arXiv subjects

Harold D. Chiang

Publications and source records attributed to Harold D. Chiang.

At least 19 recordsLinked to original sources

arXiv2026

Cross-Fitting-Free Debiased Machine Learning with Multiway Dependence

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 orthogonal moments 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. Python and R packages are available for implementing the proposed procedures.

econ.EM↗

arXiv2026

Panel Quantile Regression with Common Shocks

This paper develops an asymptotic and inferential theory for fixed-effects panel quantile regression (FEQR) that delivers inference robust to pervasive common shocks. Such shocks induce cross-sectional dependence that is central in many economic and financial panels but largely ignored in existing FEQR theory, which typically assumes cross-sectional independence and requires $T \gg N$. We show that the standard FEQR estimator remains asymptotically normal under the mild condition $(\log N)^2/T \to 0$, thereby accommodating empirically relevant regimes, including those with $T \ll N$. We further show that common shocks fundamentally alter the asymptotic covariance structure, rendering conventional covariance estimators inconsistent, and we propose a simple covariance estimator that remains consistent both in the presence and absence of common shocks. The proposed procedure therefore provides valid robust inference without requiring prior knowledge of the dependence structure, substantially expanding the applicability of FEQR methods in realistic panel data settings.

econ.EM↗

arXiv2026

Gaussian approximation for maximum score and non-smooth M-estimators with multiway dependence

The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a non-Gaussian limiting distribution and exhibits cube-root asymptotics, which complicates statistical inference. We show that, under multiway dependence, the maximum score estimator attains asymptotic normality at a parametric rate. We obtain this surprising result through the development of a general M-estimation theory that accommodates non-smooth objective functions under multiway dependence. We further propose and establish the validity of a bootstrap procedure for inference.

econ.EM↗

arXiv2026

Extremal Quantiles under Two-Way Clustering

This paper studies extremal quantiles under two-way clustered dependence. We show that the limiting distribution of unconditional intermediate-order tail quantiles is Gaussian. This result is notable because two-way clustering typically leads to non-Gaussian limiting behavior. Remarkably, extremal quantiles remain asymptotically Gaussian even in degenerate cases. Building on this insight, we extend our analysis to extremal quantile regression at intermediate orders. Simulation results corroborate our theoretical findings. Finally, we provide an empirical application to growth-at-risk, showing that earlier empirical conclusions remain robust even after accounting for two-way clustered dependence in panel data and the focus on extreme quantiles.

math.ST↗

arXiv2025

Empirical Likelihood for Random Forests and Ensembles

We develop an empirical likelihood (EL) framework for random forests and related ensemble methods, providing a likelihood-based approach to quantify their statistical uncertainty. Exploiting the incomplete $U$-statistic structure inherent in ensemble predictions, we construct an EL statistic that is asymptotically chi-squared when subsampling induced by incompleteness is not overly sparse. Under sparser subsampling regimes, the EL statistic tends to over-cover due to loss of pivotality; we therefore propose a modified EL that restores pivotality through a simple adjustment. Our method retains key properties of EL while remaining computationally efficient. Theory for honest random forests and simulations demonstrate that modified EL achieves accurate coverage and practical reliability relative to existing inference methods.

stat.ML↗

arXiv2025

Genuinely Robust Inference for Clustered Data

Conventional cluster-robust inference can be invalid when data contain clusters of unignorably large size. We formalize this issue by deriving a necessary and sufficient condition for its validity, and show that this condition is frequently violated in practice: specifications from 77% of empirical research articles in American Economic Review and Econometrica during 2020-2021 appear not to meet it. To address this limitation, we propose a genuinely robust inference procedure based on a new cluster score bootstrap. We establish its validity and size control across broad classes of data-generating processes where conventional methods break down. Simulation studies corroborate our theoretical findings, and empirical applications illustrate that employing the proposed method can substantially alter conventional statistical conclusions.

