Abstract
Likelihood ratio tests of over-identifying restrictions on the common trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained) maximum likelihood estimation are presented, and asymptotic properties sketched. The techniques are illustrated using the analysis of the PPP and UIP between Switzerland and the US.
Highlights
The duality between the common trends representation and the vector equilibrium-correction model-form (VECM) in cointegrated systems allows researchers to formulate hypotheses of economic interest on any of the two
Johansen (1991), and the Johansen Representation Theorem, for the case of I(2) systems, see Johansen (1992). Both representation theorems show that the loading matrix of the common stochastic trends of highest order is a basis of the orthogonal complement of the matrix of cointegrating relations
This paper focuses on I(2) vector autoregressive (VAR) systems, and it considers the situation where economic hypotheses are entertained for the factor loading matrix of the I(2) trends
Summary
The duality between the common trends representation and the vector equilibrium-correction model-form (VECM) in cointegrated systems allows researchers to formulate hypotheses of economic interest on any of the two. Johansen (1991), and the Johansen Representation Theorem, for the case of I(2) systems, see Johansen (1992) Both representation theorems show that the loading matrix of the common stochastic trends of highest order is a basis of the orthogonal complement of the matrix of cointegrating relations. This paper focuses on I(2) vector autoregressive (VAR) systems, and it considers the situation where (possibly over-identifying) economic hypotheses are entertained for the factor loading matrix of the I(2) trends It is shown how they can be translated into hypotheses on the cointegrating relations, which appear in the VECM representation; the latter forms the basis for maximum likelihood (ML) estimation of I(2) VAR models. Economic hypotheses may directly imply restrictions on the cointegrating vectors in τ, in some cases it is more natural to formulate restrictions on the I(2) loading matrix τ⊥ This is illustrated by the two following examples
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