Testing for a Valid Normalization of Cointegrating Vectors in Vector Autoregressive Processes

Abstract

This article develops test procedures for checking the validity of general normalizing restrictions imposed on cointegrating vectors in vector autoregressive processes. Such test procedures are of importance because normalizing restrictions, possibly combined with overidentifying restrictions, are often necessary for a proper interpretation of cointegrating vectors. The null hypothesis of our tests assumes that the employed normalization is valid or, alternatively, that certain linear combinations of the considered series are not cointegrated. The asymptotic distribution theory of these tests agrees with that of likelihood ratio tests for cointegration. The practical usefulness of the proposed tests is demonstrated by Monte Carlo simulation and an empirical application to interest-rate data.

KEY WORDS:

• Cointegration
• Identification
• Interest rates
• Vector autoregression