77127
THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3: 541-62
Guidelines on Searching for a Dalton-Improving
Tax Reform: An Illustration
with Data from Indonesia
Shlomo Yitzhaki and Jeffrey D. Lewis
This article documents the search for a Dalton-improving tax and expenditure re-
form using a methodology developed by Yitzhaki and Slemrod (1991) and Mayshar
and Yitzhaki (1995). The methodology overcomes the need to define a specific social
welfare function by searching instead for reforms that improve each social welfare
function belonging to a wide class of functions. The authors apply the method to the
energy sector of Indonesia, ignoring distributional constraints, and find that both
the subsidy on kerosene and the tax on gasoline should be reduced. But taking distri-
butional concerns into account, the present structure of energy taxes is reasonable
and the country may benefit by increasing the subsidy to kerosene, taxing electricity,
and reducing the gasoline tax. These conclusions are robust to changes in the rel-
evant parameters representing the Indonesian economy.
This article illustrates the search for a Dalton-improving tax and expenditure
reform using a methodology developed by Yitzhaki and Slemrod (1991) and
Mayshar and Yitzhaki (1995). : The goal of this methodology is to eliminate the
need to define a specific social welfare function. Instead, we search for reforms
that improve each social welfare function belonging to a wide class of functions.
Avoiding the definition of a specific social welfare function reduces the bias
often inherent in such reforms: because governments are unable to specify a
social welfare function on their own, the proposed reforms often represent the
social views of advisers, which need not coincide with those of the client govern-
ments. Although professional advice on income distribution is never value free,
use of the Dalton-improving principle reduces the significance of the value judg-
ments embedded in such advice.
Dalton-improving reforms require the same data as social welfare-based tax
reforms. Thus no savings are made with respect to data collection. But the reli-
ance on data is weaker under Dalton-improving reforms. For example, both
1. See Martina (1993) for applications of the methodology in other areas of economics.
Shlomo Yitzhaki is with the Economics Department at Hebrew University, and Jeffrey D. Lewis is
with the Financial Policy and Institutional Strategy Department at the World Bank. This article was
written while Shlomo Yitzhaki was a consultant with the World Bank's Policy Research Department. The
authors would like to thank Hamid Davoodi, Shantayanan Devarajan, and Gunnar S. Eskeland for helpful
discussions, Peter Lambert and two anonymous referees for comments on an earlier draft, and Min Zhu
for research assistance.
© 1996 The International Bank for Reconstruction and Development / THE WORLD BANK
541
542 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3
types of reforms require revenue estimates; although regular reforms may be
sensitive to the exact magnitude of these estimates, Dalton-improving reforms
are not affected if the estimates are multiplied by a constant.
I. THE SEARCH FOR A DALTON-IMPROVING REFORM
Hugh Dalton, a British economist, was the first to suggest that a transfer
from a rich person to a poor person increases social welfare (Dalton 1949).
Dalton improvement is weaker than Pareto improvement, which asserts that
society benefits if the income of at least one member increases, provided that the
incomes of all other members do not fall. By contrast, a Dalton-improving re-
form allows the income of an individual to fall, provided that the incomes of one
or more poorer individuals increase by at least the same amount.
Searching for a Dalton-improving reform first requires ranking the popula-
tion according to its economic well-being. A definition of well-being must be
agreed upon to allow determination of who is rich and who is poor; such a
distinction is needed to decide whether a transfer will increase or decrease social
welfare. The definition of well-being can be expanded; for example, Mayshar
and Yitzhaki (forthcoming) allow well-being to be affected by two parameters—
ability and needs. Given ability, the greater the needs, the lower the well-being
of a household; and, given needs, the greater the ability of the household, the
higher its well-being. This kind of extension is useful for handling family size, in
which needs increase with the number of children, or rural-urban distinctions,
in which rural populations might need less income to achieve a certain level of
well-being than do urban populations (Ravallion 1993).
The technical requirements and implications of such extensions are beyond
the scope of this article. Instead, the empirical illustration reported later uses
expenditure per capita as the sole indicator of economic well-being. Because
expenditure per capita is used only to rank households, any monotonic transfor-
mation of this measure can be used without affecting the findings.
Dalton described the effect of transfers from rich to poor—not of transfers
between equally rich or equally poor individuals. Differential treatment of equally
rich or poor individuals is referred to as horizontal inequity. In our analysis we
allow transfers to be made between individuals that are equally well-off; fur-
thermore, we assume that society is indifferent to such transfers. This assump-
tion enables us to aggregate households with equal economic well-being.2
Types of Reform
We restrict the search for a Dalton-improving reform to finding the direction
of the desired tax reform (that is, determining which taxes or subsidies will in-
2. Note that indirect taxes tend to tax equal individuals differently. For a discussion of different
interpretations of horizontal inequity, see Lambert and Yitzhaki (1995). Mayshar and Yitzhaki
(forthcoming) extend the method to deal with Dalton-improving reforms in which transfers between
certain types of individuals are not allowed.
Yitzhaki and Lewis 543
crease or decrease and in what proportions), rather than the exact magnitudes of
changes in tax rates. The methodology of a Dalton-improving reform is appli-
cable to nonmarginal reforms. However, we will restrict the application to mar-
ginal reforms. The main advantage is the smaller data requirements: the analysis
of a marginal reform relies mostly on observed data, while analysis of a
nonmarginal reform typically relies on estimated or synthetic data on households.
