR和LM统计量的渐近分布，并说明如何构造置信集。
We consider the problem of making asymptotically valid inference on structural parameters in instrumental variables regression with weak instruments. Using the localto-zero asymptotics of Staiger and Stock (1997), we derive the asymptotic distributions of LR and LM type statistics for testing simple hypotheses on structural parameters based on maximum likelihood and generalized method of moments estimation methods. In contrast to the nonstandard limiting behavior of Wald statistics, the limiting distributions of certain LM and LR statistics are bounded by a chi-square distribution with degrees of freedom given by the number of instruments. Further, we show how to construct asymptotically valid confidence sets for structural parameters by inverting these statistics.