Tatiana Komarova (London School of Economics)
A Simple Test For Monotonicity And Monotonicity-related Properties
Abstract: We develop a test for monotonicity in a nonparametric framework 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.