Energy Economics 42 (2014) 88–100

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Energy Economics

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Can carbon taxes be progressive?☆

Yazid Dissou ⁎, Muhammad Shahid SiddiquiDepartment of Economics, University of Ottawa, Social Sciences Building, 120, University (09038), Ottawa, Ontario K1N 6N5, Canada

☆ Wewould like to thank Abdelkrim Araar, Sami Bibi, JaDidic, Stefan Dodds, Jean-Yves Duclos, Paul Makdissi,Tatsiana Yakautsava and an anonymous referee for veryments and suggestions on an earlier version of this papersupport from a grant on Canadian environmental issues band Humanities Research Council (SSHRC) is acknowledg⁎ Corresponding author.

E-mail addresses: ydissou@uottawa.ca (Y. Dissou), ms(M.S. Siddiqui).

0140-9883/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.eneco.2013.11.010

a b s t r a c t

a r t i c l e i n f o

Article history:Received 29 September 2012Received in revised form 10 November 2013Accepted 18 November 2013Available online 4 December 2013

JEL classification:D58D63H23

Keywords:Climate changeCarbon taxesInequalityCGE model

Most studies have assessed the distributional impact of carbon taxes through their effects on commodityprices alone, while ignoring their impact on individual welfare brought about by changes in factor prices.Yet, the remunerations of capital and labor are not affected by these taxes similarly, and their shares inearned incomes are not uniform across households. This paper provides a comprehensive analysis of theincidence of carbon taxes on inequality by considering simultaneously the commodity and the incomechannels. We propose a decomposition of the change in individual welfare metrics. Then, we develop a gen-eral equilibrium model to assess the impact of carbon taxes on factor and commodity prices, and subse-quently their distributional impact on households, using the Lorenz and concentration curves and theGini index. Our results suggest that changes in factor prices and changes in commodity prices (especiallythose of energy commodities) have opposing effects on inequality. Carbon taxes tend to reduce inequalitythrough the changes in factor prices and tend to increase inequality through the changes in commodityprices. Hence, we find a non-monotonic (U-shaped) relationship between carbon taxes and inequality.Our results suggest that the traditional approach of assessing the impact of carbon taxes on inequalitythrough changes in commodity prices alone may be misleading. The findings cast light on the desirabilityof using both channels in the assessment of carbon taxes on inequality.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

In this paper, we provide a new assessment of the impact of carbontaxes on inequality. It is generally perceived that the imposition of car-bon taxesmay not proportionally affect themetrics of individual house-hold welfare. Asking whether a carbon tax is progressive can be seen asa provocative questioning. The reality is that the impact of a carbon taxon households (progressive or regressive) is still questionable in light ofthe differences in its incidence on inequality, particularlywhen assessedfrom both the income and commodity sides of household welfaremetrics.

Indeed, most studies have relied on the commodity channel intheir assessments of the impact of carbon taxes on household wel-fare by examining their effects on relative prices of commodities.These studies generally point to the finding that carbon taxes are re-gressive. The main reason is that the increase in the prices of energyand energy-intensive goods, brought about by the imposition of

red Carbone, Patrick Coe, SelmaMarcel Merette, Leslie Shiell,useful and constructive com-. Usual caveats apply. Financialy the Canadian Social Sciencesed.

idd062@uottawa.ca

ghts reserved.

carbon taxes, hurts the poor more than the rich, as the formerspend a larger proportion of their income on those goods than thelatter do. For example, Robinson (1985) finds that the incidence ofan industrial pollution abatement tax is heavily regressive.1 Similar-ly, Hamilton and Cameron (1994) analyze the distributional effectsof a carbon tax on Canadian households and find that the conse-quences of the tax are regressive. Wier et al. (2005) and Dinan andRogers (2002) find similar results for Denmark and the Netherlands,respectively. Kerkhof et al. (2008) and Shammin and Bullard (2009)further confirm these results for the U.S. economy. All these studieshave ignored the impact of carbon taxes on factor incomes, and ulti-mately on inequality. As long as a carbon tax policy generates differen-tiated impacts on factor remunerations, the sources of income emergeas an important element in the assessments of carbon taxation and itseffects on inequality. Taking into account the fact that the rich derivemost of their income from capital, in comparison to the poor, an assess-ment of the impact of a carbon tax policy on inequality has the potentialto provide completely new insights.

Within a general equilibrium setting, Fullerton and Heutel (2007)have shown that pollution control policies can harm the remunerationof capital more than that of labor. The main reason is that the pollutingindustries are relatively more capital intensive than other industries(see Hettige et al., 1992). Implementing policies that negatively affectthe polluting industries will be detrimental to the factor they use most

1 See also Dubin and Henson (1988).

89Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

intensively. Under these circumstances, and looking from the factor in-come perspective alone, implementing a pollution control policy couldbe progressive, as the incomes of the affluent households will be morenegatively affected than those of the poor. It is important to note thatwe are not referring to the impact of the policy on social welfare, butrather on inequality; here, we are interested in its distributional impact.Even in the event that a carbon control policy reduces the welfare of allhouseholds, it can still be progressive, if the rich are more adverselyaffected than the poor. Moreover, note that the progressiveness of acarbon tax policy, which we are referring to, does not stem from arevenue-recycling approach as argued by Burtraw et al. (2009) andBento et al. (2009).

Unfortunately, most studies found in the literature on the inci-dence of pollution control policies on inequality have exclusivelyconsidered the commodity channel, i.e., the impact of the policieson the relative prices of commodities alone.2 Yet, individual house-hold welfare depends not only on commodity prices, but also on in-come. This suggests that most analyses of the impact of carbon taxeson inequality are incomplete as they overlook an important channel,i.e., the impact of carbon taxation on inequality through factorincomes.

Our objective in this paper is to offer a more comprehensive analysisof the distributional impact of carbon taxes by considering both thecommodity and the income channels throughwhich a pollution controlpolicy might have an incidence on individual welfare, and hence on in-equality. When viewed from this more holistic perspective, there is nodefinitive answer as to the exact impact of pollution control policieson inequality. This is attributed to the presence of two opposing effects:a regressive impact via the commodity channel and a progressive im-pact via the income channel. The final impact is an empirical matterthat deserves to be investigated.

In this study, we assess the possibility of a carbon tax being pro-gressive, i.e., whether there exists some value of a carbon tax,where its positive impact on inequality through income outweighsits negative impact induced by commodity prices. We are notaware of any other paper that offers an analysis of the incidence ofcarbon taxes on inequality, while disentangling their differing effectschannels on the relative prices of commodities and factor remunera-tion. To do so, we combine general equilibrium analysis with incomedistribution analysis.3 Central to our analysis is the decomposition ofwelfare metrics into different components, which include initialtotal expenditures, the contribution of the changes in commodityprices, and the contribution of the changes in factor prices. For thispurpose, we choose equivalent income as the main household wel-fare metric and assess the contributions of the last two componentsto the change in inequality.

More specifically, we examine the incidence of a carbon tax policyon income distribution by component as well as their contribution tochanges in total inequality. To measure the effects of a carbon tax onincome distribution we follow Kakwani (1977a, 1977b), who sug-gests that the incidence of a pollution tax through a component canbe derived by comparing the Lorenz curve of initial equivalent in-come and the concentration curve of each component.4 To measure

2 One notable exception to this is the recent paper by Araar et al. (2011) that analyzesthe incidence of carbon mitigation policies on social welfare.

3 A recent U.S. study by Metcalf et al. (2010) raises the issue of considering the incomeside in the analysis of the incidence of climate change policies. Nevertheless, their analyt-ical framework is completely different from the onewe suggest in this paper. They analyzethe effects of different emissions and revenue allocating approaches on householdwelfarein terms of equivalent variation. In contrast, we consider equivalent income as the house-holdwelfaremetric and stress the importance of the distributional impact by analyzing in-equality through a decomposition method of those elements considered important inincome and spending decisions of households.

4 See also Blaylock and Smallwood (1982).

the change in post-reform5 income inequality by components, weapply the concentration indices approach. For this purpose, we firstdevelop a static, multisector computable general equilibrium (CGE)model of the Canadian economy and run several simulations withdifferent values of the carbon tax. The remainder of the paper pro-ceeds as follows. The next section provides some theoretical back-ground on the impact of carbon taxes on relative factor prices andon their incidence on inequality. We present the CGE model in thethird section and discuss the results in the following section. Thelast section concludes.

