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.