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Forskning om skattekonomi

Economic Research Programme on Taxation

Rapport 69

Jrgen Aasness Andreas Benedictow Mohamed F. Hussein

Distributional Efficiency ofDirect and Indirect Taxes

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Rapport nr. 1-49 bestilles fra Norges forskningsrd

F.o.m. nr. 50 (1998) bestilles rapportene fra:

Statistisk sentralbyrSalg- og abonnementservice2225 Kongsvinger

Telefon: 62 88 55 00Telefaks: 62 88 55 95E-post: [email protected]

Oslo, desember 2002Trykk: Statistisk sentralbyr

ISBN 82-12-01793-1ISSN 0803-2742

Copyright Statistisk sentralbyr 2002

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Abstract

Twelve different direct and indirect taxes in the Norwegian tax system are ranked according to their

distributional efficiency. The distributional efficiency of a tax change is measured by the change in an

aggregate measure of the distribution of standard of living over all individuals in the (mini)

population, divided by the change in total consumption. We focus on three measures: average standard

of living, equality and Sen-welfare. The distributional efficiency varies strongly between the tax

reforms, and the rankings are robust w.r.t. important model assumptions. For expansive tax reforms,

the ranking list according to increase in Sen-welfare per krone increase in total consumption is: (i)

Increased child benefit for families with three or more children, (ii) increased parents' tax deduction,

(iii) increased child benefit for the first child, (iv) increased parents' income deduction, (v) reduced

VAT on food, (vi) reduced tax on use of electric energy, (vii) reduced VAT on all goods, (viii)reduced taxes on tobacco, spirits and wine, (ix) reduced petrol tax, (x) reduced income tax, (xi)

reduced wealth tax, and (xii) reduced surtax.

Keywords: Consumption, equivalence scales, income, inequality, microsimulation, tax policy, welfare

JEL classification: D10 D30 H21 H22 H24

Address:

Research DepartmentStatistics NorwayP.O.Box 8131 Dep.N-0033 Oslo, [email protected]@[email protected]

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1. Introduction

The tax system affects the standard of living in different ways for different groups of the population.

This is why the effects of direct and indirect taxes on the standard of living is an important subject in

public economics, see for instance Myles (1995). In Norway, a lot of attention has been paid to the

distributional effects of direct taxes, like for instance taxation of income and wealth, while little

attention has been paid to the distributional effects of indirect taxes, like value added tax (VAT) and

commodity taxes. This is in spite of the fact that indirect taxes are the source of approximately one

third of the public tax revenue,1 and thereby have considerable effects on the standard of living.

Consumption also shows less volatility than income, and may therefore be a better indicator for the

standard of living than income. Consumption taxes may thus be relevant tools for the distributional

policy. In this paper, we compare the effects of twelve direct and indirect taxes on the standard of

living of the Norwegian population.

Our starting point is a hypothetical situation where the government wants to lead an expansive

economic policy, either through a reduction in direct or indirect taxes, or by increasing transfers or

subsidies. We assume that the government wants a specific level on the expansivity of the economic

policy, here measured by the increase in total consumption of all households.2

We calculate the

distribution of the standard of living3

over all persons in the Norwegian population, and how this

distribution responds to changes in the tax system. Furthermore, this approach allows us to determine

the effects on various characteristics of the distribution of the standard of living. We focus on threeaggregated measures of welfare: (a) Average standard of living, measured by the arithmetic mean; (b)

the equality of the standard of living, measured by 1 minus the Gini-index; and (c) Sen-welfare,

defined as the product of the average standard of living and equality.

We find that all the twelve tax reforms lead to an increase both in the average standard of living and in

Sen-welfare. Reduced surtax, income tax, wealth tax and petrol tax lead to reduced equality, while the

other tax changes lead to a more equal distribution of the standard of living. In general, an increase in

subsidies or tax-deductions directed towards families with children leads to the largest increase in both

the mean and the equality of the standard of living, and thereby the largest increase in Sen-welfare.

Then follows reduced VAT on food, and the rest of the indirect taxes. The least efficient tax changes

in this analysis are reduced taxation on income and wealth.

1 About 36 per cent of the publics' total tax revenue came from indirect taxes in 1999 (Olsen 2000, appendix, p. 69*).2 We define total consumption of a household as total consumption expenditure divided by a household specific price index.Total consumption of all households is defined as the sum of total consumption over all households in Norway. Total

consumption per person and per consumption unit are also calculated to get comparable figures.

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A reduction in taxes or an increase in transfers leads to a partial increase in the standard of living of

the households because it allows for increased private consumption. Such tax changes may also lead to

reduced public economic activity however, for instance reduced public support to kindergartens. This

will also affect the standard of living, but is not discussed here.

In this paper we do not focus on traditional efficiency issues in tax analysis, but instead we define our

measure ofdistributional efficiency separable from efficient production of consumption, by dividing

the changes in welfare by the change in total consumption. One tax reform is more distributional

efficient than another if it distributes total consumption among households in a way that makes

aggregate welfare larger. This can be achieved by reducing inequality, choosing tax reforms that favor

the poor, or by increasing average standard of living, choosing tax reforms that favor households that

are efficient producers of standard of living from their consumption expenditures. It follows from

assuming an equivalence scale different from the per capita model, that households have different

efficiency w.r.t. producing standard of living from consumption expenditures. We draw attention to

this often neglected implication of equivalences scales, and include it as an integrated part of our

distributional analysis.

Since we have a complete set of household demand relations in our model system, we could extend the

analysis to optimal reform of indirect taxes, see e.g. Ahmad and Stern (1984) and Decoster and

Schokkaert (1989), but this is left to another paper. Since our current model do not include labour

supply relations this would also introduce an assymmetry between the effects of direct and indirect

taxes. Our analysis can be considered in the tradition of incidence analysis within tax-benefit

microsimulation models, where we somewhat untraditionally analyse both direct and indirect taxes

within the same framework, and where we introduce some new analytical tools.4

When interpreting our empirical results it is important to note that we do not measure the effects of

changed behavior in labor supply and commodity demand due to local tax reforms. Such effects can

be important for, say, changes in total consumption, but we conjecture it will not be important fordistributional efficiency since we in our definition has separated away the effect of changed

consumption. We take full account of the wide differences in consumption patterns and labor supply

3 We define standard of living as total consumption of a household per consumption unit.4 The household demand system is used to derive a system of Engel functions in base year prices and predicting non-negativebudget shares for 24 commodities, adding to one, for each of the 15 000 households in the model. These budget shares areused in Laspeyres prices indexes (Pkt) for each household k and local tax reform t. Such price indexes are approximatelyequal to any utility based price index for local reforms. It is the distribution of these price indexes, and the underlyingdistribution of budget shares, that determine the distributional effects of indirect taxes in our model. The microdata used in

our simulation model do not include consumption data, but if it had we could have used the observed budget shares instead ofpredicting them. Thus our analysis focus on distributional effects and not on behavioral effects of taxation.

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among our 15 000 households, but not the changes in these patterns, since the first point is decisive for

our problem at hand, while the latter is not. It should also be mentioned that we do not take into

account regional differences in preferences, prices and availability of goods, which might influence

our results.

The model framework is presented in section 2, and in section 3 we give a brief description of the

different tax reforms considered in the analysis. The results are presented and discussed in section 4.

In the last section, we show that the main results are robust with respect to the choice of equivalence

scale, within a new and quite broad class of scales.

2. The model framework

We have used the model LOTTE-Konsum, developed at Statistics Norway.

5

LOTTE-Konsum is basedon consumer theory and econometric analysis of consumer behaviour and standard of living, and

welfare theory for aggregation of standard of living over households and individuals in a population. A

model for direct taxes, LOTTE, is used as a pre-model for LOTTE-Konsum to compute the effects of

changes in direct taxes on disposable household income, cf. Aasness et al (1995). LOTTE uses a

model population of approximately 15 000 households with about 40 000 individuals, weighted to be

representative for the Norwegian population. The effects of changes in indirect taxes on consumer

prices are calculated in another pre-model.6 Lotte-konsum calculates savings, total consumption

expenditure, consumption expenditure for 24 goods, the number of consumption units and priceindexes for each household, taking into consideration that different households have different

consumption patterns, and the different measures of distributional effects for the model population,

which represents the entire Norwegian population.

