Jørgen Aasness • Andreas Benedictow • Mohamed F. Hussein
Distributional Efficiency of
Direct and Indirect Taxes
Rapport 69
Forskning om skatteøkonomi
Economic Research Programme on Taxation
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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 Department
Statistics Norway
P.O.Box 8131 Dep.
N-0033 Oslo, Norway
[email protected]
[email protected]
[email protected]
3
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 three
aggregated 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*).
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.
2
4
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 of distributional 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 for
distributional 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.
The household demand system is used to derive a system of Engel functions in base year prices and predicting non-negative
budget shares for 24 commodities, adding to one, for each of the 15 000 households in the model. These budget shares are
used in Laspeyres prices indexes (Pkt) for each household k and local tax reform t. Such price indexes are approximately
equal to any utility based price index for local reforms. It is the distribution of these price indexes, and the underlying
distribution 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 of
predicting them. Thus our analysis focus on distributional effects and not on behavioral effects of taxation.
4
5
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 based
on 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 price
indexes 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 and
Gravningsmyhr (1996). The actual microsimulation model used in this paper is developed in 2000, see Hussein (2001) and
Aasness (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 price
equations in the general equilibrium model MSG-6, cf. Holmøy, Strøm and Åvitsland (1999).
7
The standard of living for household k, and all its members, in situation t is wkt = ckt/ek = ykt/(Pktek), where total
consumption 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.
6
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 OECDscale provides a suitable approximation, see Bojer (1977), Herigstad (1979) and Røed 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 household demand functions and aggregate individual well-being across the population.
9
The number of consumption units in household k, in base yeae prices, is defined as ek = (1-f(e)) + ez1k + f(e)z2k, where z1k
and 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, described
in 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 of
consumption units for single adult households equals 1 for any given value of e. Buhman et al (1988) used a power function
class of equivalence scales with a parameter e with a similar role as in our linear class. We prefer the linear form because the
power function exagerates the economies of scale for large households. This can be illustrated by the much used special case
of the power function which assumes that the number of consumer units is the square root of the number of persons. This
implies e.g. that 16 single persons will quadroble their standard of living by establishing a houshold collective! We find this
unrealistic. Furthermore, note that the equivalence scale can be interpreted as an ethical norm or judgement, which can be
combined 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 may
also vary with the standard of living when the relative prices are not as in the base period, cf. Aasness (1995).
7
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. If e
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 OECDscale 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 living is 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-welfare12 combines
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 additional
members in the households. In the modified equivalence scale, the cost of expanding a household by one adult is 0.5, and by
one 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 an
axiomatic 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" instead
of total consumption, but this may change if the model takes into account changes in labor supply and substitution effects in
consumption patterns.
14
Change in average standard of living per krone change in total consumption is considered as a measure of distributional
efficiency, because when a change in the tax system results in higher standard of living than another change, for a given
change 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 relatively
large positive effect on the average standard of living.
8
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 benefit is given to
all who support children under the age of 1817 and live in Norway, and can be considered as a negative
tax. 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 and taxes on tobacco, beer, spirits and wine. A 10 per cent increase is simulated for all these
taxes. 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 such
changes 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 in
Norway in 2000, but on 1st July 2001, VAT is introduced on most services.
9
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 average
standard 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 the
standard 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.
10
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-
Change in average Change in
welfare per
standard of living
krone increase
per krone increase krone increase
in total
in total
in total
consumption
consumption
consumption
equality per
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 that
in our consumption model, petrol expenses are included in the same aggregate as, among other goods and services, expenses
to 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.
11
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 Senwelfare 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 analysis
We 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.
12
F ig u re 1 . C h an g e in averag e stan d a rd o f livin g
p er kro n e in crease in to tal co n su m p tio n
S ource: L otte-konsum , N o vem ber 20 00, S tatistics N orw a y.
6
5
Change in standard of living
V A T on all
S urtax
4
V A T on food
Third child +
3
2
1
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Eq uivalence scale (e)
Figure 2. Change in equality
per krone increase in total consumption
Source: Lotte-konsum, November 2000, Statistics Norway.
8
6
VAT on all
Surtax
Change in equality
4
VAT on food
Third child
2
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
-2
-4
Equivalence scale (e)
Figure 3. Change in Sen-welfare
per krone increase in total consumption
Source: Lotte-konsum, November 2000, Statistics Norway.
4,5
4
VAT on all
Surtax
3,5
Change in Sen-welfare
VAT on food
3
Third child +
2,5
2
1,5
1
0,5
0
0
0,1
0,2
0,3
0,4
0,5
0,6
Equivalence scale (e)
13
0,7
0,8
0,9
1
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 are
also 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.
14
6. Conclusions
Twelve 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 Senwelfare, 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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16
Norges forskningsråd – Kultur og samfunn
Forskning om skatteøkonomi
Economic Research Programme on Taxation
Rapportoversikt
1989
Nr. 1
Vidar Christiansen (red.)
Rapport fra seminar om skatteøkonomisk forskning. Gol 9.-10. mai 1988
Nr. 2
Rolf Aaberge, Steinar Strøm og Tom Wennemo
Skatt, arbeidstilbud og inntektsfordeling i Sverige
Nr. 3
Vidar Christiansen og Torunn Kvinge
Optimal differensiering av kaptialbeskatning
Nr. 4
Erik Fjærli
Skattesubsidiering av selveierboliger:
– Boligpolitikk for hvem?
Nr. 5
Datagrunnlaget for skatteforskning
Rapport fra en arbeidsgruppe
Nr. 6
Vidar Christiansen og Tom Kornstad
Skattekiler på rente for personer i Norge 1986-1989
Nr. 7
Rolf Aaberge, John K. Dagsvik and Steinar Strøm
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
Samfunnsøkonomiske 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
Kåre P. Hagen and Vesa Kanniainen
Optimal Taxation of Heterogeneous Capital and Tax Neutrality
Nr. 14
Gaute Torsvik
Truverdeproblem i økonomisk politikk
Nr. 15
Øystein Aadnevik
Støtte til hushold i etableringsfasen
Nr. 16
Erik Offerdal
A Survey of the Norwegian Tax System, 1962-1987
Nr. 17
Erik Offerdal and Bjørn Helge Vatne
Forward-looking Behavior and Tax Policy Modeling
Nr. 18 Erik Offerdal
Capital Accumulation, Productivity and Economic Growth in Norway, 1962-1987
Nr. 19
Erik Offerdal
Inflation and the Nonneutrality of Capital Income Taxation
Nr. 20
Erik Offerdal
Effective Tax Rates and the Cost of Nonneutral Taxation in Norway, 1962-1987
Nr. 21
Erik Offerdal
Effective Tax Rates, Applied OGE-Models and Tax Reforms Toward Neutrality.
