Location Properties of Point Estimators in Linear Instrumental Variables and Related Models
研究了线性工具变量等模型中，从简化型分布到结构参数的映射是奇异的，这导致点估计量不能无偏、不能分位数无偏或平移等变，意味着偏差与方差的权衡不可避免。
We examine statistical models, including the workhorse linear instrumental variables model, in which the mapping from the reduced form distribution to the structural parameters of interest is singular. The singularity of this mapping implies certain fundamental restrictions on the finite sample properties of point estimators: they cannot be unbiased, quantile-unbiased, or translation equivariant. The nonexistence of unbiased estimators does not rule out bias reduction of standard estimators, but implies that the bias-variance tradeoff cannot be avoided and needs to be considered carefully. The results can also be extended to weak instrument asymptotics by using the limits of experiments framework.