Input-output model

From the structure of the input-output table of a country it is possible to develop a highly simplified model of the economy, which helps explain the structural interdependence between the various economic sectors.

Assuming a Leontief production function, the level of production that the 2th sector sells to jth (X _ij ) is a constant proportion of the production level of the jth sector (X _j ):

Therefore, the technical coefficients record the need for input of each sector to produce one unit of output in this sector.

Assuming that X _j and X _ij , (1≤ i ≤ n, 1 ≤ j ≤n) are the n+n ² endogenous variables, while the components of final demand net imports (y _i ) including consumption, investment, government spending and exports are ո exogenous variables. Thus, the model for all sectors of the economy can be represented in matrix form as:

where A is called the matrix of direct requirements, as its matrix elements indicate the rate at which input per unit of product are demanded. Then, with matrix algebra we obtain the expression of the Leontief input-output model:

Where B ≡ I-A-1 is the Leontief or total requirements (direct and indirect) matrix, which relates the output of each sector X_i to the final demand net after imports. Each b _ij element of the Leontief matrix represents the amount of production that sector і should produce to satisfy a unit of final demand net after imports of the jth product (^{Schuschny, 2005}).

Environmental extension of the input-output model

The CO₂e emission intensity of an economic sector is defined as the total CO₂e emissions per unit of production in this sector. Since CO₂e emissions for most sectors come mainly from fossil fuels, there is a direct relationship between energy use and emissions of CO₂e. However, the agriculture and livestock sector and forestry sector are an exception since most of their emissions come from other sources, not fuel use. In the agriculture and livestock sector those standing out are enteric fermentation, manure management, rice cultivation, agricultural land use, burning of agricultural waste, among other activities.

The forestry sector generates capture of CO₂e emissions, so the value of such emissions is negative.

The CO₂e emissions generated by the production of an economic sector consist of direct emissions from that sector, plus indirect emissions due to the production of goods and services by other sectors, but required by this sector. The direct emission intensity g is a vector of emissions in which each element represents the amount of direct CO₂e emissions released per unit produced in sector i⁵. So you can get vector m, the vector of intensities of direct and indirect emissions:

On the other hand, the vector of environmental tax on production є is calculated by multiplying the emission intensity of each sector by a (φ) pollutant price, expressed in US $/t emitted (^{Gemechu et al., 2014}).

Environmental extension of the Leontief price model

The input-output model also provides a framework for analyzing the structure of the prices of the various products of the economy. If p _i , are the unit prices of the sector ith-, then the cost (in terms of inputs) of a product unit of sector j is: Assuming that sectoral prices are equal to the average cost of production, the unit normalized price of production in each sector j, p _j . can be expressed as the total cost of intermediate inputs and expenditures on the total value added as follows (^{Llop, 2008}):

where t _j . is the ad ty on imports in sector j, p _j ^m is the price of imports, and m. is the import coefficient.

The impact of the introduction of an environmental tax rate (ɛ _j ) on the cost structure of sector j is evaluated by the following equation:

When defining the value added (wages, benefits) and the domestic value of the imported product, both per unit of product j as v _j , the above equation can be rewritten as:

Which in matrix form can be written as follows:

where A* is the new matrix of technical coefficients that incorporates both ad valorem taxes and environmental taxes, and v is the vector of value added per unit of production which includes wages, payment to capital, and includes imported inputs. Thus, producer prices shall be determined according to the following matrix operation:

The environmental tax also affects the consumer price index (CPI) which increases from IPC to IPC ^ɛ , where p _j . and pjε are consumer prices before and after the introduction of environmental tax, respectively, while α _j . represents the proportion of goods and services of sector j consumed in the economy. Thus, variation in the CPI can be expressed as:

The impact of the tax on private real income from the change in consumer spending goods of sector j (C _j ), can be evaluated by the expression:

This indicator can be interpreted as the change in the economic welfare of consumers after tax; any negative value reflects a situation in which there is a loss of welfare, since it indicates an increase in spending.