Any Lessons for Norway?
Nr. 22
Rolf Aaberge, John K. Dagsvik and Steinar Strøm
Labor Supply, Income Distribution and Excess Burden of Personal Income Taxation in
Sweden
1991
Nr. 23
Gaute Torsvik
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, Kåre P. Hagen og Jan G. Sannarnes
Indtægtsbeskatning og indtægtsfordeling
En empirisk analyse av indtægtsbeskatningens fordelingsvirkninger med spesiell vægt på
kapitalbeskatningens betydning
Nr. 26
Erling Holmøy and Haakon Vennemo
A General Equilibrium Assessment of a Suggested Reform in Capital Income Taxation
Nr. 27
Ragna Alstadheim
Kapitalbeskatning i en åpen økonomi
Enkelte problemstillinger knyttet til ilegging av omfordelende skatt på mobil kapital
Nr. 28
Randi Næs
Beskatning av nye finansielle instrumenter
Nr. 29
Morten Berg
Inntektsbeskatning og kamuflert konsum hos personlig næringsdrivende
1992
Nr. 30
Petter Osmundsen
Optimale finansielle beslutninger ved ulike skattesystemer; en litteraturstudie
Nr. 31
Knut H. Engedal
Strukturpolitiske konsekvenser av informasjonsproblemer i kapitalmarkedene
En vurdering
1993
Nr. 32
Gaute Torsvik
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 forskermøte i skatteøkonomi 24.-26.05. 1993
Nr. 35
Erik Fjærli
Skatt og finansiell tilpasning
En empirisk undersøkelse av finansieringsatferd og skatt i norske industriaksjeselskaper,
1987-91
Nr. 36
Jan Gaute Sannarnes
Marginalskattens betydning for porteføljesammensetningen av husholdningers sparekapital
Nr. 37
Knut Terje Fagerland
Delingsmodellen
1994
Nr. 38
Christian Andersen
Ejerformer, organisationsændringer og beskatning
Nr. 39
Christian Andersen, Nina Langbraaten og Jan Gaute Sannarnes
Skattereform, indtægtsfordeling og skattestruktur
Nr. 40
Christian Andersen og Jan Gaute Sannarnes
Intertemporal konsistens i reglene for deling av næringsinntekt
(Rapporten utgis samtidig som SNF-rapport nr. 37-94)
1995
Nr. 41
Jan Gaute Sannarnes
Delingsmodellen og incitamenter til risikotaking
Nr. 42
Skatteforum 1995
Nasjonalt forskermøte i skatteøkonomi 18.-20.01.1995
1996
Nr. 43
Christian Andersen og Jan Gaute Sannarnes
Skatteudgifter i indtægtsbeskatningen af aktieselskaber
Nr. 44
Skatteforum 1996
Nasjonalt forskermøte i skatteøkonomi 20.-22.05.1996
Nr. 45
Christian Andersen
En teoretisk model for en entreprenørs 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 økonometrisk analyse av skattereformens betydning for investeringsatferden
Nr. 48
Christian Andersen og Jan Gaute Sannarnes
Fordelingseffekter av det norske skatte- og overføringssystemet i et livsløpsperspektiv
Nr. 49
Skatteforum 1997
Nasjonalt forskermøte i skatteøkonomi 2.-4. juni 1997
1998
Nr. 50
Skatteforum 1998
Seminar om skatteøkonomi 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
Måling av progressivitet i det norske skattesystemet 1991-95
Nr. 55
Skatteforum 1999
Seminar om skatteøkonomi 30. mai – 1. juni 1999
Nr. 56
Øystein Thøgersen, Carl Edvard Gjersem, Jan Gaute Sannarnes og Wenche Irén Sterkeby
Skatt, trygd og arbeidstilbud
Nr. 57
Jørn Rattsø
Fiscal Adjustment with Vertical Fiscal Imbalance: Empirical Evaluation of Administrative
Fiscal Federalism in Norway
2000
Nr. 58
Annette Alstadsæter
Optimal skatt på avkastinga av utdanning
– Flat eller progressiv skatt på arbeidsinntekt?
Nr. 59
Jan Gaute Sannarnes og Elisabeth Steckmest
Velferdsstaten i et livsløpsperspektiv
Nr. 60
Raymond Lokshall
Merverdiavgiftsloven og vridning i produksjonstilpasningen
«Goods and Services Tax» (GST) i New-Zealand
Nr. 61
Espen Bratberg, Tor Helge Holmås and Øystein Thøgersen
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
Nr. 63
Skatteforum 2000
Seminar om skatteøkonomi 29. – 31. mai 2000
Nr. 64
Hans Fehr, Wenche Irén Sterkeby and Øystein Thøgersen:
Social security reforms and early retirement
2001
Nr. 65
Skatteforum 2001
Seminar om skatteøkonomi 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 ménages possibles.
The Pangloss critique of equivalence scales
2002
Nr. 68
Skatteforum 2002
Seminar om skatteøkonomi 29 – 30. april 2002
Nr. 69
Jørgen Aasness, Andreas Benedictow and Mohamed F. Hussein
Distributional Efficiency of Direct and Indirect Taxes
Discussion Papers No. 455, April 2006
Statistics Norway, Research Department
Fred Schroyen and Jørgen Aasness
Marginal indirect tax reform
analysis with merit good
arguments and environmental
concerns: Norway, 1999
Abstract:
We present a framework to identify and evaluate marginal tax reforms when merit good arguments
and environmental concerns are given explicit consideration. It is applied to the Norwegian indirect
tax system for 1999. The analysis shows that the reform passed in Parliament in November 2000
had a clear redistributive profile: a lowering of the VAT rate on food items and the introduction of a
VAT on services benefits households in the lowest seven deciles while the upper three deciles got
worse off. But we also argue that the aggregate demand responses triggered an increase in
greenhouse gasses. Next, we show that if the 2000 reform had been complemented with tax rates
rate changes on other products, it could have made every decile better off. Finally, we present
socially 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 the
Catholic University of Leuven (2005). We are grateful for comments from seminar participants, in
particular from Vidar Christiansen and Bjørn Sandvik, and for computational assistance from
Mohamed F. Hussein and Odd Erik Nygård. This research project has been financed by a grant from
the 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 & Business
Administration, Helleveien 30, N-5045 Bergen , Norway ([email protected]).
