Environmental Taxation, Inequality and Engel’s Law: The Double Dividend of Redistribution


Empirical evidence shows that low-income households spend a high share of their income on pollution-intensive goods. This fuels the concern that an environmental tax reform could be regressive. We employ a framework which accounts for the distributional effect of environmental taxes and the recycling of the revenues on both households and firms to quantify changes in the optimal tax structure and the equity impacts of an environmental tax reform. We characterize when an optimal environmental tax reform does not increase inequality, even if the tax system before the reform is optimal from a non-environmental point of view. If the tax system before the reform is calibrated to stylized data—and is thus non-optimal—we find that there is a large scope for inequality reduction, even if the government is restricted in its recycling options.

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  1. 1.

    We are only concerned with the (intra-generational) distribution between different households at a given point in time, since increased intra-generational inequality is one of the most commonly used arguments against environmental policy (Combet et al. 2010; Ekins 1999). For an article that considers both intra- and inter-generational distributional effects of environmental taxation see Jacobs and van der Ploeg (2010).

  2. 2.

    In this strand of literature it is argued that using environmental tax revenue for reducing distorting taxes might lead to a reduction in the gross costs of an environmental tax reform, compared to lump-sum recycling (Goulder 1995; Bovenberg 1999).

  3. 3.

    Sandmo (1975) called this principle the additivity property.

  4. 4.

    This contribution and related research is centered around the question whether the marginal cost of public funds equals unity or not. Kaplow (2004) was the first to argue that these are indeed equal to one, if Mirrleesian income taxes and optimal public good supply are set simultaneously. Jacobs and De Mooij (2015) extend Kaplow’s thesis to the case of Pigouvian taxes combined with optimal income distribution. This holds when uniform lump-sum transfers are available to the government, in which case there are no environmental double dividends possible.

  5. 5.

    This is a common approach when assessing the equity and efficiency impacts of environmental policy in a general equilibrium (see e.g. Fullerton and Heutel 2007; Fullerton and Metcalf 2001; Copeland and Taylor 1994).

  6. 6.

    Following Jacobs and De Mooij (2015), we include uniform lump-sum transfers as a possible policy instrument. We analyze the case of a government restricted to income taxes in Sect. 4.1 and find that the uniform lump-sum transfers play a significant role in optimal taxation.

  7. 7.

    Bovenberg and van der Ploeg (1994, 1996) use the terms “blue welfare” for the non-environmental welfare component, and “green welfare” for the welfare component that depends on the environmental quality, to make this important distinction. Bovenberg and van der Ploeg (1996) and Ligthart and van der Ploeg (1999), further decompose welfare in a red and a pink component which accrue to changes in public consumption and employment, respectively. Since we assume constant government spending and full employment, there are no effects on public consumption or employment in our model.

  8. 8.

    This threshold level is a consequence of the assumption that the firms allocate some of the labor to pollution abatement (see Eq. (1) and the subsequent paragraph). In Fig. 4 in Sect. 4.3 we gradually increase \(\xi \) from zero and hence demonstrate the existence of that threshold.

  9. 9.

    We use the Gini coefficient in non-environmental utility, see Sect. 2.3 for more details.

  10. 10.

    This means all equations laid out in Sect. 2 remain the same, but we add the constraint that \(L=0\).

  11. 11.

    While some kinds of inequality may indeed be detrimental for society, others motivate people to work harder, and can be beneficial (Marrero and Rodríguez 2013). However, there seems to be evidence that inequality itself can have a negative effect on efficiency (Berg et al. 2012; Kumhof et al. 2015). At least for this reason, assuming suboptimally high levels of inequality is thus a credible premise and inequality-reduction a frequent policy goal.

  12. 12.

    We refrain from displaying the results of revenue recycling through a combination of lump-sum transfers and non-linear income tax cuts, since it leads to the same outcome as the scenario with only non-linear income tax cuts. The reason for that is that the government uses all the environmental tax revenue to mitigate inequality in the income tax system and hence has no use for lump-sum transfers.

  13. 13.

    This concept is different, however, from the concept of the environmental double dividend in the sense of Goulder (1995) and Bovenberg (1999): In models with only one representative household such a (weak) dividend can occur, when recycling through income tax cuts is more efficient than lump-sum recycling. A strong double dividend, that is an increase in economic efficiency, can only occur with an inefficient pre-existing tax system. In our setting, there is also an increase in GDP (see Fig. 5, bottom) because the pre-existing income tax schedule creates an inefficient labor supply.


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The authors thank three anonymous reviewers for their encouraging and helpful comments. We further thank Ulrike Kornek and Jan Siegmeier, as well as the participants of the 2015 GGKP, the 2015 EAERE and the 2016 Tinbergen Institute conferences for insightful discussions.

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Correspondence to David Klenert.

Appendix: First-Order Conditions of Households and Firms

Appendix: First-Order Conditions of Households and Firms


By combining the households’ first-order conditions with their budget equation, the following explicit demand functions can be derived:

$$\begin{aligned} C_i= & {} \frac{\alpha }{p_C(\alpha +\beta +\gamma )}H(w,p_D,\tau _{w,i},L), \end{aligned}$$
$$\begin{aligned} D_i= & {} \frac{\beta }{p_D(\alpha +\beta +\gamma )}H(w,p_D,\tau _{w,i},L)+D_0 \end{aligned}$$
$$\begin{aligned} l_i= & {} \frac{\gamma }{(\alpha +\beta +\gamma )(1-\tau _{w,i})\phi _i w}H(w,p_D,\tau _{w,i},L), \end{aligned}$$


$$\begin{aligned} H(w,p_D,\tau _{w,i},L) = ( (1-\tau _{w,i})\phi _i w T + L - p_D D_0). \end{aligned}$$

Firms Maximizing profits of both firms yields four first-order conditions:

$$\begin{aligned} w= & {} \frac{\partial F_j(T_j,Z_j)}{\partial T_j}=\epsilon _j T_j^{(r-1)} F_j^{(1-r)} p_j, \end{aligned}$$
$$\begin{aligned} \tau _Z= & {} \frac{\partial F_C(T_C,Z_C)}{\partial Z_C}=(1-\epsilon _j) Z_j^{(r-1)} F_j^{(1-r)} p_j, \end{aligned}$$

with \(j \in \{C,D\}\).

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Klenert, D., Schwerhoff, G., Edenhofer, O. et al. Environmental Taxation, Inequality and Engel’s Law: The Double Dividend of Redistribution. Environ Resource Econ 71, 605–624 (2018). https://doi.org/10.1007/s10640-016-0070-y

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  • Environmental tax reform
  • Double dividend
  • Revenue recycling
  • Inequality
  • Distribution
  • Non-homothetic preferences

JEL Classification

  • D58
  • D62
  • E62
  • H21
  • H23