Prediction Intervals of Panel Data Approach for Programme Evaluation

ABSTRACT We consider the inference on individual and time specific treatment effects on the treated within the framework of panel data approach for programme evaluation. We formulate the target problem as constructing prediction intervals for high‐dimensional linear regressions with weakly dependent data. Post‐LASSO OLS is used for estimation, while dependent wild bootstrap and simple residual bootstrap are used for the construction of prediction intervals. The proposed prediction intervals are proved to have asymptotic validity as the number of pretreatment times goes to infinity. In the proof, we also establish the model selection consistency of LASSO for dependent data and under bootstrap measure, which may be of independent interest. Monte Carlo experiments illustrate that our method outperforms existing methods in finite samples under a wide variety of data generating processes except nonstationary data. Two empirical applications are also provided.