Jørgen Aasness, Statistics Norway, Research Department. E-mail:
[email protected]
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1
Introduction
In Norway, the indirect tax system is responsible for about one third of total
tax revenue. It consists of two parts. On the one hand, a value added tax
system that up til 2000 imposed a uniform rate of 23% on most commodities
but exempted an important set of services. On the other hand, excise taxes
that are imposed on a range of products. These taxes are based on the
products’ physical properties (% of alcohol content, motor capacity, ...) and
are motivated by environmental considerations (petrol, packaging), merit
good 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 system
was passed in the Norwegian Parliament. The general value added tax rate
was to be raised from 23 to 24% from January 2001 onwards, and became
applicable as well to most types of services from July 1, 2001 onwards. Also
from that date, the VAT rate on food and beverage items was reduced to
12%.
Tax reforms have consequences for the efficiency with which resources in
the economy are allocated, for the distribution of welfare over households,
and for the environment. ’Large’ changes in the indirect tax system, should
be evaluated by means of a microeconomic general equilibrium model. For
’small’ reforms, however, a limited amount of statistical information suffices
to identify directions of reforms that are desirable out of efficiency and/or
equity concerns. Such exercises have been performed for a number of developed and developing countries. Examples are Decoster & Schokkaert (1989,
1990) for Belgium, Madden (1995) for Ireland, Ahmad & Stern (1984) for
India, Ahmad & Stern (1991) for Pakistan, and Kaplanoglou & Newbery
(2003) for Greece.
The above described reform of the Norwegian value added tax system is
not a small one. Except for the rise in the rate non-food rate from 23 to
24 %, the nominal rate on many services was raised from 0 to 24%, while
the rate on food items was halved. In this paper, we are concerned with
an evaluation of the direction of this reform by taking the effective indirect
tax rate structure of 1999 as our starting point and analysing ’small’ or
marginal reforms. Methodologically, our framework extends the one used by
the authors referred above, by explicitly taking environmental considerations
and merit good arguments into account.
3
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 of
which are relegated to an appendix. Thereafter we present results of the tax
analysis, focusing on the ranking of commodities according to the marginal
cost of partial tax increases, and how the ranking changes with the different
household deciles and the environment. Furthermore we demonstrate the
possibilities of Pareto improving reforms. In section 4 we introduce a social
welfare function and demonstrate different types of social welfare improving
reforms. Concluding remarks are collected in section 5.
2
A theoretical framework
We consider an economy with H households whose preferences can be represented by the utility functions uh (·) (h = 1, ..., H) defined over n commodities (xi , i = 1, ..., n), tradeable on competitive markets.
The offproducer prices on these markets are given by the price vector p = (p1 , ..., pn )0 .
Household h has disposable income mh that comes from labour earnings,
replacement incomes, and capital incomes. The government imposes specific indirect tax rates ti such that the consumer price for commodity i is
qi = pi +ti (i = 1, ..., n). Facing these prices, household h demands xhi (q, mh )
units of commodity. For future reference, we denote h’s normalised price for
def
good i by π hi = mqih .
Indirect tax revenue
Aggregate demand for commodity i is given by1
X
def
xTi (q) =
xhi (q, mh ),
h
and indirect tax revenue can therefore be written as
X
def
R(t) =
tj xTj (p + t).
j
A marginal increase in tax rate i results in extra revenue for the treasury
to the amount of
n
X
∂xTj
def ∂R
= xTi +
tj
.
ri =
∂ti
∂q
i
j=1
1
Hereafter we ignore the vector of income levels (m1 , ..., mH ) as an argument in commodity demands.
4
Multiplying this expression through by qi , we obtain
qi ri = qi xTi +
n
X
t∗j εji qj xTj ,
(1)
j=1
def ∂xT
def ti
qi
where εji = ∂qji xqTi is the aggregate cross price elasticity and t∗i =
j
effective tax rate as a fraction of the consumer price.
is the
The government evaluates indirect tax reforms in terms of its effects on
household welfare and the environment.
Household welfare
Household welfare is not necessarily perceived in the same way by the
government as by the household. The reason for this perception wedge
is that the government may be convinced about the beneficial/detrimental
properties of some commodities, which households disregard when making
their purchasing decisions. The obvious examples here are alcohol and tobacco. In the empirical application, these commodities belong to the same
consumption category and we will therefore in the rest of the paper assume
that only one commodity has (de)merit properties, viz commodity n. To
model merit good arguments in the social evaluation, we follow the approach
put forward by one of us (Schroyen, 2005a,b) and take the government’s evaluation of household h’s consumption bundle as (we drop for the time being
the household index)
def
U(x−n , xn ) = u(
x
),
1 − μxn
where x−n is a shorthand for the truncated bundle (x1 , ..., xn−1 ) . The parameter μ measures to which extent good n is considered a merit good. It has
the dimension of a normalised price (a price in proportion to income), so that
μxn can be interpreted as a virtual budget share for commodity n.2 Defining
now the (uncompensated) consumer’s and government’s marginal evaluation
2
If π ci (x, u) (i = 1, ..., n) are the compensated inverse demand functions for the household (giving demand prices in proportion to income), the compensated inverse demand
functions for the government can be shown to be
Πci (x, u) = π ci (x, u) (i 6= n), and
Πcn (x, u) = π cn (x, u) + μ.
5
of commodity j, as (subscripts with u and U denote partial derivatives)
uj (x)
Uj (x)
def
and Πj (x) = P
,
k uk (x)xk
k Uk (x)xk
def
π j (x) = P
respectively, it can be shown that, to a first approximation,
Πj (x) ' π j (x) [1 + σ j wn η] (j 6= n),
Πn (x) ' π n (x) [1 + η + σ n wn η] ,
(2a)
(2b)
where σ j is the scale elasticity for commodity j (the relative change in the
demand price of commodity j due to a 1% increase in the Divisia quantity
P
def
index j wj dlog xj ), wn is the budget share of the merit good, and η = πμn ,
a dimensionless measure of the merit good argument. Merit considerations
regarding good n thus have two effects on the government’s demand prices.
First, they boost the government’s demand price for good n (relative to
the household’s demand price) with η. But second, and less obviously,
the government considers the household to be better off because of all the
inframarginal units of n consumed. This has a scale effect on all demand
prices whose importance depends on the budget share of n.