econ.EM↗

arXiv2025

Enhancing the Merger Simulation Toolkit with ML/AI

This paper develops a flexible approach to predict the price effects of horizontal mergers using ML/AI methods. While standard merger simulation techniques rely on restrictive assumptions about firm conduct, we propose a data-driven framework that relaxes these constraints when rich market data are available. We develop and identify a flexible nonparametric model of supply that nests a broad range of conduct models and cost functions. To overcome the curse of dimensionality, we adapt the Variational Method of Moments (VMM) (Bennett and Kallus, 2023) to estimate the model, allowing for various forms of strategic interaction. Monte Carlo simulations show that our method significantly outperforms an array of misspecified models and rivals the performance of the true model, both in predictive performance and counterfactual merger simulations. As a way to interpret the economics of the estimated function, we simulate pass-through and reveal that the model learns markup and cost functions that imply approximately correct pass-through behavior. Applied to the American Airlines-US Airways merger, our method produces more accurate post-merger price predictions than traditional approaches. The results demonstrate the potential for machine learning techniques to enhance merger analysis while maintaining economic structure.

econ.EM↗

arXiv2025

Maximal Inequalities for Separately Exchangeable Empirical Processes

This paper derives new maximal inequalities for empirical processes associated with separately exchangeable random arrays. For fixed index dimension $K\ge 1$, we establish a global maximal inequality bounding the $q$-th moment ($q\in[1,\infty)$) of the supremum of these processes. We also obtain a refined local maximal inequality controlling the first absolute moment of the supremum. Both results are proved for a general pointwise measurable function class. Our approach uses a new technique partitioning the index set into transversal groups, decoupling dependencies and enabling more sophisticated higher moment bounds.

econ.EM↗

arXiv2022

Inference in high-dimensional regression models without the exact or $L^p$ sparsity

This paper proposes a new method of inference in high-dimensional regression models and high-dimensional IV regression models. Estimation is based on a combined use of the orthogonal greedy algorithm, high-dimensional Akaike information criterion, and double/debiased machine learning. The method of inference for any low-dimensional subvector of high-dimensional parameters is based on a root-$N$ asymptotic normality, which is shown to hold without requiring the exact sparsity condition or the $L^p$ sparsity condition. Simulation studies demonstrate superior finite-sample performance of this proposed method over those based on the LASSO or the random forest, especially under less sparse models. We illustrate an application to production analysis with a panel of Chilean firms.

econ.EM↗

arXiv2022

Algorithmic subsampling under multiway clustering

This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for the multiway algorithmic subsample means. Consequently, we discover an additional advantage of the algorithmic subsampling that it allows for robustness against potential degeneracy, and even non-Gaussian degeneracy, of the asymptotic distribution under multiway clustering. Simulation studies support this novel result, and demonstrate that inference with the algorithmic subsampling entails more accuracy than that without the algorithmic subsampling. Applying these basic asymptotic theories, we derive the consistency and the asymptotic normality for the multiway algorithmic subsampling generalized method of moments estimator and for the multiway algorithmic subsampling M-estimator. We illustrate an application to scanner data.

econ.EM↗

arXiv2022

Empirical likelihood and uniform convergence rates for dyadic kernel density estimation

This paper studies the asymptotic properties of and alternative inference methods for kernel density estimation (KDE) for dyadic data. We first establish uniform convergence rates for dyadic KDE. Secondly, we propose a modified jackknife empirical likelihood procedure for inference. The proposed test statistic is asymptotically pivotal regardless of presence of dyadic clustering. The results are further extended to cover the practically relevant case of incomplete dyadic data. Simulations show that this modified jackknife empirical likelihood-based inference procedure delivers precise coverage probabilities even with modest sample sizes and with incomplete dyadic data. Finally, we illustrate the method by studying airport congestion in the United States.