An immediate question arises: How restrictive is the assumption of a mar-
ginal reform, and does this assumption make the methodology irrelevant for
evaluating practical tax reforms? Technically, an approximation based on know-
ing only the appropriate direction is applicable whenever first-order approxima-
tions do not lead to gross errors. But this textbook answer is not very useful.
Looking further, Willig (1976) investigated the accuracy of estimates of con-
sumer surplus from demand curves and showed that such approximations de-
pend on a commodity's share in total consumption and on income elasticities.
The smaller the share, the greater the accuracy—that is, the less a change in a
commodity's price affects the accuracy of the approximations. Similarly, the
higher the income elasticity, the less accurate are the approximations.
Also critical are the properties of Dalton-improving reforms. Empirically, it
is important that the reforms do not drastically change the household ranking.
A useful rule of thumb holds that if the reform does not change incomes by more
than 10 percent, a marginal analysis is reasonable. But if one intends to make
the poor rich and the rich poor, marginal analysis is not appropriate.
Tax-Shifting Assumptions
Tax-shifting assumptions allow for additional data savings. A general equi-
librium model is required to determine the distributional effect of the portion of
the tax absorbed by firms, households (the suppliers of factors of production),
and the economy. Most computable general equilibrium (CGE) models generally
assume that all production functions are homogeneous of degree one and that
there is perfect competition—which is equivalent to assuming that taxes are
borne by consumers. For simplicity we assume such shifting to consumers as
well, although there is nothing in the method that prevents the introduction of
complex tax shifting into the calculations.
Revenue Neutrality
It is easier to analyze revenue-neutral reforms because we can ignore the issue
of the optimal size of government activity. But ignoring this issue is another
convenient assumption and can be discarded, provided that the appropriate data—
each household's willingness to pay for public goods—are available. Partial re-
laxation of this requirement will be illustrated later.
Externalities
Ignoring externalities is yet another simplifying assumption. It should not be
difficult, however, to incorporate the effects of externalities into the calcula-
544 THE WORLD BANK ECONOMIC REVIEW, VOL 10, NO 3
tions, provided that we can obtain the appropriate data or, alternatively, make
the necessary assumptions regarding the effect of the externalities. If externali-
ties affect a public good, then we would need to know each household's willing-
ness to pay. Eskeland and Kong's (1994) framework is a good example of an
approach that can be incorporated into the search for Dalton-improving reforms.
II. CHARACTERIZATION OF A DALTON-IMPROVING REFORM
Consider a household with a well-behaved utility function «*(•), unknown to
us, and a known budget allocation, y* = Z^pc*, where q, is the consumer price of
the rth commodity; x/1 is the quantity of that commodity consumed; and y* is
the household's exogenously given income. Commodities may include faaors of
production, such as labor, in which case the consumed quantity of the commod-
ity is nonpositive. Assume that producers' prices (p, for the »th good) are given
and that t, = q: - pi are the tax rates. Then, the effect of a marginal tax reform on
the household, or marginal benefit, is
(1) MBh=-ZiX*dqi+dyh.3
A Dalton-improving reform can be viewed as the combination of the alloca-
tion of manna from heaven (arriving because of a reduction in deadweight effi-
ciency loss, or excess burden) and transfers from rich to poor households. MBh
is the first-order approximation of the effect of the reform on household h,
evaluated in monetary terms.
Under the Dalton criterion, MB} S 0 must hold for the poorest (first) house-
hold, otherwise the poorest household has not received its share of manna or a
transfer from a richer household. If MB1 < 0, the poorest household is making a
transfer to others, in violation of the Dalton criterion.
Now consider the second poorest household. The Dalton criterion restriction
on the marginal benefit to this household requires that MB1 + MB2 ;> 0, which
means that the combined first and second household "poor" must be better off.
Note that MB2 can be negative, in which case the reform involves a transfer
from the second poorest to the poorest household.
By similar reasoning, it can be shown that a Dalton-improving reform has to
fulfill the general condition
(2) XjUMB* >0,for* = l,2,3...H,
where H is the number of households in the economy.
We can offer an additional interpretation of equation 2. Consider a social
planner who wants to reduce the poverty gap but does not know who is
3. We can derive this relationship under two alternative sets of assumptions. First, the household is a
utility maximizer, and, by Roy's identity, dif()fi}tl = -X*x*, where v is the indirect utility function and X is
the marginal utility of income. The marginal benefit is the income equivalent of the change caused by the
reform. Second, no optimization is carried out by the household, and we are interested only in a Slutsky
compensation to the household.
Yitzhaki and Lewis 545
poor. To be on the safe side, it is best to reduce poverty gaps for any possible
poverty line. Equation 2 is the necessary and sufficient condition for such a
strategy.
A simple change in equation 2 will allow us to adapt the Dalton-improving
reform to more specific poverty criteria. If the social planner is willing to
commit to an upper bound for the poverty line, then equation 2 can be re-
stricted to the subset of households that are potentially poor, and all other
households can be aggregated into one group. Another poverty target is to
insist that the reform raise all incomes above a given threshold. Accommo-
dating such a restriction requires that additional constraints be imposed on
the lowest inequalities in equation 2. Such an extension is feasible but be-
yond the scope of this article.