Reintroducing the household index h, the effect of a marginal change in
ti on this household’s welfare can be shown to be given by
!
Ã
X
∂U h
(all i, h).
(3)
' (qi xi )h − η h · (qn xn )h ·
wjh σ hj εhji + εhni
−qi
∂ti
j
After dividing (3) by (1), we obtain the marginal cost of rasing one extra
krone in tax revenue through rate ti on household hs welfare (as perceived
by the government):
´
³P
h
h
h
h h h
h
(q
x
)
−
η
·
(q
x
)
·
w
σ
ε
+
ε
i i
n n
ni
j j j ji
def
P
MCih =
(all i, h),
(4)
∗
(qi xi )T + k tk · εki · (qk xk )T
where the small round brackets indicate that one only needs information on
expenditures—not on prices and quantities separately—to compute the MCih .
If MCih > MCjh , a small decrease in t∗i , accompanied by a small increase in
that compensates for the tax revenue loss, leads to a welfare improvement
for household h. The reason is simple: per krone that is lost by marginally
t∗j
6
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 greenhouse gasses. These gasses are due to the total production, distribution and
consumption of goods and services:
E(xT1 , ..., xTn ).
The effect on emissions of a tax rise on commodity i is
∂E X ∂E ∂xTk
=
.
∂ti
∂xTk ∂qi
k
Again, multiplying through by qi allows for a parameterisation in terms of
elasticities:
∂E X
=
ω k · εki ,
(5)
qi
∂ti
k
def
xT
∂E k
where ω k = ∂x
T E , the elasticity of greenhouse gas production w.r.t the conk
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 ti on
total emissions:
P
ω ·ε
E def
Pk k∗ ki
.
(6)
MCi =
T
(qi xi ) + j tj · εji · (qj xj )T
Pareto improving tax reforms
Suppose now that MCih > MCjh for all h, then the above reform may
be regarded as Pareto improving for the present generation.3 Should in
addition also MCiE > MCjE , 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
⎫
P
max{dti } P
⎬
i ri dti
h
s.t. (i)
(P1)
i MC
P i ri dtEi ≤ 0 (all h)
⎭
(ii)
MC
r
dt
≤
0
i i i
i
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 its
preferences have been distorted by the government.
7
where the dti are ’small’.
Rather than searching for ’small’ dti s, Ahmad & Stern (1984) suggest to
look instead for a set of δ i (i = 1, ..., n) where δ i is the extra revenue raised
from increasing the tax on good i; these revenue changes are then constrained
to be smaller than one in absolute value. For this purpose, we define δ i as
ri dti (all i) and checking the existence of a Pareto improving tax reform is
thus equivalent to solving
⎫
P
δ
max{δi } P
⎪
i
i
⎪
⎬
h
s.t. (i)
MC
δ
≤
0
(all
h)
i P i i
(P2)
E
(ii)
⎪
i MCi δ i ≤ 0
⎪
⎭
(iii) −1 ≤ δ i ≤ 1 (all i)
If the solution to this problem is δ i = 0 (all i), we can apply FarkasMinkowski’s lemma and solve the inverse problem, that is search for a set of
H + 1 non-negative welfare judgements (β 1 , ..., β H , β E ), such that
H
X
β h MCih + β E MCiE = 1 (all i).
(7)
h=1
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 should
equal that krone.
In the empirical part, this problem will not concern us as there is room for
Pareto improvements. Christiansen & Jansen (1978) have solved the ’inverse
problem’ for the Norwegian indirect tax system of 1975. Their approach,
however, is slightly different in that they constrain the social welfare parameters β h to be monotonically declining according to the exponential function
h
βh = β1 · ( m
)−e , where e ∈ [0, ∞) is an inequality aversion parameter (this
m1
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 reforms
in the Norwegian economy as of 1999, and use the result to evaluate the
direction 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 of
price, income and scale elasticities, tax rates, emission rates, and expenditure
8
patterns of ten representative consumers. Next we present the results of our
tax reform analysis, by proceeding in three stages. First we ignore merit good
considerations and the effects on the environment, second we introduce the
merit good argument, and finally we also take environmental externalities
into account. According the MCih expression (4) we need price and scale
elasticities at the individual level. Since we we lack this information, we
replace them with the respective aggregate elasticities.
3.1
Empirical basis
All the empirical parameters needed in our analysis of tax reforms are presented in table 1 below and in tables A1-A2 in the appendix. These parameters are taken from a comprehensive system of statistics, econometric studies
and simulation models, including both micro and macro data, compiled and
carried out by Statistics Norway.
The budget shares, Engel elasticities and direct Cournot elasticities presented in Table 1, stem from a complete demand system for a representative
household in Norway 1999, generating macro demands by multiplying with
the number of households. The cross price Cournot elasticities are presented
in table A2 in the appendix. They fulfil all restrictions following from
adding-up, homogeneity, symmetry and negativity. The macro demands can
be generated from a Gorman polar cost function with linear demographics.
Under absence of corner solutions, these macro demands can also be generated by exact aggregation from a population of households with corresponding 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 and
Mysen (1996) and the references therein. The model we used to generate tables 1 and A2
is documented in Nygard and Aasness (2003) and the references therein. Each household
in the population is assumed to have a utility function in terms of a utility tree with
55 commodities and 34 branches, at each branch the preferences can be described by a
translated CES utility function, where the ”necessity quantities” are linear functions of
the number of children and adults in the household. The demand system is calibrated
using data from household expenditure surveys and national accounts. The elasticities
are aggregated to the 14 commodities in this paper using Hicksian aggregation. The
aggregation is partly across branches of the underlying utility tree.
9
Table 1. Budget shares, income, own (uncompensated) price and scale
elasticities, effective tax rates and emission shares. Average household.
Norway 1999.
