Econometric Theory

We consider bootstrap inference in predictive (or Granger-causality) regressions when the parameter of interest may lie on the boundary of the parameter space, here defined by means of a smooth inequality constraint. For instance, this situation occurs when the definition of the parameter space allows for the cases of either no predictability or sign-restricted predictability. We show that in thi…

This study proposes a test for coefficient randomness in autoregressive models where the autoregressive coefficient is local to unity, which is empirically relevant given earlier work. Under this specification, we analyze the effect of the correlation between the random coefficient and disturbance on the properties of tests, a matter that remains largely unexplored in the literature. Our analysis…

Relatively, recent work by Jeganathan (2008, Cowles Foundation Discussion Paper 1649) and Wang (2014, Econometric Theory , 30(3), 509–535) on generalized martingale central limit theorems (MCLTs) implicitly introduces a new class of instrument arrays that yield (mixed) Gaussian limit theory irrespective of the persistence level in the data. Motivated by these developments, we propose a new semipa…

This paper proposes a consistent nonparametric test with good sampling properties to detect instantaneous causality between vector autoregressive (VAR) variables with time-varying variances. The new test takes the form of the U -statistic, and has a limiting standard normal distribution under the null. We further show that the test is consistent against any fixed alternatives, and has nontrivial …

The Least Trimmed Squares (LTS) regression estimator is known to be very robust to the presence of “outliers”. It is based on a clear and intuitive idea: in a sample of size n , it searches for the h -subsample of observations with the smallest sum of squared residuals. The remaining observations are declared “outliers”. Fast algorithms for its computation exist. Nevertheless, the existing asympt…

We establish theoretical results about the low frequency contamination (i.e., long memory effects) induced by general nonstationarity for estimates such as the sample autocovariance and the periodogram, and deduce consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We present explicit expressions for the asymptotic bias of these estimates. We show theoretically that no…

Since the implementation of the Basel III Accord, expected shortfall (ES) has gained increasing attention from regulators as a complement to value-at-risk (VaR). The problem of elicitability for ES makes jointly modeling VaR and ES a popular method to study ES. In this article, we develop model averaging for joint VaR and ES regression models that selects the two weight vectors by minimizing a ja…

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalized shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literat…

New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root, or fractional process…

A new explicit solution representation is provided for ARMA recursions with drift and either deterministically or stochastically varying coefficients. It is expressed in terms of the determinants of banded Hessenberg matrices and, as such, is an explicit function of the coefficients. In addition to computational efficiency, the proposed solution provides a more explicit analysis of the fundamenta…

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to be a finite-dimensional affine space in the frequency domain. It is demonstrated that solutions can be discontinuous with respect to the parameters of the mod…

The primary focus of this article is to capture heterogeneous treatment effects measured by the conditional average treatment effect. A model averaging estimation scheme is proposed with multiple candidate linear regression models under heteroskedastic errors, and the properties of this scheme are explored analytically. First, it is shown that our proposal is asymptotically optimal in the sense o…

We consider a causal structure with endogeneity, i.e., unobserved confoundedness, where an instrumental variable is available. In this setting, we show that the mean social welfare function can be identified and represented via the marginal treatment effect as the operator kernel. This representation result can be applied to a variety of statistical decision rules for treatment choice, including …

Mildly explosive autoregressions have been extensively employed in recent theoretical and applied econometric work to model the phenomenon of asset market bubbles. An important issue in this context concerns the construction of confidence intervals for the autoregressive parameter that represents the degree of explosiveness. Existing studies rely on intervals that are justified only under conditi…

Attrition is monotonic when agents leaving multi-period studies do not return. Under a general missing at random (MAR) assumption, we study efficiency in estimation of parameters defined by moment restrictions on the distributions of the counterfactuals that were unrealized due to monotonic attrition. We discuss novel issues related to overidentification, usability of sample units, and the inform…

In this article, we develop a novel large volatility matrix estimation procedure for analyzing global financial markets. Practitioners often use lower-frequency data, such as weekly or monthly returns, to address the issue of different trading hours in the international financial market. However, this approach can lead to inefficiency due to information loss. To mitigate this problem, our propose…

Functional linear regression has gained popularity as a statistical tool for studying the relationship between function-valued variables. However, in practice, it is hard to expect that the explanatory variables of interest are strictly exogenous, due to, for example, the presence of omitted variables and measurement error. This issue of endogeneity remains insufficiently explored, in spite of it…