Testing for Monotonicity under Endogeneity An Application to the Reservation Wage Function
This paper develops a test for monotonicity of nonparametric regression models under endogeneity, which in its generality is novel in the literature.� The test statistic, which is built upon a second order U-process, introduces 'correction terms' based on control functions that purge the endogeneity.� The test has a non-standard asymptotic distribution from which asymptotic critical values can directly be derived.� Furthermore, the test statistic is extended to accommodate multivariate (exogenous) regressors.� Consistency against general alternatives is proved and the test's finite sample properties are examined in a Monte Carlo experiment.� The test is used to formally assess the monotonicity of the reservation wage as a declining function of elapsed unemployment duration.� This relationship is difficult to measure due to the simultaneity of both variables.� Preliminary results indicate that reservation wage functions do in fact not decline monotonically.
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