  There are many environments in econometrics which require nonseparable
modeling of a structural disturbance. In a nonseparable model with endogenous
regressors, key conditions are validity of instrumental variables and
monotonicity of the model in a scalar unobservable variable. 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 specified. Our test statistic is asymptotically normally
distributed under correct specification and consistent against any alternative
model. In addition, test statistics to justify the model simplification are
established. Finite sample properties are examined in a Monte Carlo study and
an empirical illustration is provided.
