Structural analysis of vector error correction models with exogenous I(1) variables

This paper generalizes the existing cointegration analysis literature in two respects. Firstly, the problem of efficient estimation of vector error correction models containing exogenous I(1) variables is examined. The asymptotic distributions of the (log-)likelihood ratio statistics for testing cointegrating rank are derived under different intercepts and trend specifications and their respective critical values are tabulated. Tests for the presence of an intercepts or linear trend in the cointegrating relations are also developed together with model misspecification tests. Secondly, efficient estimation of vector error correction models when the short-run dynamics may differ within and between equations is considered. A re-examination of the purchasing power parity and the uncovered interest rate parity hypotheses is conducted using U.K. data under the maintained assumption of exogenously given foreign and oil prices.