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Co-summability from linear to non-linear cointegration

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  • Vanessa Berenguer Rico
  • Jesús Gonzalo

Abstract

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.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1312.

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Date of creation: Jun 2013
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Handle: RePEc:cte:werepe:we1312

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Keywords: Balancedness; Co-integration; Co-summability; Non-linear co-integration; Non-linear processes; Persistence;

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References

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Citations

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Cited by:
  1. Markus Eberhardt & Andrea F. Presbitero, 2013. "This Time They’re Different: Heterogeneity and Nonlinearity in the Relationship between Debt and Growth," Discussion Papers 2013/10, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
  2. Vanessa Berenguer Rico & Jesus Gonzalo, 2011. "Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes," Economics Working Papers, Universidad Carlos III, Departamento de Economía we1115, Universidad Carlos III, Departamento de Economía.
  3. Markus Eberhardt, 2013. "Nonlinearities in the Relationship between Debt and Growth: Evidence from Co-Summability Testing," Discussion Papers 2013/06, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
  4. Pitarakis, Jean-Yves, 2012. "Functional cointegration: definition and nonparametric estimation," MPRA Paper 38846, University Library of Munich, Germany.
  5. Berenguer-Rico, Vanessa & Gonzalo, Jesús, 2014. "Summability of stochastic processes—A generalization of integration for non-linear processes," Journal of Econometrics, Elsevier, Elsevier, vol. 178(P2), pages 331-341.

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