Carbon tax effects on the poor: a SAM-based approach

For several years, climate change and global warming have worried society and policymakers worldwide. The international organizations and governments have conducted policies and actions to reduce greenhouse gas (GHG) emissions. The most abundant long-lived greenhouse gases are carbon dioxide (CO₂), methane (CH₄) and nitrous oxide (N₂O), which are closely linked to human activities. According to the World Meteorological Organization (WMO), a specialized agency of the United Nations, CO₂ is the anthropogenic GHG that contributes the most to radiative forcing⁴, with 65% of the total. Atmospheric CO₂ has risen primarily from combustion of fossil fuels. So, a proposal to reduce CO₂ emissions is to apply a tax on the production of fossil fuels.

Different environmental issues, related to this topic, have been analyzed with multisectorial models. For instance, Perese (2010) and Siriwardana et al (2011) study the effect of a carbon tax, per metric ton of CO₂ emissions, in the United States and Australia, respectively. Perese (2010) uses an input–output price model in order to estimate the effect of a $20 tax per metric ton of CO₂ emissions, the tax is levied on the use of coal, oil and natural gas. He finds that sectors such as natural gas distribution, electricity and gasoline, report the highest price increments following the tax implementation, close to 10%, and the other sectors experience a rise in prices of around 1%. Siriwardana et al (2011) use a static and neoclassical general equilibrium model, focusing on the energy sector and using households classified by income. In the baseline simulation, the carbon tax decreases GDP by 0.68% and raises the consumer price index by 0.75%. Almost all sectors show production decrements, especially brown coal and electricity-brown coal industries. In contrast, the electricity renewable industry manifests an increment in production. Furthermore, it was found that the tax is regressive, meaning that it imposes a greater burden on the poorer households than on the richer ones.

Yusuf and Resosudarmo (2007) present an exhaustive bibliography on CGE models with households' disaggregation to analyze an impact of carbon tax, the literature is divided into analysis of developed countries where the carbon tax is found to be regressive, and few analysis of developing countries where there is a variety of results. For example, a carbon tax in Philippines slightly increases poverty, and in Pakistan is regressive, whereas in China the results are driven by the urban and rural strata, where the carbon tax is progressive given that the higher income households in the urban areas make use of fossil fuels while lower income household in rural areas use firewood. The authors state that there is the need to analyze developing countries using CGE models that consider substitutability between fossil fuel and other energy commodities, and different schemes of expending government revenue; they calibrate a CGE Model for Indonesia with rural and urban households, and found that tax regressivity is fixed if the government gives back the collected tax as a uniform cut on commodities tax rate, or using uniform transfers to households. Rausch et al (2011), use a general equilibrium model implementing a $20 USD carbon tax per ton, and analyze the effect of three different government expenditure policies to reverse the regressive effects of this tax. First, revenue is used to lower marginal income tax rates, the second policy distributes revenues in an equal per capita basis, and the third in an equal per capita income. The first and second revenue recycling do not solve the regressivity, and the third could diminish it if the main source of income of the lower income households is government transfers because they are neutral to carbon tax; while carbon tax affects wages and capital income, which is mainly the income source of middle and upper income households.

Gemechu et al (2012) employ an input-output model for estimating GHG emission intensities by economic sector for Spain. They calculate environmental tax rates by sectors, based on the estimations of both CO₂ and total GHG emissions. The highest environmental tax rate in both cases is for the cement industry.

Regarding the works that have been made for Mexico, Castillo (2010) and Bravo et al (2013) built general equilibrium models in order to analyze different alternatives to reduce CO₂ emissions. Castillo (2010) studies the economic effects of a tax in the energy sector, especially for the activities: coal and its derivatives; oil extraction; oil refining; and electricity, gas and water. The results indicate that extraction of petroleum and gas sector is the most affected in all the simulations, besides, the reduction in emissions is accompanied with a decrease in the consumer welfare and the GDP. Bravo et al (2013) analyze the economic and redistributive effects of environmental taxes on the energy inputs. Taxes are simulated for each energy sector and for all together. There are two assumptions about the elasticity of substitution between energy and other inputs: when it is rigid and when it is flexible. The results vary with each case, but in general, with this policy there are no important redistributive effects.

