Long-run Relations in a Well Defined Statistical Model for the Data Generating Process. Cointegration Analysis of the PPP and the UIP Relations

The concept of a well defined statistical model for the data generating process is given an empirical formulation in the vector autoregressive model under assumption of cointegration in an analysis of prices, interest rates and exchange rates between Denmark and Germany. The long-run relations are estimated as stationary linear combinations between the non-stationary variables and the presence of deterministic components in the common stochastic trends is investigated. Structural hypothesis on the purchasing power parity and uncovered interest rate hypothesis are tested in a full information maximum likelihood framework. Empirical support for both of these fundamental relations are found. Comparative analysis of the long-run relations based on the single equation ecm-model as well as the Engle-Granger two-step procedure are performed. The full system versus the partial system analysis approach is discussed in terms of optimal inference on the long-run parameters. By testing hypotheses on the weight coefficients it is empirically demonstrated that the full five-dimensional system cannot be reduced without loosing some efficiency.