Time-varying coefficient models have been widely used to model changing relationships of economic and financial variables. The existing literature usually specifies the time-varying coefficient vector as a stochastic stationary process, a deterministic function of time, or a unit root process....

Consider a nonseparable model Y=R(X,U) where Y and X are observed, while U is unobserved and conditionally independent of X. This paper provides the first nonparametric test of whether R takes the form of a transformation model, meaning that Y is monotonic in the sum of a function of X plus a...