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We develop a novel method of constructing confidence bands for nonparametricregression functions under shape constraints. This method can be implementedvia a linear programming, and it is thus computationally appealing. Weillustrate a usage of our proposed method with an application to the regressionkink design (RKD). Econometric analyses based on the RKD often suffer from wideconfidence intervals due to slow convergence rates of nonparametric derivativeestimators. We demonstrate that economic models and structures motivate shaperestrictions, which in turn contribute to shrinking the confidence interval foran analysis of the causal effects of unemployment insurance benefits onunemployment durations.

Linear programming approach to nonparametric inference under shape restrictions: with an application to regression kink designs