Computation and Operational Properties of Nonparametric Shape-Restricted Estimators

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Estimation and testing methods that require parametric assumptions about the functions in the models being studied have the important drawback that they may yield erroneous results when the parametric restrictions imposed are incorrect. Recently, several estimation and testing techniques have been developed that, instead of specifying parametric structures, specify nonparametric restrictions about the functions in the models. Typical restrictions used are concavity, monotonicity, and homogenity of degree one, which are properties that economic theory often implies about the shape of utility, production, profit, and cost functions. Using presently available algorithms to estimate and test nonparametric functions that satisfy shape restrictions requires more computer memory and CPU time than is available to most researchers. The major contribution of this project comes from developing algorithms for nonparametric estimating and testing that are within most applied researchers' reach. This project develops an algorithm that will make it possible (1) to estimate utility, production, profit, and cost functions, without imposing any parametric structure on these functions, and (2) to test whether imperfect data are consistent with a particular economic hypothesis, such as a minimization or maximization hypothesis. More generally, the new algorithm will allow estimation of nonparametric shape-restricted functions and tests of the hypothesis that a regression function belongs to a particular family of nonparametric functions. The algorithm will be used with actual and simulated data to study the operational properties of nonparametric methods, to compare the performance of nonparametric methods with that of their parametric counterparts, and to uncover features of estimated functions that could not have been discovered previously using parametric methods.