Nonlinear Cointegration, Misspecification and Bimodality

We derive the asymptotic distribution of the ordinary least squares estimator in a regression

with cointegrated variables under misspecification and/or nonlinearity in the regressors. We show

that, under some circumstances, the order of convergence of the estimator changes and the asymptotic

distribution is non-standard. The t-statistic might also diverge. A simple case arises when the intercept

is erroneously omitted from the estimated model or in nonlinear-in-variables models with endogenous

regressors. In the latter case, a solution is to use an instrumental variable estimator. The core results in

this paper also generalise to more complicated nonlinear models involving integrated time series.

Publicado em Econometic Reviews, v. 33, n.7, p. 713-731, 2014