On the Geometry of the Instrumental Variable Estimator*
用几何方法推导了恰好识别工具变量估计量的精确分布，直观解释了弱工具和小样本下估计量非正态形状的成因，并展示了工具质量和内生性如何影响分布形态。
Abstract I derive the exact distribution of the exact determined instrumental variable estimator using a geometric approach. The approach provides a decomposition of the exact estimator. The results show that by geometric reasoning one may efficiently derive the distribution of the estimation error. The often striking non‐normal shape of the instrumental variable estimator, in the case of weak instruments and small samples, follows intuitively by the geometry of the problem. The method allows for intuitive interpretations of how the shape of the distribution is determined by instrument quality and endogeneity. The approach can also be used when deriving the exact distribution of any ratio of stochastic variables.