Another work, using multi-sectorial models for Mexico, was developed by Chapa and Ortega (2017), in which they identify the economic activities that are CO₂ direct emitters and those that are final users of highly CO₂ polluting products. The main results show that construction, electricity, gas and water supply, inland transport and food, beverages and tobacco are the major generators of CO₂ emissions through their intermediate consumption. Furthermore, they estimate the CO₂ emissions multipliers of the economy, finding that the sector of water transport generates the highest emissions with an exogenous monetary injection; while among household types, the food poverty families in the urban areas show the highest emissions multiplier.

In this work, we developed a social accounting matrix (SAM)-based price model (see Roland-Holst and Sancho 1995) for Mexico in order to analyze the effects of a carbon tax on production costs and welfare. The model permits to assess the impact on the consumer price indexes and consumption by household type, classified according to poverty condition and strata.

With respect to public policy, it is quite important to analyze the incidence of the carbon tax according to the poverty condition of households. Poor families account for 55.1% of the population of Mexico, from which the geographical division accounts for 50.6% of the population in urban areas and 62.7% in rural areas. A carbon tax which affects transport and fuel in rural areas would affect most of the population whose budget is mostly expend on commodities and services that will be affected by the tax. In the case of urban areas, private transport and services may be the direct channel to which the household budget will be affected.

Mexico, due to its geographical location and economic development, is very vulnerable to the effects of climate change, particularly impacted by the climatic phenomena. Mexico's population vulnerability is found in the isolated rural communities as well as those that are living in the heavily populated cities. A significant global increment of temperature (+2 °C) will endanger the lives of thousands of people, their welfare and property, and limit the opportunities of development in the short and long terms.

'From 1999 to 2011 the human losses and economic damage derived from hydro meteorological phenomena are estimated in an annual average of 154 deaths and $21 368 million pesos. It is also estimated that the cumulative cost of climate change for this century may be between 3.2% and 6% of the gross domestic product.' (SEMARNAT 2012). With this perspective, it is important to strengthen measures to mitigate GHG emissions in order to reduce the consequences of its impacts. Carbon Tax represents an important measure that discourages the use of fossil fuels. The tax rate, which was enacted since 2014, is estimated according to the official information of Mexican government for sectors producing fossil fuels. Mexico is ranked 12 among all countries contributing to global emissions, it contributes only with 417 metric ton (Mton) CO₂ which represent 1.4% of global emissions of CO₂ derived from burning fossil fuels, according to (IEA 2012). The principle of the international agreement signed in Paris is precisely that all countries have to contribute to decrease carbon tax independently of their current emissions levels. Therefore, even though the impact as a country alone is low, actions per country contribute to the global reduction.

The main results suggest that, the highest impacts on prices are in the sectors of coke, refined petroleum and nuclear fuel; air transport; and inland transport. The rural households are more affected by the carbon tax than the urban ones, this is because rural families spend a higher proportion of their income on the final goods that show price increment. With respect to the distributional effects of the carbon tax, it is found that the tax is regressive in urban strata.

The document is delineated as follows. Section 2 describes the carbon tax applied in Mexico and the way in which the official carbon tax per unit are converted into tax rates applied on production. In section 3 the model is specified. In section 4 the results are discussed. The conclusions are presented in section 5.

In 2014 the Mexican Congress approved a fiscal reform that includes a carbon tax on CO₂ emissions from manufacturing, selling and burning fossil fuels in order to discourage activities which harm the environment, improve air quality and reduce respiratory illness. The justification for this tax was to internalize the social cost of the negative externalities of CO₂ emissions from fossil fuels and incentive the use of clean renewable energies. The carbon taxes are applied to fossil fuels sales, expressed in monetary units per litre or tons. The tax in pesos per unit applied in 2014 and 2015 are shown in table 1.

In order to convert the taxes per unit into tax rates applied on the output of the sectors that sell the taxed fossil fuels, we use the GHG emissions of the Mexican WIOD Release 2013 from European Commission, which involves energy use by sector and energy commodity for 40 countries for the period 1995–2009, Mexico is among these countries⁵.

