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Inconsistent VAR Regression with Common Explosive Roots

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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d17b/d1777.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1777.

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Length: 32 pages
Date of creation: Jan 2011
Date of revision:
Publication status: Published in Econometric Theory (August 2013), 29(4): 808-837
Handle: RePEc:cwl:cwldpp:1777

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Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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  1. Peter C. B. Phillips & Jun Yu, 2009. "Dating the Timeline of Financial Bubbles During the Subprime Crisis," Finance Working Papers 23051, East Asian Bureau of Economic Research.
  2. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2007. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Working Papers 222007, Hong Kong Institute for Monetary Research.
  3. Fanelli, Luca, 2007. "Present Value Relations, Granger Noncausality, And Var Stability," Econometric Theory, Cambridge University Press, vol. 23(06), pages 1254-1260, December.
  4. Paolo Paruolo & Alessandra Luati, 1997. "Nota sulla distribuzione di una base di norma unitaria del complemento ortogonale di un vettore gaussiano: il caso bidimensionale," Quaderni di Dipartimento 3, Department of Statistics, University of Bologna.
  5. Peter C.B. Phillips, 1982. "The Exact Distribution of LIML: I," Cowles Foundation Discussion Papers 658, Cowles Foundation for Research in Economics, Yale University.
  6. Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2009. "Co-integration Rank Testing under Conditional Heteroskedasticity," CREATES Research Papers 2009-22, School of Economics and Management, University of Aarhus.
  7. Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2012. "Bootstrap Determination of the Co-integration Rank in Heteroskedastic VAR Models," CREATES Research Papers 2012-36, School of Economics and Management, University of Aarhus.
  8. Magdalinos, Tassos & Phillips, Peter C.B., 2009. "Limit Theory For Cointegrated Systems With Moderately Integrated And Moderately Explosive Regressors," Econometric Theory, Cambridge University Press, vol. 25(02), pages 482-526, April.
  9. Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
  10. Phillips, Peter C.B. & Magdalinos, Tassos, 2008. "Limit Theory For Explosively Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 24(04), pages 865-887, August.
  11. Anders Rygh Swensen, 2006. "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models -super-1," Econometrica, Econometric Society, Econometric Society, vol. 74(6), pages 1699-1714, November.
  12. Fischer, Andreas M., 1993. "Weak exogeneity and dynamic stability in cointegrated VARs," Economics Letters, Elsevier, vol. 43(2), pages 167-170.
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