There are many environments in econometrics which require nonseparable
modeling of a structural disturbance. In a nonseparable model, key conditions
are validity of instrumental variables and monotonicity of the model in a scalar
unobservable. Under these conditions the nonseparable model is equivalent to
an instrumental quantile regression model. A failure of the key conditions, however,
makes instrumental quantile regression potentially inconsistent. This paper
develops a methodology for testing the hypothesis whether the instrumental
quantile regression model is correctly specied. Our test statistic is asymptotically
normally distributed under correct specication and consistent against any
alternative model. In addition, test statistics to justify model simplication are
established. Finite sample properties are examined in a Monte Carlo study and
an empirical illustration.
Nonparametric quantile regression, instrumental variable,
specication test, local alternative, nonlinear inverse problem.