Carbon Taxation, Prices and Household Welfare in New Zealand (WP 04/23)

Abstract#

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This paper examines the effects on consumer prices of a range of carbon taxes in New Zealand, using information about inter-industry transactions and the use of fossil fuels by industries. The resulting effects on the welfare of different household types and total expenditure levels are examined. The excess burdens of the carbon tax are computed for the different household types. Finally, overall measures of inequality are reported.

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, and Peter Wilson for comments on an earlier version.

Disclaimer#

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The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the authors. 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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In October 2002, the New Zealand Government announced its intention to introduce a charge on carbon dioxide (and fossil fuel) emissions from the year 2007. The charge forms part of the Government’s policy package on climate change designed to meet New Zealand’s greenhouse gas reduction target under the Kyoto Protocol. The charge will approximate international emissions prices, but will be capped at $25 per tonne of carbon dioxide. The aim of this paper is to analyse the price, welfare and inequality changes that may arise from the imposition of such a carbon tax.[1] The exact magnitude of the tax is still unknown. For this reason, the paper analyses three carbon tax rates of $7, $15 and $25 per tonne of carbon dioxide.

The analysis proceeds as follows. First, it is necessary to provide a link between a carbon tax (expressed in terms of tonnes of carbon dioxide) and the price changes of commodities; this depends on the carbon dioxide intensities of each good. These intensities in turn depend on the fossil fuels used in the production of each good and the nature of inter-industry transactions. Second, given the price changes, it is necessary to evaluate the effect on the welfare of households; this stage requires the use of a demand model. This paper uses the linear expenditure system, where the parameters vary between household types and total expenditure levels. Third, the overall evaluation of the carbon tax requires the calculation of inequality measures, involving an allowance for household composition.

Section 2 sets out the basic framework of analysis. Subsection 2.1 derives an expression for the carbon dioxide intensities of commodities. These intensities together with a carbon tax rate are then used to calculate the effective carbon tax rates on commodities and subseqent prices changes, expressions for which are derived in subsection 2.2.

Section 3 applies the framework to New Zealand. Subsection 3.1 describes the sources from which the data were gathered and the processes used to evaluate the expressions derived in section 2. Subsection 3.2 outlines the data and methodology used to analyse the demand responses of consumers. One problem relates to the different levels of aggregation used in the input-output and household demand analyses. The theory behind the various measures used to conduct the analysis is provided in Appendix B. The implied price and indirect tax changes for alternative carbon dioxide rates are then reported in subsection 3.3. As a partial equilibrium analysis, reductions in carbon dioxide emissions are assumed to be generated purely through consumer substitution. Hence, the possible effects of the carbon tax on the use of fuels and other intermediate inputs by industries are not modelled here.

Section 4 analyses the welfare and inequality effects arising from the three carbon tax rates. Welfare changes, measured in terms of equivalent variations, are examined for a range of household types and levels of total weekly expenditure. These welfare measures give an indication of the disproportionality of the impact at different total expenditure levels, for the household types. Overall measures of inequality are also computed for each household type and for all households combined. These use the individual as the basic unit of analysis and make use of adult equivalence scales in producing each individual’s level of ‘wellbeing’.

Conclusions are provided in section 5.

 

 

 

 

2 A Carbon Tax and Prices#

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The first stage of the analysis is to apply a carbon tax and examine its effects on consumer prices. This section derives the expressions used to calculate such price changes. A carbon tax is specified as a number of dollars per tonne of carbon generated by the production of each good. It is therefore necessary to translate from a tax specified in term of physical amounts of carbon into an equivalent tax imposed per dollar of expenditure by final consumers of each good. This is achieved through the carbon intensity of each good.

As with other studies of carbon taxes, the tax examined is actually considered to be imposed on carbon dioxide intensity, rather than carbon intensity. However, carbon content and carbon dioxide emissions are directly proportional by molecular weight, and the equivalent tax on carbon content can be obtained by multiplying the carbon dioxide tax by 44/12. Hence a tax is specified in terms of tonnes of carbon dioxide and consumer prices rise in proportion to their carbon dioxide intensity.

