The Trade-off Between Income Inequality and Carbon Dioxide Emissions

We investigate the theoretically ambiguous link between income inequality and per capita carbon dioxide emissions using a panel data set that is substantially larger (in both regional and temporal coverage) than those used in the existing literature. Using an arguably superior group fixed effects estimator, we find that the relationship between income inequality and per capita emissions depends on the level of income. We show that for low and middle-income economies, higher income inequality is associated with lower carbon emissions while in upper middle-income and high-income economies, higher income inequality increases per capita emissions. The result is robust to the inclusion of plausible transmission variables. JEL codes: Q0, Q1, Q3


Introduction
Reducing global poverty and mitigating climate change are two major challenges facing mankind in the twenty-first century. Economic growth leads to absolute poverty reduction, particularly if it is not associated with rising income inequality (e.g. Dollar and Kraay, 2002;Bourguignon, 2003). There is a substantial literature that investigates the relationship between income and carbon dioxide emissions (the main driver behind the increase in global surface temperature). This literature suggests that economic growth, at least up to a certain level of economic development, increases greenhouse gases (IPCC, 2014; Jakob et al., 2014).
Consequently, from the perspective of a developing country, economic growth may alleviate poverty, but intensify climate problems. A related issue is whether there is also a tradeoff between income inequality and carbon emissions, as stated by Ravallion et al. (2000). As we discuss below, the theoretical and empirical literature generates mixed results on this question, pointing to different mechanisms and effects (for a survey see Berthe and Elie, 2015). Much of this literature is, however, based on econometric methods that are biased in the presence of time-varying unobserved heterogeneity, and on older data on both inequality as well as emissions. We improve upon the existing literature in both of these respects.
A particular innovation with respect to the existing literature is that we use a group fixed effects estimator (Bonhomme and Manresa, 2015) as opposed to a standard fixed effects estimator. This grouped fixed effects estimator takes into account that different regions of the world adopt clean technologies at different rates or face different structural challenges and dynamics. Furthermore, the estimator arguably deals better with endogeneity due to unobserved heterogeneity. Finally, the within transformation associated with the standard country-based fixed effects estimator would eliminate most of the variation in the Gini data, leaving only the relatively small intertemporal variation (see the literature on the debates on inequality and growth literature, e.g. Forbes, 2000, Banerjee and Duflo, 2003, Scholl and Klasen, 2016. To the best of our knowledge, only five papers are closely related to our empirical in-vestigation of the link between per capita carbon dioxide emissions, per capita output, and inequality. There are also related studies investigating the link between inter-country inequality and emissions (e.g. Guo, 2013, Coondoo andDinda, 2008). First, Ravallion et al. (2000) use a pooled OLS model that interacts inequality with a third-order polynomial of income, a time trend, and population size. The panel data set consists of 42 countries over the period from 1975 to 1992. The authors use one (average) inequality measure per country. They find that there is a static tradeoff between reducing carbon emissions and reducing income inequality. Second, Borghesi (2006)  its square, and the Gini coefficient. Similar to Ravallion et al (2000), they find that income inequality is negatively associated with carbon emissions per capita. All three studies rely on the inequality measure from the data set described in Deininger and Squire (1996). Two further studies use the University of Texas Inequality data which proxies household inequality with the between sector wage inequality in non-agricultural sectors. Drabo (2011) finds, in a 2SLS fixed effects framework using 86 countries finds that inequality increases emissions. Gassebner et al. (2011) use extreme bound analysis for a sample of up to 120 countries in 1960-2001 and find that inequality is robustly associated with smaller CO2 emissions. The use of the UTIP data, which relates to a particular aspect of industrial wage inequality, as a proxy for overall inequality is, however, controversial and can lead to biases (Scholl, 2016).
Our analysis uses expanded and improved data from Solt (2009), which is derived from the much broader, more consistent, and more reliable WIDER 1 World Income Inequality Database. This allows us to use a larger set of countries (158) than the existing literature, and observations from 1980-2008, which is larger and more recent than most existing studies.
