When are two step estimators efficient?
利用Kruskal定理，简洁推导了含预期与非预期变量模型中两步估计量的有效性条件，并给出新结果：当前非预期变量参数始终有效，滞后非预期变量在无滞后因变量时有效。
Kruskal's theorem is used to provide simple and elegant alternative derivations of the efficiency of some two step estimators (2SE) for models containing anticipated and unanticipated variables. Several new results are established: 2SE is not efficient for a structural equation with current and lagged values of both anticipated and unanticipated variables; 2SE is always efficient for the parameter associated with the current unanticipated variable, and for the parameter associated with the lagged unanticipated variable if there is no lagged dependent variable in the expectations equation; the inclusion of additional regressors in the structural equation and contemporaneous correlation of the structural and expectations errors can both be analysed in a straightforward manner; the single-equation generalized least squares estimator can be as efficient as the systems maximum likelihood estimator.