Do Reservation Wages Decline Monotonically? A Novel Statistical Test

This paper develops a test for monotonicity of the regression function under endogeneity. The novel testing framework is applied to study monotonicity of the reservation wage as a function of elapsed unemployment duration. Hence, the objective of the paper is twofold: from a theoretical perspective, it proposes a test that formally assesses monotonicity of the regression function in the case of a continuous, endogenous regressor. This is accomplished by combining different nonparametric conditional mean estimators using either control functions or unobservable exogenous variation to address endogeneity with a test statistic based on a functional of a second order U-process. The modified statistic is shown to have a non-standard asymptotic distribution (similar to related tests) from which asymptotic critical values can directly be derived rather than approximated by bootstrap resampling methods. The test is shown to be consistent against general alternatives. From an empirical perspective, the paper provides a detailed investigation of the effect of elapsed unemployment duration on reservation wages in a nonparametric setup. This effect is difficult to measure due to the simultaneity of both variables. Despite some evidence in the literature for a declining reservation wage function over the course of unemployment, no information about the actual form of this decline has yet been provided. Using a standard job search model, it is shown that monotonicity of the reservation wage function, a restriction imposed by several empirical studies, only holds under certain (rather restrictive) conditions on the variables in the model. The test from above is applied to formally evaluate this shape restriction and it is found that reservation wage functions (conditional on different characteristics) do not decline monotonically.