ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS
推导了异方差和多工具变量条件下刀切工具变量估计量的极限分布，并给出标准误公式，发现该估计量渐近正态且标准误一致，而经典工具变量估计量在此情形下不一致。
This paper derives the limiting distributions of alternative jackknife instrumental variables (JIV) estimators and gives formulas for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994, Econometrica 62, 657–681) and the many weak instrument sequence of Chao and Swanson (2005, Econometrica 73, 1673–1691). We show that JIV estimators are asymptotically normal and that standard errors are consistent provided that $\root \of {K_n } /r_n \to 0$ as n →∞, where K n and r n denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical instrumental variables estimators as limited information maximum likelihood, bias-corrected two-stage least squares, and two-stage least squares, all of which are inconsistent in the presence of heteroskedasticity, unless K n / r n →0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of r n and K n .