Carbon Dioxide Emissions Reductions in New Zealand: A Minimum Disruption Approach (WP 04/25)

Abstract#

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Reductions in carbon dioxide emissions can come from (among other things) changes to the structure of final demands, changes in the use of fossil fuels by industry, and changes to the structure of inter-industry transactions. This paper examines the nature of the least disruptive changes, that is the minimum changes to these three components which are consistent with specified overall reductions in carbon dioxide in New Zealand. In examining the minimum changes needed, constraints are imposed on the corresponding changes in GDP growth and aggregate employment.

Acknowledgements#

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We should like to thank Statistics New Zealand, in particular Jeremy Webb, for making available its monetary and physical estimates of fuel use by industry. This information is from the Statistics New Zealand Energy Flow Account report that will be published in March 2004.  We are also grateful to Iris Claus for help with the Input-Output data.

Disclaimer#

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The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author(s).  They do not necessarily reflect the views of the New Zealand Treasury.  The New Zealand Treasury takes no responsibility for any errors or omissions in, or for the correctness of, the information contained in this Working Paper.  The paper is presented not as policy, but to inform and stimulate wider debate.

1  Introduction#

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A reduction in carbon dioxide emissions arising from the production of goods and services can come from three main sources: changes to the structure of final demand; changes to fuel mix and efficiency in production, and changes to the structure of inter-industry trading. The aim of this paper is to examine the nature of the least disruptive changes in the New Zealand economy that are necessary to achieve a target annual rate of reduction in emissions. The paper concentrates on changes in final consumer demands and changes in the quantities and mixture of fossil fuels used by industries. A situation in which emissions reductions are achieved by reducing all final demands would imply an increase in aggregate unemployment and a negative growth rate of GDP. In the case of final demand changes, constraints on GDP and employment growth are imposed: these imply that the final demands of some industries would need to increase, while other industries decline. These changes are examined using constrained minimisation techniques within an input-output framework, following the methods developed by Proops et al (1993).[1]

The constrained minimisation method does not consider a specified means of reducing emissions, such as a carbon tax.[2] It is therefore not directly concerned with determining the economic costs associated with curbing carbon dioxide emissions. Instead the method attempts to find the minimum set of structural changes required in different industries of the economy that would achieve a target level of emissions reduction whilst maintaining predetermined levels of variables like GDP growth and employment. In doing so, the method can determine the severity of the required changes.

Subsection 2.1 presents the input-output approach to modelling carbon dioxide emissions, while subsection 2.2 describes the method of allowing for constrained minimisation of disruptions. The minimum disruption approach is applied to New Zealand in sections 3 and 4. Section 3 describes the sources from which the data were gathered and the processes used to form the expressions derived in section 2, while subsections 4.1 and 4.2 analyse the minimum disruption results for respectively final demands and fuel use. Conclusions are provided in section 5.

2  An Input-Output Approach#

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This section presents the framework of analysis used to compute minimum disruption changes. Subsection 2.1 derives an expression for total carbon dioxide emissions, using an input-output approach. Subsection 2.2 derives the minimum disruption changes to final demands necessary to achieve a required rate of reduction in total emissions, and subject to growth and employment constraints. Finally, subsection 2.3 examines the changes in the fuel use coefficients required to achieve a target carbon dioxide emissions reduction.

2.1  Total Carbon Dioxide Emissions#

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Consider increasing the final consumption of a good by $1. The problem is to evaluate how much carbon dioxide this would involve. This increase in the final demand by $1 involves a larger increase in the gross, or total output, of the good - as well as requiring increases in the outputs of other goods. This is because intermediate goods, including the particular good of interest, are needed in the production process. The extent to which there is an increase in carbon dioxide depends also on the intermediate requirements of all goods which are themselves intermediate requirements for the particular good. Indeed, the sequence of intermediate requirements continues until it ‘works itself out’, that is, the additional amounts needed become negligible. This is in fact a standard multiplier process. It can be set out formally as follows.

An industry’s gross output derives from both intermediate output which serves as input to other industries and final demand. Let

 

denote the value of output flowing from industry

 

to industry

 

and let

 

denote the value of final demand, by consumers, for the output of industry

 

. The value of an industry’s gross output,

 

, may therefore be expressed as the sum of intermediate and final demands:

 

(1)    

 

 

The direct requirement co-efficient,

 

, measures the value of output from industry

 

directly required to produce $1 worth of output in industry

 

. Hence:

 

(2)     

 

 

Using (2) to write

 

and substituting the resulting expression into equation gives gross output as:

 

(3)     

 

 

Let

 

and

 

denote the n-element vectors of

 

and

 

respectively. Further, let

 

denote the

 

matrix of the direct requirement coefficients,

 

. These definitions enable the system of

 

equations described in equation (3) to be expressed in matrix notation as:

 

(4)     

 

 

Continuous substitution for

 

on the right-hand side of equation (4) produces the following geometric sequence:

 

(5)     

 

 

If the condition

 

is satisfied, the system is productive and the non-negative solution is:[3]

 

(6)     

 

 

and     

 

is the matrix multiplier required.

