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In this paper we examine a novel way of imposing shape constraints on a localpolynomial kernel estimator. The proposed approach is referred to as ShapeConstrained Kernel-weighted Least Squares (SCKLS). We prove uniform consistencyof the SCKLS estimator with monotonicity and convexity/concavity constraintsand establish its convergence rate. The competitiveness of SCKLS is shown in acomprehensive simulation study. Finally, we analyze Chilean manufacturing datausing the SCKLS estimator and quantify production in the plastics and woodindustries. The results show that exporting firms have significantly higherproductivity.

Shape constrained kernel-weighted least squares: Application to production function estimation for Chilean manufacturing industries