The WIOD 2013 Release allows the identification of the consumption of diesel, gasoline, jet fuel, coke and coal of the Mexican economy in 2008. These data are presented in Tera joules, therefore, in order to calculate the carbon tax base, we transform the consumption of diesel, gasoline and jet fuel from Tera joules to litres and, the use of coke and coal from Tera joules to tons, based on its high heating value (HHV) and density (Dens)⁶. This is done by applying the conversions described by equations (1) to (3)

$$\begin{equation} EC_{Kg}^{FF} = {{EC_{Tj}^{FF} *1000000} \over {HHV_{Mj/Kg}^{FF} }} \end{equation} \tag{ 1 }$$

$$\begin{equation} EC_{Tons}^{FF} = {{EC_{Kg}^{FF} } \over {1000}} \end{equation} \tag{ 2 }$$

$$\begin{equation} EC_{Lts}^{FF} = {{EC_{Kg}^{FF} *1000} \over {Dens_{Gr/Lts}^{FF} }} \end{equation} \tag{ 3 }$$

where:

• $EC_{Tj}^{FF}$ = consumption of fossil fuel FF expressed in Tera joules
• $HHV_{Mj/Kg}^{FF}$ = high heating value of fossil fuel FF expressed in Megajoules per Kilogram
• $EC_{Kg}^{FF}$ = consumption of fossil fuel FF expressed in kilograms
• $EC_{Tons}^{FF}$ = consumption of fossil fuel FF expressed in metric tons
• $Dens_{Gr/Lt}^{FF}$ = density of fossil fuel FF expressed in grams per liter
• $EC_{Lt}^{FF}$ = consumption of fossil fuel FF expressed in liters.

The converted taxes applied in 2014 to 2008 constant prices are shown in tables 2 and 3.

Then, we compute the potential carbon tax collection for each fossil fuel (CTRec^FF ) by multiplying the tax in 2008 constant prices (table 3) and the consumption in 2008 by fossil fuel (table 2), and converting into millions of pesos, using equations (4) and (5)

$$\begin{equation} {\mathop{\rm Re}\nolimits} vCTax^{FF} = {{EC_{Tons}^{FF} *Tax_{Pesos/Tons}^{FF} } \over {1000000}} \end{equation} \tag{ 4 }$$

for coal and coke.

$$\begin{equation} RevCTax^{FF} = {{EC_{Lt}^{FF} *Tax_{Cents/Lt}^{FF} } \over {100000000}} \end{equation} \tag{ 5 }$$

for diesel, gasoline and jet fuel.

The sectoral detail used in the SAM base of the model follows the WIOD 2013 Release⁷. Coal is classified into the WIOD sector 'Mining and Quarrying'; and the coke, refined oils and nuclear fuel are aggregated in the WIOD sector 'Coke, Refined Petroleum and Nuclear Fuel'. Therefore, the potential carbon tax collection caused by the consumption of coal is expressed as a percentage of gross output of the sector mining and quarrying; and the potential carbon tax collection caused by the consumption of refined oils and coke as a percentage of gross output of the sector coke, refined petroleum and nuclear fuel⁸. These calculations are contained in table 4. Note that the carbon tax is equal to a tax rate of 0.03% on mining and quarrying's gross output and a tax rate of 0.5% on coke, refined petroleum and nuclear fuel's gross output.

A SAM-based price model is formulated to measure the effects of a carbon tax on the sectors that produce fossil fuels. The model considers 37 economic activities according to NACE; eight types of households, classified by poverty condition and geographical area; three labour types differentiated by schooling levels; two capital types, private and public; a general government; and an aggregate of the rest of the world. The description of these classifications can be consulted in the annex 1. In general, it is assumed Leontief production functions for the economic activities, and the Cobb–Douglas utility function for the preferences of households and government. Therefore, price elasticity of demand for each final product is unitary. The model specification is contained in the annex 2.

The poverty condition of the household is based on their income to buy goods and services. The food poverty accounts for the people that even when expending all their money cannot buy the food basket (20.5%), whereas the capabilities poverty considers the food basket plus health and education services (29.1%). The patrimony poverty considers the food basket, health, education and transport services, plus house and dressing (53.2%). If we alienate each type of poverty, we have that food poverty includes 20.5% of the population, capability poverty only is 8.6% of the population, and patrimony poverty is 24.1% of the population in Mexico for the year 2014 (table 5).