 

Let

 

denote the

 

matrix of energy requirements (in PJs) for

 

industries across

 

fossil fuel types. Let

 

denote the k-element vector of CO₂ emissions (tonnes of carbon dioxide) per unit of energy (PJ) associated with each of the

 

fossil fuels.

 

Multiplying the transpose of the

 

vector by the transpose of the

 

matrix gives the following row vector which contains the carbon dioxide emissions per unit of gross output from each industry:

 

(7)    

 

 

Total carbon dioxide emissions,

 

, can then be obtained by post-multiplying the above row vector by the column vector of gross output,

 

:

 

(8)    

 

>

 

The term in square brackets gives the row vector,

 

, of the carbon dioxide intensities:

 

(9)    

 

>

 

Equation (8) is used in determining the necessary structural changes to achieve a specified reduction in emissions. Proops et al (1993, pp.11-12) identified three main areas where a change in economic structure might give rise to reductions in carbon dioxide emissions. First, there are changes to final demands,

 

. Second, there are changes to the efficiency of fuel use,

 

. Third, changes to the structure of inter-industry trading,

 

can be made.

 

The objective is to minimise the disruption to industries with regard to one of these variables while achieving a specified reduction in emissions. Disruption to any variable,

 

say, in industry

 

is measured in terms of the proportional change in that variable,

 

. In specifying an objective function, Proops et al (1993, p.228) adopted a quadratic cost function, but it is useful to consider the more general form given by:

 

(10)    

 

 

The term

 

is simply a scaling factor which drops out in differentiation. This objective function assumes that there is an equal social cost associated with a 1 percentage point change in a certain variable, irrespective of the industry.[4]

 

2.2  Disruptions to Final Demands#

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Consider first the problem of minimising the disruption to final demand. To impose no more than a constraint on the amount of emissions reduction is obviously not a case that should be considered seriously. In particular, the required final demand changes would all be negative. However, this case serves to introduce the basic approach adopted.[5]

Total emissions, when written in algebraic as opposed to matrix form are equal to

 

, so that:

 

(11)    

 

 

If

 

is the required proportional change in total carbon dioxide emissions

 

, the constraint can be written as:

 

(12)    

 

 

where

 

is

 

's share of emissions, and

 

denotes the proportional change in final demand for industry

 

. The Lagrangean for this problem is given by:

 

(13)    

 

 

Differentiation gives the set of first-order conditions:

(14)    

 

 

Multiplying equation by

 

, adding over all industries, and solving for

 

gives:

 

(15)    

 

 

Substituting this result into the first-order condition gives the solution for the required proportional reduction in output of:

(16)    

 

 

This result shows that the larger is

 

, the smaller is the dispersion in the required rates of change. Therefore, increasing the power ultimately leads toward an equalisation of the proportional changes. Furthermore, when additional constraints are imposed, the first-order conditions cannot be solved explicitly. For this reason, the quadratic form is retained in this study, and the substitution of

 

gives the result, as in Proops et al (1993, p.144), that:

 

(17)    

 

 

Carbon Dioxide and GDP Growth Targets

It is appropriate to include a constraint on GDP growth in addition to the constraint on the level of carbon dioxide emissions reduction. This constraint can be written as:

(18)    

 

 

where

 

represents the desired rate of growth, expressed as a weighted sum of the changes in final demands once again, with each weight being the proportion of that industry’s contribution to total GDP, that is

 

. The Lagrangean for this problem is:

 

(19)    

 

 

Differentiating with respect to each of the

 

gives rise to the first-order conditions:

 

(20)    

 

 

along with the two constraints relating to

 

and

 

. Using

 

from the first-order conditions and substituting into the constraints gives the resulting two simultaneous equations:

 

(21)    

 

 

If the determinant of this matrix is written as

 

, the solutions for the Lagrange multipliers are:

 

(22)    

 

 

The resulting multipliers can be substituted into the first-order conditions to solve for the

 

s; see also Proops et al (1993, pp.234-235).[6]

 

Carbon Dioxide, GDP and Employment Targets

An additional constraint concerns the rate of growth in employment,

 

. This is expressed as:

 

(23)    

 

 

where the weights

 

are the levels of employment in each industry as a proportion of total employment. Minimising the disruption to final demands subject to all three constraints simultaneously, involves the Lagrangean:

 

(24)    

 

 

In this case there are three Lagrangean multipliers, so that a set of three linear equations can be solved using matrix methods. The procedure is a simple extension of that described above; see also Proops et al (1993, pp.238-9).

