This article studies the principal component analysis (PCA) estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PCA estimators of loadings, which comes from the approximately (block) upper triangular structure of the rotation matrix. It suggests an asymmetric relationship among factors: the sparsity of the rotated loadings for a stronger factor can be contaminated by the loadings from weaker ones, but the sparsity of the rotated loadings of a weaker factor is almost unaffected by the loadings of stronger ones. Then, we propose a simple alternative to the existing penalized approaches to sparsify the loading estimators by screening out the small PCA loading estimators directly, and construct consistent estimators for factor strengths. The proposed estimators perform well in finite samples, as shown by a set of Monte Carlo simulations.

In a recent paper, Juodis and Reese (2022, Journal of Business & Economic Statistics, 40, 1191–1203) (JR) show that the application of the CD test proposed by Pesaran (2004, General diagnostic tests for cross-sectional dependence in panels, CWPE 0435, Cambridge) to residuals from panels with latent factors results in over-rejection. They propose a randomized test statistic to correct for over-rejection, and add a screening component to achieve power. This article considers the same problem but from a different perspective and shows that the standard CD test remains valid if the latent factors are weak. A bias-corrected version, CD$^{\ast}$, is proposed which is shown to be asymptotically standard normal under the null of error cross-sectional independence which has power against network-type alternatives. This result is shown to hold for pure latent factor models as well as for panel regression models with latent factors. The case where the errors are serially correlated is also considered. Small sample properties of the CD$^{\ast}$ test are investigated by Monte Carlo experiments and are shown to have satisfactory small sample properties. In an empirical application, using the CD$^{\ast}$ test, it is shown that there remains spatial error dependence in a panel data model for real house price changes across 377 Metropolitan Statistical Areas in the United States, even after the effects of latent factors are filtered out.

Panel data often contain stayers and slow movers. The literature proposes an estimator for the average partial effects (APEs) for this setting without a formal theory. The literature is also silent about inference in the presence of stayers and many slow movers. We contribute to this state of the art. First, we develop an asymptotic theory to guarantee that such an estimator is consistent in the presence of stayers and slow movers. Second, we propose its standard error. Third, we relax the existing assumption to allow for “many” slow movers. Fourth, we generalize the existing estimator. Fifth, we establish that this generalized estimator can achieve larger extents of bias reduction and hence faster convergence rates. Simulation studies demonstrate that the conventional 95% confidence interval covers the true value of the APE with 37%–93% frequencies whereas our proposed one achieves 93%–96% coverage frequencies. Using the U.S. Panel Study of Income Dynamics, we find that estimates of the marginal propensity to consume based on our generalized estimator remarkably differ in values from those of the existing estimators. Moreover, the generalized estimator achieves more than three times as small standard errors as those of the existing robust estimator.

This article presents novel methods and theories for estimation and inference about parameters in statistical models using machine learning for nuisance parameter estimation when data are dyadic. We propose a dyadic cross-fitting method to remove over-fitting biases under arbitrary dyadic dependence. Together with the use of Neyman orthogonal scores, this novel cross-fitting method enables root-n consistent estimation and inference robustly against dyadic dependence. We demonstrate its versatility by applying it to high-dimensional network formation models and reexamine the determinants of free trade agreements.

A first-order Gaussian autoregressive model is considered. The exact finite-sample joint density of the minimal sufficient statistic is derived, for any value of the autoregressive parameter. This allows us to derive explicitly the exact density of the autocorrelation coefficient and its Studentized t-ratio, whose densities were available only in the asymptotic case and not for all values of the parameter and the statistic. This article also demonstrates how to solve a general problem in statistical distribution theory (well beyond the specific case of autoregressive models), that of inverting confluent characteristic functions in multiple variables.

This article provides a general asymptotic theory for mildly explosive autoregression. We confirm that Cauchy limit theory remains invariant across a broad range of error processes, including general linear processes with martingale difference innovations, stationary causal processes, and nonlinear autoregressive time series, such as threshold autoregressive and bilinear models. Our results unify the Cauchy limit theory for long memory, short memory, and anti-persistent innovations within a single framework. Notably, we demonstrate that in the presence of anti-persistent innovations, the Cauchy limit theory may be violated when the regression coefficient approaches the local-to-unity range. Additionally, we explore extensions to models with varying drift, which is of significant interest in its own right.