III. TAX INSTRUMENTS
Equation 2 defines the target function for the tax reform, which is subject to the
constraint that the reform be revenue neutral. Each tax instrument (which may be a
tax rate, an exemption, or any aspect of the tax function) involved in the reform is
characterized by two kinds of parameters. The first parameter reflects the effect on
the target function and is later referred to as the distributional characteristics of the
instrument.4 The second parameter reflects the impact on the revenue constraint
and is referred to as the marginal efficiency cost of public funds (MECF). The MECF
reflects the cost to society of the revenue raised by changing the tax instrument.
Distributional Characteristics
Substituting equation 1 into the left-hand side of equation 2 gives
(3) IL.MB* =- ILX,*N<7, + X L V -
By changing the order of summation and dividing and multiplying by
X; = J.hxf, the "quantity demanded" of the tax base / (which for indirect taxes is
commodity i), we get
(4) X
The term YX.\xflX, is the cumulative share of commodity i consumed (held) by
the k poorest households. This term reflects the distributional characteristics of
the tax instrument. It is portrayed by the concentration curve of the commodity,
which is a variation of the well-known Lorenz curve (Kakwani 1977 describes
the properties of concentration curves).
The data required for constructing concentration curves can be found in any
survey of family expenditure. In this article we use the National Social Eco-
nomic Survey, or SUSENAS (Government of Indonesia 1990). Since we deal only
with indirect tax reforms, dy*1 = 0 for all households.
4. Feldstein (1972) coined the term distributional characteristics and showed its relevance in taxation.
546 THE WORLD BANK ECONOMIC REVIEW, VOL 10, NO. 3
Marginal Costs of Funds
An important consideration in any tax reform is the expected change in rev-
enue. In this section we show that embedded in these revenue estimates is the
estimate of the marginal deadweight loss that can be recovered through the
revenue estimates.
Government tax revenue is
(5) R(t,P,y) = l,t,xilp + t,y)
where X, (q, y) is the demand for commodity /'; y is a vector of incomes; t is a
vector of specific taxes; and consumer prices are q = p + t. Revenue neutrality
requires that
(6) dR=^iMR,dt,=0
where MR, = dR/dt, is the change in overall tax revenue resulting from a small
change in the tax rate on commodity i. As it turns out, it is convenient to work
with revenue changes expressed in monetary terms rather than with tax param-
eters, which may have different units. Hence the change in tax revenue (denoted
by 8,) that results from a change in the tax rate on commodity i (dt,) becomes
(7) 5, = MR.dt,.
The marginal tax reform, dt, could also be characterized by the vector of tax
receipts, 8. And the change in tax revenue would then be dR = X.-8,.
Substituting equation 7 into equation 4 and taking into account that dt{= dq,
and dy*1 = 0 for all h, the Dalton criterion becomes
(8) Zl,MBh=-Z,(X,
subject to S,-8, = 0.
The term XJMRj is the marginal efficiency cost of public funds. To illustrate,
we concentrate on the last inequality in equation 8, when k = H. This is the
representative consumer case in which distributional considerations are ignored.
Equation 8 becomes
(9) £ £ , MBh = -X, (X,- / MR,-) 5, subject to £ , 5, = 0.
A neutral tax reform, involving only two taxes, will reduce deadweight loss if
(10) X L MBh = -i(Xt I MR,) 8, - (X2 / MR2) 8,] = (MECF2 - MECF^ > 0.
It can be easily seen that if MECF2 > MECFU the reform will have an effi-
ciency gain only if 8] > 0, and if MECF2 < MECFU the reform will have an
efficiency gain only if 8, < 0.5
5. Note that if any two MECB are not equal, then we can design a Pareto-improving tax reform,
provided that lump-sum taxes exist.
Yitzhaki and Lewis 547
To estimate the marginal efficiency cost of public funds, two parameters for
each tax instrument must be evaluated: the marginal change in revenue, MRh
and the tax base X,, which is the expected change in tax revenue assuming no
other changes occur.
In many estimations, X, is also used as an estimate of MR,. The interpretation
in those cases is that all marginal efficiency costs of public funds are assumed to
be equal. But in this article we relax this simple assumption and use a CGE model
for Indonesia that can estimate these costs individually (Lewis 1993). A brief
description of the model is given in the appendix.
Characterization of the Solution
The problem solved is that defined in equation 8. That is, we must deter-
mine the 8,(; = 1. . .«) that satisfy the inequalities in that equation. In many
cases equation 8 will have no feasible solution or an infinite number of solu-
tions. We will be interested in finding one feasible solution, and, if possible,
characterizing the feasible set. Since the trivial solution, 8, = 0 for all /, satis-
fies the constraints, one commodity should be chosen as a numeraire, with
5 = 1 or 8 = - 1 . We must try both cases because we do not know whether the
tax on the numeraire should be increased or decreased. Also, any convex
combination of two solutions is feasible.6 Thus by finding two Dalton-
improving tax reforms, one with a positive change in the tax rate / and the
other with a negative change, we can find a Dalton-improving reform with
no change in tax rate /'. In this case we can conclude that instrument;' is not
essential for a Dalton-improving reform.
In order to search for solutions, a numerical optimization algorithm is used to
solve the following problem:
(11) Min^Max [-CMB* (6),0]2}, subject to £ , 5 , = O, 5, * 0
where CMBk = YJf,a\MBh is the cumulative marginal benefit of all households
poorer than or just as poor as household k. A feasible marginal tax reform, 8,
will be considered a solution if the value of the objective function in equation 11
is zero. Since a solution requires that the target function equal zero, it is easy to
verify that the numerical optimizer reaches a solution. The algorithm used for
the search is described in Yitzhaki (1982), but any algorithm for numerical op-
timization can be used.