Each tax reform is analysed with regard to three different measures of distributional efficiency,

focusing on the level and the equality of the standard of living. As a measure of the standard of living

for each individual in a household, we use total consumption per consumption unit in the household.7

This implies that all persons belonging to the same household has the same standard of living, a

relevant assumption in the absence of information about the internal distributions within the

5 We use the same kind of microsimulation model and approach as in Aasness (1995, 1997) and Aasness, Aslaksen andGravningsmyhr (1996). The actual microsimulation model used in this paper is developed in 2000, see Hussein (2001) andAasness (2001), and data and tax rules are updated to 2000.6 This model, called PR since it determines prices and revenues, is documented in Benedictow (2000). It is based on the priceequations in the general equilibrium model MSG-6, cf. Holmy, Strm and vitsland (1999).7 The standard of living for household k, and all its members, in situation t is wkt = ckt/ek = ykt/(Pktek), where totalconsumption of the household (ckt) is defined as ckt = ykt/Pkt, i.e total consumption expenditure (ykt) divided by a household

specific price index (Pkt), and ek is the number of equivalent adults in the household in base year prices. Aasness (1995)shows that this can be interpreted as a money metric utility. For description of Pkt see footnote 4 above.

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households.8

The households are considered as producers of standard of living for its members. We

allow for the existence of economies of scale in the households, which means that the number of

consumption units in a household is smaller than the number of persons in the household. For instance

will a household consisting of two adults need less than twice the income of a single adult to achieve

the same standard of living. They can make do with a house smaller than twice the size, and several

expenses can be shared, for instance for newspapers and electricity. Furthermore, we assume that

children need less consumption than adults to achieve the same standard of living. This is reflected in

the model by a larger increase in the number of consumption units when a household is extended with

an adult than with a child. This implies that large households, and families with children in particular,

are relatively efficient as producers of standard of living. This implication of equivalence scales is

often neglected, while we point out the consequences.

An equivalence scale is used to calculate the number of consumption units in the households.9 There

exists no generally accepted foundation for empirical determination of equivalence scales. Therefore,

the choice of equivalence scale is a controversial subject, see e.g. Buhman et al (1988), Atkinson

(1992) and Nelson (1993). Our starting point is the so-called OECD-scale, which implies that if the

cost of living for a one-person household is normalised to 1, the cost of keeping the standard of living

constant when the household is expanded with an adult is 0.7, and with a child 0.5. Several empirical

studies of Norwegian consumer expenditure surveys find support for the hypothesis that the OECD-

scale provides a suitable approximation, see Bojer (1977), Herigstad (1979) and Red Larsen and

Aasness (1996). We carry out sensitivity analyses of the results with respect to the choice of

equivalence scale. This is done by introducing the parameter e, which may be interpreted as the cost of

living for a child relative to the cost of living for a single adult, and also represents the economies of

scale in the household production, cf. footnote 9. The larger e is, the smaller are the economies of

scale, and the larger is the cost of an additional child. If there are perfect economies of scale, e equals

8 This can be rationalized by a household maximin welfare function of the individual utilities, cf. Blackorby and Donaldson(1993, p. 338). Like them we use householddemand functions and aggregate individualwell-being across the population.9 The number of consumption units in household k, in base yeae prices, is defined as e k = (1-f(e)) + ez1k + f(e)z2k, where z1kand z2k are the number of children and adults respectively, e is the cost of living for a child relative to a single adult, and f(e)is the cost of living for an additional adult relative to a single adult. The parameter e is assumed to lie in the interval [0,1].The function f(e) is the most simple linear spline function which fulfills the four special cases, for e = 0, 0.3, 0.5, 1, describedin the text and in footnote 10. This implies that f(e) = (5/3)e for e[0, 0.3], f(e) = 0.2 + e for e[0.3, 0.5], and f(e) = 0.4 +0.6e for e[0.5, 1]. Notice that the relative cost of one additional household member is constant, and that the number ofconsumption units for single adult households equals 1 for any given value of e. Buhman et al (1988) used a power functionclass of equivalence scales with a parameter e with a similar role as in our linear class. We prefer the linear form because thepower function exagerates the economies of scale for large households. This can be illustrated by the much used special caseof the power function which assumes that the number of consumer units is the square root of the number of persons. Thisimplies e.g. that 16 single persons will quadroble their standard of living by establishing a houshold collective! We find thisunrealistic. Furthermore, note that the equivalence scale can be interpreted as an ethical norm or judgement, which can becombined consistently to any household demand system in base period prices, cf. Blundell and Lewbel (1991). Thus the

equivalence scale can vary with prices, and since our underlying demand system is not IB/ESE the equivalence scale mayalso vary with the standard of living when the relative prices are not as in the base period, cf. Aasness (1995).

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0. An increase in the number of members in the household is then free of cost, and the standard of

living for each member of the household is measured by total consumption of the household. Ife

equals 1, there are no economies of scale, and the standard of living for each member of the household

is measured by total consumption divided by the number of members in the household. When e equals

0.5, we obtain an equivalence scale which is equal to the OECD-scale mentioned above.10 The OECD-

scale is employed in the analysis in section 4. We carry out sensitivity analyses in section 5, varying e

between 0 and 1.

The distribution of the standard of living over a population can be summarised in several ways. In this

paper, we focus on three simple aggregated measures: (i) Average standard of living; (ii) equality; and

(iii) Sen-welfare.Average standard of livingis measured by the arithmetic mean of total consumption

per consumption unit over all the individuals in the model population. We define equality as (1 - G),

where G is the Gini-coefficient11. The equality measure varies between 0 and 1, and the value

increases when the distribution of the standard of living becomes more equal. Sen-welfare12combines

the two measures above by multiplying them. The Sen-welfare increases when the standard of living

increases and when the distribution of standard of living becomes more equal.

We analyse the distributional efficiency of twelve expansive changes in the tax system, of which seven

are changes in direct taxes and five are changes in indirect taxes. The tax reforms are evaluated in

accordance with the changes in the three distributional measures presented above, per krone change in

total private consumption.13

The resulting ratios are denoted distributional efficiency, and the changes

are to be interpreted as marginal, comparable changes, which allows us to rank the tax reforms

according to distributional efficiency.14

Before we present the results of the simulations, we take a

brief look at the direct and indirect taxes included in this analysis.

10

Eurostat (1997, p. 86) recommends the use of the standard OECD scale, as mentioned in the text, but has also developed a"modified OECD-scale" as a response to critics claiming that the standard OECD-scale gives to much weight to additionalmembers in the households. In the modified equivalence scale, the cost of expanding a household by one adult is 0.5, and byone child 0.3. When e equals 0.3, we have an equivalence scale that is equal to the modified OECD-scale.11 The Gini-coefficient is the most common measure of inequality in the economic literature, see Aaberge (2001) for anaxiomatic foundation of the Gini-coefficient.12 An axiomatic foundation for Sen-welfare is given in Sen (1974).13 The main results are robust towards the use of real disposable income or total tax revenue as "resource measures" insteadof total consumption, but this may change if the model takes into account changes in labor supply and substitution effects inconsumption patterns.14 Change in average standard of living per krone change in total consumption is considered as a measure of distributionalefficiency, because when a change in the tax system results in higher standard of living than another change, for a givenchange in total consumption, it is due to the distributional effects of the tax changes: An expansive tax reform that to a large

extent affects large households, which are the most efficient producers of standard of living, will therefore have a relativelylarge positive effect on the average standard of living.

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3. Tax reforms

Surtax is a progressive tax on high incomes, and is levied on personal income without any deductions.

Income tax is the common tax on income to the tax distribution fund. It has a flat tax rate, and is

proportional to net income less income deductions, if applicable. Wealth tax is a progressive tax, and

is levied on net wealth. We simulate a reduction of one percentage point for each of these taxes.15

Parents' tax deduction is a deduction in the income tax for parents or others with custody of children

under the age of 19, and is calculated per child. If the recipient does not have taxable income, the

corresponding amount is given as a transfer payment. We simulate an increase of 10 per cent.Parents'

income deduction is, within a specified limit, given for documented childcare expenses for children

under the age of 1216

. We simulate a 10 per cent increase of the initial value. Child benefitis given to

all who support children under the age of 18

17

and live in Norway, and can be considered as a negativetax. Single parents have the right to child benefit for one more child than the actual number of children

in the household. The child benefit is higher for child number three and above than for the two first

children. An additional benefit is given for children under the age of three. We analyse two alternative

changes in the child benefit, a 10 per cent increase for the first child and a 10 percent increase for the

third child and above.

