COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1053

"Nonlinear Econometric Models with Deterministically Trending Variables"

Donald W. K. Andrews and C. John McDermott

August 1993

This paper considers an alternative asymptotic framework to standard sequential asymptotics for nonlinear models with deterministically trending variables. The asymptotic distributions of generalized method of moments estimators and corresponding test statistics are derived using this framework. The asymptotic distributions are shown to be the same with deterministically trending variables as with non-trending variables. That is, the distributions are normal and chi-squared respectively. The asymptotic covariance matrices of the estimators, however, are found to depend on the form of the trends. These findings provide a justification for the use of standard asymptotic approximations in nonlinear models even when the variables have deterministic trends.

Keywords: Asymptotics, Deterministic trend, Generalized method of moments estimator, Hypothesis test, Nonlinear econometric model, Time Trend

JEL Classification: 211