Tests of Additive Derivative Constraints - Stoker, Thomas M. (Review of Economic Studies, 1989)
This paper proposes nonparametric tests of additive constraints on the first and second derivatives of a model E(y|x) = g(x), where the true function g is unknown. Such constraints are illustrated by the economic restrictions of homogeneity and symmetry, and the functional form restrictions of additivity and linearity. The proposed tests are based on estimates of regression coefficients, that statistically characterize the departures from the constraint exhibited by the data. The coefficients are based on weighted-average derivatives, that are reformulated in terms of derivatives of the density of x. Coefficient estimators are proposed that use nonparametric kernel estimators of the density and its derivatives. These statistics are shown to be √N consistent and asymptotically normal, and thus are comparable to estimators based on a (correctly specified) parametric model of g(x).