Limiting an increase in global temperatures requires deep changes to be made to the structure of the economy. Attaining the RCP 1.9 target Representative Concentration Pathway with radiative forcing of 1.9 W/m2 in 2100 Total CO2 emissions under the ‘intermediate challenges’ Shared Socioeconomic Pathway (SSP2) scenario
At the same time, models that link the size of the greenhouse effect to the structure of the economy (known as integrated assessment models (IAMs)) predict that change of this structure will be associated with economic cost. IAMs (including computable general equilibrium (CGE) models) are designed to describe the structure of global or regional economy (the structure may be constituted by the following elements, among others: use of resources, production technologies, expected innovations, consumption and trade patterns) and simulate its change under low-carbon pathways. The models used in the IPCC 5th Assessment Report suggest that the global cost of an ambitious mitigation scenario (limiting greenhouse gas stock to 430−480 ppm CO2 eq) would be in the range of 2–4% of annual GDP in 2050 (IPCC, 2014). Mitigation costs in terms of reduced consumption were also found in regional studies (see, for instance, Kiuila, 2018 and Antosiewicz et al., 2020).
However, IAMs provide no insight on how these costs will materialise in the budgets and welfare of households. To what extent will the burden of climate policy affect households through an increase in prices of consumption goods (consumption channel) and to what extent through changes in productivity and wages (wage channel)?
The relevance of this question stems from the heterogeneity of households. If consumers were homogeneous, the distinction between consumption and wage channels would not matter in general equilibrium: increase in consumption price index and drop in wage has exactly the same effect on real income and welfare. However, when each household is differently affected by changes in prices and wages, the distinction between the two channels is necessary for determining the ultimate distribution of burden of the transition across society.
The purpose of this article is to review the existing literature and devise a new conceptual framework for understanding how the change in households’ welfare due to climate policy depends on their pattern of consumption and allocation of labour. Our analysis will focus on the effects that are induced by carbon tax. We consider all effects in general equilibrium setting, that is, we will analyse not only the consequences of changes in prices of carbon-intensive goods, but also the changes of all prices and wages in the economy, including those associated with the production of carbon-free goods.
Although our endeavour is purely theoretical, it has two direct practical motivations. First, it addresses the question of whether potential compensation for the losers of low-carbon transition should be based purely on criteria related to consumption of carbon-intensive goods (such as energy) or also on consumption of other goods and employment in carbon-free and carbon-intensive sectors. Such compensation is feasible, because it could be, at least partly, financed by revenue from carbon tax. It can be partly financed also by foreign governments or supranational organisations that are willing to encourage and support the de-carbonisation in regions where the costs of low-carbon transition are high. An example of the planned compensation fund is a Just Transition Fund in the European Union (European Commission, 2020), which is financed from the common EU budget.
Second, our study sheds new light on the interpretation of cost projections generated by IAMs. Specifically, we use our framework to argue that general equilibrium IAMs that assume homogeneity across labour types are not able to show the costs of climate policy that affect households through the wage channel. As a result, such models underestimate the total macroeconomic costs of climate policy.
Indeed, the results of our study show that households employed in carbon-intensive sectors need to be compensated to prevent them from being worse off after the transition, even though predictions of standard economic models would deny there is such a need. The reason for this compensation is that workers will lose part of their productivity (and labour income) after moving from their current first-best choice of sector to the second-best. Moreover, we argue that households that do not consume carbon-intensive goods and are not employed in sectors producing these goods do not require any compensation, even when all general equilibrium effects are taken into account.
The remaining part of this article is structured as follows: in Section 2 we review the literature, focusing on works related to general equilibrium modelling of labour market and welfare in the context of climate policy. Section 3 presents the set-up of our model and the key theoretical results. Section 4 concludes the article.
The literature review consists of two parts. We first survey a broader stream of research on the economic effects of climate policies, discussing how our study fits into that context. Subsequently, we analyse in more detail the contributions that take a similar methodological perspective to the one adopted in our work, namely the top-down, general equilibrium setting. While we do not explicitly follow the ways in which labour heterogeneity has been addressed in the CGE models, as reviewed below, the discussion of related methodological concepts facilitates exposition of our approach.
