Testing non-nested semiparametric models: an application to Engel curves specification

Abstract

This paper proposes a test statistic for discriminating between two partly non linear regression models whose parametric components are non-nested. The statistic has the form of a J-test based on a parameter which artificially nests the null and alternative hypotheses. We study in detail the realistic case where all regressors in the nonlinear part are discrete and then no smoothing is required on estimating the nonparametric components. We also consider the general case where continuous and discrete regressors are present. The performance of the test in finite samples is discussed in the context of some Monte Carlo experiments. The test is well motivated for specification testing of Engel curves. We provide an application using data from the 1980 Spanish Expenditure Survey.