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Measuring the Effect of Economic Growth on Countries’ Environmental Efficiency: A Conditional Directional Distance Function Approach

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Abstract

Using a recently developed probabilistic approach of a conditional directional distance function, we measure the effect of economic growth on countries’ environmental efficiency in carbon dioxide emissions for a sample of 99 countries over the period of 1980–2010. Our approach directly accounts for the exogenous factors influencing countries’ environmental production; therefore, we do not impose the separability condition on the estimated environmental efficiencies. When examining the entire sample as well as the sample of developed countries, our results reveal an inverted U-shaped relationship between countries’ GDP per capita and environmental efficiency. However, when examining the relationship for the sample of developing countries, the results reveal an N-shaped form. Moreover, our results show that countries ratifying the Kyoto Protocol tend to have higher efficiency scores, implying that their mitigation activity is less costly.

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Notes

  1. For empirical evidence examining the EKC hypothesis, see, among others, the studies by Selden and Song (1994, 1995), Grossman and Krueger (1995), Hilton and Levinson (1998), Halkos (2003), Cassou and Hamilton (2004), Harbaugh et al. (2002), Maddison (2006) and Tsurumi and Managi (2010).

  2. According to Kumbhakar and Lovell (2000), a frontier analysis is based on the estimation of the long-run equilibrium relationship between environmental output and environmental production factors and not on the dynamic adjustments toward the equilibrium.

  3. These studies are based on the environmental production framework introduced by Färe et al. (1989). For a literature review on the subject, see Tyteca (1996, 1997).

  4. In their regression setting, they incorporated other variables that, according to the authors, can influence countries’ environmental performance. These variables were population density, environmental research and development expenditures and share of manufacturing in GDP.

  5. Zaim and Taskin (2000) used the same inputs and outputs without including any other control variables in their parametric and nonparametric regression analyses.

  6. In their parametric regression setting, they also used a dummy for export composition, the share of polluting exports in total exports and an openness index defined as the ratio of total exports and imports to GDP.

  7. They used three pollutants as bad outputs in the estimated environmental production function (carbon dioxide, methane and nitrous oxide).

  8. Typically, the suggestion by Chung et al. (1997) of setting a direction vector \(d=\left( {0,d_y ,-d_\xi } \right) \) is followed, implying output orientation aiming to reduce bad outputs and simultaneously expand good outputs. This is the most common assumption made when measuring environmental performance; however, it must be noted that the choice of direction is an open research question and is subject to the demand and specific characteristics of the analysis at hand. To model the directional distance function, a direction vector \(d=\left( {y_y ,-d_\xi } \right) \) is used where \(d_y =1\) and \(-g_\xi =-1\) and the efficiency score for a country is obtained either from:

    $$\begin{aligned}&\beta \left( {x,y,\xi ;d_y ,d_\xi } \right) =\max \beta \\&s.t.\left( {y+\beta d_y ,\xi -\beta d_\xi } \right) \in P\left( x \right) \end{aligned}$$

    or from solving linear problem (11). Efficiency is then indicated when \(\beta \left( {x,y,\xi ;d_y ,d_\xi } \right) =0\) and inefficiency when \(\beta \left( {x,y,\xi ;d_y ,d_\xi } \right) >0\).

  9. For innovative applications in environmental problems applying DEA, see Hernandez-Sancho et al. (2000), Hoang and Alauddin (2012) and Camarero et al. (2013).

  10. Directional distance functions can also be calculated using parametric approaches. See, for instance, the work by Hoang and Coelli (2011).

  11. In terms of measuring environmental performance, Picazo-Tadeo et al. (2012) and Murty et al. (2012) suggest that CRS is a suitable assumption. However, if a researcher wants to impose VRS, he or she should be aware of several operationalization aspects regarding the presented linear program (Kuosmanen 2005; Färe and Grosskopf 2009; Kuosmanen and Podinovski 2009).

  12. To choose the optimal bandwidths, we adopt the algorithm by Bădin et al. (2010, p. 640), which is based on the Least Squares Cross-Validation (LSCV) criterion (Hall et al. 2004; Li and Racine 2007, 2008). Furthermore, for the calculation of environmental efficiencies (for both conditional and unconditional), we have used the ‘FEAR’ package, which is an integrated program in the language R (Wilson 2008).

