Research Interest

Econometric Theory and Applications

• Robust inference for big data (including clustered data);

• Machine learning methods;

• Nonstandard parameter inference, subsampling;

• Uniform inference, threshold regression.

Job Market Paper

“Uniform Inference in High-Dimensional Threshold Regression Models.” Jiatong Li and Hongqiang Yan.

Abstract:

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and l1 estimation errors for the Lasso estimator of the slope parameters and the threshold parameter, accommodating heteroskedastic non-subgaussian error terms and non-subgaussian covariates. Next, we derive the asymptotic distribution of tests involving an increasing number of slope parameters by debiasing (or desparsifying) the Lasso estimator in cases with no threshold effect and with a fixed threshold effect. We show that the asymptotic distributions in both cases are the same, allowing us to perform uniform inference without specifying whether the model is a linear or threshold regression. Additionally, we extend the theory to time series data under the near-epoch-dependence assumption. Finally, we demonstrate the consistent performance of our estimator in both cases through Monte Carlo simulations, and we apply the proposed estimator to empirical analyses of cross-country economic growth rates and the effect of a military news shock on US government spending.

Keywords: high-dimensional data, lasso, near-epoch-dependence, threshold models, uniform inference, tests.

JEL Codes: C12, C13, C24.

Publications

“Algorithmic subsampling under multiway clustering.” Harold D. Chiang, Jiatong Li, Yuya Sasaki.

Econometric Theory (11 July 2023): 1-44.

Abstract:

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 multiway algorithmic subsample means. We show that algorithmic subsampling allows for robustness against potential degeneracy, and even non-Gaussian degeneracy, of the asymptotic distribution under multiway clustering at the cost of efficiency and power loss due to algorithmic subsampling. Simulation studies support this novel result, and demonstrate that inference with algorithmic subsampling entails more accuracy than that without algorithmic subsampling. We derive the consistency and the asymptotic normality for multiway algorithmic subsampling generalized method of moments estimator and for multiway algorithmic subsampling M-estimator. We illustrate with an application to scanner data for the analysis of differentiated products markets.

Keywords: algorithmic subsampling, data sketching, multiway clustering, robustness against degeneracy, scanner data.

JEL Codes: C2, C3, C55.

Working Paper

“Inference for threshold parameter in high-dimensional threshold regression models.” Jiatong Li.

Abstract:

This paper develops a valid inference for the threshold parameter in high-dimensional threshold regression models. I derive the asymptotic distributions of the threshold parameter estimator under three specifications: kink, diminishing jump, and fixed jump, with the latter two representing discontinuities. These distributions are shown to be continuous, satisfying the necessary conditions for applying the subsampling method. To estimate the convergence rate of the threshold parameter when the specification at the threshold point is unknown, I apply the subsampling method. This method is further used to construct confidence intervals. I demonstrate the performance of these confidence intervals through Monte Carlo simulations. I apply the proposed inference method to support the validity of splitting the countries into different regimes when analyzing their growth behavior and defining the state of the economy when estimating the impulse response to a military news shock in the US government spending.

Keywords: high-dimensional data, inference, lasso, subsampling, threshold models.

JEL Codes: C18, C24, C46.