Robust estimation with many instruments

TL;DR: In this article, leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity are proposed for the analysis of variance and tests of linear restrictions in models with many regressors.

TL;DR: In this article, the Sargan test statistic for over-identifying restrictions is shown to be the same as the MD criterion test statistic, and the equivalence results also apply to the efficient two-step generalized method of moments and robust optimal MD estimators and criterion functions, allowing for general forms of heteroskedasticity.

TL;DR: This article proposed a data-driven procedure that exploits heterogeneity in the first-stage correlation between an instrument and an endogenous variable to improve the asymptotic mean squared error (MSE) of instrumental variable estimators.

TL;DR: In this article, the authors propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model and compare the conventional F statistic to a critical value that corrects for many restrictions.

TL;DR: In this article, the authors developed asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero.

TL;DR: In this article, a new approach toward a theory of robust estimation is presented, which treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators that are asyptotically most robust (in a sense to be specified) among all translation invariant estimators.

TL;DR: In this paper, the authors prove consistency and asymptotic normality of maximum likelihood estimators under weaker conditions than usual, such that the true distribution underlying the observations belongs to the parametric family defining the estimator, and the regularity conditions do not involve the second and higher derivatives of the likelihood function.

TL;DR: In this paper, the authors developed asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero.