A comparison of autoregressive distributed lag and dynamic OLS cointegration estimators in the case of a serially correlated cointegration error

Abstract

Summary This paper deals with a family of parametric, single-equation cointegration estimators that arise in the context of the autoregressive distributed lag (ADL) models. We particularly focus on a subclass of the ADL models, those that do not involve lagged values of the dependent variable, referred to as augmented static (AS) models. The general ADL and the restricted AS models give rise to the ADL and dynamic OLS (DOLS) estimators, respectively. The relative performance of these estimators is assessed by means of Monte Carlo simulations in the context of a triangular data generation process (DGP) where the cointegration error and the error that drives the regressor follow a VAR(1) process. The results suggest that ADL fares consistently better than DOLS, both in terms of estimation precision and reliability of statistical inferences. This is due to the fact that DOLS, as opposed to ADL, does not fully correct for the second-order asymptotic bias effects of cointegration, since a ‘truncation bias’ always remains. As a result, the performance of DOLS approaches that of ADL, as the number of lagged values of the first difference of the regressor in the AS model increases. Another set of Monte Carlo simulations suggests that the commonly used information criteria select the correct order of the ADL model quite frequently, thus making the employment of ADL over DOLS quite appealing and feasible. Additional results suggest that ADL re-emerges as the optimal estimator within a wider class of asymptotically efficient estimators including, apart from DOLS, the semiparametric fully modified least squares (FMLS) estimator of Phillips and Hansen (1990, Review of Economic Studies 57, 99–125), the non-linear parametric estimator (PL) of Phillips and Loretan (1991, Review of Economic Studies 58, 407–36) and the system-based maximum likelihood estimator (JOH) of Johansen (1991, Econometrica 59, 1551–80). All the aforementioned results are robust to alternative models for the error term, such as vector autoregressions of higher order, or vector moving average processes.