This intensity, defined by

 

measures the tonnes of carbon dioxide emissions per dollar of final consumption of the output from industry

 

. Therefore, a carbon dioxide tax of

 

which is placed on carbon dioxide emissions is equivalent to an ad valorem tax-exclusive rate on the

 

^th commodity group of

 

, where:[2]

 

(1)    

 

 

As the intensity is expressed in terms of each dollar’s worth of the output that contributes to final demands, the total amount of carbon dioxide arising from all industries,

 

, is given by:

 

(2)    

 

 

where

 

is the value of final demand for industry

 

for

 

. The terms

 

and

 

denote corresponding column vectors and the prime indicates transposition.

 

The carbon dioxide intensities depend in a direct way on the types and amounts of fossil fuels used by each industry, and the emissions per unit of those fossil fuels. However, the problem is complicated by the need to consider the total output of each industry, rather than merely the amount of that output which is consumed, that is the final demand. This problem is examined in subsection 2.1. Having obtained the equivalent tax rates, the next stage is to obtain an expression for the overall tax rate imposed on each unit of the good consumed. This is discussed in subsection 2.2.

2.1  Carbon Intensities#

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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:

 

(3)    

 

 

The direct requirement co-efficient,

 

, measures the value of output from industry

 

directly required to produce $1 worth of output in industry

 

. Hence:

 

(4)    

 

 

Using (4) to write

 

and substituting the resulting expression into equation (3) gives gross output as:

 

(5)    

 

 

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 (5) to be expressed in matrix notation as:

 

(6)    

 

 

Continuous substitution for

 

on the right-hand side of equation (6) produces the following geometric sequence:

 

(7)    

 

 

If the condition

 

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

 

(8)    

 

 

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:

 

(9)    

 

 

Total carbon dioxide emissions,

 

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

 

:

 

(10)    

 

 

This may be compared with (2) above. The term in square brackets gives the row vector,

 

, of the carbon dioxide intensities:

 

(11)    

 

 

This expression can then be used together with a selected carbon tax rate to calculate the effective carbon tax rates given by equation (1).

The expression in (11) is in fact a simplified form of that obtained by Proops et al (1993) and Symons et al (1994) and used by Cornwell and Creedy (1997). The present analysis abstracts from carbon dioxide emissions arising directly from the consumption of goods and services, which are small compared with those arising from production.[4]

2.2  Effective Tax Rates#

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The carbon tax is imposed in addition to pre-existing indirect taxes. Hence it is necessary to obtain an expression for the post-carbon tax equivalent indirect tax rates. Let

 

denote the tax-exclusive price of commodity

 

_, where the subscript has been dropped for convenience. Prior to the imposition of the carbon tax, the existing ad valorem tax rate is

 

and therefore the tax-inclusive price of commodity

 

,

 

, is defined by:

 

(12)    

 

 

The carbon (dioxide) tax is effectively a tax on final consumption at the rate,

 

, which is the resulting proportional increase in the price of the good. Hence, the new tax-inclusive price of commodity

 

,

 

, is given by:

 

(13)    

 

 

The overall effective ad valorem tax rate on commodity

 

_,

 

_, may therefore be calculated from the expression:

 

(14)    

 

 

In the following analysis the effects of shifting from

 

to

 

are examined. The term

 

, as the effective carbon tax on consumption, measures the proportional price increase for each good.

 

 

 

 

 

3 Application to 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. Subsection 3.1 describes the data used to determine the carbon dioxide intensity,

 

of the output from each of New Zealand’s industries. Subsection 3.2 describes the data used to analyse the demand responses and welfare changes arising from the imposition of the carbon tax. Section 3.3 reports the effective tax rates and price changes arising from alternative carbon dioxide tax rates.

 

3.1  Fuel use and carbon content#

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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).[5] 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 National 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 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.

3.2  Household Demands#

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The first stage in the analysis of the impact of price changes on households is to estimate the relationships between budget shares and total household expenditure for a range of household types. Household expenditure data from the Household Economic Survey (HES) for the years 1995, 1996, 1997, 1998 and 2001 were adjusted to 2001 prices using the consumer price index (CPI).[6] Over this period there were very few changes in indirect taxes. The surveys were then pooled to form one large database.