Changes in sectoral prices induced by the environmental tax could also be reflected in the total production. These effects can be evaluated under the assumption that the monetary values of sectoral output before and after the introduction of the tax will remain constant at the original levels⁶. Therefore, the new sectoral production of sector j after the environmental tax ( Xjε) has been introduced can be calculated as:

By taking into account that prices on the benchmark equilibrium are normalized equal to 1 (that is, p _j =1) and using the proportionality assumption of the input-output model, in which the total emissions of CO₂e of each sector are directly linked to the total output of this sector, we can approximate the new sectoral emissions ( Ejε) as the multiplication of new production with direct emissions per unit of production (g_j)⁷:

Finally, the tax collection (R) is evaluated as:

Economic data used

This research used data from the statistical yearbook "Cuentas Nacionales de Chile 2008-2012" (National Accounts of Chile 2008-2012), Central Bank of Chile, and specifically the Input-Output Table 2010 (IOT 2010) was used. To make information manageable 111 economic activities of the IOT 2010 in 34 sectors were added, resulting in a square matrix of a 34x34 dimension.

The sectors used are: Agriculture and Livestock, Forestry, Aquaculture, Fisheries, Coal, Oil and Gas, Copper, Rest of Mining, Food Industry, Textiles and Leather, Wood, Pulp, Fuel, Chemical Industry, Non-Metallic Mining, Basic Metals Industry, Metalworking Industry, Furniture, Other industries, Electricity, Water, Construction, Trade and Hotels, Passenger Transport, Transportation, Telecommunications, Financial Services, Services, Public Administration, Public Education, Private Education, Public Health, Private Health and Other Services (Anex).

Environmental emission data

CO₂e is a measure used to indicate the possibility of global warming associated with each of GHGs, ie, in addition to CO₂, it also includes the effects of methane (CH₄), nitrous oxide (N O) and other long life GHG compared to a reference gas, usually CO₂. The Global Warming Potential (GWP) of these gases can be calculated for periods of 20, 100 or 500 years and 100 years is the most frequent value. For example, the 100-year GWP of CH₄ is 25 and ΝΟ_χ is 298; that is, the emission of 1 million Mg of methane is equivalent to emitting 25 million Mg CO_2e (^{World Bank, 2014}).

Due to the variability and unreliability of official data reported by the Pollutant Release and Transfer Register (PRTR) in Chile, emissions were estimated using other sources of information. Thus, CO₂ and CO₂e emissions for the 34 sectors were obtained with data of fuels used and extracted from various sources such as industrial survey ENIA and National Energy Balance (BNE).

To transform fuel consumption data into CO₂ emissions we used emission factors (EPA, 2014). Then to calculate CO₂e emissions the procedure was similar, but also emissions multiplied by a conversion GWP factor for CO₂, CH4 and N₂0 using a horizon of 100 years (^{United Nations Convention Framework on Climate change, 2014}).

For the agriculture and livestock sector and forestry sector, data for CO₂ emissions were estimated from fuel use and emissions data of CO₂e were obtained from the report "Complementos у actualización del inventario de Gases de Efecto Invernadero (GEI) para Chile en los sectores de Agropecuario, uso del suelo, cambio de uso del suelo y silvicultura, y residuos antrópicos" (Accessories and updated inventory of Greenhouse Gases (GHG) for Chile in the sector of agriculture, land use, land use change and forestry, and anthropic waste) prepared by the Institute of Agricultural Research ^{INIA (2010)}. Within CO₂e emission data we took into account the capture of emissions obtained from the source "Suelos forestales y plantaciones forestales" (Forest soils and forest plantations), presented in the report. The CO₂e emissions associated with livestock were estimated from the information extracted from the report "Producción Pecuaria, Periodo 2008-2013 y Primer Semestre 2014" (Livestock Production, 2008-2013 and First Half 2014) (^{Instituto Nacional de Estadística, 2014}/National Institute of Statistics, 2014). To estimate emissions from this sector average GHG emission intensities for beef, small ruminants, pig, chicken, milk and egg were used, obtained from the report "Enfrentando el Cambio climático a través de la Ganadería" (Confronting climate change through Livestock) prepared by FAO (2013).

For the validation of estimates of CO₂e there is no official figure available for comparison. However, according to World Bank statistics emissions for 2010 in Chile were 72.2 million Mg of CO₂, very close to the value of the emission estimates made in this study of 72.0 million Mg of CO₂.