There has been an emerging literature on just transition and the distributional consequences of climate policies. One strand of this literature is descriptive studies that analyse the difficulties associated with moving labour away from carbon-intensive sectors (Spencer et al., 2018, Sartor, 2018, Swilling et al., 2016, Leipprand and Flachsland, 2018, Turnheim and Geels, 2012 and Skoczkowski et al., 2020).
The second strand is studies that analyse the impact of climate policy on households in different income deciles using microdata (e.g. Levinson, 2019, Davis and Knittel, 2019, Cronin et al., 2019, da Silva Freitas et al., 2016, Bureau, 2011, Antosiewicz et al., 2020). Those models, however, do not account for changes in wages (with few exceptions, such as the study by da Silva Freitas et al., 2016 and Antosiewicz et al., 2020). Moreover, they consider only changes in prices that are directly induced by the change in carbon tax and do not account for feedback between changes of demand and changes of all prices in general equilibrium.
Numerical IAMs used in designing socially optimal transition pathways generate predictions by considering either cost-minimising choice between a large set of technologies (bottom-up approach) or the optimal decisions of firms and consumers in general equilibrium (top-down approach, which we review below). The recent article by Baran et al. (2020) demonstrated with an analytical model that the costs of transition projected by bottom-up models ignore the costs associated with frictional movement of labour across sectors. Our study develops an analytical model that extends this argument to costs projected by top-down CGE models.
CGE models have been workhorses of numerous studies of economic effects of climate policies, largely due to their detailed, industry-level representation of energy demand and supply, and greenhouse gas emissions. However, as noted by Boeters and Savard (2013, p. 1645), labour market has not been in the focus of the CGE modelling field, and this also holds in the case of climate- and energy-related applications. Common simplifying assumptions include homogeneity of labour force and fixed labour supply.
The starting point of the theoretical approach proposed in this article is the explicit differentiation between productivity of the same person employed in different sectors. To our knowledge, such a specific setting has not been explored so far. Yet, various related concepts are present in the CGE field. These include, inter alia, heterogeneous agents, welfare decomposition, and labour adjustment costs. Below we briefly review these methodological viewpoints.
One straightforward way to distinguish different labour varieties is by means of constant elasticity of transformation (CET) function (Boeters and Savard, 2013, p. 1659–1660). The basic formulation assumes that aggregate labour supply – e.g. total available hours of work – is allocated between two or more ‘uses’, to maximise total labour income, given relative wages. Such an approach allows the capturing of (i) differences in wages of distinct labour varieties and (ii) costs for the economy that are related to reallocation of labour between occupations or sectors, e.g. invoked by tax policy. On the other hand, since this formulation relies – at least in a literal interpretation – on the assumption of a representative agent who earns income from all labour varieties, it does not allude to the explicit analysis of welfare effects for distinct household or worker groups.
Dixon and Rimmer (2002, p. 289–299) propose a framework in which labour market adjustment costs are recognised explicitly. Adjustment costs are associated with year-to-year flows of people between different states in the labour market, such as between occupations, regions or industries of employment, from or into unemployment, or from or into labour force. For example, a flow of a worker from one occupation to another one may impose a cost related to training, modelled in terms of productivity loss in a given year. Notably, such an approach requires a dynamic model setting. Adjustment costs are temporary (one-off) – contrary to the CET-based formulations, in which changes in allocative efficiency are sustained. In the approach proposed by Dixon and Rimmer (2002, p. 289–299), aggregate adjustment cost generally depends on the rate of structural changes – in case that rate is low, adjustment will largely be accommodated by retirements and inflows of new workers, whereas with larger changes, labour force movements will impose a higher adjustment cost.
The above-mentioned approaches introduce labour disaggregation; yet, they stick to the (multiple) representative agent’s paradigm. With recent advances in trade theory, pioneered by Melitz (2003), a new perspective on heterogeneity has made its way to the CGE field. CGE models introducing Melitz in place of the standard, Armington specification of foreign trade (see Balistreri and Rutherford, 2013; Dixon et al., 2016) assume that each industry is composed of a continuum of firms with different productivities. Productivity distribution is characterised by probability density. An implication of such a framework is that, for example, increase in trade protection has an adverse effect on productivity in domestic trade-exposed industries, because trade barriers allow certain less productive firms to remain in the market.