Table 2 shows the household types used.[7] In each case households were further divided into smoking (S) and non-smoking (NS) households; a positive weekly expenditure on tobacco (group 17 in Table 3) was sufficient for the household to be designated as a smoking household. The division into smoking and non-smoking households, for examination of all commodity groups, was found substantially to improve the fit of most of the budget share relationships.[8] Table 2 also gives the arithmetic mean total weekly household expenditure for each household type.

It was necessary to express all existing indirect taxes in terms of a tax-exclusive ad valorem tax rate. While this is straightforward for most commodity groups, for which only GST applies, the translation is more complex where an excise tax is also imposed, as these are typically based on units of the commodity rather than values.

It was not possible, mainly because of estimation difficulties, to use all the separate and highly detailed HES commodity categories. Instead, these were consolidated into 22 commodity groups. Table 3 shows the commodity groups used and the effective ad valorem tax-exclusive percentage rates, at 2001. The rates shown in Table 3 were taken from Young (2002). Where several HES categories were combined, the effective rates also required the computation of a weighted average of the individual components. Table 3 clearly indicates the high effective rates on petrol, cigarettes and tobacco and alcohol. These high rates are typically rationalised on merit good and externality grounds.[9]

The demand responses were calculated using the 22 commodity group classification discussed above. However, the price changes arising from the carbon tax are given for a 49 industry group classification. The calculated price changes cannot therefore be directly used to evaluate the demand responses and welfare changes. Table A4 provides the translation between the two classifications.

It may be thought that the demand model, and welfare changes, should explicitly allow for external effects. For example, suppose there is a small community in which some people hate noise and smoke, while others play loud music and burn domestic rubbish in their gardens. The people who hate smoke and noise are forced to dry their washing indoors and insulate their houses with double glazing. Taxes on smoke and noise mean that budget allocations change - those who do not need to spend on indoor drying and insulation change their allocation away from these goods.[10] Those who made noise and smoke have to spend money on devices to avoid creating the externalities, and adjust their allocations elsewhere because of income effects. Any attempt to evaluate the welfare and distributional effects of such taxes must allow for these external effects on consumption patterns and thus of course utility functions. However, the case considered in this paper is closer to a situation in which no one makes noise or smoke, but households use electricity and gas for heating and cooking. However, there are no smoke-belching coal-fired electricity generating plants near houses, and the people in the community are not aware (since it is far from visible) that their use of electricity produces effects on the air of other communities or on the ozone layer which may affect them eventually, but whose effects are remote and not evident. A tax on carbon emissions produces differential price changes for all goods according to their carbon intensities. The cleaner air elsewhere does not enter utility functions. An evaluation of the welfare and distributional effects of the tax is not subject the problems of the first case above. The government, however, believes that there are benefits to being part of an international agreement, and believes that some other communities will benefit from cleaned air. Its decision to impose the tax involves a balancing of the costs imposed by the price changes against the overall gains from emissions reductions.

3.3  Taxes and Prices#

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In view of the uncertainly regarding the precise charge on carbon dioxide that will come into effect from the year 2007, three carbon tax rates of $7, $15 and $25 per tonne of carbon dioxide are examined here. As the values of final demands are measured in thousands of dollars, a tax rate of, for example, $7 translates into a value of

 

of 0.007.

 

The left side of Table 4 shows the effective carbon tax rates for 22 commodity groups. These calculations were made for each of the three carbon tax rates, expressed in thousands of dollars per tonne of carbon dioxide. Displayed on the right side of Table 4 are the new effective ad valorem tax rates. When wishing to analyse the effects of the carbon taxes on commodity prices, the values of

 

are not directly comparable because the existing ad valorem tax rates,

 

, differ across the commodity groups. Attention is therefore turned to the effective carbon tax rate,

 

.

