Abstract: In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients and generalizations of this notion like a known nonlinear functional relationship. They also allow to test for degeneracy of the distribution of a random coefficient, i.e., whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We analyze their power against both global and local alternatives in large samples and through a Monte Carlo simulation study. Finally, we apply our framework to analyze the specification in a heterogeneous random coefficients consumer demand model.

Key Words: Nonparametric speci cation testing, random coecients, unobserved heterogeneity, sieve method, characteristic function, consumer demand