Also, in this type of model, two main assumptions are built: (i) a price shock on an industry i can be completely and instantaneously transmitted to downstream industries; therefore, the effects could be overestimated; (ii) the technical coefficients are fixed, so the cost reduction efforts made by manufacturers through technology change are not taken into account.⁹ The model parameters are calculated with the method known as calibration, based on the SAM made by Chapa and Ortega (2017) for the Mexican economy, with reference to the year 2008¹⁰. This method assumes that the SAM represents a benchmark equilibrium, where initial prices are equal to one, so that the model replicates the data of the SAM. Figure 1 presents a schedule of the effects that the model allows to calculate and analyze. The carbon tax increases the unit costs and prices of mining and petroleum products, directly; then the unit costs and prices of the downstream industries also rise; goods prices and wages in rural and urban strata increase; the wages increment is transmitted to unit costs and prices; then, there are two contrary effects on household's consumption demands, the wage increment (positive) and the goods prices increment (negative); finally, the tax collection increases and therefore the public income and expenditure (surplus is fixed)¹¹.

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The simulation takes into account two opposite carbon tax effects on consumption, saving and welfare: the price effect related to rising products and services prices (negative) and the income effect associated to wages increment (positive). The carbon tax implies a direct increment of 0.03% on the mining and quarrying's unit cost and an increase of 0.5% on the coke, refined petroleum and nuclear fuel's unit cost.

4.1. Price effect

4.2. Income effect

4.3. Impact on consumption, saving and welfare

4.4. Impact on government revenue and expenditure

In this work a SAM-based price model was built for the Mexican economy, in order to assess the impact of a carbon tax on production cost, consumer prices, household consumption and government revenue. There is no antecedent of any model of this kind that considers households by the official poverty condition and geographical area.

According with the tax law approved by the Mexican Congress for the CO₂ emissions from manufacturing, selling and burning fossil fuels, the tax rates estimated for this model are 0.5% for the coke, refined petroleum and nuclear fuel sector, and 0.03% for the sector of mining and quarrying.

The highest rise in price is for the sector 'coke, refined petroleum and nuclear fuel', due to the direct impact of the tax; but by indirect effect, the most affected sectors are air transport and inland transport; because of their close relationship with the former sector.

The carbon tax effect on consumption and welfare by household poverty condition differs by strata. In the rural strata, it is not a defined pattern. However, in the urban strata, the carbon tax is regressive, consumption and welfare reductions are higher as the household income decreases. This is caused by the household expenditure pattern: expenditure share in inland transport and petroleum products, services and products that show larger price increments, are higher as the household income decreases.

Given the importance that public transportation has on the expenditure share of the poor households, and it is part of one feature of passing from capability to patrimonial poverty, it will be a twofold beneficial public policy to transfer subsidies for those transport services using clean energies and it will operate like a subsidy for the poor and non-poor households when they use clean energy services. The carbon tax revenues that Mexico can raise from carbon pricing could be used to reduce poverty, over and above reducing the policy's regressive impact on low-income groups. Future analysis should be done using CGE models like Yusuf and Resosudarmo (2007), to account for different model simulations where alternative means to recycle carbon tax revenue is allowed; for the time being we have advanced in this area of study by first performing an analysis using an I-O model, then the current paper uses a SAM-based price model and further research will incorporate a CGE analysis.

Therefore, this research contributes to the discussion with its regressive thesis which is contrary to Boyd and Ibarrarán (2002) who found progressive effects on welfare, Bravo et al (2013) who found non-redistributive effects, and Ibarrarán et al (2011) who found a U shape in costs for four different types of households.

The results of this research are conditioned to the following assumptions: there is no substitution between fossil fuels and renewable resources and price elasticity demand is unitary. However, substitutability of fossil fuel by renewable energy seems unlikely in Mexico in the short term. By the end of 2014, the installed capacity of renewable energies reached 25% (16 240 MW) and the generation of renewable energy and efficient co-generation represented 18% (55 003 GWh) of the total (SENER 2015). Investment in technologies for renewable energy will be possible in near future with more transparent regulation given that in the administrative period of 2006–2012, three regulatory instruments were published, creating the legal framework for the use of renewable energy: the Law for Sustainable Use of Energy, the Law for the Use of Renewable Energies and for the Financing of Energy Transition, and the Law for the Promotion and Development of the Bioenergy.

