Co-summability from linear to non-linear cointegration
While co-integration theory is an ideal framework to study linear relationships among persistent economic time series, the intrinsic linearity in the concepts of integration and co-integration makes it unsuitable to study non-linear long run relations among persistent processes. This drawback hinders the empirical analysis of modern macroeconomics, which often addresses asymmetric responses to policy interventions, multiplicity of equilibria, transitions between regimes or polynomial approximations to unknown functions. In this paper, to cope with non-linear relations and consequently to generalise co-integration, we formalise the idea of co-summability. It is built upon the concept order of summability developed by Berenguer-Rico and Gonzalo (2013), which, in turn, was conceived to address non-linear transformations of persistent processes. Theoretically, a co-summable relationship is balanced -in terms of the variables involved having the same order of summability- and describes a long run equilibrium that can be non-linear -in the sense that the errors have a lower order of summability. To test for these types of equilibria, inference tools for balancedness and cosummability are designed and their asymptotic properties are analysed. Their finite sample performance is studied via Monte Carlo experiments. The practical strength of co-summability theory is shown through two empirical applications. Specifically, asymmetric preferences of central bankers and the environmental Kuznets curve hypothesis are studied through the lens of co-summability.
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.:
- Charles I. Jones, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, Oxford University Press, vol. 110(2), pages 495-525.
- Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
- Qiying Wang & Peter C. B. Phillips, 2009.
"Structural Nonparametric Cointegrating Regression,"
Econometric Society, vol. 77(6), pages 1901-1948, November.
- Peter C.B. Phillips, 1985.
"Understanding Spurious Regressions in Econometrics,"
Cowles Foundation Discussion Papers
757, Cowles Foundation for Research in Economics, Yale University.
- Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
- Jalil, Abdul & Mahmud, Syed F., 2009. "Environment Kuznets curve for CO2 emissions: A cointegration analysis for China," Energy Policy, Elsevier, vol. 37(12), pages 5167-5172, December.
- Donald W. K. Andrews & Patrik Guggenberger, 2009. "Hybrid and Size-Corrected Subsampling Methods," Econometrica, Econometric Society, vol. 77(3), pages 721-762, 05.
- Joon Y. Park & Peter C. B. Phillips, 1999.
"Nonlinear Regressions with Integrated Time Series,"
Working Paper Series
no6, Institute of Economic Research, Seoul National University.
- Berkes, Istv n & Horv th, Lajos, 2006. "Convergence Of Integral Functionals Of Stochastic Processes," Econometric Theory, Cambridge University Press, vol. 22(02), pages 304-322, April.
- Gonzalo, Jesús & Pitarakis, Jean-Yves, 2006.
"Threshold effects in cointegrating relationships,"
UC3M Working papers. Economics
we20060621, Universidad Carlos III de Madrid. Departamento de Economía.
- Gonzalo, J. & Pitarakis, J., 2005. "Threshold effects in cointegrating relationships," Discussion Paper Series In Economics And Econometrics 0506, Economics Division, School of Social Sciences, University of Southampton.
- Campbell, John & Yogo, Motohiro, 2006.
"Efficient tests of stock return predictability,"
3122601, Harvard University Department of Economics.
- John Y. Campbell & Motohiro Yogo, 2003. "Efficient Tests of Stock Return Predictability," NBER Working Papers 10026, National Bureau of Economic Research, Inc.
- John Y. Campbell & Motohiro Yogo, 2002. "Efficient Tests of Stock Return Predictability," Harvard Institute of Economic Research Working Papers 1972, Harvard - Institute of Economic Research.
- Gonzalo, Jesus & Pitarakis, Jean-Yves, 2010.
"Regime Specific Predictability in Predictive Regressions,"
29190, University Library of Munich, Germany.
- Jesús Gonzalo & Jean-Yves Pitarakis, 2011. "Regime-Specific Predictability in Predictive Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 229-241, June.
- Pitarakis, Jean-Yves & Gonzalo, Jesús, 2010. "Regime specific predictability in predictive regressions," UC3M Working papers. Economics we097844, Universidad Carlos III de Madrid. Departamento de Economía.
- Gonzalo, Jesus & Pitarakis, Jean-Yves, 2010. "Regime specific predictability in predictive regressions," Discussion Paper Series In Economics And Econometrics 0916, Economics Division, School of Social Sciences, University of Southampton.
- Martin Lettau & Stijn Van Nieuwerburgh, 2006.
"Reconciling the Return Predictability Evidence,"
2006 Meeting Papers
29, Society for Economic Dynamics.
- Perman, Roger & Stern, David I., 2003.
"Evidence from panel unit root and cointegration tests that the Environmental Kuznets Curve does not exist,"
Australian Journal of Agricultural and Resource Economics,
Australian Agricultural and Resource Economics Society, vol. 47(3), September.
- Roger Perman & David I. Stern, 2003. "Evidence from panel unit root and cointegration tests that the Environmental Kuznets Curve does not exist," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 47(3), pages 325-347, 09.
- Anders Møller Christensen & Heino Bohn Nielsen, 2009. "Monetary Policy in the Greenspan Era: A Time Series Analysis of Rules vs. Discretion," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(1), pages 69-89, 02.
- Richard H. Clarida & Jordi Gali & Mark Gertler, 1998. "Monetary policy rules in practice," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
- Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1373-1403, October.
- Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
- Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
- Nickell, Stephen, 1985. "Error Correction, Partial Adjustment and All That: An Expository Note," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 47(2), pages 119-129, May.
When requesting a correction, please mention this item's handle: RePEc:cte:werepe:we1312. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ana Poveda)
If references are entirely missing, you can add them using this form.