Nonlinear Econometric Models with Deterministically Trending Variables
提出一种替代渐近框架，用于处理含确定性趋势变量的非线性模型，证明广义矩估计量的渐近分布与无趋势变量时相同（正态和卡方），但协方差矩阵依赖于趋势形式，为实际应用中的标准渐近近似提供了理论依据。
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.