Budget
Income
Own price
Scale
Effective
i
Commodity group
share
elasticity
elasticity
elasticity
tax rate
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Food and non-alcoholic drinks
Alcohol and tobacco
Clothing and footwear
Gross rents
Electricity
Fuels
Health
Private transport
Public local transport
Public distant transport
Post and telecommunication
Other goods
Other services
Direct purchases abroad
Sum (weighted)
.143
.046
.055
.155
.028
.005
.026
.094
.017
.010
.022
.151
.181
.067
1
0.31
0.94
1.16
1.13
0.42
0.18
0.74
1.39
0.87
1.77
0.31
1.03
1.20
1.52
1
-0.21
-0.75
-0.51
-0.61
-0.26
-0.48
-0.32
-0.84
-0.66
-1.65
-0.28
-0.53
-0.62
-0.92
-4.36
-0.44
-0.15
-0.19
-3.98
-5.10
-1.35
0.04
-0.50
0.13
-2.76
-0.40
-0.08
-0.12
-1
.21
.69
.19
.02
.28
.23
.08
.42
.00
.05
.18
.17
.11
.00
The price elasticities for the representative household in tables 1 and A1
are our estimates of the εji in the formulae of section 2. Since we analyse
marginal tax reforms, the expenditures for the different households (qi xhi ) in
the year 1999 suffice to calculate the effects on the standard of living. In
order to make the analysis transparent, and comparable with similar studies
for European countries, we have constructed ten households to represent the
Norwegian population of households in 1999. The expenditure patterns of
these ten representative households are presented in table A2 in the appendix.
Household expenditures are derived from a microsimulation model which is
calibrated to the same 1999 consumption data as the macro model, so that
the 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 (see
Schroyen, 2005b, on the algorithm). Their interpretation is the percent
change in the demand
price of a commodity for a 1% increase in the Divisia
P
quantity index ( j 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
10
Emission
share
.320
.020
.020
.018
.022
.084
.011
.294
.037
.016
.006
.094
.057
0
1
tax as a fraction of the final consumer price for the year 1999.5
The final column gives the emission shares. Emissions include both direct
emissions from the consumers and emissions from the producers of the consumer goods, including the emissions from the production of the intermediate
goods used in the production of the consumer goods, applying input-output
techniques. The emission estimates are taken from Indahl, Sommervoll and
Aasness (2001, table 1, last column), updated to 1999 and aggregated to the
commodity 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 ignore
merit good considerations and the effects on the environment. Next, we
introduce the merit good argument, and finally we also take the negative
environmental externalities into account.
The marginal costs for the ten representative households when setting
η h = 0 are reported in table A3 of the appendix. But as we discussed
earlier, to identify the effect of reform on household hs well-being, it suffices
to compare the ranking of the different MCih . The rankings are depicted in
figure 1.
First notice how a marginal tax changes may have very different effects
on the well-being of different households. While the lower deciles would
approve of a reduction in the tax rate on food or fuel and an increase in that
on private transport or public distant transport, exactly the opposite
is true for the upper deciles. A similar finding was reported by Decoster
& Schokkaert (1989) for Belgium and Kaplanoglou & Newbery (2002) for
Greece. This should not come as a surprise since the budget share for food
falls from more than 25% for the lowest decile down to 9% for the highest
decile (cf table A2). Private and public distant transport, on the other hand
increase from less than 4% (taken together) up to almost 13%. Much less
variation 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 Norwegian
parliament in the Fall of 2000—a reduction in the VAT rate on food items,
5
These are calculated for 1999 by the input-output model integrated in the Norwegian
national accounts and large scale general equilibrium models of Statistics Norway. See
e.g. Holmøy et al (1994, 2.17.1-5)
11
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
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 telecom m unication
12. O ther goods
13. O ther services
14. Purchases abroad
10
Figure 1: Rankings of MCih (η = 0).
and introduction of VAT on services—is benefiting the first seven deciles and
making the last three deciles worse off.
Except for the first decile, all other deciles would also agree on a reduction
in the tax on private transport (excise taxes on gasoline and on cars) if
this was financed by more expensive public local transport.
Another observation is that all ten representative households would endorse lower excise taxes on alcohol and tobacco no matter how financed
through other commodity taxes (even that on health services!).
Many observers are likely to utter scepticism about these last policy proposals, arguing that the high level of excise taxes on alcoholic beverages and
tobacco serve to contain consumption patterns that put health at risk, and
that excise taxes on private transport play a Pigouvian role. In a next stage,
we therefore introduce the merit good argument and environmental concerns.
12
3.3
Introducing a merit good and environmental concerns
We single out the category alcohol and tobacco as a demerit good whose
consumption is depreciated by the government with a factor η < 0 common
for all deciles. An important question is then what value η should take. In
recent years, public opinion is unambiguously converging on the idea that
smoking is detrimental for people’s health.6 Regarding alcohol, the sale of
beverages with an alcohol content of more than 5% is restricted in Norway
to Vinmonopolet, the stated owned wine monopoly.7
As seen earlier, a zero value for η makes it possible to make all deciles
better off by lowering taxes on alcohol and tobacco, and raising the tax on
h
h
health care. From table A3, it transpires that MCalc&tob
−MChealth
is lowest
for households in the lowest decile. It turns out that −.67 is the highest value
h
h
for η such that MCalc&tob
≥ MChealth
(all h) (the inequality being binding
for the lowest decile). On the other hand, for any value of η below −.784,
h
h
we have that MCbev&tob
≤ MChealth
(all h) so that every decile’s well-being
could be improved by taxing beverages and tobacco heavier and making
health care products and services cheaper. We therefore fix η at −.70 in
the remainder of the paper. This means that the government’s marginal
willingness 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 MCih
are given in the first ten columns of figure 2 (based on table A4).
From this figure, it transpires that the government could still increase the
well-being of every decile by at least two reforms: lowering taxes on private
transport, clothes and footwear, other services and raising them on
public distant transport; and lowering taxes on alcohol and tobacco
and rasing them on gross rents. But are such reforms also to the benefit
of 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 cafés and restaurants.
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. Several
years later, this ban was abolished and Vinmonopolet got the sole right to sell spirits and
liquor.
8
Using (2b), we get that
7
Π2 (x) − π2 (x)
' (1 + σ 2 w2 ) η = [1 + (−.441)(.0464)] (.7) = −.686
π2 (x)
13
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
1 . F o o d , i n c l. n o n - a lc h o li c b e v .
3 . C lo th i n g a n d fo o tw e a r
5 . E le c tr i c i ty
7 . H e a lth
9 . P u b li c lo c a l tr a n s p o r t
1 1 . P o s t a n d te le c o m m u n i c a ti o n
1 3 . O th e r s e r v i c e s
8
9
10
Env
2 . A lc o h o l a n d to b a c c o
4 . G r o s s r e n ts
6 . F u e ls
8 . P r i v a te tr a n s p o r t
1 0 . P u b li c d i s ta n t tr a n s p o r t
1 2 . O th e r g o o d s
1 4 . P u rc h a s e s a b ro a d
Figure 2: Rankings of MCih and MCiE (η = −.7).