We study the effects of three changes in indirect commodity taxes, the petrol tax, tax on use of electric

energy andtaxes on tobacco, beer, spirits and wine. A 10 per cent increase is simulated for all thesetaxes. The petrol tax is an indirect volume tax collected from wholesale and retail. The tax on use of

electric energy is an indirect volume tax collected from the producers. The taxes on tobacco and beer

are indirect volume taxes collected from the producers, while the taxes on spirits and wine are indirect

volume taxes collected from wholesale and retail. We also study the effects of a general reduction of

the VAT from 23 to 21 per cent,18 and a reduction of the VAT on food from 23 to 21 per cent. The

results are also relevant for larger or smaller changes, also with the opposite sign, because the

distributional effects are calculated per krone change in total consumption of the households.

15 The results on the distributional efficiency are robust to variation of the size and sign of the tax changes, since suchchanges multiplies the nominator and the denominator with almost the same factor.16 There is no age limit for children with special needs, e.g. handicap.17 Before 1st May 2000, the limit was 16 years.18

We simulate a reduction of VAT on commodities subject to VAT in 2000. Most services were exempted from VAT inNorway in 2000, but on 1st July 2001, VAT is introduced on most services.

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4. Results

The model results in table 1 show that all the twelve tax reforms generate increased welfare measured

by average standard of living and Sen-welfare. Most of the reforms also lead to a more equal

distribution of the standard of living. Exceptions are reductions in surtax, income tax, wealth tax and

petrol tax, which lead to reduced equality. In general, increased child benefit and tax deductions for

parents lead to the largest increase both in the standard of living and equality, and thereby to the

largest increase in Sen-welfare. Reductions in indirect taxes cause a larger increase in Sen-welfare

than reduced direct taxes on income and wealth. This is due to the relatively favourable effect reduced

indirect taxes have on equality.

Standard of living and total consumption are measured per person. If there are no economies of scale

in the household production and the cost of living is equal for children and adults, "change in averagestandard of living per krone increase in total consumption" equals 1 for all the tax reforms. This is

illustrated in figure 1 when e = 1. Economies of scale in the household production is assumed in table

1 (e = 0.5), and it follows that all the numbers in the middle column are greater than 1.

Increased child benefit for families with three or more children tops the ranking list for change in the

average standard of living in table 1, because this reform only applies to large households with

considerable economies of scale. After the four child-related tax changes follows surtax, because

many large households pay surtax. A reduction in the wealth tax gives the smallest increase in thestandard of living, reflecting that families with children have little net wealth.

We find that increased child benefit for families with three or more children also leads to the largest

increase in equality per krone increase in total consumption. This is because (i) many households with

three or more children have a relatively low standard of living, (ii) poor families with children

experience a relatively larger increase in their standard of living than rich families with children, even

though they receive the same increase in child benefit in absolute value, and (iii) large families with

children are efficient producers of standard of living. In other words, increasing this type of child

benefit improves the standard of living for a group of people with relatively low standard of living in

an efficient way. The same factors also explain the high score of increases in parents' tax deduction

and child benefit for the first child on the list of changes in equality. Parents' income deduction yields

a lower score on equality, because relatively rich families with children benefit more from this

arrangement than poor families with children.

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Table 1: Distributional efficiency of a reduction in various taxes and an increase in child

benefit and various deductions. OECD equivalence scale (e = 0.5). Ranking number

in parentheses.

Change in Sen-

welfare per

krone increase

in total

consumption

Change in average

standard of living

per krone increase

in total

consumption

Change in

equality per

krone increase

in total

consumption

Increased child benefit for 3rd child+ 2.16 (1) 1.57 (1) 5.78 (1)

Increased tax deduction for parents 1.69 (2) 1.48 (2) 3.45 (2)

Increased child benefit for 1st child 1.55 (3) 1.45 (4) 2.72 (3)

Increased income deduction 1.23 (4) 1.47 (3) 0.76 (6)Reduced VAT on food 1.18 (5) 1.26 (7) 1.34 (4)

Reduced tax on electricity 1.11 (6) 1.23(10) 1.11 (5)

Reduced VAT on all commodities 1.00 (7) 1.26 (9) 0.31 (7)

Reduced tax on tobacco & spirits 0.96 (8) 1.22(11) 0.25 (8)

Reduced petrol tax 0.86 (9) 1.27 (6) -0.56a

(9)

Reduced income tax 0.73(10) 1.26 (8) -1.31(10)

Reduced wealth tax 0.64(11) 1.20 12) -1.59(11)

Reduced surtax 0.44(12) 1.30 (5) -3.18(12)

a This figure is particularly uncertain, and should probably have been less negative or somewhat positive. The reason is thatin our consumption model, petrol expenses are included in the same aggregate as, among other goods and services, expensesto car insurance, which has a larger income elasticity than petrol.

Source: Lotte-konsum, November 2000, Statistics Norway.

Reduced VAT on food and reduced tax on electricity both perform better than parents' income

deduction with regards to equality. These reforms also make rich households better off in absolute

value, but as poor households get the largest percentage increase in the standard of living, equality

increases. A general reduction of VAT, for all goods subject to VAT in 2000, leads to a small increase

in equality. In Norway, services have been exempted from VAT19

. These are "luxurious goods" on

average, meaning that consumption of these goods is increasing with the standard of living. An

introduction of VAT on all services would therefore lead to increased equality.

19 VAT was introduced on most services in Norway in 2001.

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A reduction of the taxes on tobacco, beer, spirits and wine by the same percentage also leads to a weak

increase in equality. According to table 1, a reduction in the petrol tax leads to reduced equality. This

result may have been caused by a weakness in the model however, as noticed in footnote a in table 1.

Reduced taxation of income and wealth, and reduced surtax in particular, leads to a considerable

reduction of equality.

Sen-welfare is defined as the product of average standard of living and equality. Thus, changes in Sen-

welfare reflect the changes in the two components. It follows that increased child benefit for families

with three or more children yields the largest increase in Sen-welfare, and thus in all the three

measures of distributional efficiency in table 1. A reduction of the surtax is performing well with

respect to average standard of living, but very poorly with respect to equality. The last effect is

dominating, and a reduction in the surtax therefore leads to the smallest increase in Sen-welfare of the

twelve tax reforms in this paper.

The results imply that if the government wants to carry out a consumption-neutral tax reform, in the

sense that total consumption of the households stays unchanged, for instance through a reduction in

the VAT on food financed through a general increase in the VAT on other goods, the net effect on

welfare is positive because a change in the VAT on food is more distributionally efficient than a

general change in the VAT.

5. Sensitivity analysisWe investigate how sensitive the results are with respect to the choice of equivalence scale by

allowing the parameter e to vary between 0 and 1. The parameter e can be interpreted both as the cost

of living for a child relative to a single adult and as representing the economies of scale in the

households, cf. footnote 9. In table 1, e equals 0.5, which corresponds to the OECD-scale. In this

section, we investigate how the choice of e affects the ranking of a selection of tax reforms; general

VAT, VAT on food, surtax and child benefit for families with three or more children.

The figures 1 to 3 show the changes in the average standard of living, equality and Sen-welfare

respectively, following a given change in total household consumption for different values of e. It is

important to emphasize that the calculations of relative changes in the average standard of living are

based on equivalence scales and the underlying assumption of economies of scale in the households. If

there are no economies of scale in the households and the living cost of a child equals the living cost

of a single adult, the number of consumption units equals the number of persons in the household.

This is illustrated in figure 1 by the fact that the relative change in the standard of living is the same

for all the tax reforms when e = 1.

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Figure 1. Change in average standard of living

per krone increase in total consumption

Source: Lotte-konsum, November 2000, S tatistics Norway.

0

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Equivalence scale (e)

Changein

standard

ofliving

VA T on al l

Surtax

VA T on fo od

Third child +

Figure 2. Change in equalityper krone increase in total consumption


-4

-2

0

2

4

6

8

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1


Changein

equality

VAT on all

Surtax

VAT on food

Third child

Figure 3. Change in Sen-welfare

per krone increase in total consumption


0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1


ChangeinSen-welfare

VAT on all

Surtax

VAT on food

Third child +

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Figure 1 shows that the ranking of the tax reforms with respect to the average standard of living is

robust towards the choice of equivalence scale. The absolute differences are increasing when the

economies of scale in the households are increasing (i.e. e is decreasing). This reflects that the more

efficient families with children are as producers of standard of living, the more welfare is achieved for

a given increase in total consumption. An increase in the child benefit for large families leads to the

largest increase in the average standard of living, and the difference increases as the economies of

scale increase.

Figure 2 shows distributional efficiency measured by the change in equality for a given change in total

consumption. The ranking is robust towards changes in e in this case also. The absolute differences are

relatively stable, except for child benefit to large families which is considerably more efficient when

the economies of scale in the households are small than when they are large. The reason is that when

the economies of scale are small (when e is large), the standard of living for large families is low,

which makes the child benefit a more efficient tax instrument for increasing equality.

Changes in Sen-welfare are presented in figure 3. Again, the ranking of the tax reforms is robust. The

absolute differences are also relatively stable, but are somewhat increasing when the economies of

scale in the households are increasing. All the tax reforms are more efficient when the economies of

scale are large.

On this background, we conclude that the choice of equivalence scale influences the size of the

distributional efficiency of the different tax reforms, but that the ranking of the tax reforms is robust.

These conclusions are valid for all the twelve tax reforms analysed in this paper.

Model simulations show that contractionary changes in the tax system (increased taxes or reduced

transfers) lead to the exact opposite ranking list compared to the expansive reforms in focus in this

paper. This means that reduced child benefit for families with three or more children yields the largest

reduction in welfare, and that increased surtax yields the smallest reduction in welfare. The results arealso robust to the magnitude of the changes in the taxes, and are therefore relevant for instance for a

halving of the VAT on food. Furthermore, the ranking of the tax reforms is not altered if we evaluate

the tax reforms per change in real disposable income or total revenue instead of total consumption of

the households. This additional information is valuable when evaluating the different policy proposals.

The more robust the results are with respect to changes in the assumptions, the stronger they stand as a

basis for policy makers when confronted with alternative changes in the tax system.

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15

6. ConclusionsTwelve different direct and indirect taxes in the Norwegian tax system are ranked according to their

distributional efficiency. This empirical case study illustrates a new approach to the analysis of the

distributional effects of direct and indirect taxes, which we find fruitful. The distributional efficiency

of a tax change is measured by the change in an aggregate measure of the distribution of standard of

living over all individuals in a mini population divided by the change in total consumption. We focus

on three aggregate measures: average standard of living, equality and Sen-welfare. The distributional

efficiency varies strongly between the tax reforms, and the rankings are robust with respect to

important model assumptions. Child benefit for families with three or more children is most efficient

in all dimensions. Other types of child benefit and tax reductions for families with children are also

relatively efficient. Reduced VAT on food and reduced electricity tax increase equality and Sen-

welfare, but are less efficient than increased child benefit and tax reductions for families with children.The least distributional efficient tax reductions, with respect to equality and Sen-welfare, are

reductions in surtax, wealth tax, and income tax.

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Norges forskningsrd Kultur og samfunn

Forskning om skattekonomiEconomic Research Programme on Taxation

Rapportoversikt

1989

Nr. 1 Vidar Christiansen (red.)

Rapport fra seminar om skattekonomisk forskning. Gol 9.-10. mai 1988

Nr. 2 Rolf Aaberge, Steinar Strm og Tom Wennemo

Skatt, arbeidstilbud og inntektsfordeling i Sverige

Nr. 3 Vidar Christiansen og Torunn Kvinge

Optimal differensiering av kaptialbeskatning

Nr. 4 Erik Fjrli

Skattesubsidiering av selveierboliger: Boligpolitikk for hvem?

Nr. 5 Datagrunnlaget for skatteforskning

Rapport fra en arbeidsgruppe

Nr. 6 Vidar Christiansen og Tom Kornstad

Skattekiler p rente for personer i Norge 1986-1989

Nr. 7 Rolf Aaberge, John K. Dagsvik and Steinar Strm

Labor Supply, Income Distribution and Excess Burden of Taxation

An Empirical Investigation of the Norwegian Tax System

Nr. 8 Vidar Christiansen

Uniform Taxation of Capital Income as a Second Best Result

1990

Nr. 9 Torunn Kvinge

Samfunnskonomiske verknader av kaptialskattlegging

Nr. 10 Tom Kornstad

Norwegian Incom Tax Reform 1986-1989

Changes in Households Marginal Rates of Substitution between Housing, Labour Supply

and other Consumption

Nr. 11 Christian Andersen

Kapitalbeskatning og afkastningskrav

Nr. 12 Knut H. Engedal

Assymetric Information in Capital Markets

A Survey

Nr. 13 Kre P. Hagen and Vesa Kanniainen

Optimal Taxation of Heterogeneous Capital and Tax Neutrality

Nr. 14 Gaute Torsvik

Truverdeproblem i konomisk politikk

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Nr. 15 ystein Aadnevik

Sttte til hushold i etableringsfasen

Nr. 16 Erik Offerdal

A Survey of the Norwegian Tax System, 1962-1987

Nr. 17 Erik Offerdal and Bjrn Helge VatneForward-looking Behavior and Tax Policy Modeling


Capital Accumulation, Productivity and Economic Growth in Norway, 1962-1987


Inflation and the Nonneutrality of Capital Income Taxation


Effective Tax Rates and the Cost of Nonneutral Taxation in Norway, 1962-1987


Effective Tax Rates, Applied OGE-Models and Tax Reforms Toward Neutrality.Any Lessons for Norway?

Nr. 22 Rolf Aaberge, John K. Dagsvik and Steinar Strm

Labor Supply, Income Distribution and Excess Burden of Personal Income Taxation in

Sweden

1991


When Groups Contribute to a Public Good:

The Importance of Institutional Framework for Making Collective Decisions

Nr. 24 Vidar Christiansen

Formueskatt

Nr. 25 Christian Andersen, Kre P. Hagen og Jan G. Sannarnes

Indtgtsbeskatning og indtgtsfordeling

En empirisk analyse av indtgtsbeskatningens fordelingsvirkninger med spesiell vgt p

kapitalbeskatningens betydning

Nr. 26 Erling Holmy and Haakon Vennemo

A General Equilibrium Assessment of a Suggested Reform in Capital Income Taxation

Nr. 27 Ragna Alstadheim

Kapitalbeskatning i en pen konomi

Enkelte problemstillinger knyttet til ilegging av omfordelende skatt p mobil kapital

Nr. 28 Randi Ns

Beskatning av nye finansielle instrumenter

Nr. 29 Morten Berg

Inntektsbeskatning og kamuflert konsum hos personlig nringsdrivende

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1992

Nr. 30 Petter Osmundsen

Optimale finansielle beslutninger ved ulike skattesystemer; en litteraturstudie

Nr. 31 Knut H. Engedal

Strukturpolitiske konsekvenser av informasjonsproblemer i kapitalmarkedeneEn vurdering

1993


Five Essays on the Dynamics of Fiscal Policy

Nr. 33 Christian Andersen og Jan Gaute Sannarnes

Diskusjon av skattereformens delingsmodell

Nr. 34 Skatteforum 1993

Nasjonalt forskermte i skattekonomi 24.-26.05. 1993

Nr. 35 Erik Fjrli

Skatt og finansiell tilpasning

En empirisk underskelse av finansieringsatferd og skatt i norske industriaksjeselskaper,

1987-91

Nr. 36 Jan Gaute Sannarnes

Marginalskattens betydning for portefljesammensetningen av husholdningers sparekapital

Nr. 37 Knut Terje Fagerland

Delingsmodellen

1994


Ejerformer, organisationsndringer og beskatning

Nr. 39 Christian Andersen, Nina Langbraaten og Jan Gaute Sannarnes

Skattereform, indtgtsfordeling og skattestruktur


Intertemporal konsistens i reglene for deling av nringsinntekt

(Rapporten utgis samtidig som SNF-rapport nr. 37-94)

1995

Nr. 41 Jan Gaute Sannarnes

Delingsmodellen og incitamenter til risikotaking


Nasjonalt forskermte i skattekonomi 18.-20.01.1995

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1996


Skatteudgifter i indtgtsbeskatningen af aktieselskaber

Nr. 44 Skatteforum 1996Nasjonalt forskermte i skattekonomi 20.-22.05.1996


En teoretisk model for en entreprenrs egenkapitalandel under asymmetrisk information og

beskatning

Nr. 46 Thomas Lie

Grunnrente og skatt i den norske vannkraftsektoren

En analyse i skattemodellen KRAFTSKATT

1997

Nr. 47 Christian Andersen, Hans Olav Husum og Jan Gaute Sannarnes

En konometrisk analyse av skattereformens betydning for investeringsatferden


Fordelingseffekter av det norske skatte- og overfringssystemet i et livslpsperspektiv


Nasjonalt forskermte i skattekonomi 2.-4. juni 1997

1998


Seminar om skattekonomi 8.-9. juni 1998

Nr. 51 Karl Ove Aarbu and Thor Olav Thoresen

The Norwegian Tax Reform; Distributional Effects and the High-Income Response

1999

Nr. 52 Andreas Haufler and Guttorm Schjelderup

Corporate tax systems and cross country profit shifting

Nr. 53 Per Tovmo and Torberg Falch

Norwegian local public finance in the 1930s

Nr. 54 Thor Olav Thoresen

Mling av progressivitet i det norske skattesystemet 1991-95


Seminar om skattekonomi 30. mai 1. juni 1999

Nr. 56 ystein Thgersen, Carl Edvard Gjersem, Jan Gaute Sannarnes og Wenche Irn Sterkeby

Skatt, trygd og arbeidstilbud

Nr. 57 Jrn Ratts

Fiscal Adjustment with Vertical Fiscal Imbalance: Empirical Evaluation of Administrative

Fiscal Federalism in Norway

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2000

Nr. 58 Annette Alstadster

Optimal skatt p avkastinga av utdanning

Flat eller progressiv skatt p arbeidsinntekt?

Nr. 59 Jan Gaute Sannarnes og Elisabeth SteckmestVelferdsstaten i et livslpsperspektiv

Nr. 60 Raymond Lokshall

Merverdiavgiftsloven og vridning i produksjonstilpasningen

Goods and Services Tax (GST) i New-Zealand

Nr. 61 Espen Bratberg, Tor Helge Holms and ystein Thgersen

Assessing the effects of early retirement programs

Nr. 62 Iulie Aslaksen and Charlotte Koren

Child Care in the Welfare State

A critique of the Rosen model


Seminar om skattekonomi 29. 31. mai 2000

Nr. 64 Hans Fehr, Wenche Irn Sterkeby and ystein Thgersen:

Social security reforms and early retirement

2001


Seminar om skattekonomi 28. 30. mai 2001

Nr. 66 Jo Thori Lind:The use of household welfare functions to estimate equivalence scales

Nr. 67 Jo Thori Lind:

Tout est au mieux dans ce meilleur des mnages possibles.

The Pangloss critique of equivalence scales

2002


Seminar om skattekonomi 29 30. april 2002

Nr. 69 Jrgen Aasness, Andreas Benedictow and Mohamed F. Hussein

Distributional Efficiency of Direct and Indirect Taxes

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Discussion Papers No. 455, April 2006Statistics Norway, Research Department

Fred Schroyen and Jrgen Aasness

Marginal indirect tax reformanalysis with merit goodarguments and environmentalconcerns: Norway, 1999

Abstract:

We present a framework to identify and evaluate marginal tax reforms when merit good argumentsand environmental concerns are given explicit consideration. It is applied to the Norwegian indirecttax system for 1999. The analysis shows that the reform passed in Parliament in November 2000had a clear redistributive profile: a lowering of the VAT rate on food items and the introduction of aVAT on services benefits households in the lowest seven deciles while the upper three deciles gotworse off. But we also argue that the aggregate demand responses triggered an increase ingreenhouse gasses. Next, we show that if the 2000 reform had been complemented with tax ratesrate changes on other products, it could have made every decile better off. Finally, we presentsocially optimal reforms, under different weights on inequality and the environment.

Keywords: indirect tax reform, merit good arguments, greenhouse gasses

JEL classification: H21, H23.

Acknowledgement: Previous versions of this paper have been presented at Skatteforum 2002(Losby), the Annual Conference of Norwegian Economists (Bergen, 2003), the 59th IIPF Congress(Prague, 2003), the 7th Nordic Seminar on Microsimulation Models (Helsinki, 2003), and at theCatholic University of Leuven (2005). We are grateful for comments from seminar participants, inparticular from Vidar Christiansen and Bjrn Sandvik, and for computational assistance fromMohamed F. Hussein and Odd Erik Nygrd. This research project has been financed by a grant fromthe Norwegian Research Council to the Institute for Research in Economics and Business

Administration (SNF) (project no 143636/510).

Address: Fred Schroyen, Department of Economics, Norwegian School of Economics & BusinessAdministration, Helleveien 30, N-5045 Bergen , Norway ([email protected]).

Jrgen Aasness, Statistics Norway, Research Department. E-mail:[email protected]

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Discussion Papers comprise research papers intended for international journals or books. A preprint of aDiscussion Paper may be longer and more elaborate than a standard journal article, as itmay include intermediate calculations and background material etc.

Abstracts with downloadable Discussion Papersin PDF are available on the Internet:http://www.ssb.nohttp://ideas.repec.org/s/ssb/dispap.html

For printed Discussion Papers contact:

Statistics NorwaySales- and subscription serviceNO-2225 Kongsvinger

Telephone: +47 62 88 55 00Telefax: +47 62 88 55 95E-mail: [email protected]

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1 Introduction

In Norway, the indirect tax system is responsible for about one third of totaltax revenue. It consists of two parts. On the one hand, a value added taxsystem that up til 2000 imposed a uniform rate of 23% on most commoditiesbut exempted an important set of services. On the other hand, excise taxesthat are imposed on a range of products. These taxes are based on theproducts physical properties (% of alcohol content, motor capacity, ...) andare motivated by environmental considerations (petrol, packaging), meritgood arguments (spirits and tobacco), or property right arguments (tapes).Excise taxes increase the value of a commodity and therefore the basis for

the value added tax on that commodity.

In the Fall of 2000, a proposal to reform the value added tax systemwas passed in the Norwegian Parliament. The general value added tax ratewas to be raised from 23 to 24% from January 2001 onwards, and becameapplicable as well to most types of services from July 1, 2001 onwards. Alsofrom that date, the VAT rate on food and beverage items was reduced to12%.

Tax reforms have consequences for the efficiency with which resources inthe economy are allocated, for the distribution of welfare over households,

and for the environment. Large changes in the indirect tax system, shouldbe evaluated by means of a microeconomic general equilibrium model. Forsmall reforms, however, a limited amount of statistical information sufficesto identify directions of reforms that are desirable out of efficiency and/orequity concerns. Such exercises have been performed for a number of devel-oped and developing countries. Examples are Decoster & Schokkaert (1989,1990) for Belgium, Madden (1995) for Ireland, Ahmad & Stern (1984) forIndia, Ahmad & Stern (1991) for Pakistan, and Kaplanoglou & Newbery(2003) for Greece.

The above described reform of the Norwegian value added tax system isnot a small one. Except for the rise in the rate non-food rate from 23 to24 %, the nominal rate on many services was raised from 0 to 24%, whilethe rate on food items was halved. In this paper, we are concerned withan evaluation of the direction of this reform by taking the effective indirecttax rate structure of 1999 as our starting point and analysing small ormarginal reforms. Methodologically, our framework extends the one used bythe authors referred above, by explicitly taking environmental considerationsand merit good arguments into account.

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In the next section we present the theoretical tools to evaluate marginal

reforms. In section 3, we first present the empirical basis for our study,including all the parameter values we use as input for the exercise, some ofwhich are relegated to an appendix. Thereafter we present results of the taxanalysis, focusing on the ranking of commodities according to the marginalcost of partial tax increases, and how the ranking changes with the differenthousehold deciles and the environment. Furthermore we demonstrate thepossibilities of Pareto improving reforms. In section 4 we introduce a socialwelfare function and demonstrate different types of social welfare improvingreforms. Concluding remarks are collected in section 5.

2 A theoretical framework

We consider an economy with H households whose preferences can be rep-resented by the utility functions uh() (h = 1,...,H) defined over n com-modities (xi, i = 1,...,n), tradeable on competitive markets. The off-producer prices on these markets are given by the price vectorp = (p1,...,pn)0.Household h has disposable income mh that comes from labour earnings,replacement incomes, and capital incomes. The government imposes spe-cific indirect tax rates ti such that the consumer price for commodity i isqi = pi +ti (i = 1,...,n). Facing these prices, household h demands xhi (q, m

h)

units of commodity. For future reference, we denote hs normalised price forgood i by hi

def= qi

mh.

Indirect tax revenue

Aggregate demand for commodity i is given by1

xTi (q)def=X

h

xhi (q, mh),

and indirect tax revenue can therefore be written as

R(t)

def

=X

j tj x

T

j (p + t).

A marginal increase in tax rate i results in extra revenue for the treasuryto the amount of

ridef=

R

ti= xTi +

nXj=1

tjxTj

qi.

1 Hereafter we ignore the vector of income levels (m1,...,mH) as an argument in com-modity demands.

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Multiplying this expression through by qi, we obtain

qiri = qixTi +

nXj=1

tj jiqjxTj , (1)

where jidef=

xTjqi

qixTj

is the aggregate cross price elasticity and tidef= ti

qiis the

effective tax rate as a fraction of the consumer price.

The government evaluates indirect tax reforms in terms of its effects onhousehold welfare and the environment.

Household welfareHousehold welfare is not necessarily perceived in the same way by the

government as by the household. The reason for this perception wedgeis that the government may be convinced about the beneficial/detrimentalproperties of some commodities, which households disregard when makingtheir purchasing decisions. The obvious examples here are alcohol and to-bacco. In the empirical application, these commodities belong to the sameconsumption category and we will therefore in the rest of the paper assumethat only one commodity has (de)merit properties, viz commodity n. Tomodel merit good arguments in the social evaluation, we follow the approach

put forward by one of us (Schroyen, 2005a,b) and take the governments eval-uation of household hs consumption bundle as (we drop for the time beingthe household index)

U(xn, xn)def= u(

x

1 xn),

where xn is a shorthand for the truncated bundle (x1,...,xn1) . The para-meter measures to which extent good n is considered a merit good. It hasthe dimension of a normalised price (a price in proportion to income), so thatxn can be interpreted as a virtual budget share for commodity n.2 Defining

now the (uncompensated) consumers and governments marginal evaluation

2 Ifci

(x, u) (i = 1,...,n) are the compensated inverse demand functions for the house-hold (giving demand prices in proportion to income), the compensated inverse demandfunctions for the government can be shown to be

c

i(x, u) = c

i (x, u) (i 6= n), and

c

n(x, u) = c

n(x, u) + .

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of commodity j, as (subscripts with u and U denote partial derivatives)

j(x)def=

uj(x)Pk uk(x)xk

and j(x)def=

Uj(x)Pk Uk(x)xk

,

respectively, it can be shown that, to a first approximation,

j(x) ' j (x) [1 + jwn] (j 6= n), (2a)

n(x) ' n(x) [1 + + nwn] , (2b)

where j is the scale elasticity for commodity j (the relative change in thedemand price of commodity j due to a 1% increase in the Divisia quantity

indexP

j wjdlog xj), wn is the budget share of the merit good, and def=

n,

a dimensionless measure of the merit good argument. Merit considerationsregarding good n thus have two effects on the governments demand prices.First, they boost the governments demand price for good n (relative tothe households demand price) with . But second, and less obviously,the government considers the household to be better off because of all theinframarginal units of n consumed. This has a scale effect on all demandprices whose importance depends on the budget share of n.

Reintroducing the household index h, the effect of a marginal change in

ti on this households welfare can be shown to be given by

qiUh

ti' (qixi)

h h (qnxn)

h

Xj

whj hj

hji +

hni

!(all i, h). (3)

After dividing (3) by (1), we obtain the marginal cost of rasing one extrakrone in tax revenue through rate ti on household hs welfare (as perceivedby the government):

M Chidef= (q

ixi)h

h

(qnxn)h

P

j wh

j hj

hji +

hni

(qixi)T +P

k t

k ki (qkxk)T

(all i, h), (4)

where the small round brackets indicate that one only needs information onexpendituresnot on prices and quantities separatelyto compute the M Chi .

IfM Chi > M Ch

j , a small decrease in t

i , accompanied by a small increase intj that compensates for the tax revenue loss, leads to a welfare improvementfor household h. The reason is simple: per krone that is lost by marginally

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lowering the tax rate on good i, welfare goes up by more then it goes down

by raising the rate on good j to make up for the tax revenue loss.

Environmental concern

Environmental concern is assumed to be focussed on the emission of green-house gasses. These gasses are due to the total production, distribution andconsumption of goods and services:

E(xT1

,...,xTn ).

The effect on emissions of a tax rise on commodity i is

Eti

=X

k

ExTk

xTkqi

.

Again, multiplying through by qi allows for a parameterisation in terms ofelasticities:

qiE

ti=X

k

k ki, (5)

where kdef= E

xTk

xTk

E, the elasticity of greenhouse gas production w.r.t the con-

sumption of good k. Dividing (5) by (1), we obtain the (probably negative)marginal cost of rasing one extra krone in tax revenue through rate t

ion

total emissions:

M CEidef=

Pk k ki

(qixi)T +P

j t

j ji (qjxj)T

. (6)

Pareto improving tax reforms

Suppose now that M Chi > M Ch

j for all h, then the above reform maybe regarded as Pareto improving for the present generation.3 Should inaddition also M CEi > M C

Ej , then also future generations, through a cleaner

environment, benefit from the reform.

To determine whether a direction of Pareto improving tax reforms exists,we should in principle solve the problem

max{dti}P

i ridtis.t. (i)

Pi M C

hi ridti 0 (all h)

(ii)P

i M CEi ridti 0

(P1)

3 Pareto improving should here be understood as when evaluated by the government.It does not necessarily mean that every household would endorse the reform, since itspreferences have been distorted by the government.

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where the dti are small.

Rather than searching for small dtis, Ahmad & Stern (1984) suggest tolook instead for a set of i (i = 1,...,n) where i is the extra revenue raisedfrom increasing the tax on good i; these revenue changes are then constrainedto be smaller than one in absolute value. For this purpose, we define i asridti (all i) and checking the existence of a Pareto improving tax reform isthus equivalent to solving

max{i}P

i is.t. (i)

PiM Chi i 0 (all h)

(ii) Pi

M CEi

i 0(iii) 1 i 1 (all i)

(P2)

If the solution to this problem is i = 0 (all i), we can apply Farkas-Minkowskis lemma and solve the inverse problem, that is search for a set ofH + 1 non-negative welfare judgements (1,...,H, E), such that

HXh=1

hM Chi + EM CEi = 1 (all i). (7)

This expression says that for an optimal tax vector, the social marginal cost

of increasing every tax rate to raise an extra krone in tax revenue shouldequal that krone.

In the empirical part, this problem will not concern us as there is room forPareto improvements. Christiansen & Jansen (1978) have solved the inverseproblem for the Norwegian indirect tax system of 1975. Their approach,however, is slightly different in that they constrain the social welfare parame-ters h to be monotonically declining according to the exponential functionh = 1 ( m

h

m1)e, where e [0,) is an inequality aversion parameter (this

function was introduced by Stern, 1977). Implicitly, they thus assumed that

the 1975 system does not allow for Pareto improvements.

3 Empirical analysis

The theory above is now applied to analyse marginal indirect tax reformsin the Norwegian economy as of 1999, and use the result to evaluate thedirection of the reform which was passed in Parliament in November 2000.We start out by presenting the empirical basis of our tax analysis, in terms ofprice, income and scale elasticities, tax rates, emission rates, and expenditure

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patterns of ten representative consumers. Next we present the results of our

tax reform analysis, by proceeding in three stages. First we ignore merit goodconsiderations and the effects on the environment, second we introduce themerit good argument, and finally we also take environmental externalitiesinto account. According the M Chi expression (4) we need price and scaleelasticities at the individual level. Since we we lack this information, wereplace them with the respective aggregate elasticities.

3.1 Empirical basis

All the empirical parameters needed in our analysis of tax reforms are pre-

sented in table 1 below and in tables A1-A2 in the appendix. These parame-ters are taken from a comprehensive system of statistics, econometric studiesand simulation models, including both micro and macro data, compiled andcarried out by Statistics Norway.

The budget shares, Engel elasticities and direct Cournot elasticities pre-sented in Table 1, stem from a complete demand system for a representativehousehold in Norway 1999, generating macro demands by multiplying withthe number of households. The cross price Cournot elasticities are presentedin table A2 in the appendix. They fulfil all restrictions following fromadding-up, homogeneity, symmetry and negativity. The macro demands canbe generated from a Gorman polar cost function with linear demographics.Under absence of corner solutions, these macro demands can also be gener-ated by exact aggregation from a population of households with correspond-ing demand functions (cf Aasness, Bye and Mysen, 1996, pp. 339-341).4

4 An earlier and more simple version of the model is described in Aasness, Bye andMysen (1996) and the references therein. The model we used to generate tables 1 and A2is documented in Nygard and Aasness (2003) and the references therein. Each householdin the population is assumed to have a utility function in terms of a utility tree with55 commodities and 34 branches, at each branch the preferences can be described by atranslated CES utility function, where the necessity quantities are linear functions ofthe number of children and adults in the household. The demand system is calibratedusing data from household expenditure surveys and national accounts. The elasticitiesare aggregated to the 14 commodities in this paper using Hicksian aggregation. Theaggregation is partly across branches of the underlying utility tree.

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Table 1. Budget shares, income, own (uncompensated) price and scale

elasticities, effective tax rates and emission shares. Average household.Norway 1999.

i Commodity group Budgetshare

Incomeelasticity

Own priceelasticity

Scaleelasticity

Effectivetax rate

Emissionshare

1 Food and non-alcoholic drinks .143 0.31 -0.21 -4.36 .21 .320

2 Alcohol and tobacco .046 0.94 -0.75 -0.44 .69 .020

3 Clothing and footwear .055 1.16 -0.51 -0.15 .19 .020

4 Gross rents .155 1.13 -0.61 -0.19 .02 .018

5 Electricity .028 0.42 -0.26 -3.98 .28 .022

6 Fuels .005 0.18 -0.48 -5.10 .23 .084

7 Health .026 0.74 -0.32 -1.35 .08 .011

8 Private transport .094 1.39 -0.84 0.04 .42 .2949 Public local transport .017 0.87 -0.66 -0.50 .00 .037

10 Public distant transport .010 1.77 -1.65 0.13 .05 .016

11 Post and telecommunication .022 0.31 -0.28 -2.76 .18 .006

12 Other goods .151 1.03 -0.53 -0.40 .17 .094

13 Other services .181 1.20 -0.62 -0.08 .11 .057

14 Direct purchases abroad .067 1.52 -0.92 -0.12 .00 0

Sum (weighted) 1 1 -1 1

The price elasticities for the representative household in tables 1 and A1

are our estimates of the ji in the formulae of section 2. Since we analysemarginal tax reforms, the expenditures for the different households (qixhi ) inthe year 1999 suffice to calculate the effects on the standard of living. Inorder to make the analysis transparent, and comparable with similar studiesfor European countries, we have constructed ten households to represent theNorwegian population of households in 1999. The expenditure patterns ofthese ten representative households are presented in table A2 in the appendix.Household expenditures are derived from a microsimulation model which iscalibrated to the same 1999 consumption data as the macro model, so thatthe aggregation restrictions presented at the start of section 2 are fulfilled in

our marginal tax analysis.

The fourth column of table 1 gives the scale elasticity for each commodity.These elasticities were obtained by inverting the direct demand system (seeSchroyen, 2005b, on the algorithm). Their interpretation is the percentchange in the demand price of a commodity for a 1% increase in the Divisiaquantity index (

Pj wj dlog xj).

The fifth column of table 1 lists the effective tax rates for all 14 categories.These rates are the sum of the value added tax, ad valorem tax and volume

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tax as a fraction of the final consumer price for the year 1999.5

The final column gives the emission shares. Emissions include both directemissions from the consumers and emissions from the producers of the con-sumer goods, including the emissions from the production of the intermediategoods used in the production of the consumer goods, applying input-outputtechniques. The emission estimates are taken from Indahl, Sommervoll andAasness (2001, table 1, last column), updated to 1999 and aggregated to thecommodity groups used in this paper.

3.2 Results ignoring merit goods and emission effects

When presenting our results, we proceed in three stages. First we ignoremerit good considerations and the effects on the environment. Next, weintroduce the merit good argument, and finally we also take the negativeenvironmental externalities into account.

The marginal costs for the ten representative households when settingh = 0 are reported in table A3 of the appendix. But as we discussedearlier, to identify the effect of reform on household hs well-being, it sufficesto compare the ranking of the different M Chi . The rankings are depicted infigure 1.

First notice how a marginal tax changes may have very different effectson the well-being of different households. While the lower deciles wouldapprove of a reduction in the tax rate on food or fuel and an increase in thaton private transport or public distant transport, exactly the oppositeis true for the upper deciles. A similar finding was reported by Decoster& Schokkaert (1989) for Belgium and Kaplanoglou & Newbery (2002) forGreece. This should not come as a surprise since the budget share for foodfalls from more than 25% for the lowest decile down to 9% for the highestdecile (cf table A2). Private and public distant transport, on the other hand

increase from less than 4% (taken together) up to almost 13%. Much lessvariation is there in the budget share for public local transport: from 1.9%for h = 1 to 1.6% for h = 10.

Figure 1 also shows that the type of reform passed in the Norwegianparliament in the Fall of 2000a reduction in the VAT rate on food items,

5 These are calculated for 1999 by the input-output model integrated in the Norwegiannational accounts and large scale general equilibrium models of Statistics Norway. Seee.g. Holmy et al (1994, 2.17.1-5)

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0123456789

1011121314

1 2 3 4 5 6 7 8 9 10

1. Food, incl. non-alcholic bev. 2. Alcohol and tobacco

3. Clothing and footwear 4. Gross rents

5. E lectricity 6. Fuels

7. Health 8. P rivate transport

9. P ublic local transport 10. P ublic distant transport

11. Post and telecommunication 12. Other goods

13. Other services 14. Purchases abroad

Figure 1: Rankings of M Chi ( = 0).

and introduction of VAT on servicesis benefiting the first seven deciles andmaking the last three deciles worse off.

Except for the first decile, all other deciles would also agree on a reductionin the tax on private transport (excise taxes on gasoline and on cars) ifthis was financed by more expensive public local transport.

Another observation is that all ten representative households would en-dorse lower excise taxes on alcohol and tobacco no matter how financedthrough other commodity taxes (even that on health services!).

Many observers are likely to utter scepticism about these last policy pro-

posals, arguing that the high level of excise taxes on alcoholic beverages andtobacco serve to contain consumption patterns that put health at risk, andthat excise taxes on private transport play a Pigouvian role. In a next stage,we therefore introduce the merit good argument and environmental concerns.

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3.3 Introducing a merit good and environmental con-

cerns

We single out the category alcohol and tobacco as a demerit good whoseconsumption is depreciated by the government with a factor < 0 commonfor all deciles. An important question is then what value should take. Inrecent years, public opinion is unambiguously converging on the idea thatsmoking is detrimental for peoples health.6 Regarding alcohol, the sale ofbeverages with an alcohol content of more than 5% is restricted in Norwayto Vinmonopolet, the stated owned wine monopoly.7

As seen earlier, a zero value for makes it possible to make all decilesbetter offby lowering taxes on alcohol and tobacco, and raising the tax onhealth care. From table A3, it transpires that M Chalc&tobM C

hhealth is lowest

for households in the lowest decile. It turns out that.67 is the highest valuefor such that M Chalc&tob M C

hhealth (all h) (the inequality being binding

for the lowest decile). On the other hand, for any value of below .784,we have that M Chbev&tob M C

hhealth (all h) so that every deciles well-being

could be improved by taxing beverages and tobacco heavier and makinghealth care products and services cheaper. We therefore fix at .70 inthe remainder of the paper. This means that the governments marginalwillingness to pay for alcohol and tobacco lies about 68.6% below that of

the consumer.8 For this parameter value, the ranking of the different M Chiare given in the first ten columns offigure 2 (based on table A4).

From this figure, it transpires that the government could still increase thewell-being of every decile by at least two reforms: lowering taxes on privatetransport, clothes and footwear, other services and raising them onpublic distant transport; and lowering taxes on alcohol and tobaccoand rasing them on gross rents. But are such reforms also to the benefitof the environment?

That question can be addressed by looking at the last ranking in figure

6 Since June 2004, smoking is no longer allowed in Norwegian cafs and restaurants.7 Vinmonopolet was established in 1922 after a general referendum in 1919 where more

than 60% of the electorate voted in favour of a ban on the sale of spirits and liquor. Severalyears later, this ban was abolished and Vinmonopolet got the sole right to sell spirits andliquor.

8 Using (2b), we get that

2(x) 2(x)

2(x)' (1 + 2w2) = [1 + (.441)(.0464)] (.7) = .686

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123456789

1 01 11 21 3

1 4

1 2 3 4 5 6 7 8 9 10 E n v

1. F oo d , inc l. no n-a lcho lic be v. 2 . A lco ho l and to b a cco

3 . C lo thing a nd fo o twe a r 4 . G ro s s re nts5 . E le c tric ity 6 . F ue ls

7 . H e a lth 8 . P riva te tra ns p o rt

9 . P ub lic lo ca l tra ns po rt 10 . P ub lic d is ta nt tra ns po rt

11. P os t and teleco mm unicat ion 12. O ther goo ds

13 . O the r s e rvice s 14 . P urcha s e s a bro a d

Figure 2: Rankings of M Chi and M CEi ( = .7).

2, indicated as Env. This column depicts the ranking of the marginalcosts for the environment, M CEi . As explained in section 2, the cost for the

environment comes in the form of greenhouse gas emissions related to theconsumption, production and distribution activities of the 14 commodities(except for purchases abroad).

