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Unit Roots, Polynomial Transformations and the Environmental Kuznets Curve

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Abstract

Time-series regressions including non-linear transformations of an integrated variable are not uncommon in various fields of economics. In particular, within the Environmental Kuznets Curve (EKC) literature, where the effect on the environment of income levels is investigated, it is standard procedure to include a third order polynomial in the income variable. When the income variable is an I(1)-variable and this variable is also included nonlinearly in the regression relation, the properties of the estimators and standard inferential procedures are unknown. Surprisingly, such problems have received rather limited attention in applied work, and appear disregarded in the EKC literature. We investigate the properties of the estimators of long-run parameters using Monte-Carlo simulations. We find that the mean of the ordinary least squares estimates are very similar to the true values and that standard testing procedures based on normality behave rather well.

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  • Gang Liu & Terje Skjerpen & Anders Rygh Swensen & Kjetil Telle, 2006. "Unit Roots, Polynomial Transformations and the Environmental Kuznets Curve," Discussion Papers 443, Statistics Norway, Research Department.
  • Handle: RePEc:ssb:dispap:443
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    1. Brock, William A. & Taylor, M. Scott, 2005. "Economic Growth and the Environment: A Review of Theory and Empirics," Handbook of Economic Growth,in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 28, pages 1749-1821 Elsevier.
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    6. Ermini, Luigi & Granger, Clive W. J., 1993. "Some generalizations on the algebra of I(1) processes," Journal of Econometrics, Elsevier, vol. 58(3), pages 369-384, August.
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    Cited by:

    1. Silvia Coderoni & Roberto Esposti, 2014. "Is There a Long-Term Relationship Between Agricultural GHG Emissions and Productivity Growth? A Dynamic Panel Data Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(2), pages 273-302, June.
    2. Coderoni, Silvia & Esposti, Roberto, 2011. "Long-Term Agricultural GHG Emissions and Economic Growth: The Agricultural Environmental Kuznets Curve across Italian Regions," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114426, European Association of Agricultural Economists.
    3. Silvia CODERONI & Roberto ESPOSTI, 2011. "Is there a Long-Term Relationship between Agricultural GHG Emissions and Productivity Growth? The Case of Italian Agriculture," Working Papers 369, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    4. J. N. Lye and J. G. Hirschberg, 2012. "Inverse Test Confidence Intervals for Turning points: A," Department of Economics - Working Papers Series 1160, The University of Melbourne.
    5. Gang Liu, 2006. "A causality analysis on GDP and air emissions in Norway," Discussion Papers 447, Statistics Norway, Research Department.

    More about this item

    Keywords

    Emissions; Environmental Kuznets Curve; Unit Roots; Monte Carlo Simulations;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products

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