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Title: A simple test for monotonicity and monotonicity-related properties Authors:  Javier Hidalgo - London School of Economics (United Kingdom)
Tatiana Komarova - London School of Economics and Political Science (United Kingdom) [presenting]
Abstract: A test for monotonicity in a nonparametric framework is developed by using partial sums empirical process. We show that the test has suitable asymptotic properties. In particular we show after appropriate transformation the asymptotic distribution is a functional of a standard Brownian motion, so that critical values are available. However, due to the possible poor approximation of the asymptotic critical values to the finite sample ones, we also describe a valid bootstrap algorithm. We show how methodology can be extended to test for other properties of the regression function such as convexity, concavity, absolute monotonicity and U-shape. We outline how this can extended to a framework when other covariates are present and no monotonicity-related properties are imposed on those. We also establish how monotonicity can be tested in the situation of endogeneity if there is a strong instrument available.