Furthermore, we argue that cross-section estimates based on pooled OLS or related methods are arguably not the most appropriate tools for this analysis, and argue that the group fixed effects estimator (Bonhomme and Manresa, 2015) is more suitable for the analysis. We also compare our analysis to a standard fixed effects estimator. 2 We find that the relationship between income inequality and emissions depends on income levels. At lower levels of incomes higher income inequality reduces emissions while at higher levels of income, the effect is reversed. The group fixed effects also generate interesting differentiated time trends linked closely to trends in energy intensity in the different groups.
The rest of the paper is structured as follows. Section 2 reviews theoretical arguments in the existing literature, emphasizing that the relationship between income inequality and emissions is ambiguous. Section 3 describes the panel data set. Section 4 outlines the fixed effects model for our setting, and reveals its shortcoming in the current context. We then argue that a group fixed effects estimator is more appropriate, and describe that model. The main results and a sensitivity analysis are presented in Section 5. Section 6 concludes.

Theory
Starting in the mid-1990's, economists have developed several theoretical arguments to explain the relationship between economic inequality and environmental degradation. For a full review, please see Cushing et al. (2015) and Berthe and Elie (2015). Here we only provide a condensed summary of this very large literature. While some of the arguments entail a positive association, namely the "equality hypothesis" proposed by Boyce (1994), Torras 2 Other papers less related to our work consider the inequality-emissions relationship for small groups of industrialized countries. Magnani (2000) uses public expenditure for environmental protection as the dependent variable, and uses only 17-52 observations for developed countries. Marsiliani and Renstrom (2003) use sulfur, nitrogen and carbon dioxide and a different inequality measure: ratio of households ranked at top 90th percentile to the median household and two panels of 7 and 10 industrialized countries over 1978-97. Finally, Fourth, Baek and Gweisah (2013) use an autoregressive distributed lag specification and U.S. data to find that income inequality is negatively associated with short and long run per capita carbon emissions.
If the second argument prevails, there will be a tradeoff between redistribution policies and environmental quality. Boyce (1994) proposes that greater inequality could increase environmental degradation via the impact on the rate of time preference and via a modified cost-benefit analysis that considers power-weighted costs and benefits. Boyce (1994) and Torras and Boyce (1998) assume that environmental quality is a public good and effective demand requires public policy solutions to this market failure. The factors which allow economies to redress market failure more efficiently are "vigilance and advocacy", as pointed out by Grossman and Krueger (1995) in earlier work. These two factors increase with per capita income because individuals gain greater power to make their demand effective through the political process. In particular, some individuals benefit from economic activities that generate pollution, whereas other citizens, adversely affected by pollution, bear net cost. The latter exercise vigilance and are in charge to demand for environmental controls, whereas the former attempt to prevent that those environmental controls are established or strengthened. Assuming that in more unequal societies those who benefit from pollution are more powerful than those who bear the cost, the benefit-cost rule will lead to predict an inefficient high level of pollution. This implies a positive correlation between income inequality and pollution. A controversial assumption they made to reach this outcome is that net benefit from polluting activities is positively correlated with individual income. However, Scruggs (1998) claims that wealthy and powerful individuals do not necessarily prefer more degradation than the rest and he also questions Boyce's underlying assumption that more democratic societies produce better environmental results than other political regimes. Also, it is unclear whether this argument, which has been formulated for environmental degradation more generally, also holds for carbon emissions. In the case of carbon emissions, costs are not only felt locally but globally and emission control is a global public good, where it is unclear that national income inequality will necessarily play a critical role in this mechanism.
In the same line of reasoning as Boyce (1994), Borghesi (2006) suggests that an increase in inequality hinders the way for public policy solutions to environmental problems and therefore greater inequality can contribute to increasing emissions. Also Marsiliani and Renstrom (2003) argue that higher inequality leads to less environmental protection and consequently Finally, the emulation theory, originally due to Veblen (1899), hypothesizes that in more unequal societies individuals in a given social class tend to compare themselves with the members of the immediately superior social class and emulate their consumption patterns.
