Autoregressive distributed lag models and cointegration

This paper considers cointegration analysis within an autoregressive distributed lag (ADL) framework. First, different reparameterizations and interpretations are reviewed. Then we show that the estimation of a cointegrating vector from an ADL specification is equivalent to that from an error-correction (EC) model. Therefore, asymptotic normality available in the ADL model under exogeneity carries over to the EC estimator. Next, we review cointegration tests based on EC regressions. Special attention is paid to the effect of linear time trends in case of regressions without detrending. Finally, the relevance of our asymptotic results in finite samples is investigated by means of computer experiments. In particular, it turns out that the conditional EC model is superior to the unconditional one.