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Testing for Common Cyclical Features in Var Models with Cointegration

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  • Alain Hecq
  • Franz Palm
  • Jean-Pierre Urbain

Abstract

We consider VAR models for variables exhibiting cointegration and common cyclical features. While the presence of cointegration reduces the rank of the long-run multiplier matrix, other types of common features lead to rank reduction of the short-run dynamics. We distinguish between strong and weak form reduced rank structures. Strong form reduced rank structures analyzed by Engle and Kozicki (1993) arise when a linear combination of the first differenced variables in a cointegrated VAR is white noise whereas in the presence of a weak form reduced rank structure, linear combinations of the first differenced variables corrected for the long-run effects are white noise. The weak form has an interest in its own. For instance, it is a necessary condition for the existence of first order codependent cycles in a VAR(2). Also, it is a necessary condition for the strong form. We also consider the mixed form which combines strong and weak forms. We discuss the model selection issues which arise from this distinction and propose a simple approach to testing for these structures using a sequence of likelihood ratio test statistics. The finite sample behavior of the sequential approach is analyzed in a Monte Carlo experiment. Finally, we illustrate the relevance of the different forms of reduced ranks with an empirical analysis of US business uctuations over the period 1954-1996.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 451.

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Date of creation: 2001
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Handle: RePEc:ces:ceswps:_451

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Keywords: Serial correlation common features; reduced rank structure; cointegration;

References

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  1. Hecq, Alain & Palm, Franz C & Urbain, Jean-Pierre, 2000. " Permanent-Transitory Decomposition in VAR Models with Cointegration and Common Cycles," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(4), pages 511-32, September.
  2. Neusser, Klaus, 1991. "Testing the long-run implications of the neoclassical growth model," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 3-37, February.
  3. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-60, Oct.-Dec..
  4. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-80, October.
  5. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September.
  6. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  7. Kunst, Robert & Neusser, Klaus, 1990. "Cointegration in a Macroeconomic System," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(4), pages 351-65, Oct.-Dec..
  8. Issler, Joao Victor & Vahid, Farshid, 2001. "Common cycles and the importance of transitory shocks to macroeconomic aggregates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 449-475, June.
  9. Anderson, Heather M. & Vahid, Farshid, 1998. "Testing multiple equation systems for common nonlinear components," Journal of Econometrics, Elsevier, vol. 84(1), pages 1-36, May.
  10. Gianluca Cubadda, 1999. "Common serial correlation and common business cycles: A cautious note," Empirical Economics, Springer, vol. 24(3), pages 529-535.
  11. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : II. New directions," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 309-341.
  12. Vahid, Farshid & Issler, Joao Victor, 2002. "The importance of common cyclical features in VAR analysis: a Monte-Carlo study," Journal of Econometrics, Elsevier, vol. 109(2), pages 341-363, August.
  13. Michel BEINE & Alain HECQ, 1999. "Inference in Codependence : Some Monte Carlo Results and Applications," Annales d'Economie et de Statistique, ENSAE, issue 54, pages 69-90.
  14. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-95, October.
  15. Vahid, Farshid & Engle, Robert F., 1997. "Codependent cycles," Journal of Econometrics, Elsevier, vol. 80(2), pages 199-221, October.
  16. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, September.
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Citations

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Cited by:
  1. Paruolo, Paolo, 2006. "Common trends and cycles in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 132(1), pages 143-168, May.
  2. Araújo, Fabio & Issler, João Victor & Fernandes, Marcelo, 2005. "Estimating the Stochastic Discount Factor without a Utility Function," Economics Working Papers (Ensaios Economicos da EPGE) 583, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  3. Miankhel, Adil Khan & Kalirajan, Kaliappa & Thangavelu, Shandre, 2010. "Integration, decoupling and the global financial crisis: A global perspective," MPRA Paper 22837, University Library of Munich, Germany.
  4. Guillén, Osmani Teixeira de Carvalho & Hecq, Alain & Issler, João Victor & Saraiva, Diogo, 2013. "Forecasting multivariate time series under present-value-model short- and long-run co-movement restrictions," Economics Working Papers (Ensaios Economicos da EPGE) 742, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  5. Osmani Teixeira de Carvalho Guillén & Alain Hecq & João Victor Issler & Diogo Saraiva, 2013. "Time Series under Present-Value-Model Short- and Long-run Co-movement Restrictions," Working Papers Series 330, Central Bank of Brazil, Research Department.
  6. Carlos Enrique Carrasco Gutierrez & Fábio Augusto Reis Gomes, 2006. "Evidence About Mercosur’S Business Cycle," Anais do XXXIV Encontro Nacional de Economia [Proceedings of the 34th Brazilian Economics Meeting] 179, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  7. Carlos Enrique Carrasco Gutierrez & Reinaldo Castro Souza & Osmani Teixeira de Carvalho Guillén, 2009. "Selection of Optimal Lag Length in Cointegrated VAR Models with Weak Form of Common Cyclical Features," Fucape Working Papers 16, Fucape Business School.
  8. Hecq Alain & Victor Issler João, 2012. "A Common-Feature Approach for Testing Present-Value Restrictions with Financial Data," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  9. Michel Beine & Bertrand Candelon & Alain Hecq, 2000. "Assessing a Perfect European Optimum Currency Area: A Common Cycles Approach," Empirica, Springer, vol. 27(2), pages 115-132, June.
  10. Osmani Teixeira de Carvalho Guillén & João Victor Issler & George Athanasopoulos, 2006. "Forecasting Accuracy and Estimation Uncertainty using VAR Models with Short- and Long-Term Economic Restrictions: A Monte-Carlo Study," IBMEC RJ Economics Discussion Papers 2006-01, Economics Research Group, IBMEC Business School - Rio de Janeiro.
  11. Alain Hecq & Franz Palm & Jean-Pierre Urbain, 2002. "Separation, Weak Exogeneity, And P-T Decomposition In Cointegrated Var Systems With Common Features," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 273-307.
  12. Paruolo Paolo, 2002. "Testing for common trends in conditional I(2) VAR models," Economics and Quantitative Methods qf0216, Department of Economics, University of Insubria.
  13. Paresh Kumar Narayan & Seema Narayan, 2008. "The role of permanent and transitory shocks in explaining international health expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 17(10), pages 1171-1186.

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