2, indicated as ’Env’. This column depicts the ranking of the marginal
costs for the environment, MCiE . As explained in section 2, the cost for the
environment comes in the form of greenhouse gas emissions related to the
consumption, production and distribution activities of the 14 commodities
(except for purchases abroad).
For each decile h we have computed the rank correlation coefficient between the MCih and MCiE . These are reported in table 2. For most deciles,
these correlations are insignificant. But it transpires that pleasing deciles
2, 3 or 4 and the environment poses a challenge. Interestingly, the rank
correlation becomes less negative (and even positive) when considering the
upper deciles.
Table 2. Rank correlation coefficient between MCih and MCiE
Decile
rankcorr(MC hi , MC E
i )
1
-.26
2
-.43
3
-.46
4
-.34
5
-.29
6
-.28
7
-.29
8
-.24
9
-.08
The impact of the 2000 reform on the environment can be readily read
E
off from the final column in figure 2: MCfEood < MCoth
serv indicates that
greenhouse gas emissions will have increased following this reform. The
explanation is that consumption of food items entails production and distribution activities which are heavy contributors to greenhouse gas emission (an
14
10
+.13
emission share of 29%). Services, on the other hand, pollute far less (3.6%
emission share). The reduced demand for services due to the introduction
of a VAT, does not compensate for the extra CO2 emissions following the
increased consumption of food items.
Notice also that the relative ranking for private transport/clothing
and footwear/other services relative to public distant transport now
switches: the environment is made worse off when reducing taxes on one of
the former category and raising them on the latter to neutralise the effect
on revenue. The same can be said about the second reform that was earlier
identified 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 reforms
are non-existent. In table 3, we show the solution to problem (P2) (with
η = −.7).
Table 3. A Pareto improving reform securing
maximal revenue (η = −.7).
i
Category
δi
1 Food & Beverages
1
2 Alcohol & Tobacco
−1
3 Clothing & Footwear
−.28
4 Gross Rents
1
5 Electricity
−1
6 Fuels
.22
7 Health
1
8 Private transport
−1
9 Public local transport
1
10 Public distant transport
1
11 Post & telecommunication −.31
12 Other goods
−1
13 Other services
1
14 Purchases abroada
0
Sum
0.9317
a
δ 14 was constrained to zero
This reform produces a maximal revenue increase of 0.93 kroner. It keeps
emissions constant and makes all deciles, except for the 1st, 9th and 10th
strictly better off. This reform is striking in several respects. First, private transport features among those commodities that can be taxed more
leniently while public local transport should be taxed heavier. Fuels and
15
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 alcohol and tobacco should be reduced, while that on health care should be
raised—and this despite the fact the government already discounts the former
category at a rate of 70% (since η = −.70).
4
Social welfare improving reforms
Above, it was established that there is room for a reform of the Norwegian
indirect tax system that makes every decile better off and reduces CO2 emissions. Two qualifications should be kept in mind. First, that ’better
off’ means as perceived by the government. Second, that we only looked at
the welfare of the representative agent in each decile: all persons in a decile
were treated identically. Should we increase the number of representative
agents, e.g. to 100, then the likelihood of finding a tax reform that furthers
the welfare of every agent would be close to zero. One can then no longer
avoid comparing the losses of some agents with the gains experienced by
others.
There is nothing that prevents
us to carry out such a welfare analysis by
P
h
calculating and comparing 10
β
MCih (all i). For this purpose, we use
h=1
the iso-elastic specification for the social marginal utility of income,
βh = β1 · (
mh −e nh
) · ( 1 ), e ∈ [0, ∞),
m1
n
normalise β 1 to 1, where mh is taken as total consumption expenditure per
equivalent adult (i.e. standard of living in table A2) and nh is the average
number of persons in a household of decile h (thus giving one welfare vote to
each person in the underlying population).9 The parameter e is the inequality aversion parameter with e = 0 reflecting efficiency with no distributional
concerns 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 do
not add the environment/future generations in the computation
of the MCi
P h
E
since this would require the selection of a β . We call h β MCih therefore
the short term social marginal cost of category i.
Figure 3 presents the rankings of the short term MCs for seven different
values 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 (lowest
decile), 1.71, 2.22, 2.44, 2.54, 2.40, 2.27, 2.14, 2.01, 2.01 (highest decile).
16
14
13
12
11
10
9
8
7
6
5
4
3
2
1
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
0
0,1
0,5
1
2
5
e
10
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 bad
one, as inequality aversion grows. Public distant transport should be
made more expensive for any value of e. The marginal cost for food exceeds
that for other services for all values of e. Earlier, it was mentioned that the
first seven deciles benefit from the 2000 reform, while the upper three deciles
loose. Figure 3 (e = 0) thus establishes that the winners’ gain outweighs
the losers’ loss.
We nowPinquire
which δ i (i = 1, ..., n) should be chosen in order to min10 P14
h
h
imise the
h=1
i=1 β MCi δ i , without deteriorating public revenue and
without increasing emissions:
⎫
P10 h P14
min{δi }
β
MCih δ i ⎪
h=1
i=1
⎪
P14
⎬
E
s.t. (i)
MC
δ
≤
0
i
i
i=1
P14
(P3)
⎪
(ii)
⎪
i=1 δ i ≥ 0
⎭
(iii) −1 ≤ δ i ≤ 1 (all i)
Column a of table 4 gives the results for the efficiency criterion. Interestingly,
the recommended policy includes a lowering of the tax on private transport
and an increase in the tax on public local and distant transport and this
benefits the environment (the constraint (i) is slack). Thus, there is no
conflict between a utilitarian perspective and concerns for the environment.
This is no longer the case when we take a maximin perspective. Column b
of table 4 presents the solution to (P3) when the weights to all but the lowest
decile are set to zero and when constraint (i) is ignored. W.r.t. the efficiency
17
solution, tax policy recommendations now change for more than half of the
commodity groups. In particular, the tax on fuels is now reduced rather
than increased. Since fuels have an extremely high marginal environmental
cost (cf last column of table A4), the consequence is a deterioration of the
environment. Imposing constraint (i) and re-optimising results in column c
of table 4. The main changes in policy recommendation are a smaller tax
reduction for fuels and a tax increase for public local transport (rather
than a status quo).
