Integrated Modied OLS Estimation and Fixed-b Inference for Cointegrating Regressions

This paper is concerned with parameter estimation and inference in a cointegrating regression, where as usual endogenous regressors as well as serially correlated errors are considered. We propose a simple, new estimation method based on an augmented partial sum (integration) transformation of the regression model. The new estimator is labelled Integrated Modi…ed Ordinary Least Squares (IM-OLS). IM-OLS is similar in spirit to the fully modi…ed OLS approach of Phillips and Hansen (1990) and also bears similarities to the dynamic OLS approach of Phillips and Loretan (1991), Saikkonen (1991) and Stock and Watson (1993), with the key di¤erence that IM-OLS does not require estimation of long run variance matrices and avoids the need to choose tuning parameters (kernels, bandwidths, lags). Inference does require that a long run variance be scaled out, and we propose traditional and …xed-b methods for obtaining critical values for test statistics. The properties of IM-OLS are analyzed using asymptotic theory and …nite sample simulations. IM-OLS performs well relative to other approaches in the literature. JEL Classi…cation: C12, C13, C32 Keywords: Bandwidth, cointegration, …xed-b asymptotics, Fully Modi…ed OLS, IM-OLS, kernel 1 Introduction Cointegration methods are widely used in empirical macroeconomics and empirical …nance. It is well known that in a cointegrating regression the ordinary least squares (OLS) estimator of the parameters is super-consistent, i.e. converges at rate equal to the sample size T . When the regressors are endogenous, the limiting distribution of the OLS estimator is contaminated by socalled second order bias terms, see e.g. Phillips and Hansen (1990). The presence of these bias terms renders inference di¢ cult. Consequently, several modi…cations to OLS that lead to zero mean Gaussian mixture limiting distributions have been proposed, which in turn makes standard asymptotic inference feasible. These methods include the fully modi…ed OLS (FM-OLS) approach of Phillips and Hansen (1990) and the dynamic OLS (DOLS) approach of Phillips and Loretan (1991), Saikkonen (1991) and Stock and Watson (1993).