2025/07/01 by Atsushi Inoue, Òscar Jordà, Inoue, Atsushi +3
Economics, Econometrics and Finance · Mathematics · #62E20 #62M10 #62P20 #Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2507.01167
openalex publication_date 2025/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Anderson-Rubin (AR) statistic for a general set of nonlinear moment restrictions. The statistic is based on the criterion function of the continuous updating estimator (CUE) for a subset of parameters not constrained under the Null. We treat the data distribution nonparametrically with parametric moment restrictions imposed under the Null. We show that subset tests and confidence intervals based on the AR statistic are uniformly valid over a wide range of distributions that include moment restrictions with general forms of heteroskedasticity. We show that the AR based tests have correct asymptotic size when parameters are unidentified, partially identified, weakly or strongly identified. We obtain these results by constructing an upper bound that is using a novel perturbation and regularization approach applied to the first order conditions of the CUE. Our theory applies to both cross-sections and time series data and does not assume stationarity in time series settings or homogeneity in cross-sectional settings.