2. Theoretical background

In this section, we present a theoretical framework to assess theimpact of a pollution tax on the relative price of capital and labor.For this purpose, we introduce a very simple model that provides agood understanding of the impact of pollution taxes on factor prices.The model will later help in building intuition of the distributionalimpact of carbon taxes on household welfare. As argued before, ageneral equilibrium setting is the most appropriate framework forcapturing the impact of a pollution tax on factor prices. The minimalrepresentation of the economic environment required for this pur-pose consists of two firms, two production factors, and one house-hold. The rationale for the sufficiency of one representativehousehold at this stage rests on our assumption that householdshave Gorman preferences, whereby, without any loss of generality,a representative consumer's preferences can be used to computetotal household demand.

In what follows, we consider a closed economy that consists of twofirms, one representative household, and the government, which has avery basic role. All agents operate in a competitive environment. Eachfirm, operating with the same constant-returns-to-scale technology,produces a single good indexed by i = (1, the clean good, and, 2, thedirty good) by combining capital and labor. For the moment, we ab-stract from the use of intermediate inputs in production activities.6 Cap-ital and labor are owned by the representative household and aresupplied in fixed quantities. The representative consumer hashomothetic preferences over the two goods and derives income fromthe ownership of primary factors and from tax revenue. Pollution is as-sumed to stem from the use of the dirty good by the representativehousehold according to a fixed proportion rule.7 The government's ob-jective is to reduce pollution by imposing a tax on the use of the dirtygood. For the sake of simplicity, we assume that the pollution tax is anad valorem tax, t, which is imposed on the value of the dirty good. Alter-natively, the pollution tax can be represented by the gross tax,τ = (1 + t).

To achieve our objective, we will first characterize the consumer'sand firms' behavior and then assess in a general equilibrium settingthe impacts of the pollution tax on the relative producer prices of thetwo goods and the relative factor price. As in most general equilibriummodels, we are interested in the changes in relative prices; hence, ourdiscussions below will mostly focus on the price and volume ratios, in-stead of their levels.

2.1. The consumer and the producer problems

Weassume that consumer preferences can be represented by awell-behaved twice-continuously differentiable and homothetic utility func-tion. Let X1 and X2 represent the consumer demand for goods 1 andgood 2, and P1 and P2, be, their associated producer prices. Due to thepresence of the tax on the dirty good, its producer price is different

5 Throughout this paper we interchangeably use the words post-policy and post-reform.6 We relax that assumption in a broader computable version of the model.7 This is a reasonable assumption, as there are no intermediate inputs used by firms.

90 Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

from its user price, which is τP2. As consumer preferences arehomothetic, at the optimum, the ratio of the demand for the two

goods X2

X1is independent of the level of income; rather it depends on

the relative price only.

X2

X1¼ f

P1

τP2

� �with f ′N0 ð1Þ

By log-differentiation of Eq. (1) we have:

dlnX1

X2

� �¼ — σd dln

P1

P2

� �— dlnτ

� �ð2Þ

where σd is by definition the elasticity of substitution between the twogoods on the demand side. Referring to Eq. (2), an increase in the pollu-tion tax, τ, will reduce the ratio of the relative demand of the dirty good(X2).

On the supply side, each firm combines capital and labor to produceoutput, Qi, using a constant-returns-to-scale technology that can be rep-resented by a well-behaved twice-continuously differentiable cost func-tion. We assume that the technology of producing the dirty good iscapital intensivewith no intensity reversal, in the sense that the orderingof the relative factor intensities in the two industries does not changewith factor prices. Assuming that the two factors are fully used, the aggre-gate output in this economy isfixed. The production possibility frontier ofthe two goods can be represented by a downward-sloping, concavetransformation curve. The concavity property stems from the combinedassumption of a constant returns to scale technology and differing capitalintensity ratios. As is well known, in a competitive environment, at agiven ratio of output prices, the optimal supply of the two goods is suchthat themarginal rate of transformation is equal to the price ratio. In par-ticular, the ratio of output depends on the ratio of output prices:

Q1

Q2¼ g

P1

P2

� �with g′N0 : ð3Þ

By log differentiation of Eq. (3) we have:

d lnQ1

Q2

� �¼ σ sd ln

P1

P2

� �with σ sN0 : ð4Þ

The parameter σs is the elasticity of substitution on the supply sidebetween the two goods. It depends on the elasticities of substitution be-tween capital and labor, on factor intensity, and on factor shares in bothfirms. Its positive sign is related to the concavity of the transformationcurve. Assuming equilibrium in the two goods markets, Eq. (4) canthus be rewritten as follows:

d lnX1

X2

� �¼ σ sd ln

P1

P2

� �: ð5Þ

We thus have two Eqs. (2) and (5), which can be used to assessthe impact of the change in the pollution tax, τ on the relative priceof the two goods. Hence, we can state our first proposition as follows.

Proposition 1. If the dirty and clean goods are substitutes in demand,firms use linear homogenous technologies, and the production of the dirtygood is capital intensive, then an increase in the pollution tax will increasethe relative producer price of the clean good.

Proof. The proof of Proposition 1 is straightforward. Assuming equilib-riumbetween demand and supply of each good, and combining Eqs. (2)and (5), it can easily be shown that:

dln P1P2

� �dlnτ

¼ σd

σd þ σ s: ð6Þ

From Eq. (2), the relative demand for the clean good increases withthe pollution tax. The intuition behind this result is that an increase inthe pollution tax increases the relative demand of the clean good,which can only bemet in equilibrium through an increase in its relativesupply. Given the shape of the transformation curve, the latter can onlyoccur through an increase in the relative price of the clean good.

We are now able to analyze the impact of the pollution tax on rela-tive factor prices. With constant-returns-to-scale technology, it is wellknown that the cost function, Ci(w,r,Qi), is linear in output and has ageneral expression that can be derived from the followingminimizationproblem:

Ci w; r;Qið Þ ¼ minKi ;Li

rKi þwLi : Fi Ki; Lið Þ≥Qif g ð7Þ

wherew, r, and Ci are, respectively, thewage rate, the rental rate of cap-ital, and the cost of production. Fi(Ki,Li) is a well-behaved productionfunction. The expression of the cost function is:

Ci w; r;Qið Þ ¼ Qici w; rð Þ: ð8Þ

At the optimum, each firm sets its price equal to its marginal costand determines the optimal level of input through cost minimiza-tion. The first-order conditions of their optimization problem are asfollows:

Pi ¼ ci w; rð Þ ð9Þ

Li ¼∂c w; rð Þ

∂w Qi ¼ aLiQi ð10Þ

Ki ¼∂ci w; rð Þ

∂r Qi ¼ aKiQ i: ð11Þ

Eq. (9) reflects the marginal cost pricing rule and Eqs. (10)–(11) arethe conditional factor demands for, respectively, labor and capital. Theparameters aLi and aKi are, respectively, labor and capital quantities re-quired to produce one unit of output i. By definition, if the productionof the dirty good (Eq. (2)) is capital intensive, the ratio of capital tolabor is higher in Firm2 than in Firm1, i.e.,aK2=aL2NaK1=aL1 or equivalent-ly, aK2=aK1NaL2=aL1 .

It is easy to show through total differentiation of Eq. (9) that the fol-lowing relations exist between the percentage changes in output andfactor prices

d ln P1ð Þ ¼ θL1d ln wð Þ þ 1−θL1ð Þd ln rð Þ ð12Þ

d ln P2ð Þ ¼ θL2d ln wð Þ þ 1−θL2ð Þd ln rð Þ ð13Þ

where θLi is the share of labor cost in the production cost of good i andhas the following expression: θLi = aLiw/Pi.

The system of Eqs. (12)–(13) has two unknowns, dln(w) and dln(r),and has a unique solution if and only if its determinant is different fromzero. Yet, using the assumption of no factor intensity reversal, it can eas-ily be shown that the determinant, which is equal to (θL1 − θL2), is dif-ferent from zero for all vectors of input prices.

