Statistical properties of the two-stage least squares estimator under cointegration

We derive the limiting properties of the two-stage least squares estimator of an equation in a dynamic simultaneous model when variables are nonstationary and cointegrated. The implication on hypothesis testing is also discussed. It is shown that in a structural equation approach what one needs to worry about are the classical issues of identification and estimation, not nonstationarity and cointegration. Conventional formulae for computing the asymptotic covariance of the 2SLS estimator and the Wald-type test statistics remain good approximations despite the fact that variables may be integrated.