 

For each of the three carbon tax rates, petrol etc (commodity group 15) faces by far the greatest price increase. Figure 1 shows the expected budget shares of total expenditure devoted to petrol, for a range of total weekly household expenditure levels, by households with two adults and two children. These are based on estimates of the budget share relationship specified in Appendix B. The inverse relationship between weekly expenditure and budget shares for both smoking and non-smoking households is indicative of the majority of types of household and shows that low-income earners spend a proportionately greater amount of their budget on petrol than high income earners. Similarly, domestic fuel and power (commodity group 6) and food (commodity group 1), both of which face substantial price rises as a result of the carbon tax, also form higher proportions of the budgets of lower-income earners. This is illustrated in Figures 2 and 3, which replicate the inverse relationship, found above, between budget shares and total expenditure.

These findings suggest that the carbon tax may have a proportionately higher impact on those households with relatively lower total household expenditure, for any given household type. However, the effect of a carbon tax is not unambiguous. The price of food consumed outside the home (commodity group 2) also rises substantially, and in this case higher-income earners spend a proportionately larger amount of their budgets on this good. Overseas travel (commodity group 13) incurs the fourth largest price increase, and its budget share increases with total expenditure.[11]

Following petrol, household services (commodity group 9) incurs the second largest price increase. This commodity group directly corresponds to the rubber, plastic and other chemical product manufacturing industry (industry no. 19), whose output has the second highest carbon content.

Figure 1 – Budget Share Allocated to Petrol by Household Type 10

 

Figure 2 – Budget Share Allocated to Food by Household Type 10

 

Figure 3 – Budget Share Allocated to Domestic Fuel and Power by Household Type 10

 

4 Welfare Analysis of a Carbon Tax#

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This section examines the effects of a carbon tax on the welfare of different household types at different levels of total weekly expenditure, along with overall inequality measures. A summary of the theory behind these welfare measures and their computation may be found in Appendix B.

4.1  Welfare Changes#

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Tables 5 and 6 summarise the welfare changes that arise from each of the three carbon tax rates. The analysis was conducted using ten expenditure levels ranging from $200 to $1400, though for convenience only three values are shown in the tables for each of the eighteen household types. The welfare changes for those households who recorded a positive weekly expenditure on tobacco are provided in Table 5, while Table 6 outlines the welfare changes for non-smoking households. The equivalent variation,

 

, is given together with its ratio to total expenditure,

 

.[12] The tables show that the welfare loss ranges from approximately 0.38 percent of total expenditure in the case of a $7 carbon tax to 1.4 percent in the case of a $25 carbon tax.

 

The relationship between

 

and

 

provides an indication of the disproportionality of the welfare impact of the carbon tax within each household type. A rising profile may be described as progressive. Within each household type, the profile of

 

with

 

is similar for each of the three carbon tax rates.

 

For nine non-smoking households and six smoking household types, the ratio

 

decreases with

 

. This suggests that the carbon tax may be slightly more regressive among non-smoking households. However, for the majority of household types, the carbon tax proves to be neither strictly regressive nor progressive. The column adjacent to

 

gives the increase in tax paid per week,

 

. The tables show that for any given carbon tax rate and level of expenditure, the increase in tax paid does not vary substantially between household types.

 

The marginal excess burden of the carbon tax,

 

, is the difference between the equivalent variation and the increase in tax paid,

 

. Households, both smoking and non-smoking, with low to moderate expenditure levels incur similar excess burdens independent of type. However among those households (smoking and non-smoking) with high levels of weekly expenditure, three groups incur significantly higher marginal excess burdens.

 

The burdens incurred by households with one child rise with expenditure at a greater rate than the burdens incurred by households with no children. Figure 4 compares the marginal excess burdens that arise from a $25 carbon tax incurred by households with one child and those with none, across one and two adult smoking households.

Relative to no children and independent of the number of adults, the addition of a child clearly increases a household’s marginal excess burden at the higher total weekly expenditure levels.

Single adult, relative to multi-adult households with higher total expenditure levels, are similarly more adversely affected by the carbon tax. Figure 5 shows the marginal excess burdens incurred by single-adult and multi-adult households with no children when a $25 carbon tax is imposed. From multi-adult to single households, the marginal excess burden clearly tilts upwards over higher levels of weekly total expenditure. This result holds regardless of the number of children in the household.