The solution to the system of equations yields:

d ln wð Þ ¼ 1−θL2ð Þd ln P1− 1−θL1ð Þd ln P2 ð14Þ

d ln rð Þ ¼ θL1d lnP2−θL2d ln P1: ð15Þ

We thus have the following propositionwith regard to the impact ofpollution tax on the relative price of factors.

Proposition 2. If the dirty and clean goods are substitutes in demand, thedirty good is capital intensive, and both firms use linear homogenous tech-nologies, then, an increase in the pollution tax increases the relative price oflabor (or decreases the relative price of capital).

91Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

Proof. The proof of this proposition is as follows.

d ln wrð Þ

d ln τð Þ ¼d ln w

rð Þd ln P1

P2

� �d ln P1P2

� �d ln τð Þ ð16Þ

Using Eqs. (6), (14), and (15), we have:

d ln wrð Þ

d ln τð Þ ¼1

θL1−θL2

σd

σd þ σ sN0: ð17Þ

The right-hand side of expression (17) has a positive sign since,θL1 N θL2, i.e., the ratio of labor to capital is higher in thefirm that producesthe clean good. The intuition behind this result follows from the onediscussed in the previous proposition and from the Stolper–Samuelsontheorem (see for example Mussa (1979)). The latter theorem suggeststhat there is a positive relationship between the relative price of a goodand the relative price of the factor used most intensively in the produc-tion of that good.

2.2. Incidence on equivalent income

In order to explain the impact of a pollution tax on welfare and in-equality, we use the equivalent income approach as suggested byKing (1983).8 We now assume that there are several householdsindexed by h = 1,2,…,H. Assume that in the reference situation,the budget constraint of the household h is characterized by (P0,Mh

0), where P0 is a vector of household's consumption prices andMh

0 is household income (total expenditures). Throughout this sec-tion, a variable's superscripts 0 and 1 refer to, respectively, beforeand after-policy levels of that variable. Referring to King (1983),equivalent income can be defined as the level of expenditure, Mh

E,at the reference price, P0, that is needed by the consumer to enjoythe same level of utility as after the reform with the prices, P1, andexpenditures Mh

1. Defining the indirect utility of the household byv = v(P,Mh), the equivalent income Mh

E can be found by solving thefollowing equation:

v P0;ME

h

� �¼ v P1

;M1h

� �: ð18Þ

Assuming Cobb–Douglas preferences, the household problem is:

maxX1 ;X2

U ¼ Xβ1X

1−β2 ð19Þ

subject to Mh≥P1X1 þ P2X2 and with 0bβb1 : ð20Þ

For a given vector of prices and income, the indirect utility functionof household h has the following expression:

v P;M1h

� �¼ M1

hβP1

� �β 1−βP2

� �1−β: ð21Þ

Considering Eqs. (18) and (21), we can write the following relation-ship between equivalent income and household income after thereform:

MEh ¼ M1

hP11

P01

!−βP12

P02

!β−1

: ð22Þ

8 An alternative measure of capturing welfare are standard of living. For more details,see Shorrocks (2004).

Using a first-order approximation, Eq. (22) can be rewritten in termsof the percentage changes (logarithmic derivatives) in the variables onits right-hand-side after the reform.

MEh ¼ M0

h 1þ d lnMhð Þ 1−βd lnP1− 1−βð Þd lnP2 þ ξ½ � ð23Þ

where ξ is the combined effect of the commodity price changes.Assuming that the consumer's total income Mh consists of labor and

capital incomes, the percentage change in his total income can be derivedas follows:

Mh ¼ wLh þ rKh ð24Þ

d lnMh ¼ θLhd lnwþ θKhd ln r: ð25Þ

Lh and Kh are the consumer endowments of, respectively, labor andcapital, and θLh, and θKh represent the shares in total income of, respec-tively, labor and capital.

Combining Eqs. (23) and (24), equivalent income, MhE, can be

decomposed as follows:

MEh ¼ M0

h þ δ1h þ δ2h þ δ3h þ δ4h ð26Þ

with

δ1h ¼ M0h θLhd lnwþ θKhd ln rð Þ ð27Þ

δ2h ¼ −βM0hd ln P1 ð28Þ

δ3h ¼ −M0h 1−βð Þd ln P2 ð29Þ

δ4h ¼ MEh− M0

h þ δ1h þ δ2h þ δ3h� �

: ð30Þ

Eq. (26) suggests that equivalent incomes after the reform can bedecomposed into five components: (i) total expenditures before thereform,Mh

0; (ii) the impact of the change in factor prices, δh1; (iii) the im-pact of the change in the price of the clean good, δh2; (iv) the impact ofthe change in the price of the dirty good, δh3; and (v) a residual that cap-tures the combined impact of changes in factor prices and in commodityprices, δh4. Since the main focus of our analysis is to evaluate the contri-bution of each component to the change in the post-policy income in-equality among households, based on Eq. (26), we can define thechange in equivalent income as dh ≡ Mh

E − Mh0 where:

dh ¼X4n¼1

δnh: ð31Þ

The overall incidence of the pollution tax policy on individual house-hold welfare will be negative if the net impact of all components isnegative.

2.3. Income distribution and inequality by components

We now investigate the impact of each component of change inhousehold equivalent income on inequality. If each component affectsall households proportionally, then there will be no change in inequal-ity. We follow Kakwani (1977a, 1977b) to examine the contribution ofeach component to the change in inequality. The incidence of taxes oninequality by income component can be analyzed by comparing theLorenz curve of initial equivalent income and the concentration curveof each component as introduced by Rao (1969) earlier. For a good un-derstanding of this comparison, it is useful to recall the intuition behindthe Lorenz and concentration curves.

Consider a population equally distributed among H householdgroups. Assume that the households are arranged in an ascending

92 Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

level of their equivalent income as follows M10≤.. Mh

0≤.. ≤ MH0 with

percentiles pj = j/H such that the mean of equivalent income acrossthe H households is μ(M0). Before the reform, the Lorenz curve of theequivalent income at p-percentile of the households may beexpressed as follows:

LM0 p ¼ h=Hð Þ ¼ 1Hμ M0� Xh

j¼1

M0j ð32Þ

where LM0 p ¼ h=Hð Þ is the cumulative percentage of total equiva-lent income held by the cumulative proportion of p householdsin the total population. For example, LM0 (0.4) = 0.2 suggeststhat the 40% poorest households hold 20% of total income of thepopulation.

On the other hand, the concentration curve can be an effective in-strument to examine the contribution of each component of equiva-lent income to post-policy variation in income inequality. Here, δhn

(n = 1,2,3,4) is the post-policy nth component, which accounts forthe variation in equivalent income of each household and can be ag-gregated for the H households in order to obtain its mean by compo-nent, μ δn

� ¼ 1H∑

Hj¼1δ

nj . The concentration curve for income

component δn is:

Cδn p ¼ h=Hð Þ ¼ 1Hμ δnð Þ

Xhj¼1

δnj ð33Þ

where Cδn p ¼ h=Hð Þ indicates the cumulative impact of the variationin equivalent income by component δn among the bottom p propor-tion of households relative to the variation in equivalent income bythe same component among all households in the rank. Notice thatby using Eq. (31), we can write the post-policy equivalent incomeof household h as Mh

E = Mh0 − (−∑ n = 1

4 δhn). Hence followingJakobsson (1973) and Kakwani (1977a), the post-policy distributionof equivalent income by each component can be estimated asfollows:

CME pð Þ−LM0 pð Þ ¼ μ δn�

μ M0� −μ δnð Þ LM0 pð Þ−Cδn pð Þ �

: ð34Þ

In Eq. (34), if LM0 pð ÞNCδn pð Þ, the incidence of δthn component ismore concentrated towards the top percentile income groups.Hence, post-policy equivalent income, in this case, will be moreequally distributed than initial income (see Kakwani, 1977a). Thisindicates that the incidence of a carbon tax policy on household in-come through the component δn is progressive. In other words, ifthe concentration curve of a component δn is below the Lorenzcurve, the low income households are affected relatively less thanthe rich households. Hence the contribution of component δn isprogressive.9

In addition to analyzing progressivity, the Lorenz and concentrationcurves can also be used to estimate income inequality by components(see Kakwani, 1977a). A widely used measure of income inequality isGini index (IG), which is one minus twice the area under the Lorenzcurve. Similarly, the concentration index (IC) is defined as one minustwice the area under the concentration curve.