In general, there may be several (or an infinite number of) solutions to
equation 11, and we do not have a methodology for finding all of them. For
each numerical problem that we solve, we may find one solution. But it can
be shown that the set of solutions forms a convex cone, implying that for a
small number of instruments we can characterize the whole efficient set. For
example, if only three tax rates are considered, then there will be only one
6. To see this, note that a "solution" means that the cumulative gain is nonnegative for all k
(5Li_,AlB* 2 0). Imagine that you have found two such solutions. Then any convex combination of the two
will also be nonnegative for all k.
548 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3
independent variable, and the efficient set will form a segment on the real
line. Searching for extreme solutions enables us to wholly characterize the
efficient set.
The set of solutions to equation 11 defines the feasible set of Dalton-improving
reforms. In general, we will be satisfied if we find one solution that belongs to
the set. If the set includes more than one solution and we can characterize the
whole set, the question to be asked is how to choose among solutions. One
possibility is to add other constraints. For example, we could require that a
Dalton improvement take place for both rural and urban populations or, alter-
natively, for several subgroups of the population, such as different-size house-
holds (see Mayshar and Yitzhaki, forthcoming). Another possibility is to choose
a Dalton-improving reform that maximizes the number of beneficiaries—mak-
ing it the most "populist" option. Those extensions are beyond the scope of this
article.
IV. MORE ON DISTRIBUTIONAL CHARACTERISTICS
Ignore, for the time being, the marginal cost of funds. We can assume that
taxes are lump sum, or that their marginal efficiency costs of public funds
are equal. The distributional characteristics of a tax instrument are described
by a concentration curve. The concentration curve of commodity / depicts
the cumulative share of aggregate expenditure on that commodity against
the ranking order of households, which are arranged in increasing order of
economic well-being. The concentration curve is constructed analogously to
the Lorenz curve, except that the vertical axis represents the cumulative share
of a tax base (commodity) rather than income. By construction, each con-
centration curve extends from zero (for h = 0) to 1 (for h = H). The income
elasticity of the commodity can be inferred from the curvature: if the con-
centration curve is convex, then the income elasticity is greater than zero; if
the curve is concave, the elasticity is negative; and if it is a straight line, the
elasticity is zero. An inferior good will thus have a concentration curve above
the diagonal, and the curve of a neutral good will coincide with the 45-
degree line. If the income elasticity is one, the Lorenz and the concentration
curves will be identical, and if the elasticity is greater than one, the concen-
tration curve will fall below the Lorenz curve. Since income elasticity can
change over the range of the income distribution, it is possible for the con-
centration curve to follow an irregular path between the starting point (0, 0)
and the ending point (1,1) (figure 1).
In general, concentration curves tend to intersect, making it difficult to deter-
mine the characteristics of the appropriate Engel curve from their movements.
This, in turn, makes it difficult to grasp the intuition and logic of Dalton-
improving reforms. Fortunately, we can derive necessary conditions for Dalton-
improving reforms using modified versions of regular income elasticities. For
this purpose it is convenient to summarize the curvature of the concentration
Yitzhaki and Lewis 549
Figure 1. Distributional Characteristics of Commodities
Cumulative share of consumption
Cumulative share of households
Note Cumulative share of households is from the lowest- to the highest-income.
r| is the (Gini) Income elasticity of commodities.
curve by a coefficient, known as the Gini income elasticity of a commodity.7
Construction of this coefficient is as follows.
The area between the Lorenz curve and the 45-degree line is equal to cov[y,
F(y)]/[iy, where \iy and F(y) are the mean and the cumulative distribution of
expenditure per capita, respectively. The term cov[y,, F(y)] resembles a variance
measure, but with a cumulative distribution substituted for the variate. Sim-
ilarly, the area between a concentration curve of commodity x, and the 45-
degree line is equal to cov[x,, F{y)]/\ih where n, is the mean expenditure on com-
modity /. Given the basic components that resemble the coefficient of variation
and the covariance, the Gini income elasticity of a commodity is
CQv[Xj,F{y)]\Ly
(12)
cov\y,F(y)]\ii
There are three interpretations of %:
• T|, is equal to the area between the 45-degree line and the concentration
curve divided by the area between the 45-degree line and the Lorenz curve;
7. See Lerman and Yitzhaki (1994), Yitzhaki (1994), and the references therein for the derivation of
the coefficient and other alternative interpretations of those coefficients.
550 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3
• T), is equal to a weighted average of the income elasticity of commodity /,
with the weights derived from the Gini coefficient (Yitzhaki 1994);
• T), is equal to the ratio of the Gini regression coefficient of the marginal
propensity to spend on commodity / divided by the average propensity. To
see thatr), resembles an elasticity, note that b,- cov[x(, F(y)]/cov[y,, F(y)] is
the Gini regression coefficient of the slope of the regression curve of x as a
function of y, which can be interpreted as a weighted average of the marginal
propensity to spend, while u , / ^ is the average propensity.8
An important property of this parameter is that a value greater or smaller
than 1 determines whether a change in the tax on the commodity raises or low-
ers the Gini index of income inequality (Lerman and Yitzhaki 1994). Moreover,
comparing the Gini income elasticities to each other and to 1 permits us to
evaluate the impact of a tax on the Gini coefficient of economic well-being
(Yitzhaki 1994).
