发表机构
FGV EPGE; MIT Department of Economics; University of Pittsburgh（巴西圣保罗基金会经济与应用研究学院; 麻省理工学院经济学系; 匹兹堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种多项式方法，通过特征值或代数消元求解线性IV模型中CU-GMM目标函数的全局最小值，从而支持过度识别和CLR检验。
AI 中文摘要
本文刻画了线性工具变量模型中连续更新广义矩方法（CU-GMM）目标函数的全局最小值。我们允许在异方差、自相关或聚类情形下的最优权重矩阵。我们证明该目标函数是两个多项式的比值。对于一个内生回归元，CU-GMM目标函数的驻点是伴随矩阵的实特征值。将其目标值与无穷远处的值进行比较即可得到全局最小值，这扩展了经典的特征向量方法以用于有限信息最大似然。对于多个内生回归元，代数消元和对实解的检验可在有限多个候选目标值（包括边界值）中识别出最小值。伽罗瓦理论排除了即便只有一个内生回归元和两个工具变量时的一般根式公式，而数值求根仍然是可能的。找到全局最小值使我们能够计算过度识别检验和似然比检验，包括条件似然比（CLR）检验。
英文摘要
This paper characterizes the global minimum of the continuously updating generalized method of moments (CU-GMM) objective in linear instrumental variables models. We allow optimal weighting matrices under heteroskedasticity, autocorrelation, or clustering. We show that the objective is a ratio of polynomials. For one endogenous regressor, stationary points of CU-GMM objective function are real eigenvalues of a companion matrix. Comparing their objective values with the value at infinity gives the global minimum, extending the classical eigenvector approach to limited information maximum likelihood. With multiple endogenous regressors, algebraic elimination and checks for real solutions identify the minimum among finitely many candidate objective values, including boundary values. Galois theory rules out general formulas by radicals even with one endogenous regressor and two instruments, while numerical root finding remains possible. Finding the global minimum allows us to compute overidentification and likelihood ratio tests, including the conditional likelihood ratio (CLR) test.