In this way, more unequal societies might have a higher propensity to consume more polluting intensive goods and services (such as big cars, long-distance vacations, etc.) that are associated to a higher MPE and therefore to higher emissions in comparison to egalitarian societies. The marginal propensity to emit will be higher at all income levels.
In summary, the theoretical literature is ambiguous about the sign of the relationship between inequality and emissions that is conditioned to a number of underlying assumptions, see alsoCushing et al. (2015) and Berthe and Elie (2015). In this respect, we aim to contribute with a novel empirical approach to shed light on some of the above mentioned theories. The contrasting theoretical arguments also suggest that the relationship is probably heterogeneous across countries, leading to different levels of emissions across countries, as well as to differences in income and inequality elasticities. In fact, some theories suggest that high inequality is associated with more emissions in richer countries, while the relationship might be reversed in poorer countries. For example, Gassebner et al (2008) relate rising inequality in rich countries to industrial decline and reduction of political power of the industrial producers. This implies limited influence to stop stringent environmental regulations demanded by consumers in rich countries. Our specification below will enable us to examine a non-monotonic relationship, such as the one implied by their mechanism.

Data
We use an unbalanced panel data set with annual measurements from 1980 to 2008, covering 158 countries. The total number of observations is 3966. This data set is much more extensive than those used in the existing literature on the relationship between income inequality, GDP, and carbon emissions. The corner stone of our data set are the Gini coefficients from the Standardized World Income Inequality Database (SWIID) by Solt (2009). For the SWIID, a missing data algorithm was used to fill in the Gini measurements and to make the data from different sources comparable. Solt (2009) differentiates between before and after tax income inequality. Many high income countries apply strong redistributive policies, which lead to overall lower after-tax income inequality than before tax income inequality. We use after-tax income inequality measure because we are interested in the effect of redistributive policies, and want to account for those already in place.
The data on carbon dioxide emissions are from the Oak Ridge National Laboratory data set, which covers emissions from fossil fuel, natural gas consumption, and cement manufacturing (Boden et al. 2012). This data set is widely used in the literature but faces two major shortcomings, see e.g. Borghesi (2006  Finally, we use the Polity measure, see Marshall and Cole (2011), which is a measure of state fragility that ranges from +10 (strongly democratic) to −10 (strongly autocratic). An overview of the variables, with summary statistics, are given in Table 1.

Econometric model
This section describes the fixed effects model and the group fixed effects model, which we use to investigate empirically the relationship between emissions, GDP, and income inequality.
We will argue that, for our empirical application, the group fixed effects estimator, proposed by Bonhomme and Manresa (2015), is an attractive alternative to the commonly used fixed effects estimator. The results for both models are described in Section 5.
For country i at time t, let e it be log CO 2 emissions per capita, and let y it denote log GDP per capita. Furthermore, let g it denote the log of the Gini coefficient, which is our preferred measure of income inequality. Additional explanatory variables are collected in a vector X it . A useful starting point for our analysis is the following fixed effects model: with the standard assumptions on the error term u it , and allowing for an unrestricted relationship between the country-and time-specific effects (α i , λ t ) and the covariates ("fixed effects"). The quadratic specification in (y it , g it ) serves as an approximation to a general, nonlinear relationship between emissions, GDP, and income inequality. The squared income inequality term is omitted, as it is highly correlated with g it , and our results are not sensitive to its omission.