When total expenditure levels exceed $600 per week, the marginal excess burdens incurred by couples where the head of the household is aged over 65 (household type 2) are substantially greater than those incurred by couples where both are aged under 65 (household type 8). Figure 6 compares the marginal excess burdens between these two smoking household types and shows that the two lines begin to diverge at the expenditure level of $600 per week in the case of a $25 carbon tax.

The marginal welfare cost of a tax, defined as

 

, measures the marginal excess burden per dollar of additional tax revenue. For all three carbon taxes, the variation in this measure is very similar and lies between approximately 18 and 25 cents per dollar of additional tax revenue.

 

Figure 4 – Marginal Excess Burdens: The Addition of a Child

 

Figure 5 – Marginal Excess Burdens: Single versus Multi-Adult Households

 

Figure 6 – Marginal Excess Burdens: The Presence of a 65+ Adult

 

The welfare measures in Tables 5 and 6 were based on three levels of total weekly expenditure. These expenditure levels were chosen for illustrative purposes. Within each household type, there is considerable variation. Table 7 reports the welfare changes at arithmetic mean weekly total expenditure levels for each household type (shown in Table 2), for the case of a $25 carbon tax. The welfare loss is about 1.3 percent for the $25 carbon tax, while the marginal welfare cost varies between approximately 15 and 18 cents for smoking households and 13 and 15 cents for non-smoking households per dollar of additional tax revenue.

4.2 Inequality Measures#

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The relationship between

 

and

 

was used in the previous section to provide a measure of the progressivity, in terms of the disproportionality, of the impact of the carbon tax. However, this indicator does not reflect information concerning the distribution of changes, involving the numbers of households at the various total expenditure levels. Furthermore, this measure only allows comparisons between households in the same demographic group. This section derives a measure of the redistributive effect of the carbon tax which as a summary measure permits comparisons across different demographic groups.

 

The redistributive effect of the tax change can be examined using the distribution of money metric utility,

 

, before and after the imposition of the carbon tax. A suitable money metric is defined as the value of total expenditure,

 

, which, at some reference set of prices,

 

, would give the same utility as the actual total expenditure.[13] For present purposes, the pre-change prices are used as the reference prices.

 

An important feature of the inequality measures reported here is that they refer to the inequality of individual (money metric) utilities. Each individual in a household is given that household’s value of ‘wellbeing’,

 

where

 

is the adult equivalent size. The inequality measure reported is the Atkinson measure,

 

, which is based on the additive welfare function:[14]

 

(15)    

 

 

where

 

is the number of individuals in the

 

^th household (

 

) and

 

is increasing and concave.[15] Inequality is defined as the proportional difference between the equally-distributed-equivalent,

 

, and the arithmetic mean,

 

. Hence,

 

is the money measure per equivalent adult which, if received by every person, produces the same social welfare as the actual distribution, and:

 

(16)    

 

 

Although this may be used with any form of

 

, the most common form is:

 

(17)    

 

 

where

 

is the degree of constant relative inequality aversion of a disinterested judge. For

 

, the expression in (17) becomes

 

. Thus:

 

(18)    

 

 

The coefficient

 

is a measure of relative inequality aversion which, as the degree of concavity of

 

reflects the judge’s view of the ‘wastefulness’ of inequality. The value of

 

is often linked to a judge’s tolerance of the loss involved (using a ‘leaky bucket’) in making a transfer from a richer to a poorer individual.[16] Adult equivalence scales are based on the following function:

 

(19)    

 

 

where

 

and

 

respectively are the number of adults and children in the household. The parameter

 

measures the size of children relative to adults, and the term

 

reflects economies of scale in consumption.[17] On the use of this form, see Jenkins and Cowell (1994, p.894). The results reported here use the values

 

and

 

. These values were found to be approximately the median of a large range of scales used in the literature. For a detailed sensitivity analysis of inequality measures to the choice of the adult equivalence scale see Creedy and Sleeman (2004). A comparison with these results suggests that inequality rises with

 

. Profiles of inequality for variations in

 

are found to be U-shaped and the value of 0.75 corresponds roughly to the minimum inequality measure, for a given value of

 

.

