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线性IV模型中持续更新GMM的多项式方法AI 解读

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…

离散近似下条件似然比检验的性质AI 解读

The conditional likelihood ratio (CLR) test is a valuable tool for inference under weak identification, with appealing theoretical properties in both linear and non-linear settings. Its implementation nevertheless requires minimizing a non-convex objective function, a difficulty long recognized even in the linear IV setting. While grid-based methods that provide a practical approximation may perform well in particular designs, such procedures do not guarantee that the…

弱识别下的置信集：理论与实践AI 解读

We develop new methods for constructing confidence sets and intervals in linear instrumental variables (IV) models based on tests that remain valid under weak identification and under heteroskedastic, autocorrelated, or clustered errors. In practice, researchers typically recover such sets by grid search, a procedure that can miss parts of the confidence region, truncate unbounded sets, and deliver misleading inference. We replace grid inversion with exact and…

工具变量回归中渐近最优检验的功效界与效率损失AI 解读

We characterize the maximal attainable power-size gap in overidentified instrumental variables models with heteroskedastic or autocorrelated (HAC) errors. Using total variation distance and Kraft's theorem, we define the decision theoretic frontier of the testing problem. We show that Lagrange multiplier and conditional quasi likelihood ratio tests can have power arbitrarily close to size even when the null and alternative are well separated, because they do not fully…

过度识别工具变量模型的稳健条件 Wald 推断AI 解读

For the over-identified linear instrumental variables model, researchers commonly report the 2SLS estimate along with the robust standard error and seek to conduct inference with these quantities. If errors are homoskedastic, one can control the degree of inferential distortion using the first-stage F critical values from Stock and Yogo (2005), or use the robust-to-weak instruments Conditional Wald critical values of Moreira (2003). If errors are non-homoskedastic, these…