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Ana Jesús López and Rigoberto Pérez

1. INTRODUCTION The achievement of environmental sustainability has been established as a Millennium Development Goal (MDG), including a wide variety of targets referred to the access of drinking water, the reduction of biodiversity loss or the improvement of lives of slum dwellers. According to these targets, the principles of sustainable development should be included into country policies. Furthermore, since the carbon dioxide emissions have increased by more than 46 per cent since year 1990, special attention must be paid to the evolution and prospects of environmental indicators. More specifically, the goal is to complete negotiations on a new international agreement by 2015 and begin implementation in 2020, taking decisive steps towards averting irreversible changes in the global climate system. In the described context, this paper focuses on the evolution and perspectives of environmental indicators, providing empirical evidence about the suitability of two different models: the Environmental Kuznets Curve (EKC) and the Environmental Logistic Curve (ELC). With this aim, we estimate EKC and ELC from a world database including 178 countries and 68 years, also computing ex-post environmental forecasts for the period 2008-2013. Once the forecasting accuracy is analysed, ex-ante forecasts are also provided, allowing the definition of alternative environmental scenarios. The paper is organised as follows: in the next section, we briefly describe the methodological framework while the third one refers to the estimation procedures and results, including the environmental forecasts. The fourth section summarises the main findings and the paper ends with the main bibliographical references. 2. METHODOLOGICAL APPROACH The Environmental Kuznets Curve (EKC) assumes that environmental quality initially worsens with the increases in per-capita income, but then improves after an Income Turning Point (ITP) so that at high-income levels economic growth leads to environmental improvement. This model is inspired in the inverted U-shaped relationship between inequality and per-capita income proposed by Simon Kuznets [1], according to which inequality increases in the first levels of economic growth and then decreases after a certain point of return. The Environmental Kuznets Curve was first proposed by Grossman & Krueger [2] and has led to a controversial debate both theoretically and empirically. In general terms, the proposed model for the Environmental Kuznets Curve is a polynomial function given by the expression: Yt   0  1 X t   2 X t 2   3 X t 3  ut

where, given a year t, Xt represents the level of economic development, usually measured through the per capita Gross Domestic Product (GDPpc) while Yt denotes the corresponding indicator of environmental degradation. Since regressions that allow levels 2


of indicators to become zero or negative are inappropriate, a restriction can be applied by introducing the EKC variables in logarithmic terms. The empirical studies referred to the EKC provide a wide diversity of findings, since the results are sensitive to the available information, the considered pollution indicators, the proposed functional form and the econometric methodology. Some recent surveys and meta-analyses can be found in Cavlovic et al. [3], He [4], Jordan [5], Bo [6], Koirala et al. [7] and López et al. [8], among others. With regard to the environmental logistic curve, Sobhee [9] suggested the logistic model with the aim of describing three different stages in which environmental degradation first accelerates, then decelerates and finally falls. Although this proposal is still bas ed in a third degree polynomial EKC, an Environmental Logistic Curve (ELC) could also be specified in a time series context following the logistic curve works by Verhulst [10] and Pearl [11]. The logistic model describes the time evolution of a variable as: Yt  Y0 

k

 

1  c e  rt

where Y0 denotes the initial level, k refers to the saturation level and r is related to the rate of growth. According to this model the level of pollution growth is approximately exponential at the initial stage; then a saturation begins, the growth slows and at maturity growth stops. The logistic curve is usually estimated through the procedures developed by Verhulst and Pearl, requiring only three observations. Nevertheless, from an econometric perspective the logistic model can be estimated through non-linear least squares (NLS), provided that the sample size is high enough. Therefore, in this paper we propose a two-stage procedure, starting with the Verhulst method followed by a non-linear least squares estimation. 3. EMPIRICAL APPLICATION The empirical application has been developed from a database of 178 countries during the period 1940-2013. The dependent variable is defined as the country per capita CO2 emissions (metric tons of CO2) calculated from dividing the total CO2 with the total population of the countries, and the corresponding information comes from the CDIAC (Carbon Dioxide Information Analysis Center). The database also includes the Income per person, defined as the Gross Domestic Product per capita by Purchasing Power Parities (in international dollars, fixed 2005 prices). These series come from the International Comparison Program (ICP) by the World Bank and they have been expanded with the projections provided by the International Monetary Fund (IMF). The inflation and differences in the cost of living between countries have also been taken into account. The Environmental Kuznets Curve (EKC) and logistic models have been estimated until 2007 leading to a wide range of results, with regard to both the shape and the goodness of fit. In global terms the estimated models provide a satisfactory goodness of fit in most of 3