V. DISTRIBUTIONAL CHARACTERISTICS OF COMMODITIES IN INDONESIA
The data we used came from the Indonesian Sample of Family Expenditure
for 1990 (Government of Indonesia 1990). Expenditure per capita is used as a
proxy for a household's economic well-being, and an individual is treated as the
relevant unit by assigning a weight according to the number of individuals in the
household. In order to simplify the calculations, the sample population is di-
vided into 94 cells, each with 500 households (except for the last, which has 79
households).
As explained above, the marginal efficiency costs of public funds are calcu-
lated using a CGE model, derived from the 1985 social accounting matrix for
Indonesia. One practical problem that arises when using two separate sources
of data is the mismatching of classifications and levels of aggregation. On one
hand, the family expenditure survey does not distinguish between imported and
locally produced goods, although the CGE model was designed primarily to deal
with such trade issues. On the other hand, the twenty-six-sector CGE model lacks
the commodity detail of the expenditure survey. For example, it includes only
one food processing sector, but the level of disaggregation in the survey goes as
far as to distinguish between different types of cigarettes. To overcome this
problem, we limited our search for Dalton-improving reforms to three com-
modities that are similarly defined in both data sources: electricity, kerosene,
and gasoline. We also limited our analysis to the excise taxes or subsidies that
were levied on these products. Historically, these rates have varied substan-
tially. In 1980-81, for example, total subsidies to domestic fuel use averaged 17
to 18 percent of government routine expenditure, or nearly 2 percent of gross
8. For those who feel more comfortable with ordinary least squares (OLS), note thatfc(can be interpreted
as an instrumental variable estimator of the slope of the regression curve when F(y) is used as an instrument
for y.
Yitzhaki and Lewis S51
Figure 2. Concentration Curves of Energy-Producing Items, Indonesia
Cumulative share of consumption
1.0
0.8 -
0.6 -|
45-degree line
0.4 -
0.2 -
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cumulative share of households
Note: Cumulative share of households Is from the lowest- to the highest-Income.
Source: Authors' calculations.
domestic product (GDP); but by 1985 (the year of the data used in this study) the
total subsidy had dropped to only about 3 percent of routine expenditure.
The commodity with the lowest concentration curve is gasoline, indicating
that gasoline has the highest income elasticity, which is greater than 1 (figure 2).
Next comes electricity, with a concentration curve that is also below the Lorenz
curve, meaning that the income elasticity of electricity is, on average, greater
than 1. The concentration curve of kerosene is below the diagonal and above the
Lorenz curve, which means that the income elasticity is bounded by 0 and 1.
The (Gini) income elasticity of kerosene is 0.59, indicating that kerosene is a
necessity, whereas electricity has an income elasticity of 1.61 and gasoline 2.30
(table 1). As shown in Yitzhaki (1991), these are consistent estimates of the
appropriate population parameters, and the asymptotic distribution converges
Table 1. Gini Income Elasticities of Commodities, Indonesia
Elasticity Kerosene Electricity Gasoline Q~c'g-' V-cig.b
Income elasticity 0.59 1.61 2.30 0.26 0.56
(0.07) (0.05) (0.14) (0.09) (0.07)
Note-. Income elasticity is calculated with respect to expenditure per capita. The population includes
all Indonesian households separated into 94 groups, each with 500 observations, except for the last
group. Households are ordered according to expenditure per capita. Jackknife standard errors arc reponed
in parentheses (see Yitzhaki 1991).
a. Q-cig. is the income elasticity of purchased quantity of regular rolled cigarettes.
b. V-cig. is the income elasticity of expenditure on regular rolled cigarettes.
Source: Government of Indonesia (1990); authors' calculations.
552 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3
to the normal. We can see from the standard errors that the income elasticities
of these commodities differ significantly from one another.
The income elasticity of regular rolled cigarettes is included in order to dem-
onstrate some of the properties of the analysis. The difference between the in-
come elasticity of quantity sold of regular rolled cigarettes and the income elas-
ticity of expenditure on this commodity (0.56-0.26) indicates that the income
elasticity of price paid is 0.3 (the difference between the two).9
VI. DALTON-IMPROVING REFORMS
To begin the search for Dalton-improving reforms, we ask the following ques-
tion: Is it possible to have a revenue-neutral Dalton-improving reform that is
based on the change in the taxation of one commodity? The answer is yes, if we
can tax the quality of the commodity.
To see this, consider the following case. A specific subsidy (that is, a subsidy
to the quantity consumed) and an ad valorem tax are simultaneously imposed
on the same commodity. The rates are defined so that the reform is neutral
(§Quant. = -^Expend.)- Since the marginal cost of funds for each of these two taxes
should be equal, the way of finding such a tax reform is by plotting the differ-
ence between the concentration curves of quantity consumed and expenditure
on that commodity. The vertical difference between the concentration curves
(the DCC curve) is the cumulative marginal benefit from the reform. If the curve
is nonnegative, then a revenue-neutral, one-commodity tax reform is identified.
The DCC curve for regular rolled cigarettes shows that the cumulative gain is
positive—thus a Dalton-improving reform exists (figure 3). The bottom 70 per-
cent of the population could gain up to 8 cents for each dollar of tax paid by the
top 30 percent of the population.
