Quantile control method: Causal inference with one treated unit via random forest

Abstract

The synthetic control and regression control methods are popular approaches for estimating treatment effects in panel data with one treated unit but often rely on placebo tests for informal inference. Chen, Xiao, and Yao (Forthcoming, https://doi.org/10.1016/j.jeconom.2024.105789) propose the quantile control method (qcm), which constructs confidence intervals for treatment effects by estimating the 2.5% and 97.5% quantiles of the counterfactual outcomes through quantile regressions. In particular, a nonparametric ensemble machine learning method known as quantile random forest is used to implement quantile regressions. It is robust to heteroskedasticity, autocorrelation, and model misspecifications and easily accommodates high-dimensional data. Simulations showed that qcm confidence intervals enjoy excellent empirical coverage in finite samples. In this article, we introduce the qcm command, which easily implements qcm, and illustrate its use by revisiting the examples of the economic impact of German reunification on West Germany and the effect of carbon taxes on CO2 emissions in Sweden.