One approach to express the post-policy change in inequality oftotal equivalent income by each component is the application ofthe exact decomposition approach, explained by Araar et al.(2011), Araar (2008), Duclos and Araar (2006), and Kakwani(1977b).10 Following these studies, the policy-induced change in

9 For details see Kakwani, 1977a.10 For a further reference, see Section 2.6 of Araar (2008), chapter 12 of Duclos and Araar(2006), and Section 3 of Kakwani (1977b).

total income inequality with respect to a variation in one of its com-ponents can be expressed as:

IGME pð Þ−IGM0 pð Þ ¼Xn

μ δn�

μ M0� IGM0 pð Þ−ICδn pð Þ �

: ð35Þ

The right hand side of Eq. (35) indicates that the change in totalincome inequality due to a variation in the nth source depends onthe average size and on the concentration index. In other words,under a tax policy reform, if IGM0 pð ÞbICδn pð Þ, then the nth componentis more concentrated towards the higher income groups and contrib-utes to a reduction in inequality. The opposite results is obtainedwhen IGM0 pð ÞNICδn pð Þ. Summing the contributions of all individualcomponents equals the left hand side of Eq. (35), which is the differ-ence between pre- and post-reform Gini indices.11

3. The numerical model

We develop a static, multi-sector, small open general equilibriummodel to assess the distributional impact of a carbon tax in light of thetheoretical discussions presented in the section above. A noticeable de-parture of this numerical model, from the analysis presented above isthat, not only dowe havemore than two commodities, we also consideran open economy that trades goods and services with the rest of theworld. The model is in the tradition of computable general equilibriummodels used to assess climate change policy options in several coun-tries. In particular, it has bearingwith some recent interesting contribu-tions to the literature on the general equilibrium modeling of climatechange within a multi-sector and static setting, such as that of Araaret al. (2011) and Bohringer and Rutherford (2010). We assume thathouseholds have Gorman polar form utility functions. Hence, we use arepresentative household to model their preferences. In addition tohouseholds, the economy consists of firms, the government and therest of the world. The economy is disaggregated into 39 industries,indexedby j, and 43 commodities indexedby i. The number of commod-ities is larger than that of industries, because some industries, such asthe oil and gas industry produce more than one commodity (in thiscase, crude oil and natural gas).12

We assume that the use of fossil fuels generates carbon dioxide(CO2), the level of which the government desires to regulate using a car-bon tax as a policy instrument. All agents consider prices as given andmust respect their budget constraints. It is worthmentioning that in ad-dition to the impact of the pollution tax on the consumption good as ex-plained in our theoretical discussions, we also have a direct impact ofthe tax on fossil fuels that are used as intermediate inputs. Hence, thecarbon tax will also have a direct impact on the producer prices ofnon-fossil-fuel goods. The magnitude of the increase in the producerprice of a good following the imposition of a carbon tax is related toits carbon intensity. Finally, capital and labor are assumed to be mobileacross industries.

In order to avoid the black-box syndrome related to CGE models, inwhat follows, we provide a description of the key behavioral features ofthe economic agents as well as the resource constraints they face. Webelieve that a discussion of these featureswill allow the reader to under-stand the intuition behind the numerical results of the model.13

3.1. Households

The representative household is assumed to have Cobb–Douglaspreferences over the 43 commodities. The household does notvalue leisure, hence, its labor supply, LS, is inelastic, and hence,

11 In a pre-reform case, the Gini coefficient and the concentration ratio will be the same.12 See Section 4 for details of industries and commodities.13 The details of the nesting structure and model algebra are available from the authorsupon request.

Fig. 1. An overview of production structure of sectors.

Table 1Sectors specifications.

I. Energy-related industries II. Non-energy related industries

Coal AgricultureCrude oil FoodNatural gas ConstructionGas pipeline TextileRefineries Wood-Gasoline Transport equipment-Diesel Other manufacturing-Liquefied petroleum Wholesale-Other refineries Retail tradeElectricity CommunicationPulp-paper EducationPrinting Government sectorChemical Non-profit organizationMining HealthRubber AccommodationPlastic Electric productsNon-metallic metals Storage

93Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

total labor supply in the economy is exogenous. Similarly, the totalsupply of the capital stock in the economy is fixed. The representa-tive household derives income from wages, capital income, transfersfrom the government, and net transfers from the rest of the world. Itpays taxes on income and consumption goods and saves a fixed frac-tion of its disposable income. The representative household's prob-lem is to choose the optimal combination of consumption goods bymaximizing its utility function subject to the budget constraint:

maxCi

∏n

i¼1Cβii with

Xi

βi ¼ 1

subject to

∑iPci Ci≤ 1—t f

� �wLs þ RK� þ TRG

—TRfr—S ≡M ð36Þ

where M; Pci ; and Chi , are, respectively, total expenditures, the

price and, the demand for the consumption good; tf, is the householdincome tax rate; w, is the wage rate; and, LS is the household's laborsupply. RK is the return to capital received by each household fromthe firms, while, TRG, TRfr, and S, are, respectively, transfers fromthe government, net transfers from the rest of the world (in worldprices), and savings.14 Moreover, βi is a parameter of the utility func-tion. As discussed below, the consumption good is a composite of do-mestically produced and imported goods, and its price incorporatesthe effects of carbon taxes that have been imposed on the use of in-termediate inputs during its production.

It is straightforward to show that the demand for each commodityby each household has the following expression:

Pci Ci ¼ βiM: ð37Þ

14 It is important to note that in the absence of an income tax and saving, the total expen-ditures,M, are identical to the concept of total income that we used in our analysis of thedecomposition of household equivalent incomes in the previous section.

As saving is a fixed fraction of disposable income, it can be expressedas follows:

S ¼ s 1−t f� �

wLs þ RK� þ TRG−eTRfr

h i: ð38Þ

Finally, the return to capital, RK, is the dividend payment receivedfrom firms whose value is lower than the total remuneration of capitalin the economy, as firms keep a fixed proportion, 1-βKE, for investmentpurposes. Hence, RK has the following expression:

RK ¼ βKE 1−tbð ÞXj

rKdj ð39Þ

where r, and Kjd, are, respectively, the rental rate of capital, and the sec-

toral demand for capital by each industry, while tb refers to the tax onentrepreneurial earnings.

3.2. Production

The representative firm in each industry has access to a linear ho-mogeneous production function to produce a composite good thatcan be sold in the domestic and the exports markets. The productiontechnology is assumed to be weakly separable, and combines capital,labor, fossil inputs and non-fossil inputs to produce the gross output.The weak separability property of the technology is captured by thenested structure of production as depicted in Fig. 1. An interestingfeature of the separability is that it makes it possible to account forthe substitution possibilities that are offered to firms, as far as theuse of energy products is concerned. This distinction is all the moreimportant in the context of a pollution tax that is based on the carboncontent of the fuel used.

As shown in Fig. 1, at the top level of the production structure, thecomposite of output is a constant elasticity of substitution (CES) aggre-gate of the composite of value-added and energy, KELj, and of the com-posite of intermediate inputs INTj. At the second level, the compositeKELj is a Cobb–Douglas aggregate of labor, Ljd, and a composite of capitaland energy KEj. At the third level of the nesting structure, the sectoralcapital stock Kj is combined with the composite of energy inputs, Ejthrough a CES aggregation function to produce KEj. The composite of en-ergy input is a CES function of electricity and an aggregate of fossil fuels.The latter is another CES combination of coal, natural gas, and the com-posite of refined petroleum products. The composite of intermediate

Steel FireOther metals Business serviceMachinery Other servicesTransport services Fishing and forestry beverage tobacco amusement

Table 2Decomposition of value added and CO2 emissions by industries in the base case.