In the future, any development on our model could be improved with a new disaggregation, currently coal is included in the sector 'Mining and Quarrying', and this has low weight in the gross output of the sector, therefore, the carbon tax effects associated to coal production could be overlooked, particularly, in the sector of other non-metallic minerals where the cement production is classified. Coal is not employed in electricity generation in Mexico. However, at least in qualitative terms, the model achieves to capture the main economic sectors that are fossil fuels intensive such as transport services, electricity and other non-metallic minerals.

We thank the research assistance of Erika Casamadrid and Esther Santos.

A2.1. Unit cost functions: prices

The SAM-based price model assumes that each sector or economic activity produces only a good or a service using a Leontief technology, with constant returns to scale, that employs in fixed proportions other goods or services (domestic or imported), as well as primary factors (labour and capital). The production function is:

$$\begin{equation} Y_j = Min\left( {{{X_{ij} } \over {a_{ij} }},{{M_j } \over {m_j }},{{LA_{lj} } \over {la_{lj} }},{{KA_{kg} } \over {ka_{kj} }}} \right) \end{equation}$$

where Y_j is the total production of the economic activity j; X_ij is the expenditure made for the sector j to buy inputs from the sector i; M_j is the imports of the sector j; L_lj are the remunerations paid by sector j to the type of work l; K A_kj is the capital payment made by sector j to the type of capital k; a_ij is the percentage of the total production dedicated by the sector j to get inputs from the sector i, also known as technical coefficient; m_j is the production percentage of sector j used to buy foreign goods (technical coefficients associated to imports); la_lj is the production proportion of sector j employed for paying to the type of work l; and ka_kj the production proportion of sector j dedicated to pay to the type of capital k.

According with these assumptions, the profits earned by each economic activity are zero, so that the price of the goods sold by sector j is equal to the unit cost after taxes, see equation (6)

$$\begin{equation} PY_j = {{\left( {\sum\limits_{i = 1\forall i \ne j}^{37} {a_{ij} *PY_i + m_j *(PM_j + TM_j ) + (1 + TSB_j + TPN_j )*\sum\limits_{e = 1}^2 {\sum\limits_{l = 1}^3 {la_{lj} *W_e *n_{el} + \sum\limits_{k = 1}^2 {ka_{kj} *R} } } } } \right)*(1 + TPS_j + CTax_j )} \over {(1 - a_{ij\forall i = j} *(1 + TPS_j + CTax_j ))}} \end{equation} \tag{ 6 }$$

where TPS_j is the net tax rate on products for sector j; CTax_j is the carbon tax on gross output of sector j; PM_j is the aggregate price of imported goods of sector j (it is considered exogenous); TM_j is the import tariff rate paid by sector j; W_e is the wage for the area e (rural or urban); n_el is the l type work proportion in the area e; TSB_j is the rate of employer contribution paid by sector j; TPN_j is the net tax on production; and R is the capital yield.

On the other hand, the wage W_e , described by equation (7), for the area e is indexed to the consumer price index CPI_e of the area e:

$$\begin{equation} W_e = 1 + g_e *\Delta CPI_e \end{equation} \tag{ 7 }$$

where g_e indicates the degree which wages are indexed, taking a value between 0 and 1 (0 when the wage is exogenous to the model and 1 when it is endogenous); and ∆CPI_e is the change in the consumer price index of the area e.

The consumer price index CPI_e for the area e is calculated with the prices of the final goods, using equation (8)

$$\begin{equation} CPI_e = \sum\limits_{j = 1}^{37} {\vartheta _{ej} *PY_j } \end{equation} \tag{ 8 }$$

where ϑ_ej is the percentage that final good j represents from the total consumption of area e.

At the benchmark equilibrium all prices are equal to one: the goods prices, the price of imported goods, the wages, and the yield of capital.