2.3  Disruptions to Fuel-use Coefficients#

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As an alternative to minimising changes to the vector of final demands, consider minimising the change in fuel-use coefficients subject to a carbon dioxide emissions-reduction target. The direct fuel-use coefficients are embodied in the matrix,

 

. The objective is to minimise:

 

(25)    

 

 

where

 

represents the proportional change in the production fuel requirement per unit of total demand of fuel

 

in industry

 

. The change is minimised subject to the constraint that a target proportional reduction,

 

, in carbon dioxide emissions, attributable to changes in the production fuel-use coefficients, is achieved. Given that total emissions are

 

, differentiation gives:

 

(26)    

 

 

This can be rewritten as:

(27)    

 

 

Hence

 

is a weighted row and column sum of the production fuel-use-coefficients, with each weight given by

 

, that is the proportional contribution to emissions of fuel

 

in industry

 

. The Lagrangean is therefore:

 

(28)    

 

 

Following Proops et al (1993, pp.241, 144), solving this yields:

(29)    

 

 

3  Fuel Use and Carbon Content in New Zealand#

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This section outlines the data and approach used to evaluate the expressions, derived in the previous section, for New Zealand.

The “Inter Industry Study of 1996” from New Zealand’s System of National Accounts provided inter-industry flows in value terms for a 49 industry group classification (IGC).[7] These flows were divided by each industry’s gross output to produce the direct requirement coefficients which were then collected to form the

 

 

matrix.

 

By subtracting each industry’s intermediate output from their gross output, the Accounts were also used to compile the 49-element

 

vector of final demands.

 

The

 

matrix was constructed from New Zealand’s Energy Flow Accounts which provided the energy use arising from the fossil fuels, expressed in physical terms (PJs), for the year ended March 1996 based on the Energy Account Industry Classification (EAIC). The translation between the Energy Account Industry Classification (EAIC) and the 49 industry group classification (IGC) which was used for the analysis is provided in Table A1. Only those fuels for which at least one industry recorded a positive expenditure were incorporated, which provided nine fossil fuels for analysis. Table A2 provides information about the demands for these fuels which are expressed in physical terms and based on the 49 industry group classification (IGC). Dividing these figures by each industry’s gross output provided the required elements of the

 

 

matrix.

 

Compiling the 9-element

 

vector of carbon dioxide emissions entailed obtaining data from multiple sources. Table 1 outlines the carbon dioxide emission factors for each of the nine fossil fuels analysed, along with their sources.

 

The resulting values of

 

,

 

and

 

were used to calculate the 49-element

 

vector of carbon dioxide intensities, using the expression

 

derived in subsection 2.1. The results of this calculation are provided in Table A3.

 

It is not surprising that petroleum and industrial chemical manufacturing (industry no. 18), which demands the greatest quantity of fuel across all industries, recorded by far the highest carbon content of 3.64 tonnes of carbon dioxide per dollar of gross output. Rubber, plastic and other chemical product manufacturing (industry no. 19) and basic metal manufacturing (industry no. 21) which respectively demand the largest quantities of natural gas and coal record similarly high carbon contents of 1.83 and 1.40 tonnes of carbon dioxide per dollar of gross output. The only other industry to record a carbon content in excess of 1, was electricity generation and supply (industry no. 26) with 1.21.

4  Minimum Disruption Calculations#

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This section applies to New Zealand the minimum disruption approach described in section 2.

4.1  Final Demands#

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Table 2 provides the annual changes to the elements of the final demand vector,

 

, which minimise disruptions to final demand while satisfying the constraints described. All values are expressed in percentage terms. Additionally, Table 2 gives the final demand, carbon intensity and employment weight of each industry.

 

Column 4 of Table 2, labeled

 

only, represents the results of the minimum disruption approach where the only constraint is a 1 percent reduction in carbon dioxide emissions. Accordingly, all industries are required to reduce their final demand. The largest annual rate of reduction in final demand is for petroleum and industrial chemical manufacturing (industry no. 18) at -2.141 percent, followed by rubber, plastic and other chemical product manufacturing (industry no. 19) at -1.491 percent and construction (industry no. 29) at -1.462 percent.

