FUNCTIONAL FORM MISSPECIFICATION IN REGRESSIONS WITH A UNIT ROOT
研究了单位根回归模型中函数形式误设时非线性最小二乘估计量的极限性质，发现估计量的收敛行为取决于真实模型与拟合模型的相对大小，误设可能导致收敛速度变慢和极限分布改变。
We examine the limit properties of the nonlinear least squares (NLS) estimator under functional form misspecification in regression models with a unit root. Our theoretical framework is the same as that of Park and Phillips (2001, Econometrica 69, 117–161). We show that the limit behavior of the NLS estimator is largely determined by the relative orders of magnitude of the true and fitted models. If the estimated model is of different order of magnitude than the true model, the estimator converges to boundary points. When the pseudo-true value is on a boundary, standard methods for obtaining rates of convergence and limit distribution results are not applicable. We provide convergence rates and limit theory when the pseudo-true value is an interior point. If functional form misspecification is committed in the presence of stochastic trends, the convergence rates can be slower and the limit distribution different than that obtained under correct specification.