Estimation and Inference in Time Series with Omitted I(1) Variables

Standard cointegration analysis yields spurious results when relevant I(1) variables are omitted from the model. As an alternative, an unobserved components approach is proposed where the error term is modelled as the sum of a transitory and a random walk component. The latter should capture omitted I(1) variables and is allowed to be correlated with the observed I(1) variables. Provided that the model is correctly specified and identified, the long-run relation between the non-cointegrated variables can be estimated consistently with maximum likelihood using the Kalman filter. The robustness of this approach to the integration properties of the error terms is supported for small samples via an extensive Monte Carlo study. The proposed methodology is applied to testing purchasing power parity.