A2.2. Consumption demands

Households make their decisions of consumption and savings following a process of optimization in three levels. In all the levels, the households preferences are represented by Cobb–Douglas utility functions, that are homogeneous of degree one. First, households determine the aggregate consumption and saving that maximize their utility, subject to their disposable income. The consumer problem is the following:

$$\begin{equation} MaxHC_h^{\gamma _H } S_h^{(1 - \gamma _h )} \end{equation}$$

$$\begin{equation} \matrix{ {s.a.DI_h } \hfill & = \hfill & {PHC_h *(1 + VAT_h + TPSH_h )*HC_h } \hfill \cr {} \hfill & {} \hfill & { + PS*S_h } \hfill \cr } \end{equation}$$

where HC_h is the aggregate consumption of household h; VAT_h is the value added tax rate that each household h pays; TPSH_h is the tax rate on products paid by household h; S_h is the saving of household h; PHC_h is the price of aggregate consumption of household h; PS is the price of saving and; DI_h is the disposable income of household h.

Therefore, the optimal levels of consumption in equation (9) and savings in equation (10) are in function of the prices and the disposable income:

$$\begin{equation} HC_h = {{\gamma _h *DI_h } \over {PHC_h (1 + VAT_h + TPSH_h )}} \end{equation} \tag{ 9 }$$

$$\begin{equation} S_h = {{(1 - \gamma _h )*DI_h } \over {PS}}. \end{equation} \tag{ 10 }$$

On the other hand, the price of savings depends on the percentage of private investment assigned to each economic activity (ϕ_j ) and the sectoral prices (PY_j ) calculated using equations (11):

$$\begin{equation} PS = \sum\limits_{j = 1}^{37} {\phi _j *PY_j } \end{equation} \tag{ 11 }$$

where $\sum\limits_{j = 1}^{37} {\phi _j = 1}$.

While the disposable income also can be expressed as a function of the factor payments, as in equation (12), which are taxable; the government transfers and the foreign transfers:

$$\begin{equation} \matrix{ {DI_h } \hfill & = \hfill & {(W_e *LH_h + R*KH_h )*(1 - TIN_h )} \hfill \cr {} \hfill & {} \hfill & { + Trans_h + Rem_h } \hfill \cr } \end{equation} \tag{ 12 }$$

where LH_h is the labour endowment of the household h; W_e is the wage of strata e, households 1 to 4 are in the rural strata and the remaining in the urban strata; KH_h is the capital endowment of household h; R is the capital yield; TIN_h is the income-tax paid by the household h; Trans_h are the government transfers to household h; and Rem_h are the remittances to household h.

In the second level of the optimization process, households choose how much to consume in domestic and foreign goods, subject to the aggregate consumption determined in the previous step. The optimization problem is the following:

$$\begin{equation} Max\;d_h DC_h^{\beta _h } MH_h^{(1 - \beta _h )} \end{equation}$$

$$\begin{equation} \matrix{ {s.a.\;HC_h } \hfill & = \hfill & {GPI_h *DC_h } \hfill \cr {} \hfill & {} \hfill & { + PMC*(1 + TMC_h )*MH_h } \hfill \cr } \end{equation}$$

where DC_h is the domestic consumption of household h; MH_h are the total imports of household h; d_h is the Cobb–Douglas utility function coefficient; GPI_h is the price of domestic consumption; PMC is the price of imports of consumption goods, that is exogenous; and TMC_h is the import tariff paid by household h.

Then, the optimal levels of domestic consumption and imports depend on their prices and the aggregate consumption, see equations (13) and (14) respectively:

$$\begin{equation} DC_h = {{\beta _h *HC_h *PHC_h } \over {GPI_h }} \end{equation} \tag{ 13 }$$

$$\begin{equation} MH_h = {{(1 - \beta _h )*HC_h } \over {PMC*(1 + TMC_h )}}. \end{equation} \tag{ 14 }$$

The price of aggregate consumption (PHC_h ) results from introducing the optimal levels of domestic consumption and imports into the unit consumption expenditure function of equation (15)

$$\begin{equation} PHC_h = \left( {{1 \over {d_h }}} \right)*\left( {{{GPI} \over {\beta _h }}} \right)^{\beta _h } *\left[ {{{PMC*(1 + TMC_h )} \over {(1 - \beta _h )}}} \right]^{(1 - \beta _h )} \end{equation} \tag{ 15 }$$

