Publication: Co-summability from linear to non-linear cointegration
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2013-06
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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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Keywords
Balancedness, Co-integration, Co-summability, Non-linear co-integration, Non-linear processes, Persistence