As demonstrated by Dixon et al. (2016), with a choice of a specific distribution of firm productivity levels – namely the Pareto distribution – the micro-founded model is transformed into straightforward aggregate equations. In the same vein, other authors have shown that constant elasticity of substitution (CES) demand functions can be interpreted as an aggregate representation of a discrete choice model of heterogeneous individuals (Anderson et al., 1987, 1988; Matveenko, 2020). Similarly, Growiec (2013) provides a micro-foundation for CES production functions with factor-augmenting technical change. Our article follows an analogous general strategy.
CGE-based studies that considered low-carbon transition, leaning towards the labour-market perspective, sometimes did so by examining the impact on unemployment (see, for example, Küster et al., 2007 and Böhringer et al., 2012). In some studies, the picture of employment/unemployment effects is enriched with equity impacts. Huang et al. (2020) adopt such a perspective, as they simulate clean energy transformation in China using the CGE framework, addressing equity issues in the context of migration and urbanisation. An example of a simulation study in a more comprehensive theoretical setting, beyond typical CGE models, is the work by Rengs et al. (2020). They use an agent-based model with interacting heterogeneous households and firms, subject to bounded rationality, to study the effects of different scenarios of carbon taxation and the use of carbon tax revenues. They show that alternative combinations of policy instruments may lead, for example, to similar environmental outcomes with varying impacts on unemployment. The multi-agent setting (5,000 households, 250 firms) allows explicit tracking of distributional consequences of policies.
It is not a very frequent practice to report and decompose CGE model results in the field of climate policy analysis in terms of welfare effects, using equivalent variation (EV) measures, although relevant methodological approaches have been proposed in the literature. Hanslow (2000) provides a general framework for a comprehensive decomposition of a change in welfare, breaking it down into, among other things, contribution of a change in endowments, terms of trade, asset prices, allocative efficiency, technical efficiency, etc. Huff and Hertel (2001) formulate a similar decomposition, tailored to the well-known GTAP model. Dixon and Rimmer (2008) is an example of welfare decomposition related to unilateral tariff change. In the context of climate policy analysis, welfare decomposition techniques have been applied by, for example, Böhringer (2000) and Böhringer and Rutherford (2000). The latter work tracks welfare changes in specific countries to specific policy instruments, such as emission taxes or emission caps, as applied by other countries.
We believe that this article adds to the CGE literature in two aspects. First, it provides micro-foundations – distribution of individual productivities and preferences and a corresponding discrete-choice labour supply model – for the analysis of sectoral allocation of labour, and its consequences for aggregate productivity. Second, it provides a decomposition of the impact of ‘dirty’ goods taxation on aggregate welfare, in a theoretical general equilibrium setting, referring to the characteristics of the distributions of productivity and preferences.
To compute cost of climate policy for individuals, we will determine EV, i.e. the amount of money that would need to be deducted from income of an individual in the situation with no policy to set his or her utility to the same level as in the situation when the policy is present.
In the first step, we will derive EV as a function of prices and incomes, using money metric indirect utility function. Next, we determine the equilibrium changes in prices and income for each individual resulting from the implementation of a policy. At this stage we also make assumptions regarding the distribution of types of individuals with respect to their preferences and human capital.
It is emphasised that the model developed in this section is meant to imitate the logic of top-down models; however, its structure is far less detailed. Indeed, our intention is to simplify the model to the level that ensures tractability and allows us to construct a micro-founded narrative.
We assume that consumer derives utility from two goods, dirty (subscriptd) and clean (subscriptc). This simple distinction is borrowed from the literature of directed technological change. In the context of climate policy, dirty goods could stand for a composite of carbon-intensive goods, such as fuels used for transportation, fuels for heating or coal-based electricity. Clean goods stand for the composite of carbon-neutral goods, including energy derived from carbon-free sources. In Section A1 in Appendix, we provide an alternative specification with consumers deriving utility from a variety of goods, each produced using a Cobb–Douglas technology that combines carbon-intensive and carbon-free inputs. Although this alternative specification is more realistic and closer to the specification of the top-down models, it also adds to complexity of the model applied in this article. Since, as we demonstrate in Appendix, the predictions of the two specifications are the same, in the main text of this article we use the simpler specification with just two goods.
