  We develop a novel method of constructing confidence bands for nonparametric
regression functions under shape constraints. This method can be implemented
via a linear programming, and it is thus computationally appealing. We
illustrate a usage of our proposed method with an application to the regression
kink design (RKD). Econometric analyses based on the RKD often suffer from wide
confidence intervals due to slow convergence rates of nonparametric derivative
estimators. We demonstrate that economic models and structures motivate shape
restrictions, which in turn contribute to shrinking the confidence interval for
an analysis of the causal effects of unemployment insurance benefits on
unemployment durations.
