Exogeneity in Vector Error Correction Models with Purely Exogenous Long‐Run Paths

Abstract

Existing exogeneity conditions of literature are only sufficient and imply ‘overly strong’ constraints on long‐run parameters. This paper presents some new results on exogeneity in vector error correction models. A key concept of the analysis is the ‘purely exogenous long‐run path’, i.e. a cointegrating vector only including ‘exogenous’ variables. Extending earlier results of Johansen, S. (1992). ‘Cointegration in partial systems and the efficiency of single‐equation analysis’, Journal of Econometrics, Vol. 52, pp. 389–402 and of Toda and Phillips (1991). Vector Autoregressions and Causality, Cowles Foundation Discussion Paper, No. 977 among others, we propose a framework based on two canonical representations of the long‐run matrix, which can constitute a suitable basis to formulate a necessary and sufficient condition for non‐causality as well as a condition for strong exogeneity. An interesting property is that the statistics involved in the sequential procedures for testing these conditions are distributed as χ2 variables and can, therefore, easily be calculated with the usual statistical computer packages, which makes our approach fully operational, empirically. Finally, the power and size distortions of the sequential test procedures are analysed using Monte Carlo experiments.