Carbon Pricing in Residential and Non-Residential Sectors: Household Inequality and Compensation Strategies

JAVIER FERRI FRANCISCA HERRANZ-BÁEZ

Documento de Trabajo 2025/14

Diciembre de 2025

fedea

Las opiniones recogidas en este documento son las de sus autores y no coinciden necesariamente con las de Fedea.

Javier Ferri^a,b Francisca Herranz-Báez^a

^aUniversity of Valencia, Spain ^bFedea, Spain

December, 2025

Abstract

This paper analyzes the macroeconomic and distributional impacts of carbon pricing policies targeting both residential and non-residential sectors. Using a model that incorporates nominal price rigidities, sectoral labor adjustments, and financial frictions tied to housing collateral, we uncover critical transmission mechanisms afecting household welfare. Our analysis highlights the distinct efects on borrowers and lenders: carbon pricing in the non-residential sector reduces labor demand and wages, disproportionately impacting borrowers, while residential carbon pricing lowers housing prices, tightening credit constraints for borrowers but imposing higher welfare costs on lenders who own more housing assets. We explore compensation strategies, particularly the allocation of carbon dividends. An equal distribution initially stabilizes consumption for borrowers but becomes less efective as emissions decline and carbon revenues shrink. Robustness checks show that factors like labor mobility, firm markups, and debt distribution significantly influence inequality. Flexible prices can mitigate early consumption inequality, while a higher share of debt among borrowers afects policy eficiency and the required carbon price levels. Our findings underscore the need for sector-specific carbon pricing and adaptive compensation mechanisms to balance eficiency and equity.

Keywords: carbon emissions, TANK, inequality, compensation policies.

JEL Classification: E27, H23, Q58, D63

^∗This paper has been financed by the Conselleria de Innovación, Universidades, Ciencia y Sociedad Digital through grant CIPROM/2023/39 (Generalitat Valenciana). It also forms part of the projects PID2023-152348NB-I00, funded by MCIN/AEI/10 13039/501100011033, and TED2021-132629B-J00. funded bv MCIN/AEI/10 13039/501100011033 and the European Union NextGenerationEU/PRTR. Javier Ferri acknowledges financial support from Fedea, Fundación Rafael de Pino, and BBVA Research. Francisca Herranz-Báez acknowledges financial support from the University of Valencia through the “Atracció de Talent” grant. We thank Javier Andrés, Pilar Beneito, José E. Boscá, Rafael Doménech, Santiago Rubio, Margarita Rubio, and participants at JIDAE 2024 (Valencia), ICMAIF 2025 (Rethymno), WEAI 2025 (San Francisco), SMN 2025 (Madrid), RES (Birmingham), and EWMES 2025 (Nicosia) for helpful comments on earlier drafts of this paper.

1 Introduction

The transition to climate neutrality stands as one of the central macroeconomic challenges for advanced economies. The European Union and other developed regions have committed to ambitious emission reduction targets that are essential for mitigating the efects of climate change and for reaching net zero emissions by 2050. Carbon pricing has emerged as a key instrument for advancing these objectives. However, the design and quantitative evaluation of climate policies continue to focus predominantly on emissions from the production sector, even though emissions generated by households through heating, cooling, and energy use represent an important component of total emissions. Since public support for environmental policies depends critically on their distributional consequences European Environmental Bureau (2022); European Commission (2021); Marcu et al. (2023), understanding how carbon pricing afects diferent households is essential for shaping socially acceptable transition strategies.

This paper contributes to this discussion by analysing the transition toward a net zero emissions economy within an Environmental Dynamic General Equilibrium framework that features two productive sectors, endogenous housing production, household heterogeneity, and a distinction between residential and non residential emissions. We incorporate limited household heterogeneity through the structure of Two Agent New Keynesian models, which separates financially unconstrained households from credit constrained households whose consumption and borrowing decisions depend on collateral and income.² This environment allows us to study the efects of carbon pricing through several channels, including changes in consumer spending patterns, factor prices, and borrowing capacity, and connects to the broader Environmental Dynamic General Equilibrium literature that examines the interaction between climate policies and economic frictions Fischer & Springborn (2011); Heutel (2012); Annicchiarico & Di Dio (2015); Coenen et al. (2018); Ferrari & Landi (2022).

Carbon pricing generates distinct macroeconomic adjustments depending on the sector where emissions occur. When applied to the non residential sector, carbon pricing primarily raises production costs, reduces labor demand, and lowers household income, which depresses consumption and aggregate activity. When applied to the residential sector, carbon pricing also afects the price of housing services, which modifies the value of the housing stock. The decline in housing prices reduces collateral values for credit constrained households and restricts their borrowing capacity, amplifying the fall in their consumption. These mechanisms highlight the importance of distinguishing across emission sources when evaluating the macroeconomic efects of climate mitigation policies.

Borrowers and lenders experience diferent welfare consequences during the transition.

²For a discussion on the aggregate implications of Two Agent New Keynesian models compared with Heterogeneous Agent New Keynesian models, see Debortoli & Galí (2024).

Borrowers are more sensitive to fluctuations in labor income and aggregate economic activity, while lenders are more afected by movements in housing prices and housing investment. The direction and magnitude of these welfare diferences vary depending on whether carbon pricing targets residential or non residential emissions. This finding reinforces earlier evidence that household heterogeneity has important consequences for the incidence of carbon taxation and that analyses that omit heterogeneity may misrepresent the distributional efects of climate policy Dinan & Rogers (2002); Metcalf et al. (2008); Hassett et al. (2009); Fullerton & Heutel (2007); Araar et al. (2011); Rausch et al. (2011); Mathur & Morris (2014); Rausch & Schwarz (2016).

The composition of household types shapes the efectiveness of carbon pricing. A larger share of credit constrained households increases their sensitivity to fluctuations in housing prices and therefore strengthens the response of residential emissions to carbon taxation. In the non residential sector, lenders respond more strongly to changes in profits induced by the carbon tax, so a reduction in their population share weakens this mechanism. The degree of indebtedness in the economy therefore influences the cost efectiveness of sector specific mitigation policies.

The distribution of carbon tax revenues also plays a crucial role in shaping the transition path. Equal per capita transfers help stabilise the consumption of credit constrained households during the early phases of the transition, when carbon revenues are relatively large. As emissions decline and revenues shrink, however, the insurance provided by these transfers weakens and inequality increases. Distributional outcomes improve substantially when carbon dividends are allocated entirely to borrowers. In this case, consumption inequality decreases from the outset, with the consumption Gini coeficient showing the most pronounced improvement, and this redistribution does not diminish the efectiveness of carbon pricing in reducing emissions. These dynamics reveal periods of heightened distributional tension and suggest that targeted support may be needed as the economy approaches net zero emissions.

The remainder of the paper is organised as follows. Section 2 presents the model. Section 3 describes the calibration strategy. Section 4 reports the results, including macroeconomic efects, heterogeneity in household responses, robustness exercises, and alternative revenue recycling schemes. Section 5 concludes with policy implications and avenues for future research.

2 The Model

We develop a Dynamic General Equilibrium model with environmental externalities, nominal rigidities, and two representative household types to assess the macroeconomic and distributional efects of carbon pricing. The model captures the EU as a single-region economy with two production sectors—non-residential (consumer and investment goods)

and residential (housing construction)—and a population composed of two household types: patient (lenders) and impatient (borrowers). This structure follows the Two-Agent New Keynesian (TANK) framework, as in Iacoviello (2005). Carbon emissions arise from two sources: the production of goods in the non-residential sector and the use of housing services by households, such as heating, cooling, and cooking. These emissions accumulate into a carbon stock that impairs productivity over time. Full model equations are provided in the online Appendix.

Households difer in their discount rates. Patient households (with higher lend to impatient households , who borrow to smooth consumption. Both types consume goods and housing services, supply labor to both sectors, and generate residential emissions. Utility is derived from consumption, housing services (proportional to housing stock), and disutility from labor. Labor is allocated across sectors via a CES aggregator with elasticity

Residential emissions for each household type are given by:

\[e _ {h t} ^ {i} = (1 - u _ {h t} ^ {i}) \varphi_ {1 h} (h _ {t} ^ {i}) ^ {1 - \varphi_ {2 h}}, i \in \{l, b \}\tag{1}\]

where is the household’s abatement efort, reflects emissions intensity, and captures building energy eficiency. These emissions represent fossil fuel use for essential residential services. Emissions can be reduced through abatement, which is costly:

\[z _ {h t} ^ {i} = \theta_ {1 h} (u _ {h t} ^ {i}) ^ {\theta_ {2 h}} h _ {t} ^ {i}, i \in \{l, b \}\tag{2}\]

The optimal abatement level is given by:

\[u _ {h t} ^ {i} = \left(\frac {\tau_ {h t} \varphi_ {1 h}}{\theta_ {1 h} \theta_ {2 h} (h _ {t} ^ {i}) ^ {\varphi_ {2 h}}}\right) ^ {\frac {1}{\theta_ {2 h} - 1}}, \quad i \in \{l, b \}\tag{3}\]

showing that abatement increases with the carbon tax and decreases with housing size and the curvature of the abatement cost function. Abatement efort difers between households according to housing tenure

Impatient households face a collateral constraint that limits borrowing:

\[b _ {t} ^ {b} \leq \kappa \mathbb {E} _ {t} \left[ \frac {q _ {t + 1} \pi_ {t + 1} h _ {t} ^ {b}}{r _ {t}} \right]\tag{4}\]

linking their credit access to the expected resale value of housing. This constraint afects both intertemporal consumption and housing investment. When binding, it weakens their ability to smooth consumption or invest in energy-eficient housing improvements.

Carbon pricing interacts with this constraint. A residential carbon tax increases the efective user cost of housing—via both emissions charges and abatement costs —which depresses housing values and tightens borrowing limits. As a result, the policy has asymmetric efects: borrowers reduce consumption and housing investment more sharply than lenders, whose behavior remains unconstrained.

The non-residential sector is composed of monopolistically competitive firms that produce output using capital and labor. Production generates emissions:

\[e _ {c t} = (1 - u _ {c t}) \varphi_ {1 c} y _ {t} ^ {1 - \varphi_ {2 c}}\tag{5}\]

where is firm-level abatement efort. Firms reduce emissions only when facing a production carbon tax , which increases marginal cost and reduces demand for inputs.

Housing is produced by perfectly competitive construction firms using capital and labor. These firms productivity is negatively afected by the economy-wide carbon stock . The government imposes sector-specific carbon taxes and , recycles revenues via lump-sum transfers, and maintains constant public consumption. Emissions accumulate as:

\[x _ {t} = (1 - \delta^ {x}) x _ {t - 1} + e _ {c t} + e _ {h t} + e ^ {\mathrm{row}},\tag{6}\]

and reduce productivity through a quadratic damage function, following Heutel (2012). Monetary policy follows a standard Taylor rule responding to deviations of inflation from target. The resource constraint reflects the use of output for consumption, investment, housing production, abatement, and price adjustment costs.

3 Calibration

We calibrate the model to replicate certain macroeconomic and environmental ratios of the EU-27 economy for 2019, the year preceding the COVID-19 crisis. While most parameters utilized in the calibration are drawn from previous literature or derived from the model’s steady-state equations, we uniquely estimate the elasticity of residential emissions to housing stock using data specific to the EU-27. Our model incorporates the emission functions proposed by Heutel (2012) and Annicchiarico & Di Dio (2015). However, what distinguishes our work in the literature on E-DGE models is our consideration of how residential emissions are contingent upon the housing stock owned by households. Estimating this parameter specifically for the EU-27 ensures a more accurate representation of the dynamics of residential emissions and their relationship with housing characteristics. Below, we provide detailed information on the strategy followed to calibrate the parameters in the model.

Figure 1: Residential emissions generated in EU-27 + UK Annual emissions over the period 1990:2017 and total floor area for housing

3.1 Estimating the Elasticity of Residential Emissions

To set the elasticity parameter in the emission function, we study how carbon dioxide emissions from dwellings vary with the housing stock. Specifically, we estimate the following regression model:

\[\log (e _ {h i t}) = \beta_ {0} + \beta_ {1} \log (h _ {i t}) + \gamma_ {i} + \gamma_ {t} + u _ {i t}\tag{7}\]

where and represent country and time fixed efects, respectively, and is our parameter of interest.

We use annual country-level data on residential emissions and house floor area for the 27 countries of the European Union plus the United Kingdom over the period 1990–2017. More particularly, our dependent variable is direct emissions produced by the combustion of fossil fuels in homes, principally by heating and cooling systems. Emissions data are taken from national residential emissions reported to the UNFCCC and the EU Greenhouse Gas Monitoring Mechanism³, and residential floor area by country is sourced from the and the EU Building Stock Observatory of the European Commission⁵.