Direct and indirect emissions of CO ₂ e

In a scenario in which the final demand of sectors experienced an increase of one million dollars, for example, if the agriculture and livestock sector has an increase in its final demand of one million dollars (equivalent to 0.0126 % of agriculture and livestock GDP), the direct and indirect effects on all productive sectors would result in an increase of 3429 t of CO₂e (2872 direct t and 557 indirect t).

Regarding CO₂e emissions, the sectors that produce a greater direct impact are: Agriculture and Livestock (2872 Mg), Electricity (1741 Mg), Oil and Natural Gas (1641 Mg), Passenger Transport and Transport (1620 Mg). Those who produce a greater indirect impact are: Forestry (2065 Mg), Electricity (1287 Mg), Water (1193 Mg), Food Industry (892 Mg) and Aquaculture (635 Mg). The sectors with the greatest overall impact of CO₂e emissions are: Agriculture and Livestock (3429 Mg), Electricity (3028 Mg), Passenger Transport (1773 Mg), Oil and Gas (1734 Mg) and Water (1200 Mg).

Direct emissions from the forestry sector have a negative value because the capture of GHG is greater than the direct emissions from fuel use and indirect emissions, creating a favorable balance capture. The wood sector has a negative value of indirect and total emissions, since this sector is an important consumer of the forestry sector inputs and emits directly only 23 t.

Simulation of tax rates on CO ₂ e

The environmental extension of the Leontief price model allows assessment of environmental taxes, as the total effect of emissions is reflected in the cost of production of all the sectors involved.

Figure 1 Environmental indicators of direct and indirect emissions of CO₂e by the increase in the final demand of one million dollars. (Cuentas Nacionales de Chile 2008-2012 ^{Banco Central de Chile, 2013}). 

While the agriculture and livestock sector receives the tax burden directly, other sectors are also affected indirectly as a result of sectoral interactions due to input demand.

Five tax values were simulated on emissions of CO₂ and CO₂e , US$l/Mg, US$5/Mg, US$10/ Mg, US$30/Mg (close to the world average value of CO₂ tax) [1] and US$130/Mg (close to the world maximum values of the CO₂ tax). These values are used to estimate the rate of environmental tax associated with the intensity of CO₂e emissions in the agriculture and livestock sector which correspond respectively to 0.40 %, 1.99 %, 3.98 %, 11.94 % and 51.75 % of the products prices of this sector (Table 1).

Table 1 Changes in production prices due to tax payment on emissions of CO₂e in the agriculture and livestock sector. 

Data obtained from Cuentas Nacionales de chile 2008-2012 (^{Banco Central de Chile, 2013}).

The agriculture and livestock sector has the largest variation in prices because it is the sector where the tax is applied directly. For example, the price increases by 4.68 % for a tax of US$10/Mg of CO₂e and 66.12 % for a tax of US$130/t of CO₂e, ie approximately 0.48 % per dollar of tax.

In addition, there is a change in the sectoral prices of forestry [1], food industry, wood and aquaculture because an environmental tax in the agricultural sector affects the cost of inputs demanded by these sectors (which have not undergone direct taxation from CO₂e).

Other economic and environmental indicators that can be obtained with the model correspond to the CPI variation, the increase in spending, total revenue and variation in CO₂e emissions associated with changes in production.

Taxing the agriculture and livestock sector in Chile seems reasonable as it is the sector that emits more CO₂e Mg. However, the results showed that it would generate small reductions of emissions in various tax scenarios. Although tax revenue increases, the private economic welfare would be diminished by the rise in the price of goods consumed (Table 2). In addition, we observed that the effects on the CPI are not negligible for higher taxes, a result explained by the share of agriculture and livestock products in the consumer basket (3-1 % fraction of expenditure according to the data of Final Consumption reported in National Accounts).

Table 2 Economic and environmental variables under the new tax on CO₂e emissions. 

Data from Cuentas Nacionales de chile 2008-2012 (^{Banco Central de Chile, 2013}).

The results obtained showed that an environmental tax of US$30 on CO₂e emissions in the agriculture and livestock sector (value close to the average in countries that have implemented a CO₂ tax) would lead to an increase in the consumer price index (CPI) of 1.01 %, an increase in spending of US$1282.4 million, a total tax revenue of US$1473-6 million and a reduction in CO₂e emissions associated with a variation in the production of only 4.04 %. In addition, production of the agriculture and livestock sector and the total output of the economy would be reduced by 0.61 % and 0.03 %, respectively.