Testing for monotonicity under endogeneity

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 finite sample properties of the test 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, which has implications for underlying job search models. This relationship is difficult to measure due to the simultaneity of both variables. Results for UK data indicate that reservation wage functions do in fact not decline monotonically thereby contradicting some partial equilibrium job search models.