Testing a Parametric Model Against a Semiparametric Alternative

This paper describes a method for testing a parametric model of the mean of a random variable <italic>Y</italic> conditional on a vector of explanatory variables <italic>X</italic> against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional moments tests based on finitely many moment conditions. The results of Monte Carlo experiments and an application illustrate the usefulness of the new test.