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.
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Length: 30 pages Date of creation: May 1991 Date of revision: Publication status: Published in Oxford Economic Papers (1993), 59: 229-255 Handle: RePEc:cwl:cwldpp:978
Find related papers by JEL classification: C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Sims, Christopher A, 1980.
"Macroeconomics and Reality,"
Econometrica,
Econometric Society, vol. 48(1), pages 1-48, January.
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Toda, Hiro Y & Phillips, Peter C B, 1993.
"Vector Autoregressions and Causality,"
Econometrica,
Econometric Society, vol. 61(6), pages 1367-93, November.
[Downloadable!] (restricted)
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