Monotonicity in a scalar unobservable is a now common assumption when modeling heterogeneity in structural models. Among other things, it allows one to recover the underlying structural function from certain conditional quantiles of observables. Nevertheless, monotonicity is a strong assumption...

This paper explores a paradox discovered in recent work by Phillips and Su (2009). That paper gave an example in which nonparametric regression is consistent whereas parametric regression is inconsistent even when the true regression functional form is known and used in regression. This appears...