³https://www.eea.europa.eu/en/datahub/datahubitem-view/3b7fe76c-524a-439a-bfd2 -a6e4046302a2

Table 1: Estimation of emission elasticity with respect to floor area

Standard errors in parenthesis. ∗∗ ; ∗ ∗ ∗

Figure 1 presents the relationship between annual emissions from dwellings and total residential floor area across all countries during the sample period. It can be observed that, in the pooled scenario, residential emissions increase with floor area over the period considered. However, it is evident from the figure that this relationship varies significantly by country.

Table 1 displays the estimations. The Newey-West estimator addresses potential autocorrelation and heteroskedasticity in the error terms. We present the estimation without fixed efects, followed by models with country and time fixed efects, respectively. The no-fixed-efects estimation produces a coeficient substantially larger than those obtained with fixed efects, highlighting the influence of cross-country diferences in residential floor area on carbon emissions. In column (2), after introducing country fixed efects, the coeficient becomes negative, indicating that once we control for time-invariant, countryspecific characteristics, emissions per unit of floor area have decreased in Europe over the past 30 years. When time fixed efects are added to control for common trends afecting carbon emissions over time, the coeficient remains significant, suggesting that emissions increase by 0.4688% for every 1% increase in residential floor area⁶. Overall, our findings emphasize the importance of technological developments that reduce emissions per unit of dwelling floor area (column 2). Including time efects partially controls for technolog ical progress, reversing the sign of the elasticity. However, given the importance of this parameter, we will include it in our sensitivity analysis in the simulations results later.

In a study by Cong et al. (2015), the authors find that, depending on the region, the elasticity of carbon emissions from buildings per square meter in China varies from 0.3382 to 0.6175, an interval that includes the value obtained in our preferred estimation.

⁴https://www.eea.europa.eu/data-and-maps/figures/trends-in-heating-energy -consumption-2

⁵https://energy.ec.europa.eu/topics/energy-efficiency/energy-efficient-buildings/ eu-building-stock-observatory en

⁶An alternative specification with robust standard errors yields similar results

When the elasticity is measured in emissions per square meter on a per capita basis, it varies from 0.418 to 0.8098. Brounen et al. (2012) find that the elasticity of residential gas consumption per square meter in the Netherlands is 0.295, accounting for housing construction period and thermal characteristics. This value is slightly lower than ours and falls outside the range reported by Cong et al. (2015), but it exclusively accounts for residential gas emissions⁷. Also focusing exclusively on gas consumption, Alberini et al. (2011) report that the elasticity of residential heating gas consumption per square foot in the US is 0.22. In view of the previous results in the literature, we set the value of the elasticity to 0.4688, according to our estimation in column (3).

3.2 Parameters and Targeted Ratios

This section describes the values of the parameters used to obtain the numerical solution. The model is calibrated to the EU-27 setting by using parameters from previous studies and by fixing target values for the steady-state values of selected model variables to determine the remaining parameters.

General Parameters and Target Steady-State Values. We take some of the parameters from the European Central Bank’s New Area-Wide Model II Coenen et al. (2018) used for policy analysis. Specifically, we set the inverse elasticity of labor to wages to , the elasticity of substitution among final goods to , price adjustment costs in consumption goods to , capital adjustment costs in manufacturing and construction to and , the capital depreciation rate in consumer goods production to , and the parameters of the Taylor rule and to 0.93 and 2.74, respectively. Following Iacoviello & Neri (2010), we set the housing stock depreciation rate to per year.

The steady-state rate of time preference for patient households is set at 1% per quarter, corresponding to an annual interest rate of 4%. For impatient households, the discount rate is set roughly at 3 percentage points per quarter. Following Bielecki & St¨ahler (2022), we set the loan-to-value ratio to the standard value and the share of constrained households to . For the elasticity of substitution between labor types and the elasticity of housing production to capital , we use the estimated values for the EU-27 from Hinterlang et al. (2022), fixing them at 1 and 0.255, respectively.

To calibrate the model, we match the steady-state ratios of economic aggregates to GDP with the corresponding values for the EU-27 in the year 2019. The ratios are obtained from Eurostat. The steady-state ratios of residential investment and nonresidential investment to GDP are 5.2% and 18.9%, respectively. In the residential sector, corporate gross fixed capital formation is equivalent to 0.604% of GDP. Government spending (which is determined exogenously in our model) represents 21.4% of GDP in steady state. Additionally, the weight of the labor force working in the residential sector is targeted at 7.2%. For simplicity, we assume that lump-sum taxes are initially distributed equally on a per capita basis between lenders and borrowers, such that Table 2 shows the general parameters and exogenous variables that are set and calibrated.

⁷As indicated in the Guidelines for National Greenhouse Gas Inventories Intergovernmental Panel on Climate Change (IPCC) (2006), emissions of each greenhouse gas from stationary sources are calculated by multiplying fuel consumption by the corresponding emission factor. Therefore, the emissions of a fossil fuel are directly proportional to its consumption, making the elasticity of emissions per area straightforwardly comparable to the elasticity of consumption per area.

Table 2: Macroeconomic parameters

Environmental Parameters. Most of the environmental parameters are taken from Gibson & Heutel (2023) and adjusted to the units of the model, as total GDP is normalized to 1 (in millions of euros), and therefore, most of the variables are interpreted in terms of million euros of total production. Moreover, we impose values for emissions in both sectors , and the atmospheric carbon dioxide stock x. According to data from the Global Monitoring Laboratory, the carbon stock in the atmosphere in 2019 is set at . The steady-state ratios of the EU-27 annual emissions in 2019 for consumption goods firms and the residential sector are obtained from the UNFCCC and the EU Greenhouse Gas Monitoring Mechanism. The steady-state values of annual emissions in the manufacturing and residential sectors are 3284.548 and 317.035 equivalent, respectively.

Table 3: Environmental parameters

From Gibson & Heutel (2023), we take the elasticity of emissions to output in manufacturing, . We also use their value for the pollution stock decay rate 7 which assumes a half-life of atmospheric carbon dioxide of 50 years, as well as their coefficients of the damage and abatement cost functions. From Equation (6) we obtain The atmospheric carbon stock is measured in gigatons (GtC) per million euros of GDP (in constant 2015 euros). After scaling the damage function coeficients with respect to the EU-27 GDP in 2019 to match the production losses reported by Gibson & Heutel (2023), we impose , and . In the abatement cost function, we choose , corresponding to a total share of abatement costs over production of 7.4% when the emission reduction share is 100%. Similarly, is calibrated to ensure that the cost of abating 100% of residential emissions in the steady state is equivalent to 7.4% of housing production. Specifically, , which in the steady state simplifies to . According to equation (2) under full abatement, , meaning that

The cost elasticities to abatement, and , are set to 2.6 from Nordhaus (2018). Finally, the calibration of the elasticity of carbon emissions to the housing stock is based on the estimation of the log of residential emissions on the log of dwelling floor area, as shown in Section 3.1.

Table 3 summarizes the environmental parameters recovered from previous studies and those that result from the calibration strategy.

4 Results

The adoption of the European Climate Act (European Commission, 2021) transformed the political commitment of the 2019 Green Deal (European Commission, 2019) into a legal obligation. EU countries are thus required to reduce greenhouse gas emissions by at least 55% below 1990 levels by 2030, with the goal of achieving climate neutrality by 2050. The building sector is a critical area for addressing climate and environmental challenges; therefore, the EU will extend the existing EU Emissions Trading Scheme to include emissions from the residential sector. The objective is to achieve a 43% reduction in emissions from buildings by 2030 compared to 2005 levels. While the introduction of a carbon price on residential emissions rightly encourages cost-efective emissions reductions and incentivizes behavioral change, it also imposes a burden on consumers.

In this section, we present simulation results on the macroeconomic efects of policies that require households to pay for their housing emissions while also pricing carbon emissions from the production of other consumption goods and services. After analyzing these macroeconomic impacts, we focus on the diferential efects between household types to uncover the inequality efects on key components of household welfare: consumption, housing holdings, and leisure time. Furthermore, we explore government strategies to alleviate the efects of carbon pricing policies during the transition to climate neutrality. Specifically, we evaluate measures to lessen the burden on households by utilizing carbon revenues from environmental policies to address redistributive issues.

4.1 Carbon Pricing

The transition to zero emissions is simulated by imposing a linear increase in the carbon price in both the residential and consumer goods production sectors. Starting from an initial steady state where no environmental policy is anticipated, an emissions pricing path is suddenly announced, and agents respond with perfect foresight until the new steady state is reached. We designate period 1 as 2019Q4, when the government introduces emission prices. The carbon price for residential emissions and production emissions increases linearly over 120 quarters, with a discontinuity before the halfway point, ensuring that emission reduction targets are met by 2030 and climate neutrality is achieved by 2050. Our intermediate targets include a 43% reduction in housing emissions by 2030 relative to 2005 levels and a 55% reduction in carbon emissions from the non-residential sector by 2030 compared to 1990 levels. Considering that the absorption rate used in the calibration implies that terrestrial ecosystems are able to absorb 25% of global emissions,⁸ achieving NZE by 2050 requires a 75% reduction in both residential and non-residential emissions by 2050 relative to 2019 levels.

⁸This figure is consistent with observations over the past 50 years (see Brienen et al. (2020)

4.1.1 Macroeconomic impacts

Our simulations isolate the gross impacts of carbon pricing policies on greening the economy, without accounting for the efects of technological improvements on energy use or carbon emissions per unit of energy. In our model, agents adjust their allocation of resources for emissions reduction in response to increases in carbon prices. Consequently, the carbon prices depicted in Figure 2 represent an upper bound of those required to meet emissions reduction targets.

In the absence of technological change, the carbon price would need to increase by approximately €460 per ton of in the non-residential sector, and by €260 per ton of in the residential sector. This increase would be accompanied by a more pronounced acceleration in the carbon price in the residential sector after 2030.

The environmental policy reduces atmospheric carbon stock by 1.36% by 2050. 9 However, the additional tax burden on households and firms during the transition period, leads to an approximate 7.45% decrease in aggregate GDP. This decline in GDP is accompanied by substantially lower levels of investment and consumption.

Firms in the consumer sector, faced with the additional costs of the carbon price, reduce their demand for labor and capital, thereby decreasing production. Capital in the non-residential sector declines by over 10%. Similarly, housing production is adversely afected, primarily due to the demand-side efects of carbon pricing. The carbon price targeting emissions from housing deters housing demand by increasing the costs associated with emissions pricing and abatement, leading to a 3% reduction in residential investment and a significant 8.7% decrease in housing prices. The adjustment in housing prices reflects not only weakened demand but also an oversupply of capital and labor resulting from reduced overall production. Idle factors of production experience a decrease in their prices, which firms pass on as lower product prices, particularly in the construction sector. Consequently, price behavior difers notably between the two production sectors. While inflation in consumer goods production remains relatively stable—since the cost factors pushing prices upward are ofset by weaker aggregate demand—housing prices decline, primarily due to the negative demand impact on this sector.

Aggregate consumption is adversely afected by declining incomes, abatement costs incurred by households during the transition, and deteriorating credit conditions. In our baseline calibration, consumption decreases by 8% by 2050, with abatement costs representing 3.4% of GDP upon achieving NZE. Since changes in housing prices are not incorporated into the Central Bank’s policy framework, monetary policy does not respond to declines in housing prices as it does to consumer goods inflation. Consequently, the monetary policy tool is less efective in mitigating the adverse aggregate efects on GDP resulting from reduced consumption by borrowers, which is further exacerbated by declining housing prices and the resulting deterioration in credit conditions.

⁹This figure reflects only Europe achieving NZE, without contributions from other countries.

Figure 2: Macroeconomic Impacts of Carbon Pricing Policies

The results are presented as percentage deviations from their expected trajectories in the absence of environmental policies, except for emission prices, which are denominated in euros, inflation, measured in basis points, and abatement costs, expressed as percentage points of GDP.

To further investigate the impact of carbon pricing on household consumption and other economic decisions, the next subsection disaggregates the efects by household type, analyzing the responses of borrowers and lenders to the emissions reduction policy.

4.1.2 Impact by household type

Figure 3 displays the percentage deviations of household-related variables relative to the no-policy scenario, highlighting the diferential impacts of the carbon pricing policy across household types. In our benchmark scenario, depicted in Figure 3a, government carbon revenues are distributed equally among household types as a carbon dividend that ofsets their tax burden.

Credit-constrained households exhibit the highest abatement efort, measured as the percentage of residential emissions reduced each period. This behavior results from the optimal abatement path, as detailed in equation (3), which indicate that abatement efort is inversely related to housing stock. The intuition behind this outcome is that households invest in abatement to mitigate the negative impact of increased carbon prices on their housing stock, as reducing housing serves as an alternative to ofsetting higher carbon costs. Since borrowers own fewer houses than lenders, reducing housing would result in a greater utility loss for borrowers than for lenders due to the decreasing marginal utility of housing. Consequently, borrowers find it optimal to exert greater abatement efort. In contrast, despite lower abatement eforts by lenders, they incur slightly higher abatement costs because they own more houses.

