rcm: A command for the regression control method

The regression control method, also known as the panel-data approach for program evaluation (Hsiao, Ching, and Wan, 2012, Journal of Applied Econometrics 27: 705–740; Hsiao and Zhou, 2019, Journal of Applied Econometrics 34: 463–481), is a convenient method for causal inference in panel data that exploits cross-sectional correlation to construct counterfactual outcomes for a single treated unit by linear regression. In this article, we present the rcm command, which efficiently implements the regression control method with or without covariates. Available methods for model selection include best subset, lasso, and forward stepwise and backward stepwise regression, while available selection criteria include the corrected Akaike information criterion, the Akaike information criterion, the Bayesian information criterion, the modified Bayesian information criterion, and cross-validation. Estimation and counterfactual predictions can be made by ordinary least squares, lasso, or postlasso ordinary least squares. For statistical inference, both the in-space placebo test using fake treatment units and the in-time placebo test using a fake treatment time can be implemented. The rcm command produces a series of graphs for visualization along the way. We demonstrate the use of the rcm command by revisiting classic examples of political and economic integration between Hong Kong and mainland China (Hsiao, Ching, and Wan 2012) and German reunification (Abadie, Diamond, and Hainmueller, 2015, American Journal of Political Science 59: 495–510).

回归控制法（regression control method），又称项目评估的面板数据方法（panel-data approach for program evaluation）（Hsiao、Ching与Wan，2012，《应用计量经济学杂志》(Journal of Applied Econometrics) 27: 705–740；Hsiao与Zhou，2019，《应用计量经济学杂志》(Journal of Applied Econometrics) 34: 463–481），是面板数据因果推断的便捷手段，其利用截面相关性，通过线性回归为单个干预单元构建反事实结果。本文提出rcm命令，可高效实现带协变量或无协变量场景下的回归控制法。模型选择的可选方法包括最优子集回归、套索回归（lasso）、向前逐步回归与向后逐步回归；可选的模型选择准则包括修正赤池信息准则（corrected Akaike information criterion）、赤池信息准则（Akaike information criterion）、贝叶斯信息准则（Bayesian information criterion）、修正贝叶斯信息准则（modified Bayesian information criterion）以及交叉验证（cross-validation）。估计与反事实预测可通过普通最小二乘法、套索回归或后套索普通最小二乘法完成。针对统计推断，可实现基于虚假干预单元的空间安慰剂检验（in-space placebo test）以及基于虚假干预时点的时间安慰剂检验（in-time placebo test）。rcm命令在运行过程中会生成一系列可视化图表。我们通过重新审视香港与内地政治经济一体化的经典案例（Hsiao、Ching及Wan，2012）以及德国统一案例（Abadie、Diamond及Hainmueller，2015，《美国政治学杂志》(American Journal of Political Science) 59: 495–510），演示了rcm命令的使用方法。