The Spurious Effect of Unit Roots on Exogeneity Tests in Vector Autoregressions: An Analytical Study

Hiro Y. Toda and Peter Phillips

No 978, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper analyzes whether inclusion of a statistically independent random walk in a vector autoregression can result in spurious inference. The problem was raised originally by Ohanian (1988). In a Monte Carlo simulation based on the VAR's estimated by Sims (1980b, 1982), Ohanian found that block exogeneity of the genuine variables with respect to an artificially generated random walk variable was rejected too often. In the present paper we attempt a full analytical study of this problem. It can be shown that if the genuine variables are nonstationary, the Wald statistic for testing the block exogeneity hypothesis does not have the usual asymptotic chi-square distribution. This result is consistent with Ohanian's finding. Furthermore, the derived asymptotic distribution is free of nuisance parameters so that we can unambiguously determine the effect of including the random walk. Interestingly, it can also be shown that if the genuine variables of the model are stationary, the asymptotic distribution is still chi-square in spite of the inclusion of the random walk.

Keywords: Random walk; exogeneity; vector autoregressions; unit roots; Wald tests (search for similar items in EconPapers)
JEL-codes: C32 C51 C52 (search for similar items in EconPapers)
Pages: 30 pages
Date: 1991-05
Note: CFP 854.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Oxford Economic Papers (1993), 59: 229-255

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