In this paper, we develop methods for statistical inferences in a partially identified nonparametric panel data model with endogeneity and interactive fixed effects. Under some normalization rules, we can concentrate out the large-dimensional parameter vector of factor loadings and specify a set of conditional moment restrictions that are involved with only the finite-dimensional factor parameters along with the infinite-dimensional nonparametric component. For a conjectured restriction on the parameter, we consider testing the null hypothesis that the restriction is satisfied by at least one element in the identified set and propose a test statistic based on a novel martingale difference divergence measure for the distance between a conditional expectation object and zero. We derive a tight asymptotic distributional upper bound for the resultant test statistic under the null and show that it is divergent at rate-N under the global alternative. To obtain the critical values for our test, we propose a version of multiplier bootstrap and establish its asymptotic validity. Simulations demonstrate the finite sample properties of our inference procedure. We apply our method to study Engel curves for major nondurable expenditures in China by using a panel dataset from the China Family Panel Studies.

It is common to assume in empirical research that observables and unobservables are additively separable, especially when the former are endogenous. This is because it is widely recognized that identification and estimation challenges arise when interactions between the two are allowed for. Starting from a nonseparable IV model, where the instrumental variable is independent of unobservables, we develop a novel nonparametric test of separability of unobservables. The large-sample distribution of the test statistics is nonstandard and relies on a Donsker-type central limit theorem for the empirical distribution of nonparametric IV residuals, which may be of independent interest. Using a dataset drawn from the 2015 U.S. Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for some commodities.

This paper introduces a new class of time-varying vector moving average processes of infinite order. These processes serve dual purposes: (1) they can be used to model time-varying dependence structures, and (2) they can be used to establish asymptotic theories for multivariate time series models. To illustrate these two points, we first establish some fundamental asymptotic properties and use them to infer the trending term of a vector moving average infinity process. We then investigate a class of time-varying VARX models. Finally, we demonstrate the empirical relevance of the theoretical results using extensive simulated and real data studies.

This paper considers semiparametric sieve estimation in high-dimensional single index models. The use of Hermite polynomials in approximating the unknown link function provides a convenient framework to conduct both estimation and variable selection. The estimation of the index parameter is formulated from solutions obtained by the routine penalized weighted linear regression procedure, where the weights are used in order to tackle the unbounded support of the regressors. The resulting index parameter estimator is shown to be consistent and sparse, and the asymptotic normality for the estimators of both the index parameter and the link function is established. To perform variable selection in the ultra-high dimension case, we further suggest a forward regression screening method, which is shown to enjoy the sure independence screening property. This screening procedure can be used before the penalized variable selection to reduce the burden of dimensionality. Numerical results show that both the variable selection procedures and the associated estimators perform well 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.

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 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.