This article develops a new test to detect changes in generalized autoregressive conditionally heteroscedastic (GARCH(1,1)) processes without imposing a stationary assumption. Specifically, the procedure tests the null hypothesis of a GARCH process with constant parameters, either in (strictly) stationary or explosive regimes, against the alternative hypothesis of parameter changes. We derive the limiting distribution of the test statistics and establish their asymptotic consistency. Monte Carlo simulations show that the proposed test has good size control and high power. We demonstrate a prototype application on a small group of stocks and report a further extensive application to more than ten thousand U.S. stocks.

This article proposes a local projection (LP) residual bootstrap method to construct confidence intervals for impulse response coefficients of AR(1) models. Our bootstrap method is based on the LP approach and involves a residual bootstrap procedure applied to AR(1) models. We present theoretical results for our bootstrap method and proposed confidence intervals. First, we prove the uniform consistency of the LP-residual bootstrap over a large class of AR(1) models that allow for a unit root, conditional heteroskedasticity of unknown form, and martingale difference shocks. Then, we prove the asymptotic validity of our confidence intervals over the same class of AR(1) models. Finally, we show that the LP-residual bootstrap provides asymptotic refinements for confidence intervals on a restricted class of AR(1) models relative to those required for the uniform consistency of our bootstrap.

We propose a one-to-many matching estimator of the average treatment effect based on propensity scores estimated by isotonic regression. This approach is predicated on the assumption of monotonicity in the propensity score function, a condition that can be justified in many economic applications. We show that the nature of the isotonic estimator can help us to fix many problems of existing matching methods, including efficiency, choice of the number of matches, choice of tuning parameters, robustness to propensity score misspecification, and bootstrap validity. As a by-product, a uniformly consistent isotonic estimator is developed for our proposed matching method.

Detecting multiple structural breaks at unknown dates is a central challenge in time-series econometrics. Step-indicator saturation (SIS) addresses this challenge during model selection, and we develop its asymptotic theory for tuning parameter choice. We study its frequency gauge—the false detection rate—and show it is consistent and asymptotically normal. Simulations suggest that a smaller gauge minimizes bias in post-selection regression estimates. For the small gauge situation, we develop a complementary Poisson theory. We compare the local power of SIS to detect shifts with that of Andrews’ break test. We find that SIS excels when breaks are near the sample end or closely spaced. An application to U.K. labor productivity reveals a growth slowdown after the 2008 financial crisis.

We investigate the properties of the linear two-way fixed effects (FE) estimator for panel data when the underlying data generating process (DGP) does not have a linear parametric structure. The FE estimator is consistent for some pseudo-true value and we characterize the corresponding asymptotic distribution. We show that the rate of convergence is determined by the degree of model misspecification, and that the asymptotic distribution can be non-normal. We propose a novel autoregressive double adaptive wild (AdaWild) bootstrap procedure applicable for a large class of DGPs. Monte Carlo simulations show that it performs well for panels of small and moderate dimensions. We use data from U.S. manufacturing industries to illustrate the benefits of our procedure.

We contribute to the recent debate on the instability of the slope of the Phillips curve by offering insights from a flexible time-varying instrumental variable (IV) approach robust to weak instruments. Our robust approach focuses directly on the Phillips curve and allows general forms of instability, in contrast to current approaches based either on structural models with time-varying parameters or IV estimates in ad-hoc sub-samples. We find evidence of a weakening of the slope of the Phillips curve starting around 1980. We also offer novel insights on the Phillips curve during the recent pandemic: The flattening has reverted and the Phillips curve is back.

We consider spline-based additive models for estimation of conditional treatment effects. To handle the uncertainty due to variable selection, we propose a method of model averaging with weights obtained by minimizing a J-fold cross-validation criterion, in which a nearest neighbor matching is used to approximate the unobserved potential outcomes. We show that the proposed method is asymptotically optimal in the sense of achieving the lowest possible squared loss in some settings and assigning all weight to the correctly specified models if such models exist in the candidate set. Moreover, consistency properties of the optimal weights and model averaging estimators are established. A simulation study and an empirical example demonstrate the superiority of the proposed estimator over other methods.

