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High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether individual covariates have additional contributions given the latent factors or more generally a set of variables. Our test statistics are based on the estimated partial derivative of the regression function of the candidate variable for screening and a observable proxy for the latent factors. Hence, our test reveals how much predictors contribute additionally to the non-parametric regression after accounting for the latent factors. Our derivative estimator is the convolution of a deep neural network regression estimator and a smoothing kernel. We demonstrate that when the neural network size diverges with the sample size, unlike estimating the regression function itself, it is necessary to smooth the partial derivative of the neural network estimator to recover the desired convergence rate for the derivative. Moreover, our screening test achieves asymptotic normality under the null after finely centering our test statistics that makes the biases negligible, as well as consistency for local alternatives under mild conditions. We demonstrate the performance of our test in a simulation study and two real world applications., Comment: 80 pages, 14 figures

The Arellano-Bond estimator is a fundamental method for dynamic panel data models, widely used in practice. However, the estimator is severely biased when the data's time series dimension $T$ is long due to the large degree of overidentification. We show that weak dependence along the panel's time series dimension naturally implies approximate sparsity of the most informative moment conditions, motivating the following approach to remove the bias: First, apply LASSO to the cross-section data at each time period to construct most informative (and cross-fitted) instruments, using lagged values of suitable covariates. This step relies on approximate sparsity to select the most informative instruments. Second, apply a linear instrumental variable estimator after first differencing the dynamic structural equation using the constructed instruments. Under weak time series dependence, we show the new estimator is consistent and asymptotically normal under much weaker conditions on $T$'s growth than the Arellano-Bond estimator. Our theory covers models with high dimensional covariates, including multiple lags of the dependent variable, common in modern applications. We illustrate our approach by applying it to weekly county-level panel data from the United States to study opening K-12 schools and other mitigation policies' short and long-term effects on COVID-19's spread.

We investigate the significance of change-point or jump effects within fully nonparametric regression contexts, with a particular focus on panel data scenarios where data generation processes vary across individual or group units, and error terms may display complex dependency structures. In our setting the threshold effect depends on a specific covariate, and we permit the true nonparametric regression to vary based on additional latent variables. We propose two uniform testing procedures: one to assess the existence of change-point effects and another to evaluate the uniformity of such effects across units. Even though the underlying data generation processes are neither independent nor identically distributed, our approach involves deriving a straightforward analytical expression to approximate the variance-covariance structure of change-point effects under general dependency conditions. Notably, when Gaussian approximations are made to these test statistics, the intricate dependency structures within the data can be safely disregarded owing to the localized nature of the statistics. This finding bears significant implications for obtaining critical values. Through extensive simulations, we demonstrate that our tests exhibit excellent control over size and reasonable power performance in finite samples, irrespective of strong cross-sectional and weak serial dependency within the data. Furthermore, applying our tests to two datasets reveals the existence of significant nonsmooth effects in both cases.

Beta-sorted portfolios -- portfolios comprised of assets with similar covariation to selected risk factors -- are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little is known of their statistical properties in contrast to comparable procedures such as two-pass regressions. We formally investigate the properties of beta-sorted portfolio returns by casting the procedure as a two-step nonparametric estimator with a nonparametric first step and a beta-adaptive portfolios construction. Our framework rationalize the well-known estimation algorithm with precise economic and statistical assumptions on the general data generating process and characterize its key features. We study beta-sorted portfolios for both a single cross-section as well as for aggregation over time (e.g., the grand mean), offering conditions that ensure consistency and asymptotic normality along with new uniform inference procedures allowing for uncertainty quantification and testing of various relevant hypotheses in financial applications. We also highlight some limitations of current empirical practices and discuss what inferences can and cannot be drawn from returns to beta-sorted portfolios for either a single cross-section or across the whole sample. Finally, we illustrate the functionality of our new procedures in an empirical application.