For each decile h we have computed the rank correlation coefficient be-tween the M Chi and M C

Ei . These are reported in table 2. For most deciles,

these correlations are insignificant. But it transpires that pleasing deciles2, 3 or 4 and the environment poses a challenge. Interestingly, the rankcorrelation becomes less negative (and even positive) when considering theupper deciles.

Table 2. Rank correlation coefficient between M Chi and M CEiDecile 1 2 3 4 5 6 7 8 9 10

rankcorr(M Chi , M CEi ) -.26 -.43 -.46 -.34 -.29 -.28 -.29 -.24 -.08 +.13

The impact of the 2000 reform on the environment can be readily readoff from the final column in figure 2: M CEfood < M C

Eoth serv indicates that

greenhouse gas emissions will have increased following this reform. Theexplanation is that consumption of food items entails production and distri-bution activities which are heavy contributors to greenhouse gas emission (an

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emission share of 29%). Services, on the other hand, pollute far less (3.6%

emission share). The reduced demand for services due to the introductionof a VAT, does not compensate for the extra CO2 emissions following theincreased consumption of food items.

Notice also that the relative ranking for private transport/clothingand footwear/other services relative to public distant transport nowswitches: the environment is made worse offwhen reducing taxes on one ofthe former category and raising them on the latter to neutralise the effecton revenue. The same can be said about the second reform that was earlieridentified as Pareto improving. Taxing (imputed) gross rents heavier while

cutting on the tax on alcohol and tobacco goes at the cost of more CO2-pollution. However, this does not mean that Pareto improving reformsare non-existent. In table 3, we show the solution to problem (P2) (with = .7).

Table 3. A Pareto improving reform securingmaximal revenue ( = .7).

i Category i1 Food & Beverages 12 Alcohol & Tobacco 13 Clothing & Footwear .284 Gross Rents 15 Electricity 16 Fuels .227 Health 18 Private transport 19 Public local transport 1

10 Public distant transport 111 Post & telecommunication .3112 Other goods 113 Other services 114 Purchases abroada 0

Sum 0.9317a 14 was constrained to zero

This reform produces a maximal revenue increase of 0.93 kroner. It keepsemissions constant and makes all deciles, except for the 1st, 9th and 10thstrictly better off. This reform is striking in several respects. First, pri-vate transport features among those commodities that can be taxed moreleniently while public local transport should be taxed heavier. Fuels and

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other services are categories that should be taxed more heavily, but so is

food (unlike what the 2000 reform did). And strikingly, the tax on alco-hol and tobacco should be reduced, while that on health care should beraisedand this despite the fact the government already discounts the formercategory at a rate of 70% (since = .70).

4 Social welfare improving reforms

Above, it was established that there is room for a reform of the Norwegianindirect tax system that makes every decile better off and reduces CO2-emissions. Two qualifications should be kept in mind. First, that betteroff means as perceived by the government. Second, that we only looked atthe welfare of the representative agent in each decile: all persons in a decilewere treated identically. Should we increase the number of representativeagents, e.g. to 100, then the likelihood offinding a tax reform that furthersthe welfare of every agent would be close to zero. One can then no longeravoid comparing the losses of some agents with the gains experienced byothers.

There is nothing that prevents us to carry out such a welfare analysis bycalculating and comparing P10h=1 hM Chi (all i). For this purpose, we usethe iso-elastic specification for the social marginal utility of income,

h = 1 (mh

m1)e (

nh

n1), e [0,),

normalise 1 to 1, where mh is taken as total consumption expenditure perequivalent adult (i.e. standard of living in table A2) and nh is the averagenumber of persons in a household of decile h (thus giving one welfare vote toeach person in the underlying population).9 The parameter e is the inequal-ity aversion parameter with e = 0 reflecting efficiency with no distributionalconcerns while e puts zero weight on all but the lowest decile (Rawls).

For practical purposes, this last case can be studied by taking e = 10. We donot add the environment/future generations in the computation of the M Cisince this would require the selection of a E. We call

Ph

hM Chi thereforethe short term social marginal cost of category i.

Figure 3 presents the rankings of the short term M Cs for seven differentvalues of e. Thus private transport and public local transport change

9 The average household size in each of the ten deciles are as follows: 1.70 (lowestdecile), 1.71, 2.22, 2.44, 2.54, 2.40, 2.27, 2.14, 2.01, 2.01 (highest decile).

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1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0,1 0,5 1 2 5 10

e

1. Food, incl. non-alcholic bev.2. Alcohol and tobacco

3. Clothing and footwear

4. Gross rents

5. Electricity

6. Fuels

7. Health

8. Private transport

9. Public local transport

10. Public distant transport

11. Post and telecommunication

12. Other goods

13. Other services

14. Purchases abroad

Figure 3: Short term social marginal cost rankings for different e values.

from resp. a bad and good candidate for a tax increase to a good and badone, as inequality aversion grows. Public distant transport should bemade more expensive for any value of e. The marginal cost for food exceedsthat for other services for all values ofe. Earlier, it was mentioned that thefirst seven deciles benefit from the 2000 reform, while the upper three deciles

loose. Figure 3 (e = 0) thus establishes that the winners gain outweighsthe losers loss.

We now inquire which i (i = 1,...,n) should be chosen in order to min-imise the

P10

h=1

P14

i=1 hM Chi i, without deteriorating public revenue and

without increasing emissions:

min{i}P

10

h=1 hP

14

i=1 M Chi i

s.t. (i)P

14

i=1 M CEi i 0

(ii)

P14

i=1 i 0(iii) 1 i 1 (all i)

(P3)

Column aof table 4 gives the results for the efficiency criterion. Interestingly,the recommended policy includes a lowering of the tax on private transportand an increase in the tax on public local and distant transport and thisbenefits the environment (the constraint (i) is slack). Thus, there is noconflict between a utilitarian perspective and concerns for the environment.This is no longer the case when we take a maximin perspective. Column bof table 4 presents the solution to (P3) when the weights to all but the lowestdecile are set to zero and when constraint (i) is ignored. W.r.t. the efficiency

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solution, tax policy recommendations now change for more than half of the

commodity groups. In particular, the tax on fuels is now reduced ratherthan increased. Since fuels have an extremely high marginal environmentalcost (cf last column of table A4), the consequence is a deterioration of theenvironment. Imposing constraint (i) and re-optimising results in column cof table 4. The main changes in policy recommendation are a smaller taxreduction for fuels and a tax increase for public local transport (ratherthan a status quo).

Table 4. Optimal i values ( = .7, Lagrange multipliers with (i) and(ii) in brackets).

i Categorya

Efficiencyb

Rawlsc

Rawls+env.1 Food and non-alc. bev. 1 1 12 Alcohol and tobacco 0 1 13 Clothing and footwear 1 1 14 Gross Rents 1 1 15 Electricity 1 1 16 Fuels 1 1 .277 Health 1 1 18 Private transport 1 1 19 Public local transport 1 0 1

10 Public distant transport 1 1 111 Post and telecommunication 1 1 112 Other goods 1 1 .7313 Other services 1 1 114 Purchases abroada 0 0 0

Sum 0 (1.53) 0 (.04) 0 (.03)Ph

hP

i M Chi i 1.66 .32 .26P

i M CEi i 2.61 2.73 0 (.021)

a 14 was constrained to zero

5 Conclusion

We have presented a framework to identify and evaluate marginal tax reformswhen merit good arguments and environmental concerns matter. We nextapplied the analysis on the Norwegian indirect tax system for 1999. Ouranalysis showed that the reform passed in Parliament in November 2000 hada clear redistributive profile: a lowering of the VAT rate on food items, andthe introduction of VAT on services benefited households in the lowest seven

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deciles while the upper three deciles got worse off. But we also argued that

an increase in greenhouse gasses has resulted from the aggregate demandresponses.

We then showed that if the 2000 reform had been complemented with taxrates rate changes on other products (as specified in table 3), it could havemade every decile better off. We have also studied social welfare improvingreforms by computing an inequality averse weighted average of the marginalwelfare costs of the ten deciles and arrived at similar conclusions.

It is important to stress the limitations of our analysis. First, we havebeen concerned with marginal tax reformschanges in the indirect tax rates

in a neighbourhood of the existing1999indirect tax structure. To evaluatefinite changes in the tax structure, it no longer suffices to have local infor-mation about behavioural responses of economic agents in the form of priceelasticities. An explicit system of demand equations for each d