In the third level of the optimization process, households decide how much they consume of each final good, maximizing their utility, given the prices of final goods (PY_j ), subject to the domestic consumption chosen before:

$$\begin{equation} Max\;b_h \prod\limits_{j = 1}^{37} {GC_{jh} \alpha _{jh} } \end{equation}$$

$$\begin{equation} s.a.DC_h = \sum\limits_{j = 1}^{37} {PY_j *GC_{jh} } \end{equation}$$

where $\sum\limits_{j = 1}^{37} {\alpha _{jh} = 1}$, and b_h is the coefficient of the Cobb–Douglas function. Besides, GC_jh is the household h consumption of good j and; DC_h is the domestic consumption of household h.

So the optimal level of domestic consumption of good j is calculated using equation (16)

$$\begin{equation} GC_{jh} = {{\alpha _{jh} *DC_h *GPI_h } \over {PY_j }}. \end{equation} \tag{ 16 }$$

In order to estimate the price of domestic consumption of household h (GPI_h ), which is a kind of consumer price index, the optimal levels of GC_jh are introduced into the unit domestic consumption expenditure function as in equation (17)

$$\begin{equation} GPI_h = {1 \over {b_h *\prod\limits_{j = 1}^{37} {\left( {{{\alpha _{jh} } \over {PY_j }}} \right)^{\alpha _{jh} } } }}. \end{equation} \tag{ 17 }$$

It can be noted that the consumption side is linked to the production side through the prices of final goods, the wages, and the return on capital.

A2.3. Government consumption and public finances

The government behaves like any other consumer in the model. It follows a process of optimization in two levels, and its preferences are represented by a Cobb–Douglas utility function, that is homogeneous of degree one. In the first level, it determines domestic consumption and imports, subject to the total spending in goods and services. The government maximization problem is the following:

$$\begin{equation} Max\;DGvC^\varepsilon \;MG^{(1 - \varepsilon )} \end{equation}$$

$$\begin{equation} s.a.\;TGvC = PGovC*DGvC + PMC*MG \end{equation}$$

where DGvC is the government spending in domestic goods and services; MG are the imports; TGvC is the total spending in goods and services; PGovC is a weighted average price which is compound of domestic goods and services prices that the government consumes; and PMC is the price of imports.

The optimal levels of government domestic consumption and imports are a function of the prices and the total spending in goods and services are calculated using equation (18) and (19):

$$\begin{equation} DGvC = {{\varepsilon *TGvC} \over {PGovC}} \end{equation} \tag{ 18 }$$

$$\begin{equation} MG = {{(1 - \varepsilon )*TGvC} \over {PMC}}. \end{equation} \tag{ 19 }$$

In the second level, the government maximizes its utility by deciding how much consume of every domestic good/service, subject to government domestic consumption obtained before:

$$\begin{equation} Max\;f\prod\limits_{j = 1}^{37} {GovC_j^{\delta _j } } \end{equation}$$

$$\begin{equation} s.a.\;DGvC = \sum\limits_{j = 1}^{37} {PY_j *GovC_j } \end{equation}$$

where $\sum\limits_{j = 1}^{37} {\delta _j = 1}$, and f is the coefficient of the Cobb–Douglas function. In addition, GovC_j is the government consumption of final good j.

Then, using equation (20), the optimal level of government consumption in good j is:

$$\begin{equation} GovC_j = {{\delta _j *DGovC} \over {PY_j }}. \end{equation} \tag{ 20 }$$

The price of government domestic consumption (PGovC) is estimated by introducing the optimal levels of consumption of final goods into the unit government domestic expenditure function, see equation (21)

$$\begin{equation} PGovC = {1 \over {f*\prod\limits_{j = 1}^{37} {\left( {{{\delta _j } \over {PY_j }}} \right)^{\delta _j } } }}. \end{equation} \tag{ 21 }$$