 

Tables 8, 9, and 10 give the pre and post-carbon tax Atkinson measure of inequality for each of the 18 household groups for both smoking and non-smoking households. Although a range of values of

 

were used, the results are reported for the relative inequality aversion coefficient of 1.2, which represents substantial aversion to inequality. Despite this, the percentage increases in inequality were small. Indeed some falls in inequality were recorded. For the top carbon tax rate of $25, the overall redistributive effect of the tax was an increase of just 0.345 percent. This overall effect also reflects the relative numbers of households in the various demographic groups, as well as the distribution of total expenditure among households. By lowering the aversion to inequality or by focussing attention on the lower tax rates, the overall effect of the carbon tax becomes trivial.

 

5 Conclusions#

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This paper has analysed the potential effects on consumer prices in New Zealand arising from the imposition of three carbon tax rates, namely $7, $15 and $25 per tonne of carbon dioxide. The resulting effects of those price changes on the welfare of a range of household types and total expenditure levels were examined. Finally, the effects on a summary measure of inequality, within each demographic group and over all groups combined, were reported. The price changes were computed using information about inter-industry transactions and the welfare effects were examined using data from pooled Household Economic Surveys. The linear expenditure system was used to model the demand responses of consumers, from which the welfare and inequality effects were calculated.

Households with relatively low total expenditure were found to spend a proportionately greater amount of their income on carbon intensive commodities such as petrol and domestic fuel and power. Despite this, the distributional effect of the carbon tax was not unambiguous, in view of the substantial price increases for several commodity groups on which households with relatively higher total expenditure spend proportionately more.

The ambiguity of the distributional effect of the carbon tax was confirmed by the welfare measures which show that for the majority of households types, the relative burden of the carbon tax (the equivalent variation divided by total expenditure) does not vary monotonically with total expenditure; over some ranges it is regressive while for other ranges of total expenditure it was progressive.

The marginal excess burdens arising from the carbon tax were generally small. However, for three groups, the burdens rose relatively more quickly with expenditure, beyond total expenditure levels of approximately $600 per week. These groups were households with one child relative to households with no children, single adult households relative to multi-adult households and households where the head of a couple was aged over 65 relative to couples where both were aged under 65.

Inequality measures were obtained for a range of degrees of aversion to inequality. Even for very high aversion, the top carbon tax rate of $25 was found to give rise to a very small redistributive effect.

The marginal welfare cost of the carbon tax was found to lie between 18 and 25 cents per dollar of additional tax revenue for all three carbon tax rates.

Appendix A: The Data#

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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.

 

 

Placements were made by locating the commodity group which contained the output of the industry concerned.

Appendix B: Welfare Changes and Demand Elasticities#

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This appendix describes the computation of the welfare measures and the method used to compute the required parameters for each demographic group and total expenditure level. Only the main results are stated, as their derivations are available elsewhere.[18] The basis of the approach is the use of the linear expenditure system to model households’ behaviour. The total expenditure of each household is assumed to remain fixed when prices of goods and services change. Thus, possible changes in production (associated with the changing structure of demands) and factor prices, along with the distribution of income, are ignored.

The direct utility function for the linear expenditure system is:

(B1)     

 

 

with

 

and

 

Here,

 

and

 

are respectively the total and the committed consumption of good

 

If

 

is the price of good

 

and

 

is total household expenditure, the budget constraint is

 

In the present context, the parameters of the utility function differ according to both household type and total expenditure, as discussed further below. The next two subsections define equivalent variations and money metric utility, which are used in the distributional analyses.

 

Equivalent Variations

The equivalent variation,

 

, is defined in terms of the expenditure function as

 

where

 

is the minimum expenditure required to reach utility level

 

at prices

 

Defining the terms

 

and

 

respectively as

 

and

 

, the indirect utility function,

 

, is:

 

(B2)     

 

 

The expenditure function is found by inverting this and substituting

 

for

 

to get:

 

(B3)     

 

 

Suppose that the vector of prices changes from

 

to

 

. Substituting for

 

using (B3) and assuming that total expenditure remains constant at

 

gives:

 

(B4)     

 

 

Substituting for

 

using equation (B2)

 

into (B4) gives:

 

(B5)     

 

 

The term

 

is a Laspeyres type of price index, using

 

s as weights. The term

 

simplifies to

 

which is a weighted geometric mean of price relatives.[19] A convenient feature of the present approach is that the expression for the equivalent variation requires only the percentage changes in prices to be specified.

