Model selection (MS) and model averaging (MA) are two popular approaches when many candidate models exist. Theoretically, the estimation risk of an oracle MA is not larger than that of an oracle MS because the former is more flexible, but a foundational issue is this: Does MA offer a substantial improvement over MS? Recently, seminal work by Peng and Yang (2022) has answered this question under nested models with linear orthonormal series expansion. In the current paper, we further respond to this question under linear nested regression models. A more general nested framework, heteroscedastic and autocorrelated random errors, and sparse coefficients are allowed in the current paper, giving a scenario that is more common in practice. A remarkable implication is that MS can be significantly improved by MA under certain conditions. In addition, we further compare MA techniques with different weight sets. Simulation studies illustrate the theoretical findings in a variety of settings.

This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the cases of identically and heterogeneously distributed observations. Our analysis is nonparametric in the sense that the relationship between the regressand and the regressors is not specified. The main results of this paper show that the empirical risk minimizer achieves the optimal performance (up to a logarithmic factor) in a dependent data setting.

We propose a new approach to the semiparametric analysis of panel data binary choice models with fixed effects and dynamics (lagged dependent variables). The model under consideration has the same random utility framework as in Honoré and Kyriazidou (2000, Econometrica 68, 839–874). We demonstrate that, with additional serial dependence conditions on the process of deterministic utility and tail restrictions on the error distribution, the (point) identification of the model can proceed in two steps, and requires matching only the value of an index function of explanatory variables over time, rather than the value of each explanatory variable. Our identification method motivates an easily implementable, two-step maximum score (2SMS) procedure – producing estimators whose rates of convergence, in contrast to Honoré and Kyriazidou’s (2000, Econometrica 68, 839–874) methods, are independent of the model dimension. We then analyze the asymptotic properties of the 2SMS procedure and propose bootstrap-based distributional approximations for inference. Evidence from Monte Carlo simulations indicates that our procedure performs satisfactorily in finite samples.

This paper proposes a nonparametric test to assess whether there exist heterogeneous quantile treatment effects (QTEs) of an intervention on the outcome of interest across different sub-populations defined by covariates of interest. Specifically, a consistent test statistic based on the Cramér–von Mises type criterion is developed to test if the treatment has a constant quantile effect for all sub-populations defined by covariates of interest. Under some regularity conditions, the asymptotic behaviors of the proposed test statistic are investigated under both the null and alternative hypotheses. Furthermore, a nonparametric Bootstrap procedure is suggested to approximate the finite-sample null distribution of the proposed test; then, the asymptotic validity of the proposed Bootstrap test is theoretically justified. Through Monte Carlo simulations, we demonstrate the power properties of the test in finite samples. Finally, the proposed testing approach is applied to investigate whether there exists heterogeneity for the QTE of maternal smoking during pregnancy on infant birth weight across different age groups of mothers.

Recently, Kurisu and Otsu (2022b, Econometric Theory 38(1), 172–193) derived the uniform convergence rates for the nonparametric deconvolution estimators proposed by Li and Vuong (1998, Journal of Multivariate Analysis 65(2), 139–165). This article shows that faster uniform convergence rates can be established for their estimators under the same assumptions. In addition, a new class of deconvolution estimators based on a variant of Kotlarski’s identity is also proposed. It is shown that in some cases, these new estimators can have faster uniform convergence rates than the existing estimators.

Cointegrating polynomial regressions (CPRs) include deterministic variables, integrated variables, and their powers as explanatory variables. Based on a novel kernel-weighted limit result and a novel functional central limit theorem, this paper shows that the fully modified ordinary least squares (FM-OLS) estimator of Phillips and Hansen (1990, Review of Economic Studies 57, 99–125) is robust to being used in CPRs. Being used in CPRs refers to a widespread empirical practice that treats the integrated variables and their powers, incorrectly, as a vector of integrated variables and uses textbook FM-OLS. Robustness means that this “formal” FM-OLS practice leads to a zero mean Gaussian mixture limiting distribution that coincides with the limiting distribution of the Wagner and Hong (2016, Econometric Theory 32, 1289–1315) application of the FM estimation principle to the CPR case. The only restriction for this result to hold is that all integrated variables to power one are included as regressors. Even though simulation results indicate performance advantages of the Wagner and Hong (2016, Econometric Theory 32, 1289–1315) estimator, partly even in large samples, the results of the paper give an asymptotic foundation to “formal” FM-OLS and thus enlarge the usability of the Phillips and Hansen (1990, Review of Economic Studies 57, 99–125) estimator implemented in many software packages.

We consider inference for possibly misspecified GMM models based on possibly nonsmooth moment conditions. While it is well known that misspecified GMM estimators with smooth moments remain $\sqrt {n}$ consistent and asymptotically normal, globally misspecified nonsmooth GMM estimators are $n^{1/3}$ consistent when either the weighting matrix is fixed or when the weighting matrix is estimated at the $n^{1/3}$ rate or faster. Because the estimator’s nonstandard asymptotic distribution cannot be consistently estimated using the standard bootstrap, we propose an alternative rate-adaptive bootstrap procedure that consistently estimates the asymptotic distribution regardless of whether the GMM estimator is smooth or nonsmooth, correctly or incorrectly specified. Monte Carlo simulations for the smooth and nonsmooth cases confirm that our rate-adaptive bootstrap confidence intervals exhibit empirical coverage close to the nominal level.