Sectors Share in total value added(in%)

Share of sectors in totalCO2 emissions (in%)

Decomposition of sectoral total emissions shares bytheir use of fossil fuel (in%)

Labor Capital Coal Oil Gas

EnergyElectricity 27.20 72.80 20.21 16.90 1.61 1.69Oil and gas 14.09 85.91 13.21 0.00 3.21 10.00Gas pipeline 19.08 80.92 1.57 0.00 0.06 1.51Coal 38.32 61.68 0.17 0.06 0.09 0.02Refineries 44.29 55.71 4.70 0.01 4.14 0.55

Non-energy commoditiesAccommodation 80.24 19.76 0.39 0.00 0.19 0.20Agriculture 38.88 61.12 2.10 0.00 1.77 0.33Amusement 73.87 26.13 1.09 0.00 1.07 0.02Beverage 33.20 66.80 0.11 0.00 0.03 0.07Chemical 43.85 56.15 2.91 0.00 0.15 2.76Communication 49.14 50.86 0.29 0.00 0.17 0.12Construction 81.05 18.95 1.78 0.01 1.75 0.02Education 90.29 9.71 0.08 0.00 0.05 0.03Electric products 78.76 21.24 0.07 0.00 0.01 0.07Fire 37.89 62.11 3.33 0.00 1.19 2.13Fishing and forestry 71.68 28.32 0.36 0.00 0.35 0.01Food 51.62 48.38 0.65 0.00 0.14 0.51Government sector 86.30 13.70 2.92 0.00 1.48 1.44Health 78.62 21.38 0.29 0.00 0.21 0.08Machinery 64.95 35.05 0.19 0.00 0.04 0.14Metals (other) 68.80 31.20 0.30 0.00 0.04 0.26Mining 30.60 69.40 1.04 0.00 0.68 0.36Non-metallic metals 57.48 42.52 2.88 1.10 0.84 0.94Non-profit 95.81 4.19 0.42 0.00 0.12 0.30Other manufacturing 57.66 42.34 0.05 0.00 0.01 0.04Other services 77.46 22.54 0.36 0.00 0.24 0.13Plastic 59.33 40.67 0.13 0.00 0.02 0.11Printing 66.41 33.59 0.05 0.00 0.01 0.05Pulp-paper 65.66 34.34 1.69 0.03 0.63 1.03Retail trade 77.93 22.07 1.38 0.00 0.80 0.58Rubber 71.58 28.42 0.06 0.00 0.02 0.04Business service 81.31 18.69 0.80 0.00 0.590 0.21Steel 48.53 51.47 4.10 0.19 2.52 1.39Storage 89.48 10.52 0.24 0.00 0.21 0.03Textile 73.47 26.53 0.10 0.00 0.02 0.08Tobacco 28.39 71.61 0.01 0.00 0.00 0.00Transport Equipment 58.95 41.05 0.43 0.01 0.06 0.36Transport Services 76.39 23.61 8.22 0.00 8.01 0.21Wholesale 68.15 31.85 2.28 0.00 1.91 0.37Wood 50.55 49.45 0.41 0.00 0.13 0.28Households – – 18.65 0.00 0.13 0.28

94 Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

inputs is a CES function of a composite of a C-D aggregate ofmotive fuelsand a Leontief aggregate of the othermaterial inputs. An overview of theproduction structure is depicted in Fig. 1.

The representative firm pays taxes net of subsidies on gross out-put and maximizes profits in order to determine the optimal levelsof inputs. The traditional principle of equalizing the marginal prod-uct of the input to its price applies in this setting. Note that theprice of a composite input is its dual price, which is obtained througha cost-minimization principle. An increase in the carbon tax will notonly reduce the demand for the fossil fuel, but will also trigger a cascad-ing increase in the dual prices of composite inputs and will eventuallylead to an increase in the producer price of the composite good.

As mentioned previously, the representative firm produces a com-posite good that is made of the domestic good and the export good.Both are imperfect substitutes and their production technology is cap-tured by a concave transformation curve. Notably, a constant elasticityof transformation (CET) function is used to transform the gross outputinto sales in the domestic market and the export market. The represen-tative firm uses a revenue-maximizing principle subject to the techno-logical constraint (represented by the transformation curve) todetermine the optimal allocation of gross output into sales in the two

markets. For example, at the optimum, everything else equal, the in-crease in the relative price of exports will reduce the ratio of domesticsales to those in foreign markets.

Finally, the representative firm returns a fixed proportion, βKE ofthe return to physical capital to households as dividend payment,pays business income taxes and uses the remainder for investmentpurposes.

3.3. Government, international trade, equilibrium conditions and closurerules

The government collects direct and indirect taxes from households,firms, and international trade activities, including pollution activities.The government enacts exogenous transfers to households and pur-chases fixed quantities of goods.

The carbon tax is implemented as an excise tax on the use of fossilfuels (by all agents) that is related to its carbon content. Assumingthat Emiti is the emissions factor related to the use of fossil fuel i, i.e.,the quantity (in tons) of CO2, emitted by one unit of the fossil fuel, Pq

is the carbon tax expressed in $ per ton of CO2, and Pci is the user price

Table 3External elasticity parameters.

Sectors Fossil fuels (FF) (refinedpetroleum, gas, coal)

Energy (i.e. FF andelectricity)

Capital &energy (KE)

KE & labor(KEL)

KEL &material

Material & motivefuels (KELM)

Elasticity oftransformation (CET)

EnergyElectricity 0.90 0.50 0.66 1.00 0.50 0.30 0.75Oil and gas 0.38 0.70 1.45 1.00 0.40 0.34 0.75Gas pipeline 2.46 0.75 0.94 0.65 0.5 0.3 0.75Coal 0.38 0.78 0.63 1.00 0.70 0.78 0.75Refineries 2.50 0.76 1.29 1.00 0.90 0.30 0.75

Non-energyAccommodation 1.93 1.03 0.60 1.00 0.40 0.41 0.75Agriculture 1.17 1.08 0.35 1.00 0.70 0.34 0.75Amusement 1.93 1.03 0.60 1.00 0.4 0.41 0.75Beverage 0.88 1.05 0.37 1.00 0.4 0.42 0.75Chemical 0.73 0.93 1.26 1.00 0.40 0.37 0.75Communication 1.93 1.03 0.60 1.00 0.40 0.41 0.75Construction 1.93 1.03 0.60 1.00 0.40 0.41 0.75Education 1.93 1.03 0.60 1.00 0.40 0.41 0.75Electric products 0.88 1.05 0.37 1.00 0.4 0.42 0.75Fire 1.93 1.03 0.6 1.00 0.4 0.41 0.75Fishing and forestry 1.17 1.08 0.35 1.00 0.7 0.34 0.75Food 0.88 1.05 0.37 1.00 0.40 0.42 0.75Health 1.93 1.03 0.60 1.00 0.40 0.41 0.75Machinery 0.88 1.05 0.37 1.00 0.40 0.42 0.75Metals (Other) 0.88 1.05 0.37 1.00 0.4 0.42 0.75Mining 0.43 0.83 0.64 1.00 0.70 0.65 0.75Non metallic metals 1.20 0.86 0.37 1.00 0.40 0.36 0.75Other manufacturing 0.88 1.05 0.37 1.00 0.40 0.42 0.75Other services 1.935 1.03 0.6 1.00 0.40 0.41 0.75Plastic 0.73 0.93 1.26 1.00 0.40 0.37 0.75Printing 1.07 0.78 0.23 1.00 0.40 0.64 0.75Pulp-paper 1.07 0.78 0.23 1.00 0.40 0.64 0.75Retail trade 2.52 0.49 0.50 1.00 0.40 0.83 0.75Rubber 1.55 0.70 0.38 1.00 0.40 0.72 0.75Business service 1.93 1.03 0.6 1.00 0.40 0.41 0.75Steel 0.88 1.05 0.37 1.00 0.40 0.42 0.75Storage 1.93 1.03 0.6 1.00 0.40 0.41 0.75Textile 0.88 1.05 0.37 1.00 0.40 0.425 0.75Tobacco 0.88 1.05 0.37 1.00 0.40 0.42 0.75Transport equipment 0.88 1.05 0.37 1.00 0.40 0.42 0.75Transport services 2.52 0.49 0.50 1.00 0.40 0.83 0.75Wholesale 1.93 1.03 0.60 1.00 0.40 0.41 0.75Wood 0.88 1.05 0.37 1.00 0.40 0.42 0.75

Note: i) Elasticity of substitution among alternate motive oil across sectors is Cobb–Douglas. ii) Elasticity of substitution among alternate non-motive oil across sectors is Cobb–Douglas iii) Armington elasticity between domestic and imported non-energy products is 2, while for energy products are 4 iv) Elasticity of substitution among domestic supplyand exports of non-energy product is 2, while for energy product is 4.

95Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

(net of the carbon tax) of fossil fuel, then, the gross-of-carbon-tax priceof the fossil fuel, Pic is: P

ci ¼ P

ci þ PqEmiti.

15

Hence, the total proceeds of the carbon taxes are PqΣiEmiti ∙ YDi,where YDi, is the total demand for each commodity by households,firms and government. To disentangle the true effects of carbon taxeson inequality and to ensure pollution tax neutrality, we elect not to re-turn the carbon taxes' proceeds to households. We instead return theseproceeds to government saving.

The representative firm produces a composite good that is com-prised of the domestic good and the export good. Both are imperfectsubstitutes and their production technology is captured by a concavetransformation curve. Notably, a constant elasticity of transformation(CET) function is used to transform the gross output, YSi, into sales indomestic market, DYSi, and exports, YXi. Using a revenue-maximizingprinciple subject to the technological constraint (represented by thetransformation curve), it is possible to determine the optimal allocationof gross output into sales in the two markets. At the optimum, every-thing else equal, an increase in the relative price of exports reducesthe ratio of domestic sales to those in foreign markets.

Total demand for each commodity, YDi, is a CES composite of the de-mand for domestically produced goods DYDi and the imported goods

15 Emiti equals to zero for non-fossil fuel goods.

YMi. A cost-minimization principle makes it possible to determine theoptimal allocation of the composite between its two components. Atthe optimum, an increase in the relative price of the imported good re-duces its relative demand.

The general equilibrium of this economy is represented by a vec-tor of price and quantity variables such that all agents maximizetheir objective functions while respecting their respective budgetconstraints, and all markets clear. In equilibrium, the following con-ditions should be met: i) zero profit or no arbitrage conditions by allrepresentative firms; ii) income balance conditions, in which house-hold income and government revenuemust be equal to its respectiveexpenditure; iii) market clearing conditions, which implies equilib-rium in the labor market, the capital market, the domestic goodsmarket, and the foreign exchange market.

The model is real in the sense that changes in nominal variables donot have any impact on real variables; only relative prices matter. Themodel's numeraire is the nominal exchange rate (currency conversionfactor). Besides, we also assume that foreign saving is exogenous. Thelevel of total real investment is kept fixed by endogenizing thehousehold's saving rate.16

16 Thanks to an anonymous referee for suggesting the latter closure rule.

Table 4Aggregate impacts of different values of carbon tax ($ per ton of CO2).

% Change relative to base case

$15 $30 $50 $100 $150

Real GDP at market price −0.10 −0.22 −0.41 −0.89 −1.35Real consumption −0.17 −0.40 −0.73 −1.58 −2.42

energy goods −6.17 −11.23 −16.79 −26.96 −34.01Non-energy goods 0.19 0.26 0.25 −0.04 −0.50Energy-intensive goods −0.57 −1.17 −1.96 −3.82 −5.49Non-energy-intensive goods 0.26 0.39 0.45 0.30 −0.05

Real exports −0.52 −0.85 −1.16 −1.65 −1.98Energy goods −2.02 −3.63 −5.30 −7.88 −8.92Non-energy goods −0.27 −0.39 −0.47 −0.61 −0.82Energy-intensive goods −2.75 −4.80 −6.96 −10.92 −13.79Non-energy-intensive goods 1.61 2.95 4.46 7.22 9.03

Real imports −0.58 −0.96 −1.31 −1.85 −2.22Energy goods −10.27 −17.52 −24.76 −36.67 −44.21Non-energy goods 0.11 0.24 0.39 0.66 0.81Energy-intensive goods 0.20 0.43 0.74 1.42 1.96Non-energy-intensive goods 0.03 0.04 0.04 −0.09 −0.33

Rental rate of capital −1.27 −2.35 −3.60 −6.09 −8.03Nominal wage rate −0.37 −0.68 −1.05 −1.85 −2.55Ratio of rental rate of capital towage

−0.91 −1.69 −2.58 −4.32 −5.62

Consumer price index 0.30 0.63 1.10 2.31 3.58Consumer price index(non energy goods)

0.00 0.00 0.00 0.00 0.00

Consumer price index(energy goods)

0.17 0.34 0.57 1.15 1.73

Reduction in total emissions −14.52 −23.31 −31.58 −44.71 −52.87

Table 5Impact of different carbon taxes on consumption prices (% change relative to base case).

Sectors $15 $30 $50 $100 $150

EnergyElectricity 2.57 4.42 6.39 10.18 13.22Oil and gas 8.94 18.04 30.31 61.43 92.99Gas pipeline −0.63 −1.12 −1.65 −2.63 −3.31Coal 83.06 166.14 276.95 554.00 831.07Refineries 9.71 19.24 31.72 62.23 92.21

Non-energyAccommodation −0.29 −0.53 −0.79 −1.31 −1.69Agriculture −0.01 0.02 0.11 0.41 0.79Amusement −0.33 −0.60 −0.91 −1.54 −2.03Beverage −0.35 −0.62 −0.93 −1.49 −1.87Chemical 1.04 1.97 3.06 5.22 6.84Communication −0.50 −0.91 −1.37 −2.31 −3.04Construction 0.39 0.78 1.30 2.51 3.60Education −0.27 −0.49 −0.73 −1.21 −1.58Electric products −0.05 −0.09 −0.13 −0.23 −0.30Fire −0.59 −1.07 −1.62 −2.71 −3.53Fishing and forestry 0.37 0.75 1.27 2.54 3.75Food −0.14 −0.21 −0.27 −0.26 −0.16Health −0.38 −0.70 −1.06 −1.81 −2.41Machinery −0.04 −0.07 −0.12 −0.20 −0.26Metals (other) 0.13 0.22 0.31 0.48 0.63Mining 0.03 0.14 0.34 0.96 1.64Non−metallic metals 0.19 0.36 0.60 1.20 1.79Other manufacturing −0.04 −0.06 −0.08 −0.09 −0.07Other services −0.28 −0.51 −0.76 −1.25 −1.63Plastic 0.16 0.31 0.49 0.84 1.07Printing −0.09 −0.14 −0.18 −0.21 −0.21Pulp-paper 0.53 1.03 1.66 3.12 4.42Retail trade −0.30 −0.55 −0.82 −1.37 −1.79Rubber 0.04 0.09 0.16 0.33 0.47Business service −0.34 −0.62 −0.94 −1.57 −2.08Steel 1.25 2.13 3.05 4.78 6.12

96 Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

4. Data structure and CGE results

To simulate the base case, we construct a social accountingmatrix(SAM), which is based on the Canadian national economic accountsfor the year 2004. The SAM is a reconciliation of input–output (IO)data with macroeconomic national accounts data and captures a bal-ance of income and expenditure flows among industries, house-holds, government, and the rest of the world for each account. TheIO table contains 39 industries and 43 commodities. The list of indus-tries is available in Table 1. For analytical reasons, we categorize allindustries into either energy-related or non energy-related sectors.Data on carbon dioxide (CO2) emissions are taken from StatisticsCanada. As indicated in the previous section, we align emissions in-ventory with economic data by calculating the emission factor ofeach fuel.17

We obtain household income and expenditure information from theCanadian “Social Policy Simulation Database” (SPSD), which is a data-base that comprises a transformation of four data sources into a singlenon-confidential and publicly used micro data file. The SPSD processuses the Canadian Survey of Labour and Income Dynamics (SLID) as ahost dataset and maps it with the other dataset (i.e., Personal IncomeTax Return data, Employment Insurance (EI), and the Survey of House-hold Spending) based on some similar records or categorical matchingamong different dataset.18 The database contains 72,687 observationsof household incomes and expenditures for the base year 2004. House-hold expenditures in the SPSD are disaggregated into 49 personal ex-penditure categories.

