Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data

Abstract

This paper proposes a doubly robust two-stage semiparametric differencein-difference estimator for estimating heterogeneous treatment effects with high-dimensional data. Our new estimator is robust to model miss-specifications and allows for, but does not require, many more regressors than observations. The first stage allows a general set of machine learning methods to be used to estimate the propensity score. In the second stage, we derive the rates of convergence for both the parametric parameter and the unknown function under a partially linear specification for the outcome equation. We also provide bias correction procedures to allow for valid inference for the heterogeneous treatment effects. We evaluate the finite sample performance with extensive simulation studies. Additionally, a real data analysis on the effect of Fair Minimum Wage Act on the unemployment rate is performed as an illustration of our method. An R package for implementing the proposed method is available on Github. 1

Asymptotic Normality in Linear Regression with Approximately Sparse Structure

“…(iv) Finally, in order to prove (27), we show that the cumulants κ (p) j , generated by K(t; p), satisfy κ (p)…”

“…[19,20] for model selection problems in autoregressive time series models; refs. [21][22][23][24][25][26][27][28] for applications on inference of high-dimensional models and high-dimensional instrumental variable (IV) regression models; or [29][30][31][32][33] for recent applications of high-dimensional and sparse methods with financial and economic data. Performing Monte Carlo simulations, we find that the empirical distributions of the corresponding statistic approach the limiting distribution reasonably quickly even for large values of and c. These results suggest that the assumption of sparse structure can be included in the applications and statistical tests, thus, could be further extended following the literature on testing for sparsity or construction of signal-to-noise ratio estimators (see, e.g., [7,[10][11][12]).…”

Asymptotic normality in linear regression with approximately sparse structure

“…Similar structures of the vector β are often found in the literature when approximate sparsity of the coefficients in the linear regression model (1.1) is assumed. See, e.g., Ing (2020) and Cha et al (2021) for a broader view towards sparsity requirements and its' implications to specific high-dimensional algorithms; Shibata (1980) and Ing (2007) for model selection problems in autoregressive time series models; or Belloni et al (2012), Javanmard and Montanari (2014), Zhang and Zhang (2014), Caner and Kock (2018), Belloni et al (2018), Gold et al (2020), Ning et al (2020), Guo et al (2021) for applications on inference of high-dimensional models and high-dimensional instrumental variable (IV) regression models. Performing Monte Carlo simulations, we find that the empirical distributions of the corresponding statistic approach the limiting distribution reasonably quickly even for large values of ρ and c, suggesting that the assumption of sparse structure can be included in the applications and statistical tests.…”