We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identification, and show that the means and the variances and covariances of the random coefficients are identified from the first two conditional moments of the response given the covariates if the support of the covariates, excluding the intercept, contains a Cartesian product with at least three points in each coordinate. We also discuss identification of higher-order mixed moments, as well as partial identification in the presence of a binary regressor. Next, we show the variable selection consistency of the adaptive LASSO for the variances and covariances of the random coefficients in finite and moderately high dimensions. This implies that the estimated covariance matrix will actually be positive semidefinite and hence a valid covariance matrix, in contrast to the estimate arising from a simple least squares fit. We illustrate the proposed method in a simulation study.

This study investigates the identification and inference of quantile treatment effects (QTEs) in a fuzzy regression discontinuity (RD) design under rank similarity. Unlike Frandsen et al. (2012, Journal of Econometrics 168, 382–395), who focus on QTEs only for the compliant subpopulation, our approach can identify QTEs and average treatment effect for the whole population at the threshold. We derived a new set of moment restrictions for the RD model by imposing a local rank similarity condition, which restricts the evolution of individual ranks across treatment status in a neighborhood around the threshold. Based on the moment restrictions, we derive closed-form solutions for the estimands of the potential outcome cumulative distribution functions for the whole population. We demonstrate the functional central limit theorems and bootstrap validity results for the QTE estimators by explicitly accounting for observed covariates. In particular, we develop a multiplier bootstrap-based inference method with robustness against large bandwidths that applies to uniform inference by extending the recent work of Chiang et al. (2019, Journal of Econometrics 211, 589–618). We also propose a test for the local rank similarity assumption. To illustrate the estimation approach and its properties, we provide a simulation study and estimate the impacts of India’s 40-billion-dollar national rural road construction program on the reallocation of labor out of agriculture.

Econometricians have usefully separated study of estimation into identification and statistical components. Identification analysis, which assumes knowledge of the probability distribution generating observable data, places an upper bound on what may be learned about population parameters of interest with finite-sample data. Yet Wald’s statistical decision theory studies decision-making with sample data without reference to identification, indeed without reference to estimation. This paper asks if identification analysis is useful to statistical decision theory. The answer is positive, as it can yield an informative and tractable upper bound on the achievable finite-sample performance of decision criteria. The reasoning is simple when the decision-relevant parameter (true state of nature) is point-identified. It is more delicate when the true state is partially identified and a decision must be made under ambiguity. Then the performance of some criteria, such as minimax regret, is enhanced by randomizing choice of an action in a controlled manner. I find it useful to recast choice of a statistical decision function as selection of choice probabilities for the elements of the choice set.

We set up a formal framework to characterize encompassing of nonparametric models through the $L^2$ distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for the encompassing hypothesis that are fully nonparametric. Our test statistics depend on kernel regression, raising the issue of bandwidth’s choice. We investigate two alternative approaches to obtain a “small bias property” for our test statistics. We show the validity of a wild bootstrap method. We empirically study the use of a data-driven bandwidth and illustrate the attractive features of our tests for small and moderate samples.

In this paper, we consider subgeometric (specifically, polynomial) ergodicity of univariate nonlinear autoregressions with autoregressive conditional heteroskedasticity (ARCH). The notion of subgeometric ergodicity was introduced in the Markov chain literature in the 1980s, and it means that the transition probability measures converge to the stationary measure at a rate slower than geometric; this rate is also closely related to the convergence rate of $\beta $-mixing coefficients. While the existing literature on subgeometrically ergodic autoregressions assumes a homoskedastic error term, this paper provides an extension to the case of conditionally heteroskedastic ARCH-type errors, considerably widening the scope of potential applications. Specifically, we consider suitably defined higher-order nonlinear autoregressions with possibly nonlinear ARCH errors and show that they are, under appropriate conditions, subgeometrically ergodic at a polynomial rate. An empirical example using energy sector volatility index data illustrates the use of subgeometrically ergodic AR–ARCH models.

This article studies the robustness of quasi-maximum-likelihood estimation in hidden Markov models when the regime-switching structure is misspecified. Specifically, we examine the case where the data-generating process features a hidden Markov regime sequence with covariate-dependent transition probabilities, but estimation proceeds under a simplified mixture model that assumes regimes are independent and identically distributed. We show that the parameters governing the conditional distribution of the observables can still be consistently estimated under this misspecification, provided certain regularity conditions hold. Our results highlight a practical benefit of using computationally simpler mixture models in settings where regime dependence is complex or difficult to model directly.

This paper considers a model with general regressors and unobservable common factors. An estimator based on iterated principal component analysis is proposed, which is shown to be not only asymptotically normal, but under certain conditions also free of the otherwise so common asymptotic incidental parameters bias. Interestingly, the conditions required to achieve unbiasedness become weaker the stronger the trends in the factors, and if the trending is strong enough, unbiasedness comes at no cost at all. The approach does not require any knowledge of how many factors there are, or whether they are deterministic or stochastic. The order of integration of the factors is also treated as unknown, as is the order of integration of the regressors, which means that there is no need to pre-test for unit roots, or to decide on which deterministic terms to include in the model.