On the other hand, the total spending in consumption can be expressed as the difference between the government income (GvI) and the sum of the government balance (GvBal) and transfers to households (Trans_h ), see equation (22):

$$\begin{equation} TGvC = GvI - (GvBal + \sum\limits_{h = 1}^8 {Trans_h } ). \end{equation} \tag{ 22 }$$

While the government balance and the transfers to households are exogenous variables, the government income depends on its capital gains and its collection of various taxes calculated as in equation (23):

$$\begin{equation} \matrix{ {GvI} \hfill & = \hfill & {R*\sum\limits_{j = 1}^{37} {KA_{2j} + RevTSB + RevTPN} } \hfill \cr {} \hfill & {} \hfill & { + RevCTax + RevTPS + RevTM} \hfill \cr {} \hfill & {} \hfill & { + RevVAT + RevTPSH + RevTIN} \hfill \cr {} \hfill & {} \hfill & { + RevTMC + RevOt} \hfill \cr } \; \end{equation} \tag{ 23 }$$

where KA_2j is the public capital used in the economic activity j; R is the return on capital; RevTSB is the tax collected from the employer contribution; RevTPN is the revenue from the tax on production paid by economic activities; RevCtax is the revenue from carbon tax paid by economic activities; RevTPS is the revenue from the tax on products paid by economic activities; RevTM is the revenue from the import tariffs paid by economic activities; RevVAT is the revenue from the value added tax; RevTPSH is the revenue from the tax on products paid by households; RevTIN is the revenue from the income tax; RevTMC is the revenue from the import tariffs paid by households; and RevOt is the revenue from other taxes, that is an exogenous variable.

The tax collection is the result of multiplying the taxable base by the tax rate. For the tax collection from the employer contribution and the revenue from the tax on production paid by economic activities, remunerations are the taxable base using equations (24) and (25) respectively:

$$\begin{equation} RevSB = TSB_j *LA_j \sum\limits_{e = 1}^2 {\vartheta _j^e w^e } \end{equation} \tag{ 24 }$$

$$\begin{equation} RevTPN = TPN_j *LA_j \sum\limits_{e = 1}^2 {\vartheta _j^e w^e } \end{equation} \tag{ 25 }$$

where $\vartheta _j^e$ is the share of labor employed in sector j that corresponds to strata e. For the revenue from the tax on products and carbon tax paid by economic activities, the tax base is the gross output, see equations (26) and (27):

$$\begin{equation} RevTPS = \sum\limits_{j = 1}^{37} {{{TPS_j *PY_j *Y_j } \over {(1 + TPS_j + CTax_j )}}} \end{equation} \tag{ 26 }$$

$$\begin{equation} RevCTax = \sum\nolimits_{j = 1}^{37} {{{CTax_j *PY_j *Y_j } \over {(1 + TPS_j + CTax_j )}}.} \end{equation} \tag{ 27 }$$

For revenue from the import tariffs paid by economic activities and households, the respective imports are the tax base, described by equations (28) and (29):

$$\begin{equation} RevTM = \sum\limits_{j = 1}^{37} {TM_j *PM_j *M_j } \end{equation} \tag{ 28 }$$

$$\begin{equation} {\mathop{\rm Re}\nolimits} vTMC = \sum\limits_{h = 1}^8 {TMC*PMC*MH_h .} \end{equation} \tag{ 29 }$$

For the revenue from the value added tax and the revenue from the tax on products paid by households, the taxable base is the consumption of the final goods, calculated using equations (30) and (31):

$$\begin{equation} RevVAT = \sum\limits_{h = 1}^8 {{{VAT_h *PHC_h *DC_h } \over {(1 + VAT_h + TPSH_h )}}}. \end{equation} \tag{ 30 }$$

$$\begin{equation} RevTPSH = \sum\limits_{h = 1}^8 {{{TPSH_h *PHC_h *DC_h } \over {(1 + VAT_h + TPSH_h )}}.} \end{equation} \tag{ 31 }$$

Finally, for the revenue from the income tax, the taxable base is the payment for labour and capital endowments, calculated using equation (32):

$$\begin{equation} RevTIN = \sum\limits_{h = 1}^8 {TIN_h *(W_e *LH_h + R*KH_h ).} \end{equation} \tag{ 32 }$$