The purpose in presenting this example is to demonstrate the importance of
separating the tax instrument from the commodity. The same commodity could
have different tax bases depending on the nature of the change in the tax func-
tion. A good example is motor vehicles. Many developing countries (including
Indonesia) impose taxes on different properties, such as quantity (a constant
amount per vehicle), weight, engine size, and, of course, value. The different
taxes may have significant differences in their distributional characteristics, a
property that can be exploited to increase the variety of tax instruments.
VII. DALTON-IMPROVING REFORMS INVOLVING MORE THAN ONE COMMODITY
In order to search for Dalton-improving reforms that involve more than one
commodity, we need to determine the MECF of the commodities, which we cal-
9. To sec this, note that £ = PQ, where P is price and Q is quantity. Let Y be income. Then AE » PAQ +
QAP. Hence:
AE E AQ Y AP Y
+
AY Y AY Q AY P'
Yitzhaki and Lewis 553
Figure 3. The Gain from a Combination of a Subsidy and a Tax, Indonesia
Gain from regular rolled cigarettes (cents)
9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cumulative share of households
Note: The figure plots the gain at each cumulative household share of a dollar of tax paid by the
higher-income households above that level. Cumulative share of households is from the lowest- to
the highest-income.
Source: Authors' calculations.
culate using the CGE model (table 2). If the tax planner cares only about effi-
ciency, then the optimal policy is to equate the marginal efficiency costs of pub-
lic funds. Comparing the income elasticities in table 1 with the MECFs in table 2,
we see that the ranking of the two is equal, meaning that the structure of taxa-
tion of those commodities is reasonable in that a higher share of tax paid by the
poor corresponds to a lower marginal excess burden. From this result we can
conclude that the structure of Indonesian energy taxes does take into account
distributional considerations.
The cost at the margin to society of raising a dollar of revenue from the
gasoline tax is 2.7 dollars (figure 4). The burden on the poorest 50 percent of the
Table 2. Parameters for Calculations of Marginal Efficiency Costs of Public
Funds, Indonesia
Tax base, X Marginal revenue Marginal
(billions of 1985 from tax, MR efficiency costs of
Indonesian (billions of 1985 public funds,
Variable rupiah) Indonesian rupiah) MECF Initial tax rate
Kerosene 62.2 57.4 1.08 -0.48
Electricity 83.5 73.4 1.13 0.00
Gasoline 104.7 38.7 2.70 0.30
Source: Authors' calculations.
SS4 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3
population is 12 cents, and the rest is borne by the wealthier half of the popula-
tion. On the other hand, a dollar of revenue raised through a tax (reduction of
the subsidy) on kerosene costs society only 1.08 dollar, but the poorest half of
the population pays 40 cents. An economist guided by efficiency concerns would
recommend that the subsidy to kerosene be reduced and the tax on gasoline
lowered in order to reduce distortionary taxation. This measure would save
society more than 1.5 dollars for each dollar reduction in the subsidy to kero-
sene. On the other hand, the economist who cares about distribution will point
out that the burden of those taxes is not shared fairly. More of the burden of
kerosene taxation is borne by the poor, so that a transfer of a dollar of taxation
from gasoline to kerosene can be viewed as a transfer from the poor to the rich.
This divergence between policy prescriptions based on efficiency alone and those
based on equity alone confirms that the Indonesian taxes embody a reasonable
tradeoff between objectives: although efficiency considerations call for reducing
the gap in tax rates, distributional concerns point in the other direction.
Note that all curves in figure 4 intersect, meaning that it is impossible to find
a Dalton-improving neutral tax reform that involves only two commodities. On
the other hand, intersection points to the possibility of finding two different
social welfare functions, both of which conform to the Dalton criterion. One
function can justify raising the tax on one commodity and lowering the tax on
the second, while the other function can show the opposite. The ability to find
two social welfare functions that give contradicting recommendations means
that it is impossible to find a Dalton-improving reform.
Figure 4. Distributional Burden of Energy Taxes, Indonesia
Cumulative burden of 1 U.S. dollar of tax (dollars)
3.0
2.5 •
2.0 -
1.5 "
1.0 -
0.5 "
Electricity
.—— =.—
0
0 0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9 1.0
Cumulative share of households
Note: Cumulative share of households Is from the lowest- to the highest-Income. Each curve is the
concentration curve of the commodity multiplied by the marginal efficiency cost of public funds of
that commodity.
Source: Authors' calculations.
Yitzhaki and Lewis 555
Economists are neither equipped nor entitled to handle issues of fairness. In
order to reach specific conclusions, social planners must be more specific with
regard to their social preferences. We can say for certain only that the Indone-
sian taxation of the commodities we examined takes into account distributional
concerns.
Having failed to find a Dalton-improving reform that is based on two com-
modities, we must search for a three-commodity reform. In this case, we have
freedom to set only one tax: one tax change is used as a numeraire, so its value
is either 1 or - 1 , and a second tax change is determined by the budget con-
straint. Since only one variable is free and the set of efficient Dalton-improving
reforms is a cone, if a given set of Dalton-improving reforms is not empty, it
forms a closed section on an interval.
Applying the optimization algorithm to this three-commodity question, we
find that Dalton-improving, revenue-neutral reforms have the following struc-
ture: an increase in the tax on electricity and a decrease in the taxes (subsidies)
on kerosene and gasoline (table 3). Reform D (distribution) says that each dollar
reduction in the tax on kerosene is accompanied by a reduction in the tax on
gasoline by 3.5 cents and an increase in the tax on electricity by 1.035 dollars.