The SPSDdata (labor and capital incomes, transfers, direct taxes, sav-ings, and expenditures on commodities) have been adjusted to matchthe totals found in the SAM. The correspondence between the

17 Our model does not represent process emissions, i.e. GHG emissions not associatedwith the combustion of fuels.18 Details on categorical matching are explained in the “Database Creation Guide” ofSPSD/M package of Statistics Canada.

disaggregation in the SPSD and IO table data has been facilitated bythe presence of an interesting feature of the Canadian IO table, whereconsumption expenditures are presented in two dimensions (commod-ities as in themodel and personal expenditure categories as in the SPSDdata). Using a fixed proportion rule, we can thus translate changes inconsumption prices from the commodity disaggregation in the modelinto a disaggregation using personal expenditure categories as in theSPSD data. Hence, after running the model with a single representativehousehold using the model disaggregation, we then translate the com-modity price changes obtained from the CGE model into price changesaccording to the disaggregation in the SPSD data with multiple house-holds. These price changes have been used to compute the post-policyequivalent incomes.

Table 2 depicts the main characteristics of the SAM along with thesectoral distribution of CO2 emissions in the base case. As the modeldoes not have an analytical solution, we rely on numerical methods. Be-fore solving the model, we need to calibrate the model parameters, i.e.we need to recover the behavioral and policy parameters, and thevalue of unobservable variables so as to reproduce the base run situationobserved in the SAM. To do so, we rely on traditional techniques foundin the CGE literature, and use the data in the SAM, the model equationsand external elasticity parameters as presented in Table 3. The base runsituation or business-as usual (BAU) situation refers to a no-carbon taxpolicy. The model is solved numerically using the GAMS software withthe CONOPT solver.

Storage −0.09 −0.13 −0.16 −0.16 −0.12Textile −0.08 −0.14 −0.20 −0.32 −0.42Tobacco −0.49 −0.90 −1.35 −2.23 −2.89Transport equipment −0.13 −0.25 −0.38 −0.65 −0.83Transport services 0.73 1.44 2.32 4.30 6.02Wholesale −0.27 −0.46 −0.66 −1.00 −1.21Wood −0.41 −0.70 −0.98 −1.39 −1.54

Table 6Distribution of households by interval of their equivalent incomes (in Canadian dollarsbase year 2004).

Interval by households equivalentincome

Populationshare

Average equivalent incomeper capita

0–20.000 0.165 14.15120.000–40.000 0.389 29.99740.000–60.000 0.262 49.38960.000–80.000 0.120 68.97780.000–100.000 0.038 87.622100.000 and over 0.026 124.682Total population 1.000 41.824

−0.1

0.0

0.1

0.1

0.1

0.2

% S

hare

s

0.00 0.19 0.38 0.57 0.76 0.95Percentile of total expenditures

Non−parametric estimation smoothing

Fig. 2. Share of capital earnings to total equivalent income among different householdgroups.

.02

.03

.04

.05

.06

% S

hare

s

0.00 0.19 0.38 0.57 0.76 0.95

Percentile of total expenditures

Non−parametric estimation smoothing

Fig. 3. Share of energy consumption in total expenditures among different householdgroups.

97Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

4.1. Simulations

We run different simulations with varying carbon tax values toassess their impact on inequality. We consider the following valuesof a carbon tax: $15, $30, $50, $100, and $150 per ton of CO2 carbontax. The carbon tax is implemented as an excise tax on the user pricesof fossil fuels. It is important to mention that both domesticallyproduced and imported fossil fuels used by all domestic agents aresubject to the tax. We run the CGE model with the suggested taxesand obtain their impact on commodity and factor prices that arelater used to assess the impact on inequality as previously discussed.In order to provide a comprehensive understanding of distributionalimpact of the policy, we elect to use thewhole information containedin the full SPSD database of 72,687 households to analyze the inci-dence of carbon taxes on inequality.

In what follows, we first discuss the CGE results in order to have agood understanding of the impact of the carbon tax on commodityprices and factor prices, and then analyze the incidence on householdinequality with a focus on the contribution of each component to thechange in total inequality. For the sake of space, we will not discussthe sectoral impacts in details as themechanisms involved in the sector-al reallocation of resources are not very important for theunderstandingof the distributional consequences, the latter being our main focus inour study.

4.1.1. Aggregate impactTo avoid unnecessary repetition,we use the results of the simulation

with a $50 carbon tax to illustrate the aggregate impacts of carbon taxes.The first direct impact of the carbon tax is to increase the user prices ofenergy goods, which are used as intermediate inputs by firms and asfinal goods by consumers. The users decrease their demand for energygoods; and this in some cases leads to a fall in the equilibrium producerprice of energy goods depending on emissions intensity. As demand forfossil energy falls, carbon dioxide emissions decrease aswell; in the newequilibrium, total carbon dioxide emissions decrease by 31.6% in com-parison to the BAU.

The increase in energy cost stemming from the imposition of acarbon tax triggers some substitution effects among inputs andsome cascading effects on the prices of composite inputs. The lattereffects ultimately translate into higher marginal costs, and hencehigher producer prices in all industries. The magnitudes of thechanges in the producer prices are related to energy intensity inthe production of their goods. The domestic prices of energy-intensive goods are the most affected. As shown in Table 4 theindex of consumer prices of energy-intensive goods increases morethan that of non-energy intensive goods. These changes have somedistributional consequences that are discussed below.

The increase in the user prices of energy-intensive goods eventu-ally leads to a decline in their demand as final goods or as intermedi-ate inputs. Thus, we observe a change in the sectoral composition oftotal demand in the economy, where the shares of energy goods andenergy-intensive goods that are directly or indirectly related to CO2

emissions fall to the benefit of non-energy intensive goods. In reality,

this is the objective pursued by a pollution control policy: reductionof the shares of energy and energy-intensive goods in total demandin the economy. We observe an increase in the demand for non-energy goods despite the negative impact of the policy on income.

As the carbon tax increases the marginal cost of production in mostindustries, it reduces the returns to labor and capital that fall by, respec-tively, 1.05% and 3.60% in comparison to the BAU situation. The relativeprice of capital falls by 2.58%. As expected, the return to capital fallsmore than that of labor for the reasons discussed earlier. Since theenergy-producing and energy-intensive industries are relatively morecapital intensive, a fall in output in these industries will reduce the de-mand for capital more than that for labor. Since the two factors are infixed supply, their returns have no choice but to fall, with a larger mag-nitude for capital.

Following our earlier discussion this change in the relative price ofcapital and labor will have some distributional consequences that willbe analyzed later. Note that the fall in the relative return to capital isnot specific to this simulation alone. As shown in Table 4 the relativeprice of capital falls monotonically with the carbon tax. In otherwords, the higher the level of the carbon tax, the lower the relativereturns to capital. For example, with a $100 carbon tax, the relativeprice of capital falls by 4.32% as compared with 2.58% and 0.91% with,

0.2

.4.6

.81

L(p)

& C

(p)

0 .2 .4 .6 .8 1

Percentiles (p)

L(p): Pre Reform Equivalent IncomeEgalitarian (45°) line

C(p): Change in Non−Energy Prices C(p): Change in Energy Prices

C(p): Change in Factor Prices

Lorenz and Concentration Curves

Fig. 4. Lorenz and concentration curves at $15 carbon tax.

0.2

.4.6

.81

L(p)

& C

(p)

0 .2 .4 .6 .8 1

Percentiles (p)

L(p): PreReformEquivalentIncomeEgalitarian(45°)line

C(p): Change in Non−Energy Prices C(p): Change in Energy Prices

C(p): Change in Factor Prices

Lorenz and Concentration Curves

Fig. 5. Lorenz and concentration curves at $50 carbon tax.

0.2

.4.6

.81

L(p)

& C

(p)

0 .2 .4 .6 .8 1

Lorenz and Concentration Curves

98 Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

respectively, $50 and $15 carbon taxes. Overall, the $50 carbon tax re-duces GDP by 0.41% in comparison to the BAU, and has similar negativeeffects on total consumption, total exports and imports,which fall by re-spectively 0.73%, 1.16%, and, 1.31%. Total real investment does notchange because of the closure rule adopted.

4.1.2. Distributional impactIn this subsection, we use the commodity and factor prices effects

generated by the CGE model to assess the distributional impact of thecarbon tax on households. We use the household survey data in theSPSD database to conduct the analysis. As discussed earlier, we convertthe commodity price changes taken from the CGEmodel disaggregationto commodity price changes in the SPSD disaggregation as shown inTable 5.

