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Environmental Kuznets Curve: Non-Linear Panel Regression Analysis

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Abstract

This study presents an analysis of the relationship between per capita CO2 emissions as an environmental degradation indicator and per capita gross domestic product (GDP) as an economic growth indicator within the framework of the Environmental Kuznets Curve (EKC). For this purpose, non-linear panel models are estimated for the Annex I countries, non-Annex countries, and whole parties with respect to data availability of the United States Convention on Climate Change (UNFCCC) for the period 1960–2012. The empirical results of the panel smooth transition models (PSTR) show that the environmental deterioration rises in the first phase of growth for all data sets. Afterwards, the environmental degradation cannot be prevented, but the increase in the amount of environmental degradation decreases. The findings of this study give an insight regarding the differential environmental impact of economic growth between developed and developing countries. While the validity of a traditional EKC relation regarding the CO2 emissions cannot be affirmed for any group of countries in our sample, empirical results indicate the existence of multiple regimes where economic growth hampers environmental quality, but its severity decreases at each consecutive regime.

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Notes

  1. For more information about UNFCCC please visit https://unfccc.int/process-and-meetings/the-convention/what-is-the-united-nations-framework-convention-on-climate-change.

  2. For more information about UNFCCC country classifications please visit https://unfccc.int/parties-observers.

  3. As can be clearly seen from Eq. (3), this homogeneity test which is the analogous linearity test of time series is nested the quadratic form of the \( {y}_{\mathrm{i}\mathrm{t}}={\alpha}_{\mathrm{i}}+{\beta}_1{x}_{\mathrm{i}\mathrm{t}}+{\beta}_2{x}_{\mathrm{i}\mathrm{t}}^2+{\varepsilon}_{\mathrm{i}\mathrm{t}} \). Kuznets curve, hence, we are also estimating the quadratic form but not as a seperate model, but as a homogeneity test whether the model under investigation is heterogeneous (nonlinear) or not.

  4. Both tests have used the exponential smooth transition autoregressive function in their testing process; however, the economic intuition behind the function is coming from the band-TAR model. The band-TAR model has 3 regimes which we can classified as inner regime and outer regimes. If there is low arbitrage probability or possibility, the series under investigation (such as exchange rate or any other one) will not converge to the mean (or mean reverting process); however, the arbitrage possibilities are increased in the outer regimes then the series become mean reverting or converge to the mean. Hence, the assumed process locally unit root and globally stationary. This explanation is directly imitated by ESTAR process which is used by UO test; on the other hand, the EO test used the ESTAR embedded logistic smooth transition autoregressive (LSTAR) function which they are imposing the asymmetry to outer regimes by using this LSTAR function. Therefore, the EO test nests the symmetric version UO test. The EO test now assumes that in the two distinct outer regimes, the convergence to the mean is differ from each other where the UO test assumes symmetric converges from outer regimes.

  5. As it is shown in the Dijk et al. [22] \( {y}_{\mathrm{it}}={\phi}_1^{\prime }{x}_{\mathrm{it}}G\left({s}_{\mathrm{it}};\gamma, c\right)+{\phi}_2^{\prime }{x}_{\mathrm{it}}\left(1-G\left({s}_{\mathrm{it}};\gamma, c\right)\right)+{\varepsilon}_{\mathrm{it}} \). (See also Omay and Kan [74], Omay et al. [75], Omay et al. [76], and Omay et al. [77] which are using Heterogonous PSTR, Heterogeneous Panel Smooth Transition Vector Error Correction (PSTRVEC), Homogenous PSTR, and Homogenous MRPSTR, respectively). This representation shows the weighted sum of two distinct regimes. However, for the parsimony principle, the same weighted version can also be estimated by using only one transition function.\( {y}_{\mathrm{it}}={\phi}_1^{\prime }{x}_{\mathrm{it}}+{\left({\phi}_2-{\phi}_1\right)}^{\prime }{x}_{\mathrm{it}}G\left({s}_{\mathrm{it}};\gamma, c\right)+{\upvarepsilon}_{\mathrm{it}} \). This parsimony version leads to economy in representing the more than two regime cases as it is done in the second data set in our study. \( {y}_{\mathrm{it}}={\phi}_1^{\prime }{x}_{\mathrm{it}}+{\left({\phi}_2-{\phi}_1\right)}^{\prime }{x}_{\mathrm{it}}{G}_1\left({s}_{\mathrm{it}};{\gamma}_1,{\mathrm{c}}_1\right)+{\left({\phi}_3-{\phi}_2\right)}^{\prime }{x}_{\mathrm{it}}{G}_3\left({s}_{\mathrm{it}};{\gamma}_2,{c}_2\right)+{\varepsilon}_{\mathrm{it}} \). Therefore, the representation and estimation become easier; however, (ϕ2 − ϕ1)′ and (ϕ3 − ϕ2)′ are not the parameters of the distinct regime in this case, so they must be interpreted as dummy variable methodology. In the estimation phase we have obtained the (ϕ2 − ϕ1)′ = θ as one parameter such as θ. This θ parameter must be added to base regime in order to obtain the second regime, and this θ must be added to third regime in order to find the third regime.

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Authors and Affiliations

  1. Turkish Statistical Institute, Ankara, Turkey

    Hüseyin Şentürk

  2. Department of Economics, Atılım University, Ankara, Turkey

    Tolga Omay

  3. Department of Economics, TED University, Ankara, Turkey

    Julide Yildirim

  4. Department of Economics and Finance, Istanbul Gelişim University, Istanbul, Turkey

    Nezir Köse

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Şentürk, H., Omay, T., Yildirim, J. et al. Environmental Kuznets Curve: Non-Linear Panel Regression Analysis. Environ Model Assess 25, 633–651 (2020). https://doi.org/10.1007/s10666-020-09702-0

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