The first row of plots in Figure 3a illustrates the evolution of key variables influencing household welfare: consumption, housing property, and leisure (working hours). Signif icant disparities emerge in household responses concerning these variables. Borrowers, because they have a higher preference rate for the present against the future, are more responsive to government transfers (tax reductions) than lenders. As shown in the figure, lump-sum taxes decrease in a convex manner due to two opposing factors. First, the carbon tax increases over time, raising government revenues that, when rebated to households, result in lower taxes. Second, emissions decline over time, reducing the tax base. Consequently, the carbon dividend reaches an upper limit before the end of the transition period.

In the very first periods, borrowers’ consumption falls compared to lenders’, primarily due to the reduction in credit caused by the decline in the value of collateral housing through decreasing house prices (see Figure 4). Borrowers demand houses not only for the housing services they provide but also because they can be used as collateral to obtain credit. As a result, borrowers’ housing demand decreases in the initial periods. Over time, the dynamic choices of both household types diverge significantly.

Figure 3: Impact of carbon pricing policy by household type

(a) Equitable distribution of carbon dividends across the population

(b) Allocation of all carbon dividend to patient households

Variables are presented as percentage deviations from their expected trajectories in the absence of envi ronmental policy, except for abatement and abatement costs. Abatement is expressed as a percentage of emissions, and residential abatement costs are expressed as a percentage of GDP.

Patient households bear a greater tax burden from residential carbon taxes because they own more houses per capita. Additionally, they experience a reduction in profits from firm ownership as emissions prices increase, which adversely afects their consumption prospects. In contrast, impatient households face a relatively lower environmental tax burden and thus benefit relatively more from the carbon dividend, which is distributed evenly among households. After the initial negative impact of the policy announcement, this dividend ofsets their residential emissions payments and increases their disposable income. Consequently, borrowers respond by expanding their housing stock, helping to sustain their consumption.

However, as emissions are progressively reduced, the diminishing carbon dividend leads to reduced government transfers, and the significant decline in house prices weakens borrowers’ ability to use their properties as collateral, explaining the hump-shaped trajectory of houses owned by borrowers. This reduction in collateral limits both con sumption and housing demand. Labor demand decreases with economic activity, driving down wages and hours. As consumption continues to deteriorate, borrowers are compelled to increase their labor supply over time in an efort to restore income (and consumption) stability. Eventually, the increase in labor supply compensates for the decline in labor demand, as reflected in the U-shape of hours worked.

Despite the difering transition dynamics, both borrowers and lenders conclude the transition period with substantial declines in consumption, decreasing by 9% and 8%, respectively. Housing demand decreases by 2% for borrowers compared to 0.5% for lenders, while working hours decline by 0.6% for borrowers and 0.9% for lenders.

Under an alternative carbon dividend distribution, household responses exhibit signif icant changes. For illustrative purposes, Figure 3b demonstrates the impact of the carbon pricing policy on consumption, housing stock, and hours worked when credit-constrained households do not receive carbon revenues, thereby maintaining their initial lump-sum taxes at a constant level. In this scenario, lenders fully receive the carbon dividend. They allocate a portion of their additional income to sustain consumption and private bonds during the initial periods. The rebound of debt in lenders’ hands observed in Figure 4 helps support borrowers’ consumption in the early stages of the transition to NZE. However, as the transition progresses, lenders benefit from an increasing share of their income from government transfers, while the income of impatient households deteriorates without the support of those transfers. Consequently, borrowers’ consumption and credit demand shrinks, and lenders take advantage of declining house prices to redirect their savings toward housing investments.

Overall, this results in a markedly diferent trajectory for consumption, housing holdings, and working hours throughout the transition period for borrowers compared to the benchmark carbon dividend distribution illustrated in Figure 3a. Specifically, the previously observed hump-shaped patterns in borrowers’ consumption and housing stock, as well as the U-shaped pattern in working hours, disappear. Despite the significant distributional efects of allocating government revenues from carbon pricing, the overall consumption dynamics remain largely unafected. Therefore, focusing solely on aggregate outcomes can obscure substantial distributional impacts.

Figure 4: One-period debt held by borrowers Two scenarios are displayed: (a) equitable distribution of carbon dividends, and (b) allocation of all carbon dividends to patient households (ν = 0)

From the above discussion, we identify two key insights. First, the allocation method of carbon dividends significantly afects household consumption, housing, and labor re sponses, with borrowers being more sensitive to the specific dividend distribution scheme. Second, despite owning fewer houses, borrowers undertake higher abatement eforts be cause reducing their housing stock would result in a greater utility loss compared to lenders.

4.2 Sector-Specific and Combined Carbon Pricing Policies

So far, we have examined the efects of simultaneously increasing carbon prices in both the residential and non-residential sectors. This section investigates the distinct economic, distributional, and welfare implications of implementing sector-specific policies within the broader framework of achieving NZE targets.

4.2.1 Long-run efects

Table 4 compares scenarios where carbon prices are simultaneously increased in both residential and non-residential sectors with those where only the non-residential or only the residential carbon price is elevated.¹⁰

The table is organized into three sections: first, it presents the efects on a set of aggregate macroeconomic variables; second, it analyzes household-type-specific variables;

¹⁰In all cases, the carbon price trajectories follow those depicted in Figure 2.

Table 4: Impact of carbon pricing under three scenarios: combined, production-only, and residential-only policies

Note: Abatement costs z are expressed as percentage of GDP. Equivalent consumption and represent percentage of no-policy consumption that a representative consumer would forgo to achieve the same welfare level under carbon emissions policies.

and third, it provides welfare indicators. This table focuses on the long run, with the columns representing steady-state levels with and without the policy. The diferences in levels are shown in brackets as percentage deviations from the no-policy values.

The analysis reveals that, unsurprisingly given the volume of emissions in both sectors, carbon pricing in the non-residential production sector is the primary driver of economic changes. In contrast, residential carbon pricing generally has relatively modest efects on overall economic indicators. However, significant long-term efects are observed in residential investment, housing stock, and new credit, specifically due to residential emissions pricing, both in absolute and relative terms.

Residential emissions account for 8.3% of total carbon emissions in the model. However, as shown in the upper section of Table 4, the impact of a residential-specific policy on GDP or consumption is significantly lower than this share when compared to a combined policy aimed at achieving general NZE across all emission sources. This indicates that pricing residential emissions adversely afects aggregate activity much less per unit of emissions reduction than pricing non-residential emissions.¹¹ Consumption exhibits a similar pattern, decreasing by 10% under dual pricing and 9.88% under single nonresidential pricing.

¹¹For example, using the figures from table row GDP , considering that residential emissions represent 8.3% of total emissions, and that the long-run rate of reduction in emissions is the same in both sectors

The impact of becomes more pronounced when examining variables directly related to the residential sector and credit. Residential investment declines by 3.75% due to the combined environmental policies aimed at achieving climate neutrality. While general equilibrium efects from taxing carbon emissions in the non-residential sector account for a 2.24% reduction in residential investment, Table 4 indicates that 1.40% decline can be attributed to residential carbon pricing policies in isolation. Additionally, housing prices fall by approximately 0.9% under , representing over 10% of the decline caused by the combined policy of

In our model, debt (the private asset issued by borrowers) expires each period and can be interpreted as fresh credit. This credit is adversely afected by the residential carbon tax, decreasing by 2.74% in the long run. Compared to the non-residential carbon policy, taxing residential emissions reduces credit by a ratio of approximately 3 to 1 per unit of emissions reduced. Thus, the impact on housing investment, housing prices, and credit per unit of carbon reduction is significantly more pronounced for than for

In the middle section of the table, we assess the impact of carbon pricing on diferent household types by focusing on key determinants of utility: consumption, housing, and leisure. The findings are as follows: first, in the long term, the combined policy adversely afects borrowers’ consumption and housing more than lenders’, and borrowers experience a smaller increase in leisure. Overall, this indicates a relative long-term deterioration of borrowers’ welfare compared to lenders’. Second, the residential emissions pricing policy has minimal long-term efects on consumption and working hours (leisure) across all household types. Third, the residential emissions policy exerts a relatively greater negative impact on borrowers’ housing compared to lenders’, likely further exacerbating the long-term decline in borrowers’ welfare.

Next, we will examine the welfare implications of the policies in more detail. To this end, we will not only compare static solutions but also consider the full dynamics implied by the policies.

4.2.2 Welfare efects

In the bottom section of Table 4, we translate the previous results into welfare changes, this time incorporating all transition dynamics. The first row, denoted as , represents a direct measure of social welfare in terms of utility, defined as the weighted sum of (equal to 75%), we can calculate , indicating that the GDP cost of reducing emissions in the residential sector is about of that in the non-residential sector.

individual utility across household types. It is given by

\[W ^ {s} = (1 - \tau^ {b}) (1 - \beta^ {l}) W ^ {l} + \tau^ {b} (1 - \beta^ {b}) W ^ {b},\]

where and correspond to the present expected value of lifetime welfare of patient and impatient households. The weights in the functions have been chosen so that for the same constant flow of final consumption, patients and inpatients would receive the same level of utility (see Lambertini et al. (2013) or Notarpietro & Siviero (2015))

The following two rows present household-specific changes in welfare, measured in terms of consumption equivalent variation, and . More generally, the post-policy welfare of household a (where —measured as the expected present value—is given by

\[\widetilde {W} ^ {a} = \mathbb {E} _ {0} \sum_ {t = 0} ^ {\infty} (\beta^ {a}) ^ {t} \left(\ln \tilde {c} _ {t} ^ {a} + \gamma_ {h} \ln \tilde {h} _ {t} ^ {a} - \frac {(\tilde {n} _ {t} ^ {a}) ^ {1 + \eta}}{1 + \eta}\right),\tag{8}\]

The discounted sum of utility for a representative household assuming the economy is at the steady state in period 0 and remains constant throughout is

\[\overline {{W}} ^ {a} = \mathbb {E} _ {0} \sum_ {t = 0} ^ {\infty} (\beta^ {a}) ^ {t} \left(\ln (\bar {c} _ {t} ^ {a}) + \gamma_ {h} \ln \bar {h} _ {t} ^ {a} - \frac {(\bar {n} _ {t} ^ {a}) ^ {1 + \eta}}{1 + \eta}\right),\tag{9}\]

The consumption equivalent measures the percentage of consumption in the no-policy scenario that a representative consumer would be willing to forgo to achieve the same level of welfare under the carbon emissions policies. A positive value indicates a welfare loss, suggesting that the carbon pricing policy is less desirable from a welfare perspective. To determine , we solve

\[\widetilde {W} ^ {a} = \mathbb {E} _ {0} \sum_ {t = 0} ^ {\infty} (\beta^ {a}) ^ {t} \left(\ln \left(\bar {c} _ {t} ^ {a} (1 - C E ^ {a})\right) + \gamma_ {h} \ln \bar {h} _ {t} ^ {a} - \frac {(\bar {n} _ {t} ^ {a}) ^ {1 + \eta}}{1 + \eta}\right),\tag{10}\]

from which we obtain

\[C E ^ {a} = 1 - \exp \left[ (1 - \beta^ {a}) (\widetilde {W} ^ {a} - \overline {{W}} ^ {a}) \right].\tag{11}\]

Achieving NZE targets through a combined increase in carbon pricing across both sectors results in a generalized welfare loss of -15.3% relative to the no-policy scenario in utility units. In contrast, the welfare simulation for carbon pricing in the residential sector alone yields a modest welfare efect of -0.54%. Considering the residential sector’s share of emissions, this result indicates that reducing a unit of carbon emissions in the residential sector is less than half as costly in welfare terms as reducing emissions in the non-residential sector.

In terms of consumption equivalent, the long-run welfare cost in the benchmark model represents a decline of more than 10% in consumption. This cost is relatively evenly distributed across households under the combined policy. However, significant diferences emerge when comparing the impacts of taxing carbon emissions in the residential versus non-residential sectors. Specifically, the welfare cost in terms of consumption is 0.5 percentage points higher for borrowers than for lenders when the carbon price increase applies only to the non-residential sector. Conversely, when only the residential sector is subject to the carbon price increase, the welfare cost for lenders, though modest, is nearly twice that of borrowers. Therefore, a more in-depth welfare analysis contradicts the steady-state intuition that housing carbon pricing would further harm borrowers through a reduction in housing properties. When all transitional dynamics are considered from the outset of the policy, and with an equitable distribution of the carbon dividend, borrowers benefit from increased consumption, housing, and leisure during certain periods of the transition (see Figure 3a).

