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.
Andrews, Donald W.K. and McDermott, John, "Nonlinear Econometric Models with Deterministically Trending Variables" (1993). Cowles Foundation Discussion Papers. 1296.