 

The annual reductions in final demand are proportional to the carbon dioxide intensities of each industry, as seen from equation(17). Therefore, those industries whose products are most carbon intensive are required to achieve the greatest reductions in final demand, as shown by Figure 1. In addition, the changes in final demand required to achieve a 2 percent reduction in carbon dioxide emissions are simply double those for the 1 percent case. For this reason, they are not displayed in Table 2.

Figure 1 – Carbon Intensity and Changes in Final Demands with Carbon Dioxide Reductions Only

 

As mentioned in section 2, these reductions should not be viewed as realistic values to be pursued, but instead benchmarks against which later results may be compared.

Demand Changes with a GDP Growth Constraint

Column 5 reports the changes to final demand when 2 percent growth in GDP is imposed in addition to the 1 percent reduction in carbon dioxide emissions. The two constraints exert opposing influences on final demand. The GDP growth constraint prompts increases in final demand, while the carbon dioxide constraint necessitates reductions.

The objective function requires minimising the sum of the square of the proportionate changes in final demand of each industry. To achieve the GDP growth constraint, increasing the final demands of industries which have relatively larger final demands, gives smaller proportionate changes, thereby minimising the objective function. Figure 2 clearly shows the positive correlation between the final demand of an industry and its associated required change in final demand. Similarly, in achieving the carbon constraint, industries whose outputs have higher carbon contents achieve greater reductions in emissions for given reductions in final demand. The negative correlation between carbon content per dollar of output and the required change in final demand is shown in Figure 3.

An industry’s required change in final demand is therefore determined by balancing the carbon intensity of output against the level of final demand. Accordingly, ownership of owner-occupied dwellings (industry no. 41) which has the largest final demand coupled with one of the smallest carbon contents is required to achieve the largest increase in final demand of 8.4695 percent. Similarly, health and community services (industry no. 47), wholesale trade (industry no. 30), retail trade (industry no. 31) and education (industry no. 46) are all required to achieve substantial increases in final demand. All four of these industries may be classified as service industries which produce low carbon dioxide emissions, yet have high levels of final demand. Regarding industries required to reduce their final demand, petroleum and industrial chemical manufacturing (industry no. 18) and rubber, plastic and other chemical product manufacturing (industry no. 19), which have the two highest carbon intensities require the greatest reductions in final demand of respectively -9.5474 and -5.8031 percent.

Figure 2 – Final Demand and Changes in Final Demands with Growth of 2 Percent

 

Figure 3 – Carbon Intensity and Changes in Final Demands with Growth of 2 Percent

 

Column 7 of Table 2 shows the required changes to final demand when the carbon dioxide constraint is raised from 1 to 2 percent, while holding the GDP growth constraint constant. Variations in the changes to final demand which arise from raising the carbon constraint are displayed in Figure 4. If the points were all to lie on the 45 degree line, the higher carbon constraint would have no effect. However, as Figure 4 clearly shows, the higher constraint requires greater reductions to be achieved in final demand. Consequently, increases in final demand must also be accentuated so as to achieve the growth constraint. These two effects combine to increase the spread of the distribution, thereby increasing the costs of disruption. However, the relative positions of the industries are seen to change only slightly.

Figure 4 – Changes in Final Demands and Raising the CO₂ Reduction Target

 

Demand Changes with GDP and Employment Growth Constraints

Proops et al (1993, p.252) imposed a 2 percent growth constraint on both GDP and employment, ‘so that the growing productivity of labour [could] be taken into account, without needing the labour coefficients to be altered’. Both constraints, in addition to the 1 percent reduction in carbon dioxide emissions, were used to generate the results shown in column 6 of Table 2. In similar fashion to Figure 4, Figure 5 analyses the impact on the required changes to final demand caused by the employment constraint.

Figure 5 – Changes in Final Demands and the Introduction of an Employment Constraint

 

The additional constraint is seen to cause very little variation to the required changes in final demand. This should not be surprising as those industries which have the largest final demands and consequently employ the greatest proportion of workers also require the largest increases in final demands to achieve 2 percent growth in GDP. Furthermore, in achieving this growth, a certain level of growth in employment is essential. Consequently, making the employment constraint explicit makes very little difference to the required changes in final demand.