Table 6 summarizes the distribution of households by their sharesin total population and equivalent income. Average per capita equiv-alent income of households is around 42,000 Canadian dollars in2004, while around 65% of total households have income withinthe interval of [$20,000;$60,000]. Before discussing the results ofthe distributional analysis, it is important to present some character-istics of the household survey data related to energy shares in con-sumption and capital share in total earned income (labor pluscapital incomes).

Fig. 2 shows the shares of capital income in total earned income byhouseholds, who are ranked by their total expenditures. The graph isupward sloping indicating that richer households derive a larger shareof their earned income from capital. Similarly, Fig. 3 presents the energyshare in household total expenditures by households, ranked by theirtotal expenditures. The negative slope of the graph suggests that poorhouseholds spend a larger share of their total expenditures on energygoods than the rich.

We then use the price changes to compute the equivalent income,Mh

E, of each household, as well as the four components, δhn, of itschange with respect to the BAU equivalent as suggested inEqs. (23)–(26).19 Using the newly computed variables, we assessthe distributional consequences of carbon taxes. Graph 5 shows theLorenz curve of initial equivalent income, and the concentrationcurves of each of the threemain components for the case of a $50 car-bon tax.20

Referring to our decomposition in Eq. (23), it is important to notethat both factor prices and energy prices contribute negatively to

19 Recall that four components refer to the impacts of the changes in prices of, respec-tively, factors, energy goods, and non-energy goods, and to their combined effects in a re-sidual term.20 We donot present the graph of the residual component, which captures the combinedeffects of the three main components, since its magnitude is relatively negligible.

equivalent income after the reform. Fig. 5 shows that the concentrationcurve of the changes in energy commodity prices is above the Lorenzcurve. This indicates that low income households are more affectedthan the rich by the changes in energy commodity prices, and suggeststhat the impact of these changes is regressive.

The concentration curve of the component due to changes in non-energy good prices crosses and is barely above the Lorenz curve; wecannot make a clear inference on its distributional impact. In contrast,the concentration curve of the factor price change component is neatlybelow the Lorenz curve. This suggests that the incidence of the changesin factor prices is more concentrated towards high percentile incomegroups. In otherwords, poor households are less affected by the changesin factor prices, implying that the incidence of the latter changes onhousehold equivalent income is progressive. The same pattern of thecurves holds for other values of carbon taxes, as shown in Figs. 4 and 6for 15$ and $100 carbon tax.

Based on these results, it is impossible tomake anydefinite inferenceon the distributional incidence of carbon taxes on household income aswe have two opposing forces at play. The changes in factor prices con-tribute to the progressivity of the carbon taxes, while the changes incommodity prices tend tomake these taxes regressive. The final impactis an empirical matter that depends on the relative strength of the im-pact of each component; carbon taxes could be progressive, regressiveor neutral.

This is a new insight in the analysis of the distributional incidence ofcarbon taxes, since if we had ignored the impact of the changes in factor

Percentiles (p)

L(p): PreReform Equivalent IncomeEgalitarian (45°) line

C(p): Change in Non−Energy Prices C(p): Change in Energy Prices

C(p): fChange in Factor Prices

Fig. 6. Lorenz and concentration curves at $100 carbon tax.

Table 7Estimation of total inequality and its decomposition by components at different levels ofcarbon tax ($ per ton of CO2 eq.).

Carbon tax Gini coefficient Contribution of each component to change ininequality

Initial After tax Factor Energy Non-energy Residuala

15 0.31376 0.31372 −0.00022 0.00021 −0.00004 0.0000030 0.31376 0.31369 −0.00041 0.00041 −0.00007 0.0000050 0.31376 0.31368 −0.00062 0.00064 −0.00010 0.00000100 0.31376 0.31373 −0.00107 0.00120 −0.00015 0.00000150 0.31376 0.31387 −0.00144 0.00172 −0.00018 0.00000

a It refers to a combined effect mentioned in the theory.

Fig. 7. Impacts of different levels of carbon taxes on income inequality.

99Y. Dissou, M.S. Siddiqui / Energy Economics 42 (2014) 88–100

prices, we would have concluded, as in many previous studies, that car-bon taxeswere definitely regressive. We continue the analysis by quan-tifying the magnitude of the impact of each component so as to gaugetheir overall distributional incidence.

Based on our previous discussions, we provide in Table 7 an exactdecomposition of inequality change as stated in Eq. (35). With a $15carbon tax, inequality, measured by the Gini index decreases by0.00006 from 0.31376 to 0.31372. At first sight, the magnitude of thischange is comparable to that found in earlier studies by Kakwani(1977b) and Araar et al. (2011).21 Although, it might seem negligible,it is important to note that the overall impact on the change in inequal-ity is the outcome of the two main opposing effects (of almost equalmagnitudes), which are the impact of the change in factor prices, andthe impact of the change in energy prices. Nevertheless, inequality islower as the impact of factor price changes outweighs that of energyprices.

Moreover, an interesting phenomenon occurs at higher levels of thecarbon tax: the impacts of factor price and energy price changes do notmove at the same pace. At $30, the carbon tax is still progressive as theimpact of factor prices dominates that of energy prices. However, at$100, the carbon tax becomes regressive as the contribution of thechange in energy prices outweighs that of the change in factor prices. In-terestingly, Table 7 and Fig. 7 show that the link between carbon taxesand total inequality is U shaped, and thereby emphasizes the impor-tance of including changes in factor incomes within distributionalanalysis.

All these results indicate that the distributional impact of carbontaxes depends on the structure of the economy and on the level of thetaxes. For the same economy, the tax might be progressive at somelevels and become regressive at higher levels. Therefore, focusing onthe changes in the prices of energy goods alone to assess the distribu-tional consequences of carbon taxes can be misleading.

5. Conclusions

In contrast to most existing studies, we have provided a compre-hensive assessment of the impact of carbon taxes on inequality byexamining their effects on changes in both commodity and factorprices. We have used equivalent income as the welfare metrics ofchoice in the distributional incidence analysis and have proposed adecomposition of the change in themetric into different componentsrelated to changes in commodity and factor price. We have then de-veloped a static, multisector general equilibrium model to assess thedistributional impact of carbon taxes by conducting several simula-tions with different values of the carbon tax. We have used the Lorenzand concentration curves and the Gini index in the distributionalanalysis.

21 For example see Table 2 in Kakwani (1977b) for change in inequality in Canada due toState and Local taxes. Similarly, see Table 6 inAraar et al. (2011) for change in inequality inCanadadue to 15% CO2 emissions reduction alongwith a uniform subsidy on consumptiongoods.

As expected, the ratio of the rental rate of capital to the wage ratefalls following the introduction of the carbon taxes, since energy-intensive industries are capital-intensive. Our simulation results suggestthat changes in commodity prices and in factor prices brought about bythe taxes have opposite effects on inequality. While changes in com-modity prices (and especially in the prices of energy commodities) in-crease inequality, changes in factor prices reduce inequality. Thereason for such a relationship between inequality and in factor pricesis that affluent households are more affected by the fall in the relativeprice of capital to labor as they derive a higher share of their incomefrom capital. Our results strongly indicate that the total impact of carbontaxes on inequality is indeterminate, as it is context-dependent. Thatimpact may be negative, positive or nil.

We have found a non-linear (U-shaped) relationship between in-equality and carbon taxes. The relationship is negative at low levelsof the tax. This suggests that the positive impact of the changes infactor prices on inequality has outweighed the negative impact ofthe changes in commodity prices. The reverse relationship has beenobserved at high levels of carbon taxes. Our findings also suggest thatthe traditional approach of assessing the impact of carbon taxes oninequality through changes in commodity prices alone may bemisleading.

Nevertheless, some caveats to our conclusions should be men-tioned. Our analysis does not consider the environmental impact ofreduced pollution on inequality and welfare. In addition, a distinc-tion must be made between changes in inequality and changes inwelfare. Despite the decline in inequality, and abstracting from theenvironmental effects, welfare does fall for all households. Finallyour analysis did not take into account the impact of sectoral immo-bility of natural resources on factor and commodity prices andhence on inequality.

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