arXiv subjects

Lucas Z. Zhang

Publications and source records attributed to Lucas Z. Zhang.

3 recordsLinked to original sources

arXiv2026

Difference-in-Differences with Time-varying Continuous Treatments using Double/Debiased Machine Learning

We propose a difference-in-differences (DiD) framework designed for time-varying continuous treatments across multiple periods. Specifically, we estimate the average treatment effect on the treated (ATET) by comparing distinct non-zero treatment intensities. Identification rests on a conditional parallel trends assumption that accounts for observed covariates and past treatment histories. Our approach allows for lagged treatment effects and, in repeated cross-sectional settings, accommodates compositional changes in covariates. We develop kernel-based ATET estimators for both repeated cross-sections and panel data, leveraging the double/debiased machine learning framework to handle potentially high-dimensional covariates and histories. We establish the asymptotic properties of our estimators under mild regularity conditions and demonstrate via simulations that their undersmoothed versions perform well in finite samples. As an empirical illustration, we apply our estimator to assess the effect of the second-dose COVID-19 vaccination rate in Brazil and find that higher vaccination rates reduce COVID-19-related mortality after a lag of several weeks.

econ.EM↗

arXiv2025

Continuous difference-in-differences with double/debiased machine learning

This paper extends difference-in-differences to settings with continuous treatments. Specifically, the average treatment effect on the treated (ATT) at any level of treatment intensity is identified under a conditional parallel trends assumption. Estimating the ATT in this framework requires first estimating infinite-dimensional nuisance parameters, particularly the conditional density of the continuous treatment, which can introduce substantial bias. To address this challenge, we propose estimators for the causal parameters under the double/debiased machine learning framework and establish their asymptotic normality. Additionally, we provide consistent variance estimators and construct uniform confidence bands based on a multiplier bootstrap procedure. To demonstrate the effectiveness of our approach, we revisit a previous study on the 1983 Medicare Prospective Payment System reform, reframing it as a DiD with continuous treatment and non-parametrically estimating its effects.

econ.EM↗

arXiv2025

Approximate Sparsity Class and Minimax Estimation

Motivated by the orthogonal series density estimation in $L^2([0,1],μ)$, in this project we consider a new class of functions that we call the approximate sparsity class. This new class is characterized by the rate of decay of the individual Fourier coefficients for a given orthonormal basis. We establish the $L^2([0,1],μ)$ metric entropy of such class, with which we show the minimax rate of convergence. For the density subset in this class, we propose an adaptive density estimator based on a hard-thresholding procedure that achieves this minimax rate up to a $\log$ term.

econ.EM↗