Overall, our findings indicate that while carbon pricing in the non-residential sector is the primary driver of economic changes and welfare losses, residential carbon pricing—despite its modest impact on aggregate indicators—significantly afects the residential sector by reducing investment, housing stock, and credit availability. Notably, reducing emissions in the residential sector is less costly in welfare terms per unit of emissions reduced compared to the non-residential sector. Additionally, the diferential impacts on borrowers and lenders highlight important distributional efects: borrowers experience greater declines in consumption and housing under combined policies, whereas lenders bear a relatively higher welfare cost when only residential emissions are priced. These insights suggest that carbon pricing policies can have significant implications for inequality, emphasizing the importance of accounting for these diferential impacts during the transition to NZE. This objective is addressed in the next subsection.

4.3 Carbon Pricing and Inequality

The burden of carbon pricing is not distributed equally across households. If it disproportionately afects less advantaged households, it may lead to social resistance against the policies. Additionally, distributional impacts may shift throughout the transition. This section examines how these evolving distributional efects influence inequality between household types.¹²

We present in Figure 5 two policy scenarios: a combined increase in both residential and non-residential carbon prices, and a single increase in the non-residential carbon price. The diference between these scenarios approximates the inequality impact of the residential carbon policy. We maintain the benchmark of an equal per capita distribution of the carbon dividend, with the pre-policy value shown as a large solid dot at 2019.

¹²While carbon pricing policies introduce economic adjustments, their long-term benefits—ranging from reduced climate damages and health improvements to economic growth through innovation—can outweigh the short-term costs. These long-run efects are beyond the scope of this paper, which focuses primarily on the realized costs during the transition

Figure 5: Inequality in the transition to NZE Dashed line: Combined carbon pricing scenario; Solid line: Only carbon pricing on the non-residential sector

In the first subplot of Figure 5, we assess inequality based on consumption using the Gini coeficient. Given that represents the share of high-income households who consume a fraction of total consumption, the Gini coeficient is calculated as the diference between their implied percentage of total consumption and their percentage in population, that is, .¹³

The figure shows an initial increase in inequality that soon starts to decrease during the transition period as lump-sum tax reductions, which primarily benefit borrowers’ consumption, are implemented (discussed in Section 4.1.2). From 2019 until 2030, coinciding with the achievement of intermediate climate targets, the Gini coeficient decreases by 0.45 percentage points. This reduction is approximately half of the decline in the Gini coeficient of disposable income observed in the EU between 2013 and 2024, according to Eurostat¹⁴. However, after reaching a minimum around 2030, the Gini coeficient begins to rise steadily, reversing the gains in consumption distribution and resulting in the highest level of inequality when the economy reaches NZE by 2050. As previously discussed, the reduction in the carbon dividend, as carbon target gaps close, and the decline in the value of borrowers’ collateral contribute to this outcome.

Using only the ratio between lenders’ and borrowers’ consumption in the second subplot of the first row provides a similar picture to that obtained with the Gini coeficient.

¹³The same statistics is used by Rubio & Unsal (2017)

¹⁴Eurostat (2024)

Similarly, in the second row of Figure 5, we present the ratios of incomes—excluding financial incomes—and housing between the two household types. Unlike the U-shaped transition dynamics observed for consumption and housing inequality, income inequal ity displays an L-shaped pattern, decreasing and remaining lower throughout the entire transition period. We interpret the diferences between the dynamics of consumption inequality and income inequality as indicative of the significance of wealth and financial channels, which adversely afect borrowers after 2030.

The comparison of the two policy scenarios reveals that residential carbon pricing, despite its relatively moderate impact, further increases consumption inequality for ap proximately half of the transition period up to 2030, before helping to mitigate the rise in inequality in the later stages. The dynamics difer when considering the ratio of housing, as the residential carbon tax induces a shift in the distribution of houses owned by households, becoming more skewed toward lenders, especially as the tax accelerates after 2030. To explain this outcome, we show in Figure 6 the response of several variables.

Borrowers demand houses not only for housing services, as lenders do, but also because they use them as collateral for obtaining credit. The increasing carbon price leads to a decline in house prices, reducing the value of the collateralized asset, which in turn negatively impacts credit availability and consumption. Regarding housing demand, borrowers must balance the marginal disutility of reducing their housing stock to cope with higher housing costs—which is greater for them than for lenders—against the loss of capacity to convert houses into consumption through credit, a constraint that lenders do not face. The results indicate that the latter efect dominates, causing borrowers to reduce their housing stock more than lenders. However, the abatement efort is much higher for borrowers than for lenders, suggesting that, without the disutility efect mentioned before, the reduction in borrowers’ housing demand would have been even more pronounced.

Because borrowers are more impatient than lenders, they tend to convert changes in income into contemporaneous changes in consumption at a higher rate than lenders. Consequently, as the carbon dividend increases, borrowers are more likely to immediately allocate it to consumption. Over time, this leads to a substitution efect where borrowers shift from housing to consumption, a dynamic that is not observed for lenders.

Our results suggest that consumption Gini dynamics vary depending on whether taxes are applied to the residential or non-residential sector. In any case, the time-dependent response of the Gini coeficient for consumption highlights periods when inequality mitigation policies are most needed. In a realistic scenario that combines both residential and non-residential taxes, such policies are particularly crucial in both the early and later stages of the transition, especially after reaching the intermediate 2030 targets and advancing toward NZE. When the policy on residential emissions is considered in isolation, inequality relief policies are primarily needed during the initial years.

Figure 6: Residential carbon price efects Variables are presented as percentage deviations from their expected trajectories in the absence of environmental policy, except for abatement, which is expressed as a percentage of emissions.

4.3.1 Robustness of inequality dynamics

We investigate the impact of several factors on inequality dynamics, including the proportion of borrowers in the economy, the intensive margin of borrowing, the distribution of the carbon dividend, labor mobility flexibility between sectors, labor supply elasticity with respect to wages, the intensity of emissions response to housing demand and to goods and services production, and the cost of abatement in both sectors.

Figure 7 presents the Gini coeficients across diferent parameter settings, with the benchmark result included for comparison. In each subplot, only one model parameter is altered, while the growth rate of carbon emissions prices remains constant across all simulations, ensuring that any changes in inequality dynamics throughout the transition are directly attributable to specific parameter variations. However, adjustments in parameters may alter the initial equilibrium. Additionally, Figure 8 illustrates how carbon emissions dynamics respond to changes in economic conditions. Together, Figures 7 and 8 ofer a comparative assessment of the impacts on inequality (via Gini coeficients) and eficiency (via emissions reduction) of carbon pricing policies under diferent settings.

The overall picture that emerges is that, in general, the U-shaped pattern in inequality dynamics observed in the benchmark calibration holds across a wide range of diferent settings. This means that consumption inequality increases immediately after the policy announcement, then begins to decline, eventually recovering at some point. The isolated efect of residential carbon pricing also appears to remain relatively unafected across the various subplots. However, a closer examination reveals that certain factors within the

Figure 7: Consumption Gini dynamics under diferent settings Carbon pricing is implemented under two scenarios: (a) simultaneously in both the non-residential and residential sectors, and (b) exclusively in the non-residential sector.

economy induce notable diferences.

Parameters related to carbon emissions in the production sector significantly influence the trajectory of inequality over time. Economies with industries characterized by higher carbon intensity experience a marked increase in inequality during the later stages of the transition, missing out on the benefits of early-period inequality reductions. The increased production costs from carbon pricing in more carbon-intensive economies result in higher abatement efort (as Figure 8 shows, emissions fall by more for a given carbon price) reduced economic activity, lower wages, and decreased government transfers to households, disproportionately afecting borrowers—whose consumption is more dependent on current income—and widening the consumption gap between households. Consequently, technological advances that reduce are crucial not only for bridging the gap with NZE, but also for mitigating the inequality impacts of carbon emissions pricing.

Labor mobility between sectors, represented by the parameter , also significantly impacts inequality. We represent the case of an increase in . In this case, workers move from the non-residential sector, where wages experience a greater decline, to the residential sector, amplifying the drop in activity within the non-residential sector. Reduced activity in this sector lowers emissions by more, subsequently decreasing the carbon dividend, which disproportionately harms the consumption of borrower households. The positive aspect is that the accelerated decline in non-residential activity facilitates achieving the NZE target, as shown in the corresponding subplot in Figure 8. Thus, higher labor mobility between sectors creates a trade-of between eficiency in terms of emissions and consumption inequality.

Figure 8: Emissions reduction dynamics under diferent settings Carbon pricing is implemented simultaneously in both the non-residential and residential sectors. Dash lines represent the evolution of emission s in the non-residential sector, and the solid line reflects the evolution of emissions in the residential sector. Values in the legend indicate emissions reduction by 2050.

An increase in the number of credit-constrained households makes the economy more unequal but does not significantly alter the dynamics of the Gini index during the transition. However, increasing the capacity to take credit (a rise in κ) initially worsens inequality more than in the benchmark when environmental measures are first announced. The expected negative impact of the policy on housing prices has a greater efect on borrowers’ consumption when the loan-to-value ratio is higher.

Increasing the cost of abatement in the non-housing sector makes it more difi cult to reduce emissions for a given carbon price. Hence, the reduction in the tax base is mitigated as we move along the transition period, keeping carbon dividends higher and benefiting borrowers relative to lenders. Consequently, this scenario improves consumption inequality at the cost of worsening emissions reduction. In the same vein, a higher cost of abatement in the housing sector reduces the inequality impact of the carbon pricing policy compared to the benchmark when targeted at this sector. This efect is evident in the widening gap between the solid and dashed lines in the final years of the period.

Flexible prices mitigate the initial increase in consumption inequality, though they do not alter the subsequent dynamics of the consumption Gini coeficient compared to the baseline scenario. In contrast, a lower initial firm markup (higher ε) contributes to a more pronounced reduction in consumption inequality.

In a scenario where , meaning borrowers receive the entire carbon dividend, consumption inequality decreases from the outset, with the Gini coeficient showing the most pronounced change. Furthermore, this positive impact on inequality is achieved without compromising the efectiveness of the taxes in reducing emissions. The importance of ν will be explored in greater depth in Section 4.4.

Overall, these findings underscore the significant role that specific economic characteristics play in shaping inequality under carbon pricing policies. Some parameters that influence the behavior of the model economy can have a sizable efect on inequality, whether through increased lump-sum transfers or wage changes. While, in some cases, changes in the economic environment improve both the eficiency of the carbon pricing policies and their efects on consumption inequality, in other cases, the alternative settings can alter emissions reduction targets, necessitating increases in carbon pricing. The destination of the carbon dividend emerges as the most efective tool for managing inequality, highlighting the critical importance of carefully designing carbon dividend distribution and emissions pricing policies to mitigate short and long-term adverse distributional impacts.

4.3.2 Population Composition and Carbon Pricing

In this subsection, we explore whether changes in population composition can afect the carbon pricing levels needed to achieve climate goals. In the subplot corresponding to in Figure 8, we do not detect significant diferences in the efect on emissions when the share of borrowers increases, provided that the pricing pace for both residential and non-residential carbon emissions is maintained at the baseline. However, this result may obscure diferences in the tax required to achieve NZE separately in each of the two sectors.

Figure 9: Carbon emission price projections to meet NZE by 2050

(a) Variations in with set to the baseline. (b) Variations in , with set to the baseline.

Figure 9 illustrates how, under a linear policy scheme, the carbon prices needed in 2050 to satisfy the NZE for both the residential and non-residential sectors vary in diferent directions as the share of borrowers in the population, , changes. As the share of borrowers increases, the efectiveness of the emissions policy in the residential sector improves, allowing for a reduction in carbon prices. As explained earlier in this paper, borrowers exert more efort than lenders in abating residential emissions due to the greater disutility associated with reducing residential demand as an alternative. Conversely, as the number of borrowers in the population increases, a higher carbon price is needed in the non-residential sector to achieve the NZE target. Non-residential carbon emissions prices directly impact lenders’ income through the efect on firm profits, which provides an incentive to abate emissions. As the share of lenders shrinks, this incentive diminishes, and carbon prices need to increase further to achieve the same efect.

4.4 Equitable Compensation Mechanism

The preceding analysis highlights the negative consequences that carbon pricing policies can have on variables crucial for household welfare, emphasizing the need for welldesigned compensation schemes, such as carbon dividends, to alleviate these adverse impacts. While ofsetting undesired welfare efects is a vital objective, it is not the only consideration for efective climate policy. Achieving a balance among environmental goals, economic eficiency, and social equity is crucial. In this section, we explore the use of carbon dividends—lump-sum transfer rebates distributed to households—as a mechanism to compensate those afected by carbon pricing, ensuring that the financial burden of the transition is distributed more equitably.

