COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1777

Inconsistent VAR Regression with Common Explosive Roots

Peter C. B. Phillips and Tassos Magdalinos

January 2011

Nielsen (2009) shows that vector autoregression is inconsistent when there are common explosive roots with geometric multiplicity greater than unity. This paper discusses that result, provides a co-explosive system extension and an illustrative example that helps to explain the finding, gives a consistent instrumental variable procedure, and reports some simulations. Some exact limit distribution theory is derived and a useful new reverse martingale central limit theorem is proved.

Keywords: Co-explosive behavior, Common roots, Endogeneity, Forward instrumentation, Geometric multiplicity, Reverse martingale

JEL Classification: C22