Cointegration and speed of convergence to equilibrium

This paper is concerned with the time profile of the effects of shocks on cointegrating relations in the context of a multivariate VAR(p) model. It considers alternative methods of characterizing and estimating such a time profile, and in particular proposes the application of the 'persistence profile' approach introduced in Lee and Pesaran (1993). It is shown that the estimator of the persistence profile of the cointegrating relations is root-T-consistent with a limiting normal distribution. The paper also shows that the persistence profile approach is invariant to the way shocks in the underlying VAR model are orthogonalized, which is not true of the traditional impulse response analysis. The theoretical framework is applied to an exchange rate and interest rate data set, and it is found that the persistence profile of the purchasing power parity (PPP) relation converges to zero very slowly, while the persistence profile of the uncovered interest parity (UIP) relation converges to zero reasonably quickly.