Table 4. Optimal δ i values (η = −.7, Lagrange multipliers with (i) and
(ii) in brackets).
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
a
5
a
b
c
Category
Efficiency Rawls Rawls+env.
Food and non-alc. bev.
−1
−1
−1
Alcohol and tobacco
0
−1
−1
Clothing and footwear
−1
1
1
Gross Rents
1
1
1
Electricity
−1
−1
−1
Fuels
1
−1
−.27
Health
1
−1
−1
Private transport
−1
1
1
Public local transport
1
0
1
Public distant transport
1
1
1
Post and telecommunication
−1
−1
−1
Other goods
−1
1
−.73
Other services
1
1
1
Purchases abroada
0
0
0
Sum
0 (1.53) 0 (.04)
0 (.03)
P hP
h
−1.66
−.32
−.26
Ph β E i MCi δ i
−2.61
2.73
0 (−.021)
i MCi δ i
δ 14 was constrained to zero
Conclusion
We have presented a framework to identify and evaluate marginal tax reforms
when merit good arguments and environmental concerns matter. We next
applied the analysis on the Norwegian indirect tax system for 1999. Our
analysis showed that the reform passed in Parliament in November 2000 had
a clear redistributive profile: a lowering of the VAT rate on food items, and
the introduction of VAT on services benefited households in the lowest seven
18
deciles while the upper three deciles got worse off. But we also argued that
an increase in greenhouse gasses has resulted from the aggregate demand
responses.
We then showed that if the 2000 reform had been complemented with tax
rates rate changes on other products (as specified in table 3), it could have
made every decile better off. We have also studied social welfare improving
reforms by computing an inequality averse weighted average of the marginal
welfare costs of the ten deciles and arrived at similar conclusions.
It is important to stress the limitations of our analysis. First, we have
been concerned with marginal tax reforms–changes in the indirect tax rates
in a neighbourhood of the existing—1999—indirect tax structure. To evaluate
finite changes in the tax structure, it no longer suffices to have ‘local’ information about behavioural responses of economic agents in the form of price
elasticities. An explicit system of demand equations for each decile is then
required to trace out the responses.
Second, we have included only ten deciles of household groups, in order
to obtain transparency and comparability to other studies. In reality there
are more than 2 million households in the Norwegian economy, heterogenous
in many dimensions. A full scale microsimulation model might reflect this
heterogeneity in a more appropriate way, and could in principle be used in our
type of analysis. A testable conjecture is that our ten household deciles will
capture an essential part of the heterogeneity, in such a way that our results
on social welfare improving reforms are robust. Another testable conjecture
is that Pareto improving reforms would not exist in such a model with a large
degree of heterogeneity. However, our results on Pareto improving reforms in
our 10 household model would still seem to give some insight in the welfare
effects of marginal tax reform in Norway 1999.
Finally, the empirical basis used and presented in the present paper, may
of course have weaknesses of different kinds. Without doubt, improved data
and painstaking econometric work would improve this basis. But since the
main policy conclusions are based on ordinal rather than cardinal comparisons of marginal costs, we expect our model to be fairly robust to minor
improvements of the empirical basis.
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Nobay (eds) Studies in modern economic analysis (Oxford: Basil Blackwell)
21
Appendix
This appendix presents the econometric estimates of the demand responses (Table A1), the expenditure patterns for the different household
deciles (Table A2), and the computations of the marginal welfare costs (Tables A3 and A4).
The ten representative households are constructed from a micro simulation model with 26 825 individuals forming 9 964 households with weights
such that this micro population is in many dimensions a good representation
of the Norwegian population in the year 1999 (see Aasness,1997, and Aasness,
Benedictow and Hussein, 2002, and references therein for information on this
model). The households are ranked according to their standard of living, defined as their estimated latent total consumption expenditure in the year
1999 divided by the number of equivalent adults (using the OECD scale),
assuming that each person in the same household has the same standard of
living. The households are grouped in ten deciles such that the weighted
number of households is the same in each decile. The number of persons
per household varies between 1 and 13 in the micro data and between 1.70
and 2.54 among the deciles. This implies that the number of persons differ
between the different deciles. The group All in table A2 gives the expenditures of the average household in the micro population, which is equal to
the mean of the expenditures in the deciles. Thus the expenditures in group
All in table A2 multiplied by the total number of households (2 064 574) in
Norway 1999 are the macro expenditures according to the micro model. The
corresponding budget shares are equal to the macro budget shares in table 1
and A1. This is so since we have calibrated both the macro model (behind
table 1 and A1) and the microsimulation model (behind table A2) to fit the
same macro data in 1999. Otherwise the empirical basis for our marginal tax
analysis would not be consistent with the basic theory in section 2.
22
23
Commodity group
1 Food and non-alcoh. drinks
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 tranport
11 Post and telecommunication
12 Other goods
13 Other services
14 Purchases abroad
Scale elasticities
budget
share
0.143
0.046
0.055
0.155
0.028
0.005
0.026
0.094
0.017
0.010
0.022
0.151
0.181
0.067
income
elast.
0.306
0.935
1.156
1.130
0.418
0.175
0.738
1.387
0.867
1.771
0.311
1.025
1.197
1.519
p2
-0.006
-0.749
-0.030
-0.029
-0.011
-0.004
-0.019
-0.035
-0.022
-0.045
-0.008
-0.026
-0.031
-0.147
-0.441
p1
-0.212
-0.108
-0.141
-0.138
-0.051
-0.021
-0.090
-0.169
-0.106
-0.216
-0.038
-0.125
-0.146
-0.130
-4.358
-0.008
-0.023
-0.511
-0.028
-0.010
-0.004
-0.025
-0.034
-0.021
-0.043
-0.008
-0.031
-0.041
-0.050
-0.151
p3
-0.022
-0.066
-0.082
-0.614
-0.036
-0.015
-0.052
-0.098
-0.061
-0.126
-0.022
-0.080
-0.085
-0.108
-0.188
p4
-0.007
-0.021
-0.026
-0.027
-0.261
0.398
-0.017
-0.032
-0.020
-0.040
-0.007
-0.025
-0.027
-0.035
-3.977
p5
-0.001
-0.004
-0.005
-0.005
0.064
-0.483
-0.003
-0.006
-0.004
-0.008
-0.001
-0.004
-0.005
-0.006
-5.098
p6
-0.005
-0.016
-0.023
-0.019
-0.007
-0.003
-0.316
-0.023
-0.015
-0.030
-0.005
-0.019
-0.024
-0.029
-1.349
p7
-0.010
-0.029
-0.036
-0.035
-0.013
-0.005
-0.023
-0.841
0.192
0.646
0.074
-0.032
-0.037
-0.048
0.036
p8
-0.003
-0.009
-0.011
-0.011
-0.004
-0.002
-0.007
0.025
-0.662
0.002
0.002
-0.010
-0.012
-0.015
-0.501
p9
uncompensated price elasticities
Table A1. Budget shares, income elasticities and uncompensated price elasticities. Norway 1999.