This paper develops a novel method for policy choice in a dynamic setting where the available data is a multivariate time series. Building on the statistical treatment choice framework, we propose Time-series Empirical Welfare Maximization (T-EWM) methods to estimate an optimal policy rule for the current period or over multiple periods by maximizing an empirical welfare criterion constructed using nonparametric potential outcome time-series. We characterize conditions under which T-EWM consistently learns a policy choice that is optimal in terms of conditional welfare given the time-series history. We then derive a nonasymptotic upper bound for conditional welfare regret and its minimax lower bound. To illustrate the implementation and uses of T-EWM, we perform simulation studies and apply the method to estimate optimal monetary policy rules from macroeconomic time-series data.

This paper presents a new approach for the estimation and inference of the regression parameters in a panel data model with interactive fixed effects. It relies on the assumption that the factor loadings can be expressed as an unknown smooth function of the time average of covariates plus an idiosyncratic error term. Compared to existing approaches, our estimator has a simple partial least squares form and does neither require iterative procedures nor the previous estimation of factors. We derive its asymptotic properties by finding out that the limiting distribution has a discontinuity, depending on the explanatory power of our basis functions which is expressed by the variance of the error of the factor loadings. As a result, the usual ``plug-in" methods based on estimates of the asymptotic covariance are only valid pointwise and may produce either over- or under-coverage probabilities. We show that uniformly valid inference can be achieved by using the cross-sectional bootstrap. A Monte Carlo study indicates good performance in terms of mean squared error. We apply our methodology to analyze the determinants of growth rates in OECD countries.

We propose a dynamic network quantile regression model to investigate the quantile connectedness using a predetermined network information. We extend the existing network quantile autoregression model of Zhu et al. (2019b) by explicitly allowing the contemporaneous network effects and controlling for the common factors across quantiles. To cope with the endogeneity issue due to simultaneous network spillovers, we adopt the instrumental variable quantile regression (IVQR) estimation and derive the consistency and asymptotic normality of the IVQR estimator using the near epoch dependence property of the network process. Via Monte Carlo simulations, we confirm the satisfactory performance of the IVQR estimator across different quantiles under the different network structures. Finally, we demonstrate the usefulness of our proposed approach with an application to the dataset on the stocks traded in NYSE and NASDAQ in 2016.

We propose employing a debiased-regularized, high-dimensional generalized method of moments (GMM) framework to perform inference on large-scale spatial panel networks. In particular, network structure with a flexible sparse deviation, which can be regarded either as latent or as misspecified from a predetermined adjacency matrix, is estimated using debiased machine learning approach. The theoretical analysis establishes the consistency and asymptotic normality of our proposed estimator, taking into account general temporal and spatial dependency inherent in the data-generating processes. The dimensionality allowance in presence of dependency is discussed. A primary contribution of our study is the development of uniform inference theory that enables hypothesis testing on the parameters of interest, including zero or non-zero elements in the network structure. Additionally, the asymptotic properties for the estimator are derived for both linear and nonlinear moments. Simulations demonstrate superior performance of our proposed approach. Lastly, we apply our methodology to investigate the spatial network effect of stock returns.

We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH$(r,s)$ (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against an alternative where there is an 'abnormal' period with changed parameter values. During this period, the change may lead to an explosive behavior of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double supreme test for the existence of a break, and then provide an algorithm to identify the period of change. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the QMLE in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian Process. In simulations we show that the test has good size and power for reasonably large time series lengths. We apply the test to Apple asset returns and Bitcoin returns.

In this paper, we study estimation of nonlinear models with cross sectional data using two-step generalized estimating equations (GEE) in the quasi-maximum likelihood estimation (QMLE) framework. In the interest of improving efficiency, we propose a grouping estimator to account for the potential spatial correlation in the underlying innovations. We use a Poisson model and a Negative Binomial II model for count data and a Probit model for binary response data to demonstrate the GEE procedure. Under mild weak dependency assumptions, results on estimation consistency and asymptotic normality are provided. Monte Carlo simulations show efficiency gain of our approach in comparison of different estimation methods for count data and binary response data. Finally we apply the GEE approach to study the determinants of the inflow foreign direct investment (FDI) to China.

We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the $Z$-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors.