The Monetary Approach in the Presence of I(2) Components: A Cointegration Analysis of the Official and Black Market for Foreign Currency in Latin America

This paper re-examines the long-run properties of the monetary exchange rate model in the presence of a parallel or black market for U.S. dollars in two Latin American countries under the twin hypotheses that the system contains variables that are I(2) and that a linear trend is required in the cointegrating relations. Using the recent I(2) test by Rahbek et al. (1999) to examine the presence of I(2) and I(1) components in a multivariate context we find that the linear trend hypothesis could not be rejected and we find evidence that the system contains two I(2) variables for each country namely, Chile and Mexico, and this finding is reconfirmed by the estimated roots of the companion matrix (Juselius, 1995). The I(2) component led to the transformation of the estimated model by imposing long-run but not short-run proportionality between domestic and foreign money. Three statistically significant cointegrating vectors were found and, by imposing linear restrictions on each vector as suggested by Johansen and Juselius (1994) and Johansen (1995b), the order and rank conditions for identification are satisfied while the test for overidentifying restrictions was significant for either case. The main findings suggest that we reject the forward-looking version of the monetary model for each country, but the unrestricted monetary model is still a valid framework to explain the long-run movements of the parallel exchange rate in both countries. Furthermore, we test for parameter stability using the tests developed by Hansen and Johansen (1993) and it is shown that the dimension of the cointegration rank is sample dependent while the estimated coeffficients do not exhibit instabilities in recursive estimations.