CONDITIONS ON CONSISTENCY FOR TESTING HYPOTHESES UNDER RATIONAL EXPECTATION BY VECTOR AUTOREGRESSIVE MODELS AND COINTEGRATION

Abstract

The method of testing the cross-equation restrictions under the rational expectation (RE) hypothesis based upon the fitted vector autoregressive (VAR) time series models has been used. It has been applied to test the cross-equation restrictions implied by the expectation hypothesis for the term structure of interest rates, the present value relation in the stock market, and the efficiency hypothesis without risk premium in forward exchange rate market.
We point out that two conventional econometric practices of the prefiltering (or differencing) and the use of law of iterated projection are often inconsistent with the restrictions imposed by the RE hypothesis. We explore the general relation between this inconsistency problem and the cointegrated stochastic processes. New sufficient conditions for logical consistency to test the restrictions imposed by the RE hypothesis are given. We show that some cointegrated filter can be used as a possible solution in some cases. Further, we propose a necessary and sufficient condition for testing the cross-equation constraints imposed by the RE hypothesis based upon the vector autoregressive moving average (VARMA) models, which can be useful as a solution to the difficulty caused by an improper use of the law of iterated projection.