Shown in the final two columns of Table 2 and contrasted in Figure 6 are the minimum disruption changes to final demand which arise from respectively 1.5 and 2 percent growth rates in GDP and employment, holding constant a 2 percent reduction in carbon dioxide emissions. The higher growth rate of 2 percent necessitates greater increases in final demand, which are sought from those industries which already required the largest increases in the case of the 1.5 percent growth rate. The resulting rise in carbon dioxide emissions is countered almost solely by one industry, rubber, plastic and other chemical product manufacturing (industry no. 19), which is required to reduce its final demand by a further 0.8 percent. These changes at the extremes of the distribution again increase the spread which leads to further increases in the cost of adjustment.

Figure 6 – Changes in Final Demand and an Increase in the Growth Rates

 

This result is magnified when the minimum disruptions of columns 6 and 9 are contrasted. Figure 7 shows the required changes to final demand in the case of 1 and 2 percent reductions in carbon dioxide emissions, holding constant 2 percent growth rates in GDP and employment. Achieving the 1 percentage point increase in the carbon constraint clearly requires relatively greater changes in final demand than that which was required to achieve the 0.5 percentage point increase in both growth rates.

Figure 7 – Changing the CO2 Reduction Requirement, with Growth and Employment Constraints

 

4.2  Changes in Fuel Mix#

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This subsection examines the annual minimum disruption changes to fuel efficiency and use necessary to reduce carbon dioxide emissions by 1 percent.

The elements of the

 

matrix, which describe the quantity of fuel required per unit of gross output, vary subject only to the carbon reduction constraint being achieved. Consequently, the changes given in Table 3 are all non-positive values, which are again expressed in percentage terms.

 

The largest annual rate of change required is in the use of crude petroleum by petroleum and industrial chemical manufacturing (industry no. 18). The only other required change over one percent is in the use of natural gas by rubber, plastic and other chemical product manufacturing (industry no. 19). All other changes are either zero or negligible, suggesting that achieving a 1 percent reduction in carbon dioxide emissions purely through fuel substitution is feasible.

The required changes to the fuel-use coefficients are again proportional to the carbon dioxide intensity of each fuel for each industry. Consequently, the changes required for a 2 percent reduction in carbon dioxide emissions are simply double those shown in Table 3 and for this reason are not reported.

 

5  Conclusions#

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This paper examined the nature of the least disruptive changes in the New Zealand economy that are necessary to achieve a target annual rate of reduction in emissions, using a cost function that depends on the sum of the squares of the proportionate changes in final demands. The paper followed the methods first developed by Proops et al (1993), and concentrates on changes in final consumer demands and changes in the quantities and mixture of fossil fuels used by industries. A situation in which emissions are achieved by reducing all final demands would imply an increase in aggregate unemployment and a negative growth rate of GDP. To overcome this problem, constraints on GDP and employment growth were imposed, implying that the final demands of some industries need to increase while other industries decline.

The magnitude of an industry’s required change in final demand was found to be determined by the relative efficiency by which they could achieve the stated constraints. The carbon intensity of an industry’s output was balanced against its employment weight and value of final demand. The small orders of magnitude which resulted from these calculations suggest that reducing carbon dioxide emissions is economically feasible. That is, reductions can be achieved while maintaining acceptable levels of key macroeconomic variables if structural change can be encouraged in the areas indicated by this study. Further employment was found to be essential in achieving the growth constraint. Consequently, the addition of an employment constraint was found to make a negligible difference to the changes in final demand. Raising the magnitudes of the constraints was found to increase the spread of the distribution, thereby increasing the costs of adjustment. An increase in the carbon constraint of one percentage point was found to increase this cost more than increasing each of the growth constraints by 0.5 percentage points.

The required changes in the fuel use coefficients were also small, with only two industries required to reduce specific fuel demands by more than 1 percent to achieve a 1 percent reduction in carbon dioxide emissions. Again, this supports the conclusion that such reductions in carbon dioxide emissions are feasible.

Appendix#

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Statistics New Zealand provided fuel demands based on the EAIC. The above translation was used to convert the fuel demands to the 49 industry group classification. Where an industry from the EAIC incorporated multiple IGC industries, final demand was used as a weight to distribute the fuel demand of the EAIC industry to each of the IGC industries.

 

References#

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Cornwell, A. and Creedy, J. (1997) Environmental Taxes and Economic Welfare: Reducing Carbon Dioxide Emissions. Cheltenham: Edward Elgar.

Creedy, J. and Sleeman, C. (2004) Carbon Taxation, Prices and Welfare in New Zealand. New Zealand Treasury Working Paper /04.

Proops, J. L. R., Faber, .M. and Wagenhals, G. (1993) Reducing CO2 Emissions: A Comparative Input-Output Study for Germany and the UK. Heidelberg: Springer-Verlag.