Discussion Paper series, Forschungsinstitut zur Zukunft der Arbeit 6364
We propose a specification test for a wide range of parametric models for the conditional distribution function of an outcome variable given a vector of covariates. The test is based on the Cramer-von Mises distance between an unrestricted estimate of the joint distribution function of the data, and a restricted estimate that imposes the structure implied by the model. The procedure is straightforward to implement, is consistent against fixed alternatives, has non-trivial power against local deviations of order n1/2 from the null hypothesis, and does not require the choice of smoothing parameters. In an empirical application, we use our test to study the validity of various models for the conditional distribution of wages in the US.
Cramer-von Mises distance quantile regression distributional regression location-scale model bootstrap wage distribution