Consistent Estimation with a Large Number of Weak Instruments
分析当工具变量数量随样本量增大时，弱工具变量下实现一致估计的条件，发现使用大量弱工具变量可能改善某些估计量的表现，并比较了LIML、B2SLS和2SLS的一致性条件。
This paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables (IV) regression when the available instruments are weak, and the number of instruments, Kn, goes to infinity with the sample size. We show that consistent estimation depends importantly on the strength of the instruments as measured by rn, the rate of growth of the so-called concentration parameter, and also on Kn. In particular, when Kn →∞, the concentration parameter can grow, even if each individual instrument is only weakly correlated with the endogenous explanatory variables, and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature. Hence, the use of many weak instruments may actually improve the performance of certain point estimators. More specifically, we find that LIML and B2SLS are consistent when Kn/rn → 0, while 2SLS is consistent only if Kn/rn → 0, as n → ∞. These consistency results suggest that LIML and B2SLS are more robust to instrument weakness than 2SLS.