Research

Newey–West (1987) standard errors are the dominant standard errors used for heteroskedasticity and autocorrelation robust (HAR) inference in time series regression. The Newey–West estimator uses the Bartlett kernel, which is a first-order kernel, meaning that its characteristic exponent, $q$, is equal to 1, where $q$ is defined as the largest value of $r$ for which the quantity $k^{\left[r\right]}\left(0\right)={lim}_{t\to 0}{\left|t\right|}^{-r}(k\left(0\right)-k\left(t\right))$is defined and finite. This raises the apparently uninvestigated question of whether the Bartlett kernel is optimal among first-order kernels. We demonstrate that, for $q<2$, there is no optimal $q$th-order kernel for HAR testing in the Gaussian location model or for minimizing the MSE in spectral density estimation. In fact, for any $q<2$, the space of $q$th-order positive-semidefinite kernels is not closed and, moreover, all continuous $q$th-order kernels can be decomposed into a weighted sum of $q$th and second-order kernels, which suggests that there is no meaningful notion of ‘pure’ $q$th-order kernels for $q<2$. Nevertheless, it is possible to rank any given collection of $q$th-order kernels using the functional $I_q\left[k\right]={\left(k^{\left[q\right]}\left(0\right)\right)}^{1/q}\int k^2\left(t\right)dt$ with smaller values corresponding to better asymptotic performance. We examine the value of $I_q\left[k\right]$ for a wide variety of first-order estimators and find that none improve upon the Bartlett kernel. These comparisons provide additional justification for the continued use of the Newey–West estimator with testing-optimal smoothing parameters and fixed-$b$ critical values despite the lack of optimality of Bartlett among first-order kernels.

I prove a semiparametric Bernstein-von Mises theorem for a partially linear regression model with independent priors for the low-dimensional parameter of interest and the infinite-dimensional nuisance parameters. My result avoids a prior invariance condition that arises from a loss of information in not knowing the nuisance parameter. The key idea is a feasible reparametrization of the regression function that mimics the Gaussian profile likelihood. This allows a researcher to assume independent priors for the model parameters while automatically accounting for the loss of information associated with not knowing the nuisance parameter. As these prior stability conditions often impose strong restrictions on the underlying data-generating process, my results provide a more robust asymptotic normality theorem than the original parametrization of the partially linear model.

This paper presents a Bayesian inference framework for a linear index threshold-crossing binary choice model that satisfies a median independence restriction. The key idea is that the model is observationally equivalent to a probit model with nonparametric heteroskedasticity. Consequently, Gibbs sampling techniques from Albert and Chib (1993) and Chib and Greenberg (2013) lead to a computationally attractive Bayesian inference procedure in which a Gaussian process forms a conditionally conjugate prior for the natural logarithm of the skedastic function.

Inference in models where the parameter is defined by moment inequalities is of interest in many areas of economics. This paper develops a new method for improving the performance of generalized moment selection (GMS) testing procedures in finite-samples. The method modifies GMS tests by tilting the empirical distribution in its moment selection step by an amount that maximizes the empirical likelihood subject to the restrictions of the null hypothesis. We characterize sets of population distributions on which a modified GMS test is (i) asymptotically equivalent to its non-modified version to first-order, and (ii) superior to its non-modified version according to local power when the sample size is large enough. An important feature of the proposed modification is that it remains computationally feasible even when the number of moment inequalities is large. We report simulation results that show the modified tests control size well, and have markedly improved local power over their non-modified counterparts.