The spurious effect of unit roots on vector autoregressions

Hiro Y. Toda · Peter C.B. Phillips

77 citations0/0 files storedJournal of Econometrics

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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 (1980, 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. The derived asymptotic distribution is free of nuisance parameters so that we can unambiguously determine the effect of including the random walk. Some simulated critical values for the asymptotic distribution are reported. 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.

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References

1991Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models 1990Inference in Linear Time Series Models with some Unit Roots 1986Understanding spurious regressions in econometrics 1993Vector Autoregressions and Causality 1988Statistical Inference in Regressions with Integrated Processes: Part 1 1982Policy Analysis with Econometric Models 1987Interpreting Evidence on Money-Income Causality 1989Statistical Inference in Regressions with Integrated Processes: Part 2

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