Quantile control via random forest

This paper studies robust inference procedure for treatment effects in panel data with flexible relationship across units via the random forest method. The key contribution of this paper is twofold. First, we propose a direct construction of prediction intervals for the treatment effect by exploiting the information of the joint distribution of the cross-sectional units using random forest. In particular, we propose a Quantile Control Method (QCM) using the Quantile Random Forest (QRF) to accommodate flexible cross-sectional structure as well as high dimensionality. Second, we establish the asymptotic consistency of QRF under the panel/time series setup with high dimensionality, which is of theoretical interest on its own right. In addition, Monte Carlo simulations are conducted and show that prediction intervals via the QCM have excellent coverage probability for the treatment effects comparing to existing methods in the literature, and are robust to heteroskedasticity, autocorrelation, and various types of model misspecifications. Finally, an empirical application to study the effect of the economic integration between Hong Kong and mainland China on Hong Kong's economy is conducted to highlight the potential of the proposed method.