Reform E (efficiency) raises the tax on electricity by 3.26 dollars and reduces
the tax on gasoline by 2.26 dollars for every 1 dollar reduction in the tax on
kerosene. Any convex combination of those reforms is a Dalton-improving, rev-
enue-neutral reform as well.
Reform D does not result in an efficiency gain to society, but it results in a
gain to low-income groups (figure 5). To see the amount of efficiency gain, add
up the products of theMECFs and the revenue changes (in table 3): (1.0)(1.083) -
(1.035)(1.13) + (0.035)(2.70) = 0.008. Reform E results in an efficiency gain of
3.5 dollars for every dollar reduction in the tax on kerosene, but the gain is
limited to high-income groups.
Now that we have identified a set of Dalton-improving reforms, we can con-
sider the appropriate reform by introducing other considerations. Although the
nature of these considerations can vary from one country to another, a few
possibilities include the following:
• Dalton-improving reforms should not discriminate between regions or ethnic
groups. The way to incorporate such a consideration is to impose the
restriction that reforms must be Dalton-improving for each region or group.
Table 3. Structure of Revenue-Neutral Dalton-improving Reforms, Indonesia
(U.S. dollars)
Reform Kerosene Electricity1 Gasoline'
Distribution (D) -1.0 1.035 -0.035
Efficiency (E) -1.0 3.260 -2.260
a. The change in the tax on the commodity for each one-dollar reduction in the tax on kerosene.
Source-. Authors' calculations.
556 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3
Figure 5- Cumulative Gain of Two Extreme Dalton-improving Reforms,
Indonesia
Cumulative gain (U.S. dollars)
3-5
-0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cumulative share of households
Note: Cumulative share of households is from the lowest- to the highest-income.
Source: Authors' calculations.
• The set of Dalton-improving reforms was derived under the assumption
that expenditure per capita represents the ranking of economic well-being.
Most economists will probably agree that family size can affect economic
well-being, but there may be disagreement about its quantitative effect.
The same argument can be raised with respect to a rural/urban distinction.
Mayshar and Yitzhaki (forthcoming) show how to incorporate such
considerations.
• An additional consideration is popular support. To satisfy both the
economist and the politician we can, for example, search for Dalton-
improving reforms that maximize the number of beneficiaries. The major
problem in incorporating such a constraint is that, unlike the search for a
Dalton-improving reform, which can be carried out with tabulated data,
the search for a majority requires that the whole sample be examined.
Needless to say, this constraint is much less binding in the era of modern
computers.
VIH. SENSITIVITY ANALYSIS
Most of the analysis in this article was carried out without any parameteriza-
tion: no assumptions were made on the curvature of the Engel curves of the
Yitzhaki and Lewis 557
commodities, and the assumptions concerning the social welfare function are
pretty mild. The only parameters that are derived from rigorous modeling ef-
forts are the marginal efficiency costs of public funds. But revenue estimates are
routinely performed by almost all treasury departments, and they are necessary
inputs into the tax reform process. Because revenue estimates are based on a
blend of complex modeling and intuition, performing traditional statistical test-
ing is often difficult, especially if the number of parameters is large.
One way of investigating the robustness of our conclusions is to perform a
sensitivity analysis on our revenue estimates by changing the marginal efficiency
cost of public funds and observing the effect on the set of Dalton-improving
reforms. Since our results depend only on the ratios of these costs, any multipli-
cative bias in the estimates should not affect the conclusions. Also, it is clear
that if the marginal efficiency cost of public funds of kerosene is reduced and the
costs of electricity and gasoline are increased, there will be no qualitative change
in the conclusions.
Because of its magnitude, the marginal efficiency cost of public funds for
gasoline (2.7) (see table 2) is most suspect. To evaluate how strongly it shapes
the results, we reduced it gradually to see if our conclusions changed qualita-
tively. Small changes did not change the results qualitatively, and even a reduc-
tion by 40 percent (from 2.7 to 1.62) still produced a Dalton-improving reform
(—1.0 for kerosene, -1.67 for gasoline, +2.66 for electricity) and an overall effi-
ciency gain of 0.75 dollar (these results are not shown). Changing the marginal
efficiency cost of public funds of electricity by 10 percent upward and down-
ward also failed to produce any qualitative change.
An explanation for the robustness of the results can be found by reexamining
figures 2 and 3. Figure 2 shows that if the marginal efficiency costs of public
funds are equal, there can be three types of Dalton-improving reforms: subsidize
kerosene and tax electricity, subsidize kerosene and tax gasoline, or subsidize
electricity and tax gasoline. Hence, if the marginal efficiency cost of public funds
of electricity is lower than that of kerosene, the Dalton-improving reform will
consist of subsidizing kerosene and taxing electricity. Therefore the conclusion
that we should increase the subsidy to kerosene will be unaffected even if the
marginal efficiency costs of public funds of electricity and gasoline are lowered
to equal that of kerosene. On the other hand, it is worthwhile to reduce the
subsidy to gasoline because of its high marginal efficiency cost of public funds.
This result will not be affected as long as this cost continues to be higher than
that of electricity. If the marginal efficiency cost of public funds of gasoline is
below that of electricity, then the Dalton-improving reform would call for an
increase in the tax on gasoline and subsidizing electricity. But for this result to
occur, the marginal efficiency cost of public funds for electricity must rise from
1.1 to above 2.7.