Recall that the per capita lump-sum taxes paid by borrowers and lenders are denoted as and , respectively. The aggregate (weighted average) of these taxes is represented by . After the implementation of the carbon dividend policy, the lump-sum taxes for each household type equal the uniform lump-sum tax minus the household-specific carbon dividend rebate. The amount of carbon revenue that the government can allocate for tax reductions, referred to as the carbon dividend, is given by and depends on the environmental policy:

\[s _ {t} = \tau_ {h t} e _ {h t} + \tau_ {c t} e _ {c t}.\]

The adjusted lump-sum taxes for each household type, following the distribution of the carbon dividend, are expressed as:

\[t r _ {t} ^ {l} = \overline {{t r}} - (1 - \nu) \frac {s _ {t}}{1 - \tau^ {b}}\]

\[t r _ {t} ^ {b} = \overline {{t r}} - \nu \frac {s _ {t}}{\tau^ {b}}\]

where is the steady-state value of lump-sum taxes required to uniformly fund government spending in the pre-policy scenario. Hence, ν represents the proportion of the carbon dividend allocated to borrowers, while denotes the share allocated to lenders. When , the carbon dividend is distributed equally on a per capita basis between the two groups, which is our benchmark assumption. The government’s budget constraint, incorporating the post-policy lump-sum taxes and is given by:

\[\bar {g} = \tau^ {b} t r _ {t} ^ {b} + (1 - \tau^ {b}) t r _ {t} ^ {l} + \tau_ {h t} e _ {h t} + \tau_ {c t} e _ {c t}.\]

Figure 10 illustrates how diferent schemes in the distribution of carbon revenues among households impact both equity and eficiency during the transition to a NZE economy. Specifically, we analyze the present value of consumption and housing demand, along with welfare efects and the projected residential carbon price for 2050 required to achieve NZE. By adjusting the parameter the government shifts the allocation of tax relief between lenders and borrowers, thereby altering their disposable income.

The first row in Figure 10 shows the present value of consumption and housing spending as a percentage deviation from the path they would have followed without any environmental policy, where consumption and housing demand are constant and equal to their steady-state values. The present value analysis demonstrates that the carbon dividend has a greater impact on borrowers than on lenders and afects housing demand more significantly than consumption spending. This asymmetry poses a challenge for policymakers in designing compensation mechanisms, as no Pareto optimal policy exists. Redirecting revenues to lenders leads to substantial losses for credit-constrained households, with housing spending falling by as much as -15% and consumption decreasing by up to -8% compared to a scenario without carbon pricing. Conversely, lenders experience maximum losses of -10% in housing and -8% in consumption when all carbon revenues are directed to borrowers. Additionally, allocating more of the carbon dividend to borrowers raises the residential carbon emissions price projection for 2050, slightly reducing the policy’s eficiency, though this efect is relatively minor.

Figure 10: Impact on consumption, housing, welfare, and carbon emission prices when carbon revenues are redirected to reduce household taxes

Carbon pricing is implemented simultaneously in both the non-residential and residential sectors. Present values in percentage deviation from the path they would have followed without any environmental policy.

The left subplot at the bottom captures the welfare efect, including variations in consumption, housing, and working hours, expressed in terms of equivalent variations. Interestingly, the most equitable welfare impact of the environmental policy on households occurs when the carbon dividend is distributed fairly evenly. This is indicated by the intersection of the dotted and solid lines at a value for ν close to . However, the steeper slope of the line representing the welfare efects for borrowers, compared to that for lenders, suggests that starting from a homogeneous distribution of the carbon dividend, further biasing the dividend towards borrowers more than compensates for the welfare loss experienced by lenders. Under certain reasonable welfare aggregations, this adjustment could lead to an improvement in overall social welfare.

5 Conclusion

This paper provides a comprehensive analysis of the macroeconomic and distributional efects of carbon pricing policies, with a focus on the diferential impacts when these poli cies target residential versus non-residential emissions. Using an Environmental Dynamic General Equilibrium (E-DGE) model, we account for critical transmission mechanisms, including nominal price rigidities and mark-ups, sectoral labor adjustments, and financial frictions tied to housing collateral. A key innovation of our approach lies in the integra tion of borrower-lender heterogeneity within a dynamic general equilibrium framework that features two distinct production sectors. This modeling approach distinguishes our work from much of the existing literature. Unlike previous studies that often rely on static or partial equilibrium models to evaluate distributional impacts, our framework captures the dynamic interplay between climate policies and the broader economy over time.

Our findings reveal sector-specific welfare diferences. Although the overall long-term welfare cost of combined carbon pricing policies is significant - exceeding 10% in terms of consumption and distributed relatively evenly between borrowers and lenders - the impacts vary notably when emissions from each sector are taxed separately. Carbon pricing in the non-residential sector imposes a greater welfare burden on borrowers due to their increased vulnerability to declines in labor demand and economic output. In contrast, residential carbon pricing disproportionately afects lenders, resulting in nearly twice the welfare loss compared to borrowers, despite lenders’ lower abatement eforts. This outcome is driven by a more concentrated reduction in housing investment and property values, which are predominantly owned by lenders. Moreover, the eficiency of emissions reduction is higher in the residential sector, making it more cost-efective in welfare terms per unit of emissions reduced compared to the non-residential sector.

The paper also highlights the role of debt distribution in shaping the eficiency of carbon pricing policies. The efectiveness of carbon pricing in the residential sector increases when there is a higher proportion of credit-constrained borrowers, as these households are more inclined to invest in abatement to avoid severe welfare losses. However, the opposite occurs in the non-residential sector: a larger share of borrowers necessitates higher carbon prices to achieve emissions reductions because the income-driven incentives for lenders to abate diminish. These findings emphasize the need for sector-specific and well-calibrated carbon pricing strategies.

Our analysis of inequality dynamics, including robustness tests, shows that carbon pricing policies can have varying impacts depending on key economic parameters. The consumption Gini coeficient generally follows a U-shaped pattern during the transition, initially decreasing due to carbon dividends but then rising as these revenues dwindle. Sensitivity analysis reveals that factors such as labor mobility and the share of creditconstrained households significantly afect the inequality trajectory. For instance, higher labor mobility between sectors can exacerbate inequality, while increasing the proportion of borrowers makes the economy more unequal but does not alter the general pattern of inequality over time. These insights underline the importance of adaptive policy measures that can address distributional challenges, especially after intermediate climate targets are reached.

This study sets the stage for future research in several compelling areas. One promising direction is to delve deeper into the role of the labor market in shaping the efectiveness of environmental policies. This includes exploring within a dynamic general equilibrium framework labor mobility between sectors and wage dynamics, building on previous work like Fullerton & Monti (2013) and Aubert & Chiroleu-Assouline (2019). Gaining a better understanding of how shifts in employment across sectors influence the outcomes of carbon pricing policies could provide valuable insights into labor market dynamics that may either amplify or bufer the economic impacts of these policies. Another crucial avenue for research involves examining financial frictions, specifically the behavior of endoge nous loan-to-value ratios under the influence of macroprudential tools. Investigating how these financial mechanisms interact with carbon pricing policies could shed light on the trade-ofs between environmental goals and financial stability.

Additionally, expanding the model to incorporate a more diverse range of heterogeneous households, similar to the work of Andres et al. (2022), would enable a more granular analysis of distributional efects. Such a framework would better capture the varied economic realities across diferent household groups, helping policymakers design strategies that more efectively balance economic eficiency, equity, and environmental sustainability. and paving the way for more robust and inclusive strategies in the global transition to a low-carbon economy.

References

1. Alberini, A., Gans, W., & Velez-Lopez, D. (2011). Residential consumption of gas and electricity in the us: The role of prices and income. Energy Economics, 33 (5), 870–881.
2. Andres, J., Bosca, J. E., Ferri, J., & Fuentes-Albero, C. (2022). Households’ balance sheets and the efect of fiscal policy. Journal of Money, Credit and Banking, 54 (4), 737–778.
3. Annicchiarico, B., & Di Dio, F. (2015). Environmental policy and macroeconomic dynamics in a new keynesian model. Journal of Environmental Economics and Management, 69 , 1–21.
4. Araar, A., Dissou, Y., & Duclos, J.-Y. (2011). Household incidence of pollution control policies: A robust welfare analysis using general equilibrium efects. Journal of Environmental Economics and Management, 61 (2), 227-243.
5. Aubert, D., & Chiroleu-Assouline, M. (2019). Environmental tax reform and income distribution with imperfect heterogeneous labour markets. European Economic Review, 116 , 60–82.
6. Bielecki, M., & St¨ahler, N. (2022). Labor tax reductions in europe: the role of property taxation. Macroeconomic Dynamics, 26 (2), 419–451.
7. Brienen, R. J., Caldwell, L., Duchesne, L., Voelker, S., Barichivich, J., Baliva, M., . . . others (2020). Forest carbon sink neutralized by pervasive growth-lifespan trade-ofs. Nature communications, 11 (1), 4241.
8. Brounen, D., Kok, N., & Quigley, J. M. (2012). Residential energy use and conservation: Economics and demographics. European Economic Review, 56 (5), 931–945.
9. Cardi, O., & Restout, R. (2015). Imperfect mobility of labor across sectors: a reappraisal of the balassa–samuelson efect. Journal of International Economics, 97 (2), 249–265.
10. Coenen, G., Karadi, P., Schmidt, S., & Warne, A. (2018). The new area-wide model ii: an extended version of the ecb’s micro-founded model for forecasting and policy analysis with a financial sector.
11. Cong, X., Zhao, M., & Li, L. (2015). Analysis of carbon dioxide emissions of buildings in diferent regions of china based on stirpat model. Procedia Engineering, 121 , 645–652.
12. Debortoli, D., & Galí, J. (2024). Heterogeneity and aggregate fluctuations: insights from ^TANK models. National Bureau of Economic Research, 32557 , 1–47.
13. Dinan, T., & Rogers, D. L. (2002, June). Distributional Efects of Carbon Allowance-Trading: How Government Decisions Determine Winners and Losers. National Tax Journal, 55 (2), 199-221.
14. Dixit, A. K., & Stiglitz, J. E. (1977). Monopolistic competition and optimum product diversity. The American economic review, 67 (3), 297–308.
15. European Commission. (2021, December). Commission staf working document impact assessment report. accompanying the document proposal for a directive of the european parliament and of the council to improve the working conditions in platform work in the european union (Tech. Rep.). Brussels: European Commission.
16. European Environmental Bureau. (2022). Lessons from the german emissions trading system for buildings and road transport. (European Environmental Bureau)
17. Eurostat. (2024). Gini coeficient of equivalised disposable income by age. Eurostat.
18. Ferrari, A., & Landi, V. N. (2022, February). Toward a green economy: the role of central bank’s asset purchases (Temi di discussione (Economic working papers) No. 1358). Bank of Italy, Economic Research and International Relations Area.
19. Fischer, C., & Springborn, M. (2011). Emissions targets and the real business cycle: Intensity targets versus caps or taxes. Journal of Environmental Economics and Management, 62 (3), 352–366.
20. Fullerton, D., & Heutel, G. (2007). The general equilibrium incidence of environmental taxes. Journal of Public Economics, 91 (3), 571-591.
21. Fullerton, D., & Monti, H. (2013). Can pollution tax rebates protect low-wage earners? Journal of Environmental Economics and Management, 66 (3), 539–553.
22. Gibson, J., & Heutel, G. (2023). Pollution and labor market search externalities over the business cycle. Journal of Economic Dynamics and Control, 151 , 104665.
23. Hassett, K. A., Mathur, A., & Metcalf, G. E. (2009). The incidence of a u.s. carbon tax: A lifetime and regional analysis. The Energy Journal, 30 (2), 155-178.
24. Heutel, G. (2012). How should environmental policy respond to business cycles? optimal policy under persistent productivity shocks. Review of Economic Dynamics, 15 (2), 244–264.
25. Hinterlang, N., Martin, A., R¨ohe, O., St¨ahler, N., & Strobel, J. (2022). Using energy and emissions taxation to finance labor tax reductions in a multi-sector economy. Energy Economics, 115 , 106381.
26. Iacoviello, M. (2005). House prices, borrowing constraints, and monetary policy in the business cycle. American economic review, 95 (3), 739–764.
27. Iacoviello, M., & Neri, S. (2010). Housing market spillovers: evidence from an estimated dsge model. American economic journal: macroeconomics, 2 (2), 125–164.
28. Intergovernmental Panel on Climate Change (IPCC). (2006). Guidelines for national greenhouse gas inventories. IGES, Japan.
29. Lambertini, L., Mendicino, C., & Punzi, M. T. (2013). Leaning against boom–bust cycles in credit and housing prices. Journal of Economic dynamics and Control, 37 (8), 1500–1522.
30. Marcu, A., López Hernández, J. F., & De Graeve, B. (2023, January). Eu ets review. political agreement after trilogues. ERCST .
31. Mathur, A., & Morris, A. C. (2014). Distributional efects of a carbon tax in broader u.s. fiscal reform. Energy Policy, 66 , 326-334.
32. Metcalf, G. E., Paltsev, S., Reilly, J., Jacoby, H., & Holak, J. F. (2008, May). Analysis of u.s. greenhouse gas tax proposals (Working Paper No. 13980). National Bureau of Economic Research.
33. Monacelli, T., et al. (2006). Optimal monetary policy with collateralized household debt and borrowing constraints. National Bureau of Economic Research Cambridge, Mass., USA.
34. Nordhaus, W. (2018). Evolution of modeling of the economics of global warming: changes in the dice model, 1992–2017. Climatic change, 148 (4), 623–640.
35. Notarpietro, A., & Siviero, S. (2015). Optimal monetary policy rules and house prices: the role of financial frictions. Journal of Money, Credit and Banking, 47 (S1), 383–410.
36. Rausch, S., Metcalf, G. E., & Reilly, J. M. (2011). Distributional impacts of carbon pricing: A general equilibrium approach with micro-data for households. Energy Economics, 33 , S20-S33. (Supplemental Issue: Fourth Atlantic Workshop in Energy and Environmental Economics)
37. Rausch, S., & Schwarz, G. A. (2016). Household heterogeneity, aggregation, and the distributional impacts of environmental taxes. Journal of Public Economics, 138 , 43- 57.
38. Rotemberg, J. J. (1982). Monopolistic price adjustment and aggregate output. The Review of Economic Studies, 49 (4), 517–531.
39. Rubio, M., & Unsal, M. F. D. (2017). Macroprudential policy, incomplete information and inequality: the case of low-income and developing countries. International Monetary Fund.