  13. According to Podinovski and Kuosmanen (2011), the conventional output radial measures are special cases of directional distance functions. For a detailed analysis, see Chung et al. (1997) and Chambers et al. (1998).

  14. Bădin et al. (2012) showed how conditional radial distances can be used to investigate the effect of the external factors. However, Daraio and Simar (2014) extended their work by introducing all the operational aspects for computing conditional and unconditional directional distances and their robust versions.

  15. In fact, as suggested by Daraio and Simar (2014, p. 362), because \(d_x \) is set to zero (as in our case), the analysis conducted with the ratios is simplified to the analysis conducted with the conventional radial output measures.

  16. In our case, because the time variable takes values from 1980 to 2010, continuous kernels can be applied (Hayfield and Racine 2008).

  17. Based on the IMF (2012), the classification in our sample contains 28 developed and 70 developing countries.

  18. According to Johnson et al. (2013), two thirds of all cross-country empirical works use different versions of PWT. Although there have been fair critiques about the consistency and the methods applied to estimate the PWT data (especially for the older versions), Feenstra et al. (2013) suggest that the new version of PWT (v8.0) is more consistent over time and more transparent in its methods. The data can be downloaded from www.ggdc.net/pwt.

  19. The CO\(_{2}\) emissions have been extracted from the World Bank online database and can be downloaded from http://data.worldbank.org/indicator/EN.ATM.CO2E.KT/countries/1W?display=default.

  20. Note that none of the examined countries was estimated as environmentally efficient for every period in our study, and therefore, the score is less than one on average.

  21. Chimeli and Braden (2005) suggest that countries’ environmental quality and total factor productivity form a U-shaped relationship providing evidence of countries’ productivity and EKC.

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Acknowledgments

Thanks are due to co-editor Professor Christian Vossler for not only giving us the opportunity to revise our paper but also his valuable comments on an earlier version of this study. We also thank two anonymous reviewers for their helpful and constructive comments and Dr N. Tzeremes for his participation in an earlier version of this paper. This research was funded by the Specially Promoted Research of a Grant-in-Aid for Specially Promoted Research (26000001) by the Japan Society for the Promotion of Science (JSPS) and S-14 funding from the Ministry of Environment. Any remaining errors are solely the authors’ responsibility.

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Authors and Affiliations

  1. Laboratory of Operations Research, Department of Economics, University of Thessaly, Korai 43, 38333, Volos, Greece

    George E. Halkos

  2. Urban Institute & Department of Urban and Environmental Engineering, School of Engineering, Kyushu University, 44 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Shunsuke Managi

  3. QUT Business School, Brisbane QLD, 4001, Australia

    Shunsuke Managi

Authors
  1. George E. Halkos
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  2. Shunsuke Managi
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Correspondence to George E. Halkos.

Appendix

Appendix

List of the countries used in our analysis.

Developed Countries (29): AUS, AUT, BEL, CAN, CYP, DEU, DNK, FIN, FRA, GRC, HKG, ISL, IRL, ISR, ITA, JPN, KOR, LUX, MLT, NLD, NZL, NOR, PRT, SGP, ESP, SWE, CHE, GBR, USA.

Developing Countries (70): ALB, AGO, ARG, BHS, BHR, BGD, BRB, BOL, BWA, BRA, BRN, BGR, CMR, CHL, CHN, COL, CRI, CIV, DOM, ECU, EGY, SLV, ETH, GAB, GHA, GTM, GIN, HND, HUN, IND, IDN, IRN, IRQ, JAM, JOR, KEN, KWT, LBN, MYS, MEX, MNG, MAR, MOZ, NGA, OMN, PAK, PAN, PRY, PER, PHL, POL, QAT, SAU, SEN, ZAF, LKA, SDN, SUR, SYR, TZA, THA, TTO, TUN, TUR, UGA, URY, VEN, VNM, ZMB, ZWE.

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Halkos, G.E., Managi, S. Measuring the Effect of Economic Growth on Countries’ Environmental Efficiency: A Conditional Directional Distance Function Approach. Environ Resource Econ 68, 753–775 (2017). https://doi.org/10.1007/s10640-016-0046-y

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