0.000
-0.001
-0.002
-0.002
-0.001
0.000
-0.001
0.070
0.010
-1.648
0.032
-0.001
-0.002
-0.002
0.125
p10
-0.006
-0.018
-0.022
-0.021
-0.008
-0.003
-0.014
-0.006
-0.009
0.041
-0.277
-0.019
-0.023
-0.029
-2.764
p11
-0.023
-0.072
-0.104
-0.093
-0.040
-0.014
-0.066
-0.106
-0.066
-0.136
-0.024
-0.528
-0.107
-0.133
-0.396
p12
-0.024
-0.072
-0.127
-0.087
-0.032
-0.014
-0.081
-0.107
-0.067
-0.136
-0.024
-0.098
-0.620
-0.159
-0.078
p13
0.020
0.253
-0.036
-0.021
-0.008
-0.003
-0.023
-0.025
-0.016
-0.032
-0.006
-0.026
-0.038
-0.923
-0.120
p14
24
Commodity group
1 Food and non-alcoh. drinks
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
Total expenditure
Standard of living
Table A2. Arithmetic means of household expenditures
All
Decile 1 Decile 2 Decile 3 Decile 4
39824
26154
31668
35733
40010
12937
6071
7685
8733
10112
15350
3512
6873
9854
12864
43278
14360
21949
28168
34469
7938
5321
6214
6853
7536
1289
1209
1223
1210
1204
7295
3406
4523
5209
6176
26176
3633
9189
13832
19245
4657
1917
2644
3068
3719
2695
198
632
940
1481
6214
4537
5138
5526
5976
42033
13778
21881
28330
35110
50517
13306
23529
32112
40635
18841
4337
6892
8694
11581
2790474 101748
150040
188261
230115
161028
71370
95163
109653
123915
per decile.
Decile 5
42920
11525
15300
40136
8070
1214
7037
24077
4331
2068
6327
40841
47975
14759
266580
138296
Norway 1999.
Decile 6 Decile 7
42532
42266
12663
13841
16067
16981
43259
46743
8192
8338
1253
1292
7485
7940
26637
29380
4718
5106
2555
3048
6405
6493
43209
45887
51332
55176
17691
20696
283998
303187
152969
169468
Decile 8
42069
15151
18059
50723
8513
1334
8448
32486
5536
3593
6598
48980
59615
24020
325124
189155
Decile 9
42422
16889
19849
56591
8822
1383
9146
36946
6103
4299
6778
53757
66436
28329
357749
215893
Decile 10
52472
26700
34136
95882
11521
1565
13581
66331
9426
8135
8367
88562
115054
51410
583143
344401
25
1 Food and non-alcoh. beverages
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
h
h
M Calc&tobacco
− M Chealth
Table A3. M Cih (h = 1, ..., 10; i = 1, ..., 14) for η = 0. Norway
Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6
.080
.097
.109
.122
.131
.130
.114
.145
.164
.190
.217
.238
.028
.054
.077
.101
.120
.126
.036
.056
.071
.087
.102
.110
.083
.097
.107
.117
.125
.127
.110
.111
.110
.110
.111
.114
.054
.072
.083
.098
.112
.119
.023
.057
.086
.119
.149
.165
.041
.057
.066
.080
.093
.102
.006
.019
.029
.046
.064
.079
.086
.098
.105
.114
.120
.122
.039
.062
.081
.100
.116
.123
.030
.054
.073
.093
.109
.117
.021
.034
.043
.057
.072
.087
.060
.073
.082
.092
.105
.119
1999.
Decile 7
.129
.260
.133
.119
.130
.118
.126
.182
.110
.094
.123
.131
.126
.101
.134
Decile 8
.128
.285
.142
.129
.132
.122
.134
.201
.119
.111
.125
.139
.136
.118
.158
Decile 9
.129
.318
.156
.143
.137
.126
.145
.229
.131
.132
.129
.153
.152
.139
.172
Decile 10
.160
.502
.268
.243
.179
.143
.216
.411
.203
.250
.159
.252
.262
.252
.286
26
Table A4. M Cih (h = 1, ..., 10; i = 1, ..., 14) for η
Decile 1 Decile 2 Decile 3
1 Food and non-alcoh. beverages .082
.098
.111
2 Alcohol and tobacco
.057
.072
.081
3 Clothing and footwear
.028
.054
.077
4 Gross rents
.036
.056
.071
5 Electricity
.084
.098
.108
6 Fuels
.116
.115
.113
7 Health
.055
.072
.083
8 Private transport
.022
.056
.085
9 Public local transport
.042
.057
.066
10 Public distant transport
.005
.019
.028
11 Post and telecommunication
.088
.100
.107
12 Other goods
.039
.062
.081
13 Other services
.030
.053
.073
14 Purchases abroad
.026
.040
.050
= −.7, and
Decile 4
.124
.094
.101
.087
.118
.111
.098
.118
.080
.045
.115
.100
.092
.065
M CiE (×1000000) (i = 1, ..., 14).
Decile 5 Decile 6 Decile 7
.133
.131
.130
.107
.117
.128
.120
.126
.133
.101
.109
.118
.127
.129
.131
.112
.115
.119
.112
.119
.126
.148
.164
.181
.093
.102
.110
.063
.077
.092
.122
.123
.125
.116
.123
.130
.109
.117
.125
.082
.097
.113
Norway 1999.
Decile 8 Decile 9
.130
.130
.140
.156
.141
.155
.128
.143
.133
.138
.123
.127
.135
.146
.200
.227
.119
.131
.109
.131
.126
.130
.139
.153
.135
.151
.131
.153
Decile 10
.160
.246
.267
.242
.179
.141
.216
.408
.203
.248
.159
.251
.261
.275
Environm.
-.477
-.659
-.245
-.176
.144
-3.881
-.281
-1.491
-.440
-.175
-.189
-.305
-.220
-.016
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