COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 910

"Asymptotics for Semiparametric Econometric Models: III. Testing and Examples"

Donald W.K. Andrews

May 1989

This paper considers tests of nonlinear parametric restrictions in semiparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like test statistics are considered and are shown to have asymptotic chi-square distributions under the null and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios. A number of examples are given to illustrate the testing results of this paper and the estimation and stochastic equicontinuity results of the antecedents to this paper, viz. Andrews (1989b, c).

JE Classification: 211

Keywords: Lagrange multiplier test, likelihood ratio test, semiparametric model, semiparametric tests, Wald test, asymptotic theory