Appendix A The complete Model

The model portrays the European Union as a unified economic region with some degree of limited heterogeneity in both the population and the production side. The population consists of two distinct household types diferentiated by their subjective discount rates, reflecting varying levels of impatience. Households with lower discount rates are more patient and tend to save, while those with higher rates are more impatient and typically become borrowers. Both classes consume goods and services, engage in the real estate market, and contribute labor to the production of consumer goods and construction.

The economy encompasses two primary production sectors. The first is responsible for producing consumer and investment goods (also named ”consumer production goods” or ”non-residential sector” through the paper), and the second focuses on housing construction. Firms in the consumer goods sector emit greenhouse gases during production, with emissions proportionally increasing with output levels. Residential activities, such as heating and cooking, also generate carbon emissions, varying by household due to diferences in real estate ownership and the associated services houses provide.

Accumulated emissions adversely afect the economy’s productivity but do not inherently drive households or firms to reduce their carbon footprint due to the associated costs. In the absence of regulation, minimal efort is made to mitigate emissions.

To counteract this, the government implements carbon pricing policies to internalize the social costs of emissions, thereby encouraging investment in emissions reduction. These policies apply to both production and residential emissions, prompting firms and households to adjust their behaviors. The government redistributes any additional revenue from these policies back to households and can ofset the financial burden on households by adjusting the lump-sum taxation scheme to manage distributional impacts. The financing for government expenditures is sourced from general taxation and the revenues generated from carbon taxes.

Below, we outline the various components of the model. For a complete list of the model’s equations, please refer to Appendix A.

A.1 Households

As in Iacoviello(2005), there are two representative households types; of them are patient (lenders) and are impatient (borrowers). Total population is given by . We call and the exogenous proportion of lenders and borrowers in the population.

A.1.1 Patient households

Patient households, or lenders, choose consumption, housing services¹⁵ and labor to maximize the following schedule (real variables are expressed in per capita terms of the specific type of household).

\[\max _ {c _ {t} ^ {l}, h _ {t} ^ {l}, n _ {c t} ^ {l}, n _ {h t} ^ {l}, b _ {t} ^ {l}, k _ {t} ^ {l}, j _ {t} ^ {l}, u _ {h t} ^ {l}} \mathbb {E} _ {0} \sum_ {i = 0} ^ {\infty} (\beta^ {l}) ^ {i} \bigg (\ln c _ {t + i} ^ {l} + \gamma_ {h} \ln h _ {t + i} ^ {l} - \frac {(n _ {t + i} ^ {l}) ^ {1 + \eta}}{1 + \eta} \bigg)\tag{A.1}\]

subject to the real flow of funds expressed in terms of consumption goods price, , (the numeraire),

\[\begin{array}{r} c _ {t} ^ {l} + q _ {t} (h _ {t} ^ {l} - (1 - \delta^ {h}) h _ {t - 1} ^ {l}) - b _ {t} ^ {l} + j _ {c t} ^ {l} + j _ {h t} ^ {l} + \tau_ {h t} e _ {h t} ^ {l} + z _ {h t} ^ {l} = \\ w _ {c t} n _ {c t} ^ {l} + w _ {h t} n _ {h t} ^ {l} - \frac {r _ {t - 1}}{\pi_ {t}} b _ {t - 1} ^ {l} + d _ {t} - t r _ {t} ^ {l} + r _ {k t} k _ {c t - 1} ^ {l} + r _ {h t} k _ {h t - 1} ^ {l} \end{array}\tag{A.2}\]

On the utility side, represents the inverse of the patient discount factor, is real consumption per capita, is lenders’ housing units, and is labor time per person. The parameter captures housing preference and the inverse of η relates to the elasticity of labor supply to wages.

We assume imperfect substitutability, as in Iacoviello & Neri (2010), of labor across sectors, so that is a CES composite of lenders’ labor supply in the consumer goods industry and in the housing sector

\[n _ {t} ^ {l} = [ \theta^ {\frac {1}{\varepsilon_ {n}}} (n _ {c t} ^ {l}) ^ {\frac {1 + \varepsilon_ {n}}{\varepsilon_ {n}}} + (1 - \theta) ^ {\frac {1}{\varepsilon_ {n}}} (n _ {h t} ^ {l}) ^ {\frac {1 + \varepsilon_ {n}}{\varepsilon_ {n}}} ] ^ {\frac {\varepsilon_ {n}}{1 + \varepsilon_ {n}}}\tag{A.3}\]

where is a weight parameter that relates with the disutility of working in the consumption sector relative to the housing sector, and afects the proportion of patient households working hours in each sector. is the elasticity of substitution between labor supply in the two sectors, capturing the easiness of movement between sectors ¹⁶.

As for the budget constraint, patient households lend in real terms − to impatient households (where is negative). They receive back from the previous period’s loans, where is the gross real interest rate factor. They invest in new productive capital in both sectors and and receive rents from capital and labor . Since they are the owners they receive profits, , from firms operating in non-competitive markets, and pay lump-sum taxes, , in terms of consumption goods.

Households incur investment adjustment costs where h denote the consumer goods production sector and housing sector. The law of motion of private

¹⁵We make the standard assumption that the flow of residential services is proportional to the stock of housing.

¹⁶For a full discussion of this CES function see Cardi & Restout (2015).

physical capital in both sectors is given by,

\[k _ {c t} ^ {l} = (1 - \delta^ {k c}) k _ {c t - 1} ^ {l} + \left[ 1 - \frac {\Phi^ {c}}{2} \bigg (\frac {j _ {c t} ^ {l}}{j _ {c t - 1} ^ {l}} - 1 \bigg) ^ {2} \right] j _ {c t} ^ {l}\tag{A.4}\]

\[k _ {h t} ^ {l} = (1 - \delta^ {k h}) k _ {h t - 1} ^ {l} + \left[ 1 - \frac {\Phi^ {h}}{2} \bigg (\frac {j _ {h t} ^ {l}}{j _ {h t - 1} ^ {l}} - 1 \bigg) ^ {2} \right] j _ {h t} ^ {l}\tag{A.5}\]

These households incur a cost of for the acquisition of new housing services in period t and for the depreciation of their housing stock. Living in house produces carbon emissions which may be subject to taxation by the government at a rate denoted as . Houses release carbon emissions into the atmosphere which are proportional to the housing stock, but abatement efort, denoted as , reduces emissions,

\[e _ {h t} ^ {l} = (1 - u _ {h t} ^ {l}) \varphi_ {1 h} (h _ {t} ^ {l}) ^ {1 - \varphi_ {2 h}}\tag{A.6}\]

The parameter represents the carbon emissions intensity per unit of dwelling services, indicating the fossil fuel usage by housing services. The elasticity, denoted as , relates to the energy eficiency of buildings. A higher exponent indicates lower eficiency, as the rate of growth of carbon emissions increases more significantly with the growth in residential services.

Each period, households have the option to invest in their houses to reduce a fraction of their emissions. However, this action entails a cost proportional to the amount and quality of their residential holdings,

\[z _ {h t} ^ {l} = \theta_ {1 h} (u _ {h t} ^ {l}) ^ {\theta_ {2 h}} h _ {t} ^ {l}\tag{A.7}\]

where and are technological parameters of the abatement cost function.

The solution to this optimization problem yields the following first-order conditions:

\[\lambda_ {t} ^ {l} = \frac {1}{c _ {t} ^ {l}}\tag{A.8}\]

\[\begin{array}{r} \lambda_ {t} ^ {l} q _ {t} = \frac {\gamma_ {h}}{h _ {t} ^ {l}} - \lambda_ {t} ^ {l} (\tau_ {h t} (1 - u _ {h t} ^ {l}) \varphi_ {1 h} (1 - \varphi_ {2 h}) (h _ {t} ^ {l}) ^ {- \varphi_ {2 h}} + \theta_ {1 h} (u _ {h t} ^ {l}) ^ {\theta_ {2 h}} + \\ + \beta^ {l} \mathbb {E} _ {t} (\lambda_ {t + 1} ^ {l} q _ {t + 1} (1 - \delta^ {h})) \end{array}\tag{A.9}\]

\[\frac {w _ {c t}}{c _ {t} ^ {l}} = (n _ {t} ^ {l}) ^ {\eta} (\theta \frac {n _ {c t} ^ {l}}{n _ {t} ^ {l}}) ^ {\frac {1}{\varepsilon_ {n}}}\tag{A.10}\]

\[\frac {w _ {h t}}{c _ {t} ^ {l}} = (n _ {t} ^ {l}) ^ {\eta} ((1 - \theta) \frac {n _ {h t} ^ {l}}{n _ {t} ^ {l}}) ^ {\frac {1}{\varepsilon_ {n}}}\tag{A.11}\]

\[\lambda_ {t} ^ {l} = \beta^ {l} \mathbb {E} _ {t} \lambda_ {t + 1} ^ {l} \frac {r _ {t}}{\pi_ {t + 1}}\tag{A.12}\]

\[\frac {\lambda_ {c t}}{\lambda_ {t} ^ {l}} = \beta^ {l} \mathbb {E} _ {t} \frac {\lambda_ {t + 1} ^ {l}}{\lambda_ {t} ^ {l}} \bigg [ r _ {t + 1} ^ {k} + \frac {\lambda_ {c t + 1}}{\lambda_ {t + 1} ^ {l}} (1 - \delta^ {k c}) \bigg ]\tag{A.13}\]

\[\frac {\lambda_ {h t}}{\lambda_ {t} ^ {l}} = \beta^ {l} \mathbb {E} _ {t} \frac {\lambda_ {t + 1} ^ {l}}{\lambda_ {t} ^ {l}} \bigg [ r _ {t + 1} ^ {h} + \frac {\lambda_ {h t + 1}}{\lambda_ {t + 1} ^ {l}} (1 - \delta^ {k h}) \bigg ]\tag{A.14}\]

\[\begin{array}{r} 1 = \frac {\lambda_ {c t}}{\lambda_ {t} ^ {l}} \bigg [ 1 - \Phi^ {c} \bigg (\frac {j _ {c t} ^ {l}}{j _ {c t - 1} ^ {l}} \bigg) \bigg (\frac {j _ {c t} ^ {l}}{j _ {c t - 1} ^ {l}} - 1 \bigg) - \frac {\Phi^ {c}}{2} \bigg (\frac {j _ {c t} ^ {l}}{j _ {c t - 1} ^ {l}} - 1 \bigg) ^ {2} \bigg ] + \\ + \beta^ {l} \Phi^ {c} \mathbb {E} _ {t} \frac {\lambda_ {c t + 1}}{\lambda_ {t + 1} ^ {l}} \frac {\lambda_ {t + 1} ^ {l}}{\lambda_ {t} ^ {l}} \bigg [ \bigg (\frac {j _ {c t + 1} ^ {l}}{j _ {c t} ^ {l}} - 1 \bigg) \bigg (\frac {j _ {c t + 1} ^ {l}}{j _ {c t} ^ {l}} \bigg) ^ {2} \bigg ] \end{array}\tag{A.15}\]

\[\begin{array}{r} 1 = \frac {\lambda_ {h t}}{\lambda_ {t} ^ {l}} \bigg [ 1 - \Phi^ {h} \bigg (\frac {j _ {h t} ^ {l}}{j _ {h t - 1} ^ {l}} \bigg) \bigg (\frac {j _ {h t} ^ {l}}{j _ {h t - 1} ^ {l}} - 1 \bigg) - \frac {\Phi^ {h}}{2} \bigg (\frac {j _ {h t} ^ {l}}{j _ {h t - 1} ^ {l}} - 1 \bigg) ^ {2} \bigg ] + \\ + \beta^ {l} \Phi^ {h} \mathbb {E} _ {t} \frac {\lambda_ {h t + 1}}{\lambda_ {t + 1} ^ {l}} \frac {\lambda_ {t + 1} ^ {l}}{\lambda_ {t} ^ {l}} \bigg [ \bigg (\frac {j _ {h t + 1} ^ {l}}{j _ {h t} ^ {l}} - 1 \bigg) \bigg (\frac {j _ {h t + 1} ^ {l}}{j _ {h t} ^ {l}} \bigg) ^ {2} \bigg ] \end{array}\tag{A.16}\]

\[u _ {h t} ^ {l} = \left(\frac {\tau_ {h t} \varphi_ {1 h}}{\theta_ {1 h} \theta_ {2 h} (h _ {t} ^ {l}) ^ {\varphi_ {2 h}}}\right) ^ {\frac {1}{\theta_ {2 h} - 1}}\tag{A.17}\]

Equation (A.9) represents the intertemporal condition for housing demand, requiring the lender to balance the marginal utility of current consumption against the marginal benefit of housing, ofset by the marginal costs resulting from carbon taxation. These costs arise as long as the government imposes a carbon price on housing emissions, negatively afecting housing demand. From the equation, it is clear that the marginal cost of an additional unit of housing consists of two environmental components: the costs associated with emissions , which depend on the carbon tax on residential emissions, and the costs associated with abatement in housing emissions . The marginal benefit of housing, typical in models `a la Iacoviello, stems from both the direct utility gain from an additional unit of housing and the expected utility from the possibility of increasing future consumption through the resale value of real estate holdings.