Note that the quadratic income term allows the relationship between emissions and income to be non-monotonic. For example, it allows for the inverted U shape that is documented in the literature on the environmental Kuznets curve. The interaction term between income and inequality allows the relationship between income inequality and emissions to depend on income. The inclusion of the interaction term is therefore crucial, as our discussion in Section 2 led to the conclusion (see the last paragraph in that section) that the elasticity of emissions with respect to inequality depends on income. In our model, this elasticity is given by This elasticity depends on the current level of GDP per capita. 4 For example, if β 3 < 0 and without requiring the researcher to specify j(i). Rather than deciding on group membership before the analysis, it is estimated along with the other parameters in this model. Group The most important difference between the fixed effects and GFE models is the restriction on the evolution of unobserved heterogeneity. The fixed effects model allows for an effect α it = α i + λ t for country i at time t, which restricts all countries to have the same pattern over time. In contrast, the GFE model allows for an effect α it = α j(i),t , restricting the pattern to be the same for all countries within a group, but allowing different groups to have fully distinct patterns. Note that these two models are not nested.
For our setting, the GFE model is an attractive alternative to the fixed effects model. To see this, we temporarily abstract from our nonlinear world and from the influence of income inequality and consider a very simple relationship between GDP per capita (Y it ) and carbon emissions per capita (E it ), see e.g. Ikefuji et al. (2015): where σ it and µ it are the emissions-to-output ratio and abatement factors for country i at time t. The emissions-to-output ratio σ it can be seen as a technology parameter that measures the extent to which clean technology is used in the economy, or the average carbon intensity of the technology used in production. In this simple model, we would have Using a standard fixed effects model with time dummies restricts
The results from these models do not change our main findings. The starting point for the sensitivity analysis is the group fixed effects estimator. First, we estimate the model with data averaged to 3-year averages ( Table 4, first column). This increases the balance of the data, and checks that our results are not driven by short-run fluctuations. Note that our main findings are unchanged: (i) the sign of the emission-inequality elasticity is negative at low values of income, and positive for a sufficiently rich country; (ii) there is an inverted-U shaped relationship between income and carbon emissions. However, the threshold value of income is out of sample, so that both reported estimated elasticities are negative. This could be due to lack of precision because of the reduced sample size, see for example the relatively high standard error of the interaction term.
Second, we investigate whether the relationship holds even if we include some plausible transmission channels. In particular, we control for the quality of institutions that could be a proxy for environmental regulations by including the Polity measure (Table 4, column "Polity"). We also control for other transmission channels by including as additional variables the share of population living in cities, and the shares of agriculture, manufacturing, and services (Table 4, column "Channels"). The relationship holds and remains significant, even after the inclusion of plausible transmission channels. This suggests that the incomecontingent effect of inequality on emissions persists beyond these plausible transmission channels. 7 Third, we estimate a fixed effects model using the data set described in Gruen

Conclusion
Based on a substantially larger data set (in both regional and temporal coverage) than the existing literature, we investigate the theoretically ambiguous link between income inequality and emissions. We find that the relationship depends on the level of income. Using an arguably superior group-fixed effects estimator, we show that for low and middle-income economies, higher income inequality is associated with lower carbon emissions while in upper middle-income and high-income economies, higher income inequality increases per capita emissions. The result is robust to the inclusion of plausible transmission variables as well as different data sources or aggregations. Our paper also illustrates the usefulness of the group fixed effects estimator which helps to address some of the short-comings in standard panel econometric approaches to this question. 7 To the extent that the variables we include as transmission channels could be seen as critical control variables, these result suggest that our relationship is not driven by the exclusion of critical control variables.
With regard to the theoretical literature discussed above, it may be the case that the claims made by Ravallion et al. (2000) and Heerink et al. (2001)  A Results using WIID This appendix reports the results of estimating the parameters in a fixed effects using two different data sets on income inequality. The results in the main text are based on data from SWIID. Our preferred specification ( Table 2, column FE) is reprinted in the second column ("SWIID") in Table 5. The first column ("WIID") of Table 5 estimates the same fixed effects model using the data set described in Gruen and Klasen (2008), which is based on the WIID data set.
We find that the results are not driven by the choice of WIID versus SWIID (the data set used for our main results). At the same time, SWIID provides us with a substantially larger number of observations.