On the Joint and Marginal Densities of Instrumental Variable Estimators in a General Structural Equation
从工具变量估计量的条件密度出发，重新推导了内生系数估计量的联合密度，并给出了线性组合的边际密度表达式，同时将联合密度近似扩展到O(T^{-2})阶，改进了边际密度近似。
Starting from the conditional density of the instrumental variable (IV) estimator given the right-hand-side endogenous variables, we provide an alternative derivation of Phillips' result on the joint density of the IV estimator for the endogenous coefficients, and derive an expression for the marginal density of a linear combination of these coefficients. In addition, we extend Phillips' approximation to the joint density to 0( T −2 ,) and show how this result can be used to improve the approximation to the marginal density. Explicit formulae are given for the special case of no simultaneity, and the case of an equation with just three endogenous variables. The classical assumptions of independent normal reduced-form errors are employed throughout.