Estimating a treatment effect under uncertainty with application to a high‐speed railway system

Abstract

AbstractThis article proposes new treatment effect models and applies them to analyse the effect of high‐speed railways on population density. These models focus on the difference in treatment intensity across treated observations. The difference in treatment intensity occurs as a result of uncertainty over whether the treatment will be properly administered to observations. When evaluating large infrastructure, such as high‐speed railways, the introduction of infrastructure is considered as the treatment for municipalities. The treatment in such cases usually takes time and poses uncertainty whether it will be complete or not. To address such uncertainty, we extend the Roy model—a typical treatment effect model—under a reasonable assumption to enable it to incorporate observations that are treated but their treatment is not complete. Further, we allow the correlation between how these observations are determined and their outcomes and treatment assignments. This article also discusses the identification problem with respect to estimating model parameters. The proposed statistical models are applied to evaluate the effect of the Shinkansen, a high‐speed railway in Japan, on population density. The Canadian Journal of Statistics 42: 337–358; 2014 © 2014 Statistical Society of Canada