Time series of counts often display complex dynamic and distributional characteristics. For this reason, we develop a flexible framework combining the integer-valued autoregressive (INAR) model with a latent Markov structure, leading to the hidden Markov model-INAR (HMM-INAR). First, we illustrate conditions for the existence of an ergodic and stationary solution and derive closed-form expressions for the autocorrelation function and its components. Second, we show consistency and asymptotic normality of the conditional maximum likelihood estimator. Third, we derive an efficient expectation–maximization algorithm with steps available in closed form which allows for fast computation of the estimator. Fourth, we provide an empirical illustration and estimate the HMM-INAR on the number of trades of the Standard & Poor’s Depositary Receipts S&P 500 Exchange-Traded Fund Trust. The combination of the latent HMM structure with a simple INAR$(1)$ formulation not only provides better fit compared to alternative specifications for count data, but it also preserves the economic interpretation of the results.

For a multidimensional Itô semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013, The Annals of Statistics 41(3), 1462–1484) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated functional and a spot volatility estimator with a forward uniform kernel. Motivated by recent results that show that spot volatility estimators with general two-sided kernels of unbounded support are more accurate, in this article, an estimator using a general kernel spot volatility estimator as the plug-in is considered. A biased central limit theorem for estimating the integrated functional is established with an optimal convergence rate. Central limit theorems for properly de-biased estimators are also obtained both at the optimal convergence regime for the bandwidth and when applying undersmoothing. Our results show that one can significantly reduce the estimator’s bias by adopting a general kernel instead of the standard uniform kernel. Our proposed bias-corrected estimators are found to maintain remarkable robustness against bandwidth selection in a variety of sampling frequencies and functions.

In this article, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of high-frequency observations as well as time variations of coefficient processes. Specifically, we employ the Huber loss and a truncation scheme to handle heavy-tailed observations, while $\ell _{1}$-regularization is adopted to overcome the curse of dimensionality. To account for the time-varying coefficient, we estimate local coefficients which are biased due to the $\ell _{1}$-regularization. Thus, when estimating integrated coefficients, we propose a debiasing scheme to enjoy the law of large numbers property and employ a thresholding scheme to further accommodate the sparsity of the coefficients. We call this robust thresholding debiased LASSO (RED-LASSO) estimator. We show that the RED-LASSO estimator can achieve a near-optimal convergence rate. In the empirical study, we apply the RED-LASSO procedure to the high-dimensional integrated coefficient estimation using high-frequency trading data.

This article proposes a novel method for estimating quantile regression models that account for sample selection. Unlike the approach by Arellano and Bonhomme (2017, Econometrica 85(1), 1–28; hereafter referred to as AB17), which employs a parametric selection equation, our method utilizes a standard binary quantile regression model to handle the selection issue, thereby accommodating general heterogeneity in both the selection and outcome equations. We adopt a semiparametric estimation technique for the outcome quantile regression by integrating local moment conditions, resulting in $\sqrt {n}$-consistent estimators for the quantile coefficients and copula parameter. Monte Carlo simulation results demonstrate that our estimator performs well in finite samples. Additionally, we apply our method to examine the wage distribution among women using a randomly simulated sample from the US General Social Survey. Our key finding is the presence of significant positive selection among women in the US, which is notably more pronounced than the estimates produced by the AB17’s model.

This article studies the identification of complete economic models with testable assumptions. We start with a local average treatment effect ($LATE$) model where the “No Defiers,” the independent IV assumption, and the exclusion restrictions can be jointly refuted by some data distributions. We propose two relaxed assumptions that are not refutable, with one assumption focusing on relaxing the “No Defiers” assumption while the other relaxes the independent IV assumption. The identified set of $LATE$ under either of the two relaxed assumptions coincides with the classical $LATE$ Wald ratio expression whenever the original assumption is not refuted by the observed data distribution. We propose an estimator for the identified $LATE$ and derive the estimator’s limit distribution. We then develop a general method to relax a refutable assumption A. This relaxation method requires finding a function that measures the deviation of an econometric structure from the original assumption A, and a relaxed assumption $\tilde {A}$ is constructed using this measure of deviation. We characterize a condition to ensure the identified sets under $\tilde {A}$ and A coincide whenever A is not refuted by the observed data distribution and discuss the criteria to choose among different relaxed assumptions.

This article considers a three-dimensional latent factor model in the presence of one set of global factors and two sets of local factors. We show that the numbers of global and local factors can be estimated uniformly and consistently. Given the number of global and local factors, we propose a two-step estimation procedure based on principal component analysis (PCA) and establish the asymptotic properties of the PCA estimators. Monte Carlo simulations demonstrate that they perform well in finite samples. An application to the dataset of international trade reveals the relative importance of different types of factors.