econ.EM↗

arXiv2022

Many Average Partial Effects: with An Application to Text Regression

We study estimation, pointwise and simultaneous inference, and confidence intervals for many average partial effects of lasso Logit. Focusing on high-dimensional, cluster-sampling environments, we propose a new average partial effect estimator and explore its asymptotic properties. Practical penalty choices compatible with our asymptotic theory are also provided. The proposed estimator allow for valid inference without requiring oracle property. We provide easy-to-implement algorithms for cluster-robust high-dimensional hypothesis testing and construction of simultaneously valid confidence intervals using a multiplier cluster bootstrap. We apply the proposed algorithms to the text regression model of Wu (2018) to examine the presence of gendered language on the internet.

econ.EM↗

arXiv2021

Inference for high-dimensional exchangeable arrays

We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over the rectangles and subsequently develop novel multiplier bootstraps with theoretical guarantees. These theoretical results rely on new technical tools such as Hoeffding-type decomposition and maximal inequalities for the degenerate components in the Hoeffiding-type decomposition for the exchangeable arrays. We exhibit applications of our methods to uniform confidence bands for density estimation under joint exchangeability and penalty choice for $\ell_1$-penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities.

econ.EM↗

arXiv2021

Linear programming approach to nonparametric inference under shape restrictions: with an application to regression kink designs

We develop a novel method of constructing confidence bands for nonparametric regression functions under shape constraints. This method can be implemented via a linear programming, and it is thus computationally appealing. We illustrate a usage of our proposed method with an application to the regression kink design (RKD). Econometric analyses based on the RKD often suffer from wide confidence intervals due to slow convergence rates of nonparametric derivative estimators. We demonstrate that economic models and structures motivate shape restrictions, which in turn contribute to shrinking the confidence interval for an analysis of the causal effects of unemployment insurance benefits on unemployment durations.

econ.EM↗

arXiv2020

Multiway Cluster Robust Double/Debiased Machine Learning

This paper investigates double/debiased machine learning (DML) under multiway clustered sampling environments. We propose a novel multiway cross fitting algorithm and a multiway DML estimator based on this algorithm. We also develop a multiway cluster robust standard error formula. Simulations indicate that the proposed procedure has favorable finite sample performance. Applying the proposed method to market share data for demand analysis, we obtain larger two-way cluster robust standard errors than non-robust ones.

econ.EM↗

arXiv2019

Lasso under Multi-way Clustering: Estimation and Post-selection Inference

This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method based on a post-double-selection procedure and show its asymptotic validity. Our procedure can be easily implemented with existing statistical packages. Simulation results demonstrate that the proposed procedure works well in finite sample. We illustrate the proposed method with a couple of empirical applications to development and growth economics.

econ.EM↗

arXiv2019

Post-Selection Inference in Three-Dimensional Panel Data

Three-dimensional panel models are widely used in empirical analysis. Researchers use various combinations of fixed effects for three-dimensional panels. When one imposes a parsimonious model and the true model is rich, then it incurs mis-specification biases. When one employs a rich model and the true model is parsimonious, then it incurs larger standard errors than necessary. It is therefore useful for researchers to know correct models. In this light, Lu, Miao, and Su (2018) propose methods of model selection. We advance this literature by proposing a method of post-selection inference for regression parameters. Despite our use of the lasso technique as means of model selection, our assumptions allow for many and even all fixed effects to be nonzero. Simulation studies demonstrate that the proposed method is more precise than under-fitting fixed effect estimators, is more efficient than over-fitting fixed effect estimators, and allows for as accurate inference as the oracle estimator.

econ.EM↗

arXiv2019

Quantile Treatment Effects in Regression Kink Designs

The literature on regression kink designs develops identification results for average effects of continuous treatments (Card, Lee, Pei, and Weber, 2015), average effects of binary treatments (Dong, 2018), and quantile-wise effects of continuous treatments (Chiang and Sasaki, 2019), but there has been no identification result for quantile-wise effects of binary treatments to date. In this paper, we fill this void in the literature by providing an identification of quantile treatment effects in regression kink designs with binary treatment variables. For completeness, we also develop large sample theories for statistical inference and a practical guideline on estimation and inference.

stat.ME↗