Equations (A.10) and (A.11) represent the labor supply of patient workers to the manufacturing and construction sectors, respectively. Equation (A.17) delineates the optimal abatement path and is influenced by the residential carbon tax and the housing stock. The optimal household abatement equates the cost savings from reduced emissions (left-hand side) to its marginal cost (right-hand side).

A.1.2 Impatient households

Impatient households are characterized by having a relatively high discount rate, so the inverse of the discount factor . Similarly to their patient counterparts, impatient household maximizes the following utility function,

\[\max _ {c _ {t} ^ {b}, h _ {t} ^ {b}, n _ {c t} ^ {b}, n _ {h t} ^ {b}, b _ {t} ^ {b}, u _ {h t} ^ {b}} \mathbb {E} _ {0} \sum_ {i = 0} ^ {\infty} (\beta^ {b}) ^ {i} \bigg (\ln c _ {t + i} ^ {b} + \gamma_ {h} \ln h _ {t + i} ^ {b} - \frac {(n _ {t + i} ^ {b}) ^ {1 + \eta}}{1 + \eta} \bigg)\tag{A.18}\]

where is borrowers’ real consumption, denotes borrower’s holding of housing units, and is a composite of labor supply to the consumption goods sector and to the housing sector represented by the following CES function,

\[n _ {t} ^ {b} = \left[ \theta^ {\frac {1}{\varepsilon_ {n}}} (n _ {c t} ^ {b}) ^ {\frac {1 + \varepsilon_ {n}}{\varepsilon_ {n}}} + (1 - \theta) ^ {\frac {1}{\varepsilon_ {n}}} (n _ {h t} ^ {b}) ^ {\frac {1 + \varepsilon_ {n}}{\varepsilon_ {n}}} \right] ^ {\frac {\varepsilon_ {n}}{1 + \varepsilon_ {n}}}\tag{A.19}\]

Impatient households become borrowers, so in addition to the budget constraint (A.20), they face a financial constraint on the maximum amount of credit they can obtain. In particular, expression (A.21) limits the amount of borrowing, , to a fraction κ of the expected resale value of housing held by household.

\[\begin{array}{r l r} & & {c _ {t} ^ {b} + q _ {t} (h _ {t} ^ {b} - (1 - \delta^ {h}) h _ {t - 1} ^ {b}) - b _ {t} ^ {b} + \tau_ {h t} e _ {h t} ^ {b} + z _ {h t} ^ {b} =} \\ & & {w _ {c t} n _ {c t} ^ {b} + w _ {h t} n _ {h t} ^ {b} - \frac {r _ {t - 1}}{\pi_ {t}} b _ {t - 1} ^ {b} - t r _ {t} ^ {b}} \end{array}\tag{A.20}\]

\[b _ {t} ^ {b} \leq \kappa \mathbb {E} _ {t} \frac {q _ {t + 1} \pi_ {t + 1} h _ {t} ^ {b}}{r _ {t}}\tag{A.21}\]

Similar to lenders, homes owned by borrowers emit carbon emissions through the combustion of fossil fuels used in cooking and heating and cooling systems. These emissions depends on total housing services and are subject to the same price making them costly. To mitigate the expenses incurred by residential carbon pricing policy, impatient households can opt for abate emissions, . The investment in emissions reduction incurs a cost , which is contingent upon their dwelling stock. The emission and abatement cost functions for borrowers are as follows,

\[e _ {h t} ^ {b} = (1 - u _ {h t} ^ {b}) \varphi_ {1 h} (h _ {t} ^ {b}) ^ {1 - \varphi_ {2 h}}\tag{A.22}\]

\[z _ {h t} ^ {b} = \theta_ {1 h} (u _ {h t} ^ {b}) ^ {\theta_ {2 h}} h _ {t} ^ {b}\tag{A.23}\]

The first order conditions derived from maximizing the utility function provide the equations governing consumption, housing investment, labor supply, borrowing, and emissions abatement for impatient households,

\[\lambda_ {t} ^ {b} = \frac {1}{c _ {t} ^ {b}}\tag{A.24}\]

\[\begin{array}{r} \lambda_ {t} ^ {b} q _ {t} = \frac {\gamma_ {h}}{h _ {t} ^ {b}} - \lambda_ {t} ^ {b} (\tau_ {h t} (1 - u _ {h t} ^ {b}) \varphi_ {1 h} (1 - \varphi_ {2 h}) (h _ {t} ^ {b}) ^ {- \varphi_ {2 h}} + \theta_ {1 h} (u _ {h t} ^ {b}) ^ {\theta_ {2 h}} + \\ + \beta^ {b} \mathbb {E} _ {t} (\lambda_ {t + 1} ^ {b} q _ {t + 1} (1 - \delta^ {h}) + \kappa \mu_ {t} ^ {b} q _ {t + 1} \pi_ {t + 1}) \end{array}\tag{A.25}\]

\[\frac {w _ {c t}}{c _ {t} ^ {b}} = (n _ {t} ^ {b}) ^ {\eta} \bigg (\theta \frac {n _ {c t} ^ {b}}{n _ {t} ^ {b}} \bigg) ^ {\frac {1}{\varepsilon_ {n}}}\tag{A.26}\]

\[\frac {w _ {h t}}{c _ {t} ^ {b}} = (n _ {t} ^ {b}) ^ {\eta} \bigg ((1 - \theta) \frac {n _ {h t} ^ {b}}{n _ {t} ^ {b}} \bigg) ^ {\frac {1}{\varepsilon_ {n}}}\tag{A.27}\]

\[\lambda_ {t} ^ {b} = \beta^ {b} \mathbb {E} _ {t} \lambda_ {t + 1} ^ {b} \frac {r _ {t}}{\pi_ {t + 1}} + \mu_ {t} ^ {b} r _ {t}\tag{A.28}\]

\[u _ {h t} ^ {b} = \left(\frac {\tau_ {h t} \varphi_ {1 h}}{\theta_ {1 h} \theta_ {2 h} (h _ {t} ^ {b}) ^ {\varphi_ {2 h}}}\right) ^ {\frac {1}{\theta_ {2 h} - 1}}\tag{A.29}\]

Equation A.25 is the inter-temporal condition for borrowers’ housing demand, indi cating that, similar to lenders, housing demand is negatively afected by emissions and abatement costs when environmental policies come into play. Housing demand for borrowers difers from that of lenders in the term , which represents the marginal utility of relaxing the borrowing constraint. This can be influenced by environmental policies through various means, such as the impact on the housing price or the tightness of the credit constraint , which introduces a diferential in the consumption and housing demand dynamics between impatient and patient households.

A.2 Aggregation

Since our economy is composed of two representative households, the value in per capita terms of the aggregate variables may be afected by the weight of each type of household, . Aggregate per capita values are calculated as follows.

Debt issued by borrowers is fully purchased by patient households

\[\tau^ {b} b _ {t} ^ {b} = - (1 - \tau^ {b}) b _ {t} ^ {l}\tag{A.30}\]

Private physical capital inn both sectors involve exclusively patient households

\[k _ {c t} = (1 - \tau^ {b}) k _ {c t} ^ {l}\tag{A.31}\]

\[k _ {h t} = (1 - \tau^ {b}) k _ {h t} ^ {l}\tag{A.32}\]

Net per capita investment is defined for each sector as

\[j _ {c t} = (1 - \tau^ {b}) j _ {c t} ^ {l}\tag{A.33}\]

\[j _ {h t} = (1 - \tau^ {b}) j _ {h t} ^ {l}\tag{A.34}\]

Aggregate per capita consumption and housing stock depends on the borrowers and lenders mix

\[c _ {t} = \tau^ {b} c _ {t} ^ {b} + (1 - \tau^ {b}) c _ {t} ^ {l}\tag{A.35}\]

\[h _ {t} = \tau^ {b} h _ {t} ^ {b} + (1 - \tau^ {b}) h _ {t} ^ {l}\tag{A.36}\]

Likewise, aggregate per capita residential emissions and total households abatement cost are defined as,

\[e _ {h t} = \tau^ {b} e _ {h t} ^ {b} + (1 - \tau^ {b}) e _ {h t} ^ {l}\tag{A.37}\]

\[z _ {h t} = \tau^ {b} z _ {h t} ^ {b} + (1 - \tau^ {b}) z _ {h t} ^ {l}\tag{A.38}\]

Total lump-sum transfers paid by households becomes,

\[t r _ {t} = \tau^ {b} t r _ {t} ^ {b} + (1 - \tau^ {b}) t r _ {t} ^ {l}\tag{A.39}\]

We also consider diferent measures of working hours. Aggregate hours per worker in the consumption goods sector

\[n _ {c t} = \tau^ {b} n _ {c t} ^ {b} + (1 - \tau^ {b}) n _ {c t} ^ {l}\tag{A.40}\]

Aggregate hours per worker in the housing sector

\[n _ {h t} = \tau^ {b} n _ {h t} ^ {b} + (1 - \tau^ {b}) n _ {h t} ^ {l}\tag{A.41}\]

Aggregate hours per worker in the economy

\[n _ {t} = \tau^ {b} (n _ {c t} ^ {b} + n _ {h t} ^ {b}) + (1 - \tau^ {b}) (n _ {c t} ^ {l} + n _ {h t} ^ {l})\tag{A.42}\]

A.3 Producers of Consumer Goods

In our model, we distinguish between two levels of production. At the top level, there is a competitive bundler that aggregates the output of intermediate-good firms , priced at , into a single composite product . Although we use the term ’consumer goods’ for simplicity, this composite product is sold to households for both consumption and investment purposes, as well as to the government.

Aggregation Technology We assume a constant returns to scale technology `a la Dixit & Stiglitz (1977) for the aggregation of the output, described by the following expressions for the aggregate production, the aggregate production price index (PPI), and the total demand for each variety:

\[y _ {t} = \left(\int_ {0} ^ {1} y _ {j t} ^ {\frac {\varepsilon - 1}{\varepsilon}} d j\right) ^ {\frac {\varepsilon}{\varepsilon - 1}}\tag{A.43}\]

\[P _ {t} = \left(\int_ {0} ^ {1} P _ {j t} ^ {1 - \varepsilon} d j\right) ^ {\frac {1}{1 - \varepsilon}}\tag{A.44}\]

\[y _ {j t} = \left(\frac {P _ {j t}}{P _ {t}}\right) ^ {- \varepsilon} y _ {t}\tag{A.45}\]

Production at the Firm Level At the bottom level, a continuum of firms indexed by produces a diferentiated good in a monopolistically competitive market. Each firm employs a uniform production technology, specifically a Cobb-Douglas production function, where physical capital ₋₁ and labor are the inputs:

\[y _ {j t} = (1 - D (x _ {t})) a _ {t} ^ {c} k _ {j t - 1} ^ {\alpha_ {c}} n _ {j c t} ^ {1 - \alpha_ {c}}\tag{A.46}\]

where represents a technological factor common across all firms. Following Heutel(2012), we introduce a negative externality where the stock of pollutants adversely afects productivity via the damage function:

\[D (x _ {t}) = d _ {0} + d _ {1} x _ {t} + d _ {2} x _ {t} ^ {2}\tag{A.47}\]

Emissions and Abatement Following Annicchiarico & Di Dio (2015), firms emit greenhouse gases (GHGs) as a byproduct of their production processes. The volume of emissions depends on the production level and the firm’s abatement eforts. Although emissions can be reduced, the associated cost is a function of the firm’s abatement efort relative to its output. The emissions and abatement cost functions for firm j at time t are modeled as follows:

\[e _ {j c t} = (1 - u _ {j c t}) \varphi_ {1 c} (y _ {j t}) ^ {1 - \varphi_ {2 c}}\tag{A.48}\]

\[z _ {j c t} = \theta_ {1 c} (u _ {j c t}) ^ {\theta_ {2 c}} y _ {j t}\tag{A.49}\]

Similarly to the case of housing services, in these equations, the parameter denotes the carbon intensity of production, quantifying emissions per unit of output. The exponent reflects the elasticity of emissions with respect to changes in output, indicating how emissions increase with a rise in production. For the abatement costs, represents the baseline cost of reducing emissions, while captures the degree of cost increase as the efort in abatement intensifies. These parameters are uniformly applied across all firms, consistent with the model’s assumption of homogeneous abatement technologies within the production sector.