We also assume that the direct utility function takes the Cobb–Douglas form; therefore,
Later in the article, we will assume that the share parameter
Finally, we assume that the before-tax prices of dirty and clean goods are
We derive money metric indirect utility function (which is the basis for computing EV) in two steps. First, we find expenditure function and then we find indirect utility function (see Mas-Colell et al., 1995)
Expenditure function could be derived from the consumer minimisation problem: min
Next, we find an indirect utility function by inverting the function above, thus giving rise to the following equation:
We can now state the money metric indirect utility function by evaluating expenditure function at the reference price level,
When reference prices are treated as constant, money metric indirect utility function is an indirect utility function (it may be noted that the function is a simple monotonous transformation of indirect utility function in Eq. (1)). In addition, if we set reference price at the level with no policy ((1+
In this subsection, we clarify our assumption regarding the distribution of types of individuals. Next, we find general equilibrium level of prices for the aggregate economy.
Goods
Each individual possesses one unit of physical labour of type
Supposing that the compensation per efficient unit of labour in sector
Consider now workers of type
Therefore, the fraction of all workers (fraction of physical labour) who decide to choose the dirty sector,
At this step, we need to assume the functional form of
It may be noted that when
In this case, the fraction of workers who choose to work in sector
It may be noticed that
Therefore, the fraction of workers choosing sector
Two remarks follow this result. First, α determines the slope of the supply curve of physical labour in the dirty sector. We will use this interpretation of α in propositions further in the article. Second, the expression above determines the fraction of workers who wish to work in the dirty sector as a function of wages and parameters of productivity distribution. This is not the same as the supply of efficiency units delivered by those workers, because each worker could have a different productivity. We determine that supply at the beginning of the forthcoming section.
Let
It may be noted that
Using the cdf and pdf of the Frechet distribution, this could be stated as
To evaluate the integral, we note again that
Using the production function in each sector and setting
Meanwhile, demand for dirty goods could be obtained by deriving individual demand from first-order conditions to consumer’s minimisation problem and aggregating across consumer types. This results in
Since we assumed that
On the one hand, relative prices are determined by the parameters of the distribution of productivity. For instance, if a relatively large share of workers has high productivity in the dirty sector (
On the other hand, relative prices are determined by the production technology and preferences of consumers. If, on average, consumers demand more clean goods (
We notice also that this result (and indeed all other results in this article) do not require assumptions on the shape of the distribution of
The level of prices depends on the choice of numeraire. We choose the consumer price index (CPI) of the representative consumer as follows:
In this case, the prices of dirty and clean goods become Note that price of clean goods is a function of taxes because we chose the CPI of the representative consumer to be a numeraire (see Eq. (4)) in Section 3.4. Since CPI depends on taxes, the price of clean goods also depends on taxes. If, instead, we chose a numeraire that is independent of taxes (e.g. before-tax CPI), the price of clean goods would be independent of taxes.
To ensure interior solution later on, we assume
Finally, we recover levels of wages in each sector to be the following:
The result in the previous subsection allows us to state the income for individual
This, together with expression for prices evaluated above, allows us to express money metric utility as a function of our policy variable (1+
The term
The term
To analyse this last argument, we observe that individuals who chose employment in the dirty sector earlier must have received higher compensation from work in the dirty sector than in the clean sector, i.e.
We can now express the ratio of EV to individual expenditure in the reference situation of no policy, which is given by
This allows us to derive first conclusions regarding the distribution of compensation across individuals.
We emphasise that the results in point (a) of the proposition would be trivial in a partial equilibrium setting: if the prices of exclusively dirty goods vary and all other prices and wages are constant, the tax cannot affect households that do not derive utility from the consumption of dirty goods. The proposition generalises this result to general equilibrium setting.
The reason why point (a) holds in general equilibrium is the presence of constant returns to scale in production technology. If returns to scale were decreasing, an inflow of workers to the clean sector would depress the wages of those who were already there. Similarly, higher demand for clean goods would lead to an increase in its price, thus affecting those households who consumed only clean goods earlier. Constant returns to scale imply that these two mechanisms are absent. Since most CGE models assume constant returns to scale, we expect that the same result will hold also in the CGE setting.
