NONLINEAR ECONOMETRIC-MODELS WITH DETERMINISTICALLY TRENDING VARIABLES

This paper considers an alternative asymptotic framework to standard s equential asymptotics for nonlinear models with deterministically tren ding 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 variab les. That is, the distributions are normal and chi-squared respectivel y. The asymptotic covariance matrices of the estimators, however, are found to depend on the form of the trends. These findings provide a ju stification for the use of standard asymptotic approximations in nonli near models even when the variables have deterministic trends.