## Abstract

This paper uses the possibilities provided by the regression-based inequality decomposition (Fields in Res Labor Econ 22:1–38, 2003) to explore the contribution of different explanatory factors to international inequality in \(\hbox {CO}_{2}\) emissions per capita. In contrast to previous emissions inequality decompositions, which were based on identity relationships, this methodology does not impose any a priori specific relationship. Thus, it allows an assessment of the contribution to inequality of different relevant variables. In short, the paper appraises the relative contributions of affluence, sectoral composition, demographic factors and climate. The analysis is applied to selected years of the period 1993–2007. The results show the important (though decreasing) share of the contribution of demographic factors, as well as a significant contribution of affluence and sectoral composition.

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## Notes

York et al. (2003) turned that accounting equation into a stochastic regression model, allowing them to make a test hypothesis and also to introduce further determinants of the environmental impact.

These analytical decomposition methods have been applied to ecological footprint in White (2007), Teixidó-Figueras and Duro (2015) and Duro and Teixidó-Figueras (2013). For the case of \(\hbox {CO}_{2}\) emissions, Duro and Padilla (2006) made a multiplicative decomposition of the contribution of Kaya (1989) factors.

Most RBID applications analyse income inequality from a micro-approach, so there is an income-generating function, and income inequality is decomposed in terms of the typical explanatory variables of those models: race, education level, gender, age, etc. (e.g. Cowell and Fiorio 2011; Fields 2003; Gunatilaka and Chotikapanich 2009; Morduch and Sicular 2002; Wan 2004).

There are several empirical applications to income inequality comparing results obtained according to the different methods of RBID. Very often they conclude that there are no significant differences (Cowell and Fiorio 2011; Fields 2003; Gunatilaka and Chotikapanich 2009; Morduch and Sicular 2002; Wan 2004).

The semi-log model \(Ln(E)=\beta _0 +\beta _1 F_1 +\beta _2 F_2 +\cdots +\beta _k F_k +\varepsilon _i \)is equivalent to \(E=\exp (\beta _0 +\beta _1 F_1 +\beta _2 F_2 +\cdots +\beta _k F_k +\varepsilon _i )=\exp (\beta _0 )\cdot \prod \nolimits _{k=1}^k {\exp ( \beta _k F_k )}\cdot \exp (\varepsilon _i )\). Then, the contribution \({\beta }_{0}\) is null since it is a constant to each observation.

Independently of the index chosen by the researcher to assess inequality, the natural decomposition of the variance is the unique unambiguous rule given that it is the only decomposition rule that allocates indirect effects among components in a non-arbitrary way. In other words, the contribution of factor k is independent of the inequality index used (see Cowell 2000; Shorrocks 1982, 1983).

GE(2) corresponds to the Theil index with the sensitivity parameter equal to 2. It can be expressed as a linear transformation of CV. The CV is in fact a statistical dispersion index which is scale invariant and that considers all observations uniformly, regardless of its position in the distributive ranking (Duro 2012).

As can be expected the higher correlations belong to cubic and quadratic terms of GDP per capita; however, it must be taken into account that the non-collinearity assumption is about linear relationships among regressors, and despite its high correlation with linear GDP per capita, the cubic and quadratic terms are a non-linear relationship. Hence, it does not violate the basic assumption (Gujarati and Porter 2009). Nevertheless, the results suggest that a non-linear relationship between GDP and \(\hbox {CO}_{2}\) fits better, although the linear term is clearly predominant. Regarding the rest of the explanatory factors, their Variation Inflation Factors (VIF) are well within accepted standards. As a robustness check, other models have been estimated with different regressors than those in Table 3. Results obtained were virtually equivalent.

Climatologists define a climatic normal as the arithmetic average of a climate element (such as temperature) over a prescribed 30-year interval in order to filter out many of the short-term fluctuations and other anomalies that are not truly representational of the real climate. The last climatic normal available is for the period 1971–2000.

This weight is clearly lower than the obtained by Duro and Padilla (2006) with a different methodology. Their study decomposed per capita \(\hbox {CO}_{2}\) emissions inequality by a multiplicative identity (Kaya factors) using the Theil index. As a result, they obtained an affluence net contribution close to 60 %, being the main contributor to \(\hbox {CO}_{2}\) inequality. However, this difference can be explained by some methodological factors. First, the Kaya identity used in Duro and Padilla (2006) assumes elasticity proportionality by construction, while in our regression model the elasticities are allowed to vary among factors (see York et al. 2003). Second, the affluence contribution is more precisely defined and isolated in our paper, given the more detailed list of potential factors. Their study can therefore be gathering effects that in our case are separated, such as the ones associated with demographic and structure factors.

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## Acknowledgments

We are grateful for the helpful comments from three anonymous reviewers. We acknowledge the support from projects ECO2013-45380-P and ECO2012-34591 (Spanish Ministry of Economy and Competitiveness), 2014SGR950, XREPP, and XREAP (DGR).

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Duro, J.A., Teixidó-Figueras, J. & Padilla, E. The Causal Factors of International Inequality in \(\hbox {CO}_{2}\) Emissions Per Capita: A Regression-Based Inequality Decomposition Analysis.
*Environ Resource Econ* **67**, 683–700 (2017). https://doi.org/10.1007/s10640-015-9994-x

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DOI: https://doi.org/10.1007/s10640-015-9994-x

### Keywords

- \(\hbox {CO}_{2}\) emissions
- International emissions inequality
- Regression-based decomposition

### JEL Classification

- C19
- D39
- Q43