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Co-summability from linear to non-linear cointegration

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  • Berenguer Rico, Vanessa
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.

Suggested Citation

  • Berenguer Rico, Vanessa, 2013. "Co-summability from linear to non-linear cointegration," UC3M Working papers. Economics we1312, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:we1312
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    Cited by:

    1. Eberhardt, Markus & Presbitero, Andrea F., 2015. "Public debt and growth: Heterogeneity and non-linearity," Journal of International Economics, Elsevier, vol. 97(1), pages 45-58.
    2. 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).
    3. Apergis, Nicholas & Christou, Christina & Gupta, Rangan, 2017. "Are there Environmental Kuznets Curves for US state-level CO2 emissions?," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 551-558.
    4. David F. Hendry, 2020. "First in, First out: Econometric Modelling of UK Annual CO_2 Emissions, 1860–2017," Economics Papers 2020-W02, Economics Group, Nuffield College, University of Oxford.
    5. Adnen Ben Nasr & Mehmet Balcilar & Seyi Saint Akadiri & Rangan Gupta, 2019. "Kuznets Curve for the US: A Reconsideration Using Cosummability," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 142(2), pages 827-843, April.
    6. 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).
    7. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, Department of Economics and Business Economics, Aarhus University.
    8. Seref Bozoklu & A. Oguz Demir & Sinan Ataer, 2020. "Reassessing the environmental Kuznets curve: a summability approach for emerging market economies," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 10(3), pages 513-531, September.
    9. Banerjee Anurag & Pitarakis Jean-Yves, 2014. "Functional cointegration: definition and nonparametric estimation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 507-520, December.
    10. Ben Nasr, Adnen & Gupta, Rangan & Sato, João Ricardo, 2015. "Is there an Environmental Kuznets Curve for South Africa? A co-summability approach using a century of data," Energy Economics, Elsevier, vol. 52(PA), pages 136-141.
    11. Berenguer Rico, Vanessa, 2011. "Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes," UC3M Working papers. Economics we1115, Universidad Carlos III de Madrid. Departamento de Economía.
    12. Berenguer-Rico, Vanessa & Gonzalo, Jesús, 2014. "Summability of stochastic processes—A generalization of integration for non-linear processes," Journal of Econometrics, Elsevier, vol. 178(P2), pages 331-341.
    13. Shinhye Chang & Matthew W. Clance & Giray Gozgor & Rangan Gupta, 2019. "A Reconsideration of Kuznets Curve across Countries: Evidence from the Co-summability Approach," Working Papers 201970, University of Pretoria, Department of Economics.
    14. Vanessa Berenguer-Rico & Bent Nielsen, 2015. "Cumulated sum of squares statistics for non-linear and non-stationary regressions," Economics Papers 2015-W09, Economics Group, Nuffield College, University of Oxford.

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    Keywords

    Balancedness;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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