High-Dimensional Statistics for Causal Inference and Panel Data

Abstract

This dissertation develops new econometric tools for causal inference in panel data settings, with a focus on addressing key biases that arise in high-dimensional and dynamic environments. While this dissertation is motivated by the need to flexibly measure the economic impacts of climate change, the methods I develop are much more general. They apply broadly to panel data problems across empirical economics—including in labor, development, and industrial organization—where standard fixed effects estimators may fail. The first chapter identifies a previously overlooked source of bias in fixed effects panel estimators, which I term dynamic bias. This bias arises when dynamic feedback—where past outcomes influence current outcomes—is ignored in the estimating equation. I show that dynamic bias can be severe even when treatments are randomly assigned and that it often exceeds the well-known Nickell bias. To address this, I develop a bias-corrected estimator that is consistent in panels with a fixed number of time periods. I apply this method to estimate the effects of temperature shocks on GDP, where accounting for dynamic feedback reduces estimated damages substantially. The second chapter, coauthored with Max Vilgalys, proposes a flexible estimator for continuous treatment effects using panel data with fixed effects. We extend the double debiased machine learning (DML) framework to this setting and prove consistency and asymptotic normality. In an application to U.S. agriculture, we show that our estimator captures nonlinear effects of temperature on crop yields more accurately than standard linear models, estimating substantially larger damages from extreme heat. The final chapter further generalizes the methodological contribution by introducing a non-parametric estimator of the average dose-response function. Building on recent developments in DML and automatic double machine learning (ADML), I propose a novel debiasing strategy that directly estimates the bias correction term, yielding favorable theoretical properties. Together, these essays provide practical and theoretically grounded tools for applied researchers working with panel data, particularly in settings characterized by high dimensionality, continuous treatments, or dynamic feedback.