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 its empirical importance. To fill this gap, this article proposes new consistent FPCA-based instrumental variable estimators and develops their asymptotic properties in detail. Simulation experiments under a wide range of settings show that the proposed estimators perform considerably well. We apply our methodology to estimate the impact of immigration on native labor market outcomes in the US.

Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear settings, this identification hinges on the completeness condition, which requires the nonsingularity of a high-dimensional matrix or operator and may fail for finite samples or even at the population level. Regularized estimators provide a solution by enabling consistent estimation of structural or average structural functions, sometimes even under identification failure. We show that the asymptotic distribution in these cases can be nonstandard. We develop a comprehensive theory of regularized estimators, which include methods such as high-dimensional ridge regularization, gradient descent, and principal component analysis (PCA). The results are illustrated for high-dimensional and nonparametric instrumental variable regressions and are supported through simulation experiments.

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 conditional homoskedasticity/heteroskedasticity. This paper studies the problem of constructing asymptotically valid confidence intervals in a mildly explosive autoregression where the innovations are allowed to be unconditionally heteroskedastic. The assumed variance process is general and can accommodate both deterministic and stochastic volatility specifications commonly adopted in the literature. Within this framework, we show that the standard heteroskedasticity- and autocorrelation-consistent estimate of the long-run variance converges in distribution to a nonstandard random variable that depends on nuisance parameters. Notwithstanding this result, the corresponding t-statistic is shown to still possess a standard normal limit distribution. To improve the quality of inference in small samples, we propose a dependent wild bootstrap-t procedure and establish its asymptotic validity under relatively weak conditions. Monte Carlo simulations demonstrate that our recommended approach performs favorably in finite samples relative to existing methods across a wide range of volatility specifications. Applications to international stock price indices and U.S. house prices illustrate the relevance of the advocated method in practice.

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 information content of various MAR assumptions for estimation of such parameters. We propose a standard doubly robust estimator for these parameters by equating to zero the sample analog of their respective efficient influence functions. Our proposed estimator performs well and vastly outperforms other estimators in our simulation experiment and empirical illustration.

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 plug-in rules, Bayes rules, and empirical welfare maximization rules. Focusing on the application of the empirical welfare maximization framework, we provide convergence rates of the worst-case average welfare loss (regret).

This article examines high-dimensional covariates in regression discontinuity design (RDD) analysis. We introduce estimation and inference methods for the RDD models that incorporate covariate selection while maintaining stability across various numbers of covariates. The proposed methods combine a localization approach using kernel weights with $\ell _{1}$-penalization to handle high-dimensional covariates. We provide both theoretical and numerical evidence demonstrating the efficacy of our methods. Theoretically, we present risk and coverage properties for our point estimation and inference methods. Conditions are given under which the proposed estimator becomes more efficient than the conventional covariate adjusted estimator at the cost of an additional sparsity condition. Numerically, our simulation experiments and empirical examples show the robust behaviors of the proposed methods to the number of covariates in terms of bias and variance for point estimation and coverage probability and interval length for inference.

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 proposed method, called Structured Principal Orthogonal complEment Thresholding (S-POET), incorporates observation structural information for both global and national factor models. We establish the asymptotic properties of the S-POET estimator, and also demonstrate the drawbacks of conventional covariance matrix estimation procedures when using lower-frequency data. Finally, we apply the S-POET estimator to an out-of-sample portfolio allocation study using international stock market data.

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 of achieving the lowest possible squared error. Second, the convergence of the weights determined by our proposal is provided when at least one of the candidate models is correctly specified. Simulation results in comparison with several related existing methods favor our proposed method. The method is applied to a dataset from a labor skills training program.