A.3.1 Firm’s Optimization Problem

Intermediate-good firms, operating under monopolistic competition, adjust their pricing in response to the demand dynamics dictated by the final goods firm. Following Rotem berg (1982), firms incur a nominal adjustment cost when they deviate from the target inflation rate . This adjustment cost is influenced by the nominal production in the sector, represented by (with serving as the numeraire),

\[A C _ {j t} = \frac {\Phi_ {p}}{2} \left(\frac {P _ {j t}}{P _ {j t - 1}} - \bar {\pi}\right) ^ {2} P _ {t} y _ {t}\]

Firms aim to set optimal prices at period t that maximize their discounted expected profits, taking into account both the demand for their goods (A.45) and their technological capabilities (A.46). The optimization problem in real terms is formulated as:

\[\begin{array}{l} \max _ {P _ {j t}, n _ {j c t}, k _ {j c t - 1}, u _ {j c t}} \mathbb {E} _ {t} \sum_ {t = 0} ^ {\infty} (\beta^ {l}) ^ {t} \frac {\lambda_ {t} ^ {l}}{\lambda_ {0}} \left(\frac {P _ {j t}}{P _ {t}} y _ {j t} - w _ {c t + i} n _ {j c t + i} - r _ {t + i} ^ {k} k _ {j c t - 1 + i} - \right. \\ \left. \tau_ {c t} (1 - u _ {j c t}) \varphi_ {1 c} (y _ {j t}) ^ {1 - \varphi_ {2 c}} - \theta_ {1 c} (u _ {j c t}) ^ {\theta_ {2 c}} y _ {j t} - \frac {\Phi_ {p}}{2} \left(\frac {P _ {j t}}{P _ {j t - 1}} - \bar {\pi}\right) ^ {2} y _ {t}\right) \end{array}\]

The resulting first-order conditions dictate the optimal choices for capital, labor, abatement eforts, and pricing for each firm. In a symmetric equilibrium, where firms choose identical prices, inputs, and outputs, the conditions simplify as follows:

\[w _ {c t} = m c _ {t} (1 - \alpha_ {c}) \frac {y _ {t}}{n _ {c t}}\tag{A.50}\]

\[r _ {k t} = m c _ {t} \alpha_ {c} \frac {y _ {t}}{k _ {c t - 1}}\tag{A.51}\]

\[u _ {c t} = \left(\frac {\tau_ {c t} \varphi_ {1 c}}{\theta_ {1 c} \theta_ {2 c} (y _ {t}) ^ {\varphi_ {2 c}}}\right) ^ {\frac {1}{\theta_ {2 c} - 1}}\tag{A.52}\]

\[\begin{array}{r l} & {\pi_ {t} (\pi_ {t} - \bar {\pi}) = \beta^ {l} \frac {\lambda_ {t + 1} ^ {l}}{\lambda_ {t} ^ {l}} \pi_ {t + 1} (\pi_ {t + 1} - \bar {\pi}) \frac {y _ {t + 1}}{y _ {t}} +} \\ & {\qquad + \frac {\varepsilon}{\Phi_ {p}} \left[ \frac {1 - \varepsilon}{\varepsilon} + (1 - \varphi_ {2 c}) \tau_ {c t} \varphi_ {1 c} (1 - u _ {c t}) y _ {t} ^ {- \varphi_ {2 c}} + \theta_ {1 c} (u _ {c t}) ^ {\theta_ {2 c}} + m c _ {t} \right]} \end{array}\tag{A.53}\]

The variable denotes the Lagrange multiplier related to the production constraint common to all firms, and it reflects the incremental production costs associated with a unit increase in production (marginal cost).

Given a carbon tax on emissions from consumer goods production, equation (A.52) equates the value of the marginal product of abatement, , to its marginal cost, . In the absence of , firms have no incentive to abate emissions, and . This equation implies that the abatement efort is uniform across all firms; hence, emissions and abatement costs are also uniform and can be aggregated as follows:

\[e _ {c t} = (1 - u _ {c t}) \varphi_ {1 c} (y _ {t}) ^ {1 - \varphi_ {2 c}}\tag{A.54}\]

\[z _ {c t} = \theta_ {1 c} (u _ {c t}) ^ {\theta_ {2 c}} y _ {t}\tag{A.55}\]

With all firms using identical technology, aggregate production can be expressed as:

\[y _ {t} = (1 - D (x _ {t})) a _ {t} ^ {c} (k _ {c t - 1}) ^ {\alpha_ {c}} (n _ {c t}) ^ {1 - \alpha_ {c}}\tag{A.56}\]

Equation (A.53) represents the nonlinear New Phillips Curve, which links inflation to both current and future real marginal costs, with denoting the desired markup in equilibrium. In our environmental model, the marginal costs of producing an additional unit of output include , as well as costs related to pollution. In the absence of a carbon tax, the New Phillips Curve simplifies to the standard formulation.

Real profits for intermediate firms in a symmetric equilibrium are obtained using Equations (A.50) and (A.51), expressed as follows:

\[(1 - \tau^ {b}) d _ {t} = y _ {t} \left[ 1 - m c _ {t} - \tau_ {c t} (1 - u _ {c t}) \varphi_ {1 c} (y _ {t}) ^ {- \varphi_ {2 c}} - \theta_ {1 c} (u _ {c t}) ^ {\theta_ {2 c}} - \frac {\Phi_ {p}}{2} (\pi_ {t} - \bar {\pi}) ^ {2} \right]\tag{A.57}\]

A.4 Housing Construction Firms

There are many small firms owned by patient households that build identical houses in a perfectly competitive environment. The price of housing, , is perfectly flexible, and firms cannot influence it (see Monacelli et al. (2006) and Iacoviello & Neri (2010)). Construction firms produce houses using labor and capital according to a Cobb-Douglas function,

\[I H _ {t} = (1 - D (x _ {t})) a _ {t} ^ {h} (k _ {h t - 1}) ^ {\alpha_ {h}} (n _ {h t}) ^ {1 - \alpha_ {h}}\tag{A.58}\]

where is the steady-state technology factor common to all firms, and is the damage function that positively depends on the emissions stock, as defined in (A.47). The economic objective of the representative firm is to maximize profits subject to the production function

\[\max _ {n _ {h t}, k _ {h t - 1}} \sum_ {i = 0} ^ {\infty} \left(q _ {t + i} I H _ {t + i} - w _ {h t + i} n _ {h t + i} - r _ {t + i} ^ {h} k _ {h t - 1 + i}\right)\]

which yields the labor and capital demand in the construction sector,

\[w _ {h t} = q _ {t} (1 - \alpha_ {h}) \frac {I H _ {t}}{n _ {h t}}\tag{A.59}\]

\[r _ {h t} = q _ {t} \alpha_ {h} \frac {I H _ {t}}{k _ {h t - 1}}\tag{A.60}\]

Considering a constant depreciation rate for the stock of houses, the total supply of houses evolves according to,

\[h _ {t} = I H _ {t} + (1 - \delta^ {h}) h _ {t - 1}\tag{A.61}\]

A.5 Policy

The European authority sets carbon pricing for both the residential and production sectors, denoted as and respectively, in line with EU carbon emissions reduction targets. It collects carbon revenues and decides whether to allocate them to lump-sum tax reductions. We assume that the government maintains a constant and exogenous per capita level of consumption . In the absence of any environmental policy, public consumption is entirely financed through lump-sum taxes , which are initially distributed equally on a per capita basis between lenders and borrowers. When carbon taxes are introduced, government consumption are financed by lump-sum taxes and carbon revenues.

\[\bar {g} = t r _ {t} + \tau_ {h t} e _ {h t} + \tau_ {c t} e _ {c t}\tag{A.62}\]

Monetary policy is managed by the European Central Bank following a Taylor’s interest rate rule that respond to deviations of euro-zone inflation from its long-run target

(π = 1). The rule takes the form:

\[r _ {t} = \bar {r} ^ {1 - \rho} (r _ {t - 1}) ^ {\rho} (\pi_ {t}) ^ {\psi (1 - \rho)}\tag{A.63}\]

where is the steady state level of the gross interest rate, is a parameter that controls the persistence of the interest rate and represents the weight given by the ECB to inflation targeting.

A.6 Pollution Dynamics

The economic losses resulting from climate change are incorporated through the damage function (A.47), which reduces productivity in both sectors and thus dampens total production. The damage function captures the relationship between the level of carbon in the atmosphere and economic damages, measured as a percentage of final-good output. In addition, to include the reverse efects, i.e., the impact of economic activity on emissions and carbon accumulation in the atmosphere, we adopt a simplification based on models such as those of Heutel(2012) and Annicchiarico & Di Dio (2015), which assume that the concentration of carbon in the atmosphere follows the following process:

\[x _ {t} = (1 - \delta^ {x}) x _ {t - 1} + e _ {c t} + e _ {h t} + e ^ {r o w}\tag{A.64}\]

where, in each period, emissions from production of consumer goods, , and from combustion of fossil fuels in houses, , feed the stock of carbon. Additionally, we assume that emissions from the rest of the world, , also impact productivity in the European region and remain constant. The parameter measures the fraction of carbon that naturally decays in each time period.

A.7 Total Resource Constraint

The aggregation of household budget constraints leads to

\[\begin{array}{r} c _ {t} + t r _ {t} + q _ {t} (h _ {t} - (1 - \delta^ {h}) h _ {t - 1}) + j _ {c t} + j _ {h t} + \tau_ {h t} e _ {h t} + \tau^ {b} z _ {h t} ^ {b} + \\ (1 - \tau^ {b}) z _ {h t} ^ {l} = w _ {c t} n _ {c t} + w _ {h t} n _ {h t} + (1 - \tau^ {b}) d _ {t} + r _ {k t} k _ {c t - 1} + r _ {h t} k _ {h t - 1} \end{array}\]

Using the equality between production and income in both sectors¹⁷ and considering the fiscal budget condition (A.62) while defining total aggregate production as the sum of consumer goods production and housing production, , the resource constraint of the economy can be expressed as:

¹⁷The equality between production and income in consumption goods sector is given by and in house construction sector by

\[\tilde {y} _ {t} ^ {A} = c _ {t} + \bar {g} + q _ {t} (h _ {t} - (1 - \delta^ {h}) h _ {t - 1}) + j _ {c t} + j _ {h t} + z _ {c t} + z _ {h t} + \frac {\Phi_ {p}}{2} (\pi_ {t} - \bar {\pi}) ^ {2} y _ {t}\tag{A.65}\]

GDP can be expressed as:

\[G D P _ {t} = c _ {t} + \bar {g} + q _ {t} (h _ {t} - (1 - \delta^ {h}) h _ {t - 1}) + j _ {c t} + j _ {h t}\tag{A.66}\]

These equalities highlight the inherent limitations within the economy, indicating that all available resources are allocated to production, which in turn is used for consumption, investment, housing production, and to cover the costs associated with emissions abate ment and price adjustments. Therefore, our model explores how environmental policies, particularly those aimed at reducing carbon emissions, afect resource allocation across the economy. Specifically, the resources allocated to mitigate the environmental impacts of carbon emissions are represented by abatement costs in both production and housing . As the government implements carbon pricing policies to curb emissions, a significant portion of the economy’s resources is redirected towards investments in emissions reduction. This shift within the resource constraints leads to a decrease in both investment and consumption and, hence, on GDP.

Table B.1: Endogenous variables

Real wage in consumption goods sector Real wage in housing sector Labor supply to the consumption goods sector Labor supply to the housing sector Labor supply Consumption Total supply of houses Aggregate physical capital in manufacturing Aggregate physical capital in construction Aggregate investment in manufacturing Aggregate investment in construction Consumption goods production Emissions in production Abatement in manufacturing Abatement cost in manufacturing Gross domestic product Total aggregate production Real profits Marginal cost Residential investment Real housing price Domestic CPI inflation Nominal interest rate Rental rate of physical capital in production Rental rate of physical capital in construction Atmospheric carbon stock

Table B.2: Exogenous variables

Table B.3: General Parameters

Table B.4: Environmental parameters