Nonseparable models do not impose any type of additivity between the unobserved part and the observable regressors, and are therefore ideal for many economic applications. To identify these models using the entire joint distribution of the data as summarized in regression quantiles, monotonicity in unobservables has frequently been assumed. This paper establishes that in the absence of monotonicity, the quantiles identify local average structural derivatives of nonseparable models.

This paper explores the empirical content of the weak axiom of revealed preference (WARP) for repeated cross-sections. In a heterogeneous population, the fraction of consumers who violate WARP is not point identified but can be bounded. These bounds, as well as some nonparametric refinements, correspond to intuitive behavioral assumptions if there are two goods. With three or more goods, such intuitions break down, and plausible assumptions can have counterintuitive implications. We also provide estimators and confidence regions. The empirical application reveals that in the British Family Expenditure Survey, upper bounds are frequently positive but lower bounds are not significantly so.