 

Money Metric Utility

For distributional analyses of tax reforms, it is necessary to have a money metric measure of each household’s utility. A suitable money metric is defined as the value of total expenditure,

 

, which, at some reference set of prices,

 

, would give the same utility as the actual total expenditure.[20] A feature of this metric is that it ensures that alternative situations are evaluated using a common set of reference prices. It is, importantly, invariant with respect to monotonic transformations of utility. Using the expenditure function gives:

 

(B6)     

 

 

For the linear expenditure system, this is found to be:

(B7)     

 

 

The effect on welfare can be measured in terms of a change in

 

from

 

to

 

, where, as before, the indices

 

and

 

refer to pre- and post-change values respectively. If pre-change prices are used as reference prices, so that

 

for all

 

 

is simply the value of actual total expenditure after the change less the value of the equivalent variation; that is,

 

. Hence the proportionate change,

 

, is conveniently the ratio of

 

to

 

.

 

Total Expenditure Elasticities

Given cross-sectional budget data, the total expenditure elasticities, for different household types, can be obtained by first estimating the relationship, for each commodity group, between the budget shares and total household expenditure. If

 

is the budget share of the

 

^th good, a flexible specification that has been found to provide a good fit is (omitting subscripts):[21]

 

(B8)    

 

 

This form has the convenient property that, if parameters are estimated using ordinary least squares, the adding-up condition,

 

holds for predicted shares, at all total expenditure levels,

 

. With the level of disaggregation used, it was necessary to carry out a total of 792 (

 

) budget share regressions. Hence these cannot be reported here.

 

At any given level of

 

the expenditure elasticity is given by:

 

(B9)     

 

 

which can be expressed as:

(B10)    

 

 

so that

 

for

 

and converges to

 

as

 

(though of course it may exceed unity over certain ranges of

 

).

 

Demand Elasticities

For the linear expenditure system, the total expenditure elasticities are:

(B11)    

 

 

Hence, given values of

 

calculated using (B10), the corresponding value of

 

can easily be obtained using (B11), as

 

 

Cross-sectional budget data do not provide direct information about price responses. However, the own-price elasticities,

 

and cross-price elasticities,

 

are obtained using a general property of directly additive utility functions. It was shown by Frisch (1959) that:

 

(B12)     

 

 

(B13)    

 

 

In these expressions,

 

denotes the elasticity of the marginal utility of total expenditure with respect to total expenditure; this is called the Frisch parameter.

 

The computation of welfare changes does not actually require each value of

 

, but the value of

 

the committed expenditure on good

 

. Given own-price elasticities of demand for each good at each income level, obtained using (B13), the committed expenditures can be obtained by making use of the property of the linear expenditure system that:

 

(B14)    

 

 

Hence:

(B15)    

 

 

A difficulty is that household budget data cannot provide direct estimates of the Frisch parameter. It is therefore necessary to make use of extraneous information. The results reported above were obtained using a fixed Frisch parameter of -1.9.[22] However, experiments with varying Frisch parameters, allowing the absolute Frisch to fall as total expenditure rises, showed that the results were not sensitive.

Price Changes

In general the demand functions can be expressed as

 

Holding

 

constant and differentiating the demand for good

 

with respect to the prices gives:

 

(B16)    

 

 

where the dots again indicate proportionate changes and

 

is the elasticity of demand for

 

with respect to a change in the price of good

 

. The proportional change in the budget share,

 

is:

 

(B17)     

 

 

which, as total expenditure is fixed, is equivalent to the proportional change in expenditure on good

 

.

 

A convenient feature of the present approach is that the expression for the equivalent variation requires only the percentage changes in prices to be specified. The relevant terms can be expressed in terms of the

 

s. Since

 

and defining

 

it can be shown that

 

and

 

. Suppose that all prices change by the same proportion. If all prices change in the same proportion,

 

for all

 

and

 

 

References#

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