the countries, but only a small subset (27 out of 178 countries) agree with the inverted -U Environmental Kuznets Curve hypothesis. The analysis of these countries reveals that they are quite heterogeneous, including a few OECD high-income countries (Australia, Denmark, Sweden) with satisfactory model fits. Nevertheless, if this inverted-U curve is extended to the more flexible N-pattern, the list increases including several European countries (Austria, Luxembourg, Slovenia, Belgium, France, Germany, Ireland, the Netherlands, Norway, Spain and the United Kingdom) and also North America (Canada and the United States). The estimated EKC and logistic curves provide forecasts of the per capita CO2 emissions for the period 2008-2012 (ex-post) and 2013-2018 (ex-ante). The evaluation of the ex-post forecasts, according to the root of the mean square error (RMSE), the mean absolute percent error (MAPE) and the U Theil´s Index, allows a classification of countries according to the suitability of the forecasting procedures. According to these criteria, the Environmental Kuznets Curve provides the most suitable forecasts in 38% of the countries, while the logistic curve leads to more accurate results in 29% of the cases. Furthermore, there is a 13% of countries in which both procedures result to be quite similar and the remaining 20% refers to countries where none of them is suitable and therefore the corresponding environmental forecasts have been rejected. Finally, regarding the ex-ante forecasts, the EKC and logistic results can be combined in order to obtain a unique projection, paying attention to the accuracy of the corresponding ex-post forecasts. More specifically, the combined forecast has been computed as a weighted mean of the previously obtained results, with weights inversely related to the root of the mean squared error. 4. CONCLUDING REMARKS The inverted-U Environmental Kuznets Curve (EKC) assuming that environmental quality initially worsens with the increases in per-capita income, but then improves after an Income Turning Point, has been extended to more flexible models allowing the existence of N and inverted-N patterns. These third degree polynomial models have been estimated in this paper from a sample of 178 countries during the period 1940-2012, leading to a wide variety of results, most of them supporting the inverted-N shapes. As an alternative to the EKC we consider the logistic model, assuming an exponential growth of emissions at the initial stage, followed by a slower growth as the saturation begins, and finishing with a maturity stage in which growth stops. This model has been estimated in two stages, consisting in the application of the traditional Verhulst procedure followed by NLS estimation, assuming the previously estimated initial values. According to the ex-post forecasts, the EKC model results to be the most suitable one in 38% of the countries while in 29% of the cases the logistic curve provides more accurate forecasts. Both procedures perform similarly accurate in 13% of the countries while none of them results to be suitable in the remaining 20%. The accuracy of these ex-post forecasts has been considered in order to obtain ex-ante forecasts, computed as weighted combinations of EKC and logistic results . 4


REFERENCES [1] S. Kuznets, “Economic Growth and Income Inequality”. American Economic Review, 65, pp. 1-28, (1955). [2] G.M. Grossman and A.B. Krueger, “The Inverted-U: What Does It Mean?”. The Environment and Development Economics, 1 (2), pp. 119-122, (1996). [3] T.A. Cavlovic, K.H. Baker, R.P. Berrens and K. Gawande, K., ”A Meta-Analysis of Environmental Kuznets Curve Studies, Agricultural and Resource Economics Review, 29 (1), pp. 32-42, (2000). [4] J. He, “Is the Environmental Kuznets hypothesis valid for developing countries? A survey”. Working Paper 07-03. Université de Sherbrooke, (2007). [5] B.R. Jordan, “The Environmental Kuznets Curve: Preliminary Meta-Analysis of Published Studies 1995-2010”. Workshop on Original Policy Research, Georgia Tech School of Public Policy. (2010) [6] S. Bo, “A Literature Survey on Environmental Kuznets Curve”. Energy Procedia, 5, pp. 1322-1325, (2011). [7] B.S. Koirala, H. Li and R.P. Berrens, “Further Investigation of Environmental Kuznets Curve Studies Using Meta-Analysis”. International Journal of Ecological Economics and Statistics, 22 (11), pp. 15-32, (2011). [8] A.J. López, R. Pérez and B. Moreno, “Environmental costs and renewable energy: Revisiting the Environmental Kuznets Curve”, Journal of Environmental Management, 145(1), pp. 368-373, (2014). [9] S.K. Sobhee, The Environmental Kuznets Curve (EKC). A logistic curve?, Applied Economics Letters, 11, pp. 449-452, (2004). [10] P.F. Verhulst, Notice sur la loi que la population suit dans son accroissement. Math. et Phys.publ. par A. Quetelet, X, pp. 113-121, (1838). [11] R. Pearl, Introduction of medical biometry and statistics, Saunders, (1930).

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