The EV relative to households’ spending (derived in (7)) can be decomposed into three components:
The first term captures the amount of money necessary to compensate the loss of individuals on the consumption side. It may be noted that it depends only on parameters
In the last subsection we computed aggregate loss (or aggregate EV) at the economy level. Since population is normalised to unity, aggregate loss could be computed as the expected value of EV. Using Eq. (3), this can be stated as:
The first term can be evaluated using Eqs (2), (5) and (6) as:
Under independence of
Combining this with previous results in the following expression for expected money metric utility:
It may be noted also that we can find
Finally, aggregate EV relative to aggregate income in the reference situation becomes:
Indeed, empirical evidence suggests that the supply curve at the sectoral level is upward sloping, although the range of estimates is very wide. For instance, Booth and Katic (2011) and Manning (2003) estimate elasticity for monopsonies and obtained the estimates in the range 0.71–0.75. Estimation of long-run elasticity of supply using the methodology proposed by Manning (2003) and estimates of separation rates reported in Ashenfelter et al. (2010) suggest that the long-run elasticity of supply is in the range 3–8.
As before, we can decompose the expected EV relative to GDP into three parts:
The first component determines the size of a hypothetical fund that would be used to compensate individuals for the loss that is captured in the first term of expression in Eq. (8). This fund would be distributed among consumers using consumption pattern as the only criterion for distribution. The second component aggregates the compensations necessary to cover the loss captured in the second term of Eq. (8). This fund would be distributed among workers using relative loss in wages as the only criterion. The third part would be a fund that would need to use both consumption and labour criteria.
In this article, we have proposed a heterogeneous agents model, in which individual worker productivity depends on the sector of employment. Taking the climate policy analysis perspective, we have considered two broad sectors – clean (carbon-free) and dirty (carbon-intensive). Each person supplies work to the sector in which he or she obtains higher income, given individual productivity characteristics and sector-specific wages per efficient labour unit. Each worker is also characterised by specific preferences in relation to the consumption of clean and dirty goods. Distributions of productivities and preferences are represented by continuous probability density functions.
We have derived a general equilibrium solution of the above theoretical model, along with the formula for the welfare cost of dirty goods’ taxation (e.g. introduction of a carbon tax). The latter is measured in terms of EV, at both individual and aggregate economy level. Furthermore, welfare impact is decomposed to distinguish the cost on the consumption side, which is related to the increase in price of the dirty goods, and the cost related to labour income loss, which stems from productivity decline following labour reallocation.
The following conclusions can be formulated: (i) In general equilibrium, under constant returns to scale in production and the Cobb–Douglas utility function, percentage change in individual household welfare (expressed as a ratio of EV to original spending of the household) due to a carbon tax for households employed (before the tax is introduced) in the clean sector does not depend on their individual productivity, but depends on the consumption pattern. On the other hand, for households employed in the dirty sector, welfare cost depends on the share of spending on dirty goods and the slope of the sectoral supply curve that stems from the shape of productivity distribution in the population. For workers switching from dirty to clean sector, that cost additionally depends on relative productivity in the clean and dirty sectors. (ii) CGE models assuming homogeneous labour force (and thus flat sectoral supply curves) may underestimate the economy-wide cost of carbon taxation.
Envisaged next research steps include calibration of the proposed theoretical model to data, and applying it—in a wider framework of a multi-sector CGE model with energy- and emissions-accounting—to a real-world policy case. This would include a comparison of results with and without the proposed extension. An empirical approach, accompanying the theoretical formulation and allowing the estimation of model parameters, would also be an interesting avenue of further inquiry.
Implementing the complete setup of the model in Section 2 with a continuum of workers types would be challenging due to numerical issues; however, the model could use an equivalent of Eq. (4) as a reduced-form equation relating supply of labour to wages in the clean and dirty sectors.
Quantifying the total welfare loss for different groups of household would also require a more careful treatment of elasticity of substitution between clean and dirty goods. In our framework we assumed a Cobb–Douglas form of utility function, which implies that elasticity of substitution between different types of goods is one and mixed price elasticity of demand is equal to zero. Altering these elasticities could affect the welfare effects of carbon tax. Introducing a more general form of utility function, such as CES, would allow exploration of this dependence.
From a theoretical viewpoint, possible extensions could address the question of whether differential productivity of individuals’ work in the clean or dirty sectors should be interpreted as a persistent feature, or whether it should be endogenous, or, in other words, dependent on the time-scope, e.g. change with in-work training or human capital investment. One could also consider allowing for non-optimal or non-deterministic choices of the labour supply of individual workers, in relation to imperfect information or other barriers.