2025 Theses Doctoral

Essays on Econometric Inference with High-Dimensional Factor Models

My dissertation consists of three chapters that develop new methods for estimation and inference in high-dimensional econometric models. A unifying theme across all chapters is the development of theoretically grounded, computationally efficient procedures for model evaluation, testing, and estimation in the presence of latent structures, sparsity, and heterogeneity.

The first chapter proposes a new approach to test conditional independence within the framework of high-dimensional factor models. A Cauchy-weighted measure is introduced to quantify the dependence between the idiosyncratic components and develop a corresponding conditional independence test. This measure, which ranges from 0 to 1, equals 0 if and only if conditional independence is true. It is robust to extreme values and computationally efficient. The proposed test is asymptotically distribution-free under the null hypothesis and capable of detecting nonlinear dependencies under the alternative hypothesis in high-dimensional scenarios. Furthermore, this chapter demonstrates that the approach of first directly estimating the factors using pooled data, followed by performing the test, is invalid when factors are unobserved. Instead, this chapter proposes to estimate the factors within the factor-augmented regression model framework and shows that the corresponding test remains valid. Extensive simulation studies and real data analysis are conducted to validate the effectiveness of this method, demonstrating its superior performance in high-dimensional scenarios.

The second chapter examines the adequacy of a simple, interpretable factor model that relies solely on the common factor component to capture the relationship between covariates and the response variable, compared to a more complex factor-augmented sparse regression model. Existing tests, based on maximum-type statistics or data-splitting projection methods, face notable limitations: the former lose power under moderate sparsity, while the latter introduce randomness and conservatism. This chapter proposes a new projection test with penalties that eliminates data splitting, improving reproducibility and efficiency. By leveraging a penalized projection pursuit framework, the proposed method enhances signal detection under alternatives while preserving validity under the null. The asymptotic null distribution of the proposed test statistic aligns with maximum-type approaches, yet it achieves superior power for moderately sparse signals. The effectiveness and robustness of the proposed test are validated through extensive numerical studies.

The third chapter proposes a new approach to instrumental variable (IV) estimation in high-dimensional settings using scaled principal component analysis (sPCA). While traditional principal component analysis (PCA) is commonly employed to extract latent factors from large panels of instruments for IV construction, it assigns equal weight to all variables and may perform poorly when many instruments are only weakly related to the endogenous regressor. To address this limitation, the chapter adapts sPCA—originally developed for forecasting—to the IV setting. By scaling each candidate instrument according to its relevance to the endogenous variable, sPCA emphasizes informative instruments while down-weighting irrelevant ones. Within a general factor model framework that accommodates heterogeneous factor strength, the chapter establishes the consistency and asymptotic normality of the resulting IV estimator. Simulation studies show that the sPCA-based IV estimator outperforms standard PCA-based IV, especially when only a small subset of instruments is strongly relevant. The proposed method offers a supervised and robust alternative for IV estimation in high-dimensional, data-rich environments.