Research
Working Papers
“Linear Regression with Common Unobserved Heterogeneity”
with Hugo Freeman
first circulation -2026- arXiv:2610.25589
arXiv
Abstract
We study inference on common slope parameters in linear panel models with two-way unobserved heterogeneity. In linear regression, bias arises from unobserved heterogeneity that is shared between the residual and the covariates. Our common unobserved heterogeneity (CUH) estimator targets this common variation directly: it searches over functionals of the residualised outcome for variation that also resides in the covariates, and seeks to further project out only bias-inducing variation. This makes the estimator less sensitive to weak outcome factors while avoiding the complete removal of exogenous variation in covariates that is unrelated to the confounding heterogeneity. We develop a weak-factor theory based on a singular-value strength index and establish root-NT asymptotic normality of the cross-fitted CUH estimator. Under homoskedastic errors, its asymptotic variance is no larger than that of a common correlated effects factor estimator. Simulations and empirical applications illustrate the resulting bias--variance trade-off and the gains from selectively removing common variation.“Fixed-smoothing Uniform Inference for Quantile Regression”
with Antonio F. Galvao, Seunghwa Rho, Timothy J. Vogelsang, Jungmo Yoon
first circulation - 2026 - arXiv:2609.05883
arXiv R package
Abstract
This paper develops fixed-smoothing inference methods for time-series quantile regression that are robust to heteroskedasticity and autocorrelation. Our approach is uniformly valid over quantile levels and accounts for dependence over time and across quantiles. It enables uniform confidence bands, Wald and Sup-t tests for joint hypotheses, and tests of shape restrictions, providing a unified framework for assessing heterogeneity in quantile effects. Under weak dependence, uniform inference for quantile regression processes is non-pivotal because the limiting distributions depend on the long-run covariance structure across quantiles. To address this issue, we develop two complementary approaches. The uniform-in-tau method estimates this structure and simulates the non-pivotal limiting distribution. For certain tests involving finitely many quantiles, the stack-Wald method delivers pivotal fixed-smoothing inference. We establish the asymptotic validity of both approaches. Simulations show improved size control over existing HAC-based procedures while maintaining good power. An application to stock-return prediction reveals substantial heterogeneity in predictive effects.“Cross-Fitting-Free Debiased Machine Learning with Multiway Dependence”
with Harold D. Chiang
first circulation - 2026 - arXiv:2602.11333
arXiv R package Python package
Abstract
This paper develops an asymptotic theory for two-step debiased machine learning (DML) estimators in generalised method of moments (GMM) models with general multiway clustered dependence, without relying on cross-fitting. While cross-fitting is commonly employed, it can be statistically inefficient and computationally burdensome when first-stage learners are complex and the effective sample size is governed by the number of independent clusters. We show that valid inference can be achieved without sample splitting by combining Neyman-orthogonal moment conditions with a localisation-based empirical process approach, allowing for an arbitrary number of clustering dimensions. The resulting debiased GMM estimators are shown to be asymptotically linear and asymptotically normal under multiway clustered dependence. A central technical contribution of the paper is the derivation of novel global and local maximal inequalities for empirical processes indexed by general classes of functions for separately exchangeable arrays, which underpin our theoretical arguments and are of independent interest.“Inference in High-Dimensional Panel Models: Two-Way Dependence and Unobserved Heterogeneity”
Best Student Paper Award at 2024 Midwest Econometrics Group Meeting
first circulation - 2025 - arXiv:2504.18772
arXiv latest version code & replication
Abstract
Panel data allows for the modeling of unobserved heterogeneity, significantly raising the number of nuisance parameters and making high dimensionality a practical issue. Meanwhile, temporal and cross-sectional dependence in panel data further complicates high-dimensional estimation and inference. This paper proposes a toolkit for high-dimensional panel models with large cross-sectional and time sample sizes. To reduce the dimensionality, I propose a variant of LASSO for two-way clustered panels. While being consistent, the convergence rate of LASSO is slow due to the cluster dependence, rendering inference challenging in general. Nevertheless, asymptotic normality can be established in a semiparametric moment-restriction model by leveraging a clustered-panel cross-fitting approach and, as a special case, in a partial linear model using the full sample. In an exercise of estimating multiplier using panel data, I demonstrate how high dimensionality could be hidden and the proposed toolkit enables flexible modeling and robust inference.“Endogenous Control Bias and Correction with Nonparametric Methods”
with Kyoo il Kim
first circulation - 2024 - arXiv:2401.14395
arXiv code & replication
Abstract
Controls are often needed to make a treatment or instrument conditionally valid, yet they may be related to unobserved outcome determinants. We show that restricted parametric adjustment can fail to recover the structural average response even when the structural model is correctly specified. Under conditional independence and sufficient conditional treatment variation, flexible conditional mean methods identify the structural average response in a nonseparable model, while a control function extension accommodates endogenous treatments with conditionally valid instruments. We develop a specification test to guide the choice between restricted and flexible functional forms. Simulations and a China shock application illustrate the methods.“Another Look at the Linear Probability Model and Nonlinear Index Models”
with Robert S. Martin and Jeffrey M. Wooldridge (Revise & Resubmit at Econometric Reviews)
first circulation - 2023 - arXiv:2308.15338
arXiv latest version code & replication
Abstract
We reassess the linear probability model (LPM) for binary responses from the perspective of average partial effects (APEs). Under certain conditions, the LPM recovers APEs even when the true response probability is nonlinear. Outside these scenarios, we demonstrate in simulations that having a large fraction of fitted values in [0, 1] is neither necessary nor sufficient for OLS to approximate the APEs well, which contradicts the common rationale. We further investigate and refine an ad hoc trimming procedure to reduce bias for LPM, and establish its statistical properties by relating it to a numerically equivalent nonlinear least squares estimator.Publication
“Fixed-b Asymptotics for Panel Models with Two-Way Clustering”
with Timothy J. Vogelsang (Journal of Econometrics, 2024, 244(1): 105831)
first circulation - 2023 - arXiv:2309.08707
arXiv published version
STATA command: xtregtfb. Installation: type net from https://kaichengchen.github.io/statafile/ in STATA