Finally, it should be noted that Dalton-improving reforms are not sensitive to
the number of instruments considered. That is, provided that the estimates of
the marginal efficiency cost of public funds are not affected, the reforms found
558 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3
Table 4. Nonneutral Dalton-improving Reforms, Indonesia
(U.S. dollars)
Reform Revenue1 Kerosene Electricity* Gasoline1'
Distribution, D.5 0.50 -1.0 1.91 -0.41
Efficiency, E.5 0.50 -1.0 2.88 -1.38
Successful reform, R.7S 0.70 -1.0 2.38 -0.68
Failed reform, R.75F 0.75 -1.0 2.56 -0.81
a. The revenue requirement of the reform. Values are for each one-dollar reduction in the tax on
kerosene.
b. The change in the tax on the commodity for each one-dollar reduction in the tax on kerosene.
Source: Authors' calculations.
to be Dalton-improving will continue to be so even if we change additional taxes
and subsidies. Additional instruments can only increase the Dalton-efficient set,
they cannot eliminate a solution from the feasible set.
IX. NONNEUTRAL REFORMS
To analyze nonneutral reforms, we must know the public's willingness to pay
for the public goods produced by the government. Since some of the Dalton-
improving reforms brought about an efficiency gain, the question arises as to
whether it is possible to split the gain between the public and the government,
subject to the extreme and unrealistic assumption that the government "wastes"
its share. To search for such a reform, we have to change the revenue constraint
(equation 6) so that dR £ c, where c is a constant greater than zero.
We consider four reforms (table 4). The first two reforms, D.5 and E.5, are
the extreme Dalton-improving reforms, subject to the constraint that the re-
form must raise 50 cents on every dollar of subsidy to kerosene. Since kerosene
is chosen to be the numeraire, the reforms are normalized according to its sub-
sidy; however, as a result, each reform raises a different amount of tax revenue.
Alternatively, the amount of additional taxes collected could be chosen as the
numeraire, but in this case the numeraire would have to be adjusted after each
calculation. Similar to the reforms reported in table 3, reform D.5 increases the
income of the poor, and reform E.5 primarily increases efficiency. Comparing
table 3 with table 4 reveals that the set of nonneutral Dalton-improving reforms
that raise revenue by 50 cents to each dollar of subsidy is contained within the
set of Dalton-improving reforms that are revenue neutral. The range of change
in electricity taxation has declined from 1.035-3.26 dollars to 1.91-2.88 dol-
lars, which may indicate that the distributionally oriented reforms are more
sensitive to revenue neutrality than reforms concerned with efficiency.
Given the possibility of raising revenue and satisfying the Dalton criterion,
we are tempted to ask how much more revenue can be extracted. From the last
two rows of table 4, we see that when the revenue requirement was raised to 70
cents, we could still find Dalton-improving reforms. Reform R.7S reports the
changes in taxes that are required. However, an attempt to raise 75 cents failed
Yitzhaki and Lewis 559
Figure 6. Cumulative Gain of Revenue-Raising Reforms, Indonesia
Cumulative gain (cents)
35
Increases revenue by 70 cents
30 for each dollar of subsidy
25 • Increases revenue by 75 cents
for each dollar of subsidy
20 -
15 -
10
-5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cumulative share of households
Note The lines show the cumulative gains to the public for reforms raising $0.70 and $0.75 In
revenue for each dollar of subsidy. Cumulative share of households Is from the lowest- to the
highest-income.
Source: Authors' calculations.
to find a Dalton-improving reform—reform R.75F is the best reform that could
be found, although it is not a Dalton-improving reform. Examining the cumula-
tive gains to the public (ignoring additional revenue) of reforms R.7S and R.75F
(figure 6), we see that reform R.7S continues to generate a cumulative gain of 35
cents, mainly for the top three deciles, a gain of 5 cents for the lowest two
deciles, and a loss of 5 cents to the middle class. Although reform R.75F does
generate 75 cents, it hurts the second to the sixth deciles (the cumulative gain
curve is declining), while the rich still receive 30 cents.
X. FURTHER RESEARCH AND CONCLUSIONS
The sensitivity analysis carried out suggests that the recommended direc-
tions for tax reform are robust with respect to variation in the marginal effi-
ciency costs of public funds. The question is whether these recommendations
are sensitive to other assumptions.
We could argue, for example, against aggregating rural and urban popula-
tions because of concerns that urban and rural economic welfare are not compa-
rable—a higher income may be needed in the city for households to reach the
same level of economic well-being as in rural areas—or transfers between urban
areas and rural areas (or the reverse) cannot be made for political reasons. These
S60 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 3
Table 5. Gini Income Elasticities
Variable All Urban Rural
Kerosene 0.59 0.21 0.55
Electricity 1.61 1.12 1.37
Gasoline 2.30 1.90 2.62
Note: Income elasticity is calculated with respect to expenditure; households are ordered according to
expenditure per capita.
Source: Authors' calculations.
two concerns can be handled by imposing additional constraints on the Dalton-
improving reform (Mayshar and Yitzhaki forthcoming).
We can evaluate the sensitivity of our results to the aggregation of rural
and urban households by calculating Gini income elasticities (table 5). There
are significant differences in income elasticities (and hence in the shape of
the Engel and concentration curves) between rural and urban populations.
The overall income elasticity of kerosene and electricity is bigger than the
income elasticity in either rural or urban areas, indicating that the Engel
curve of the full population is steeper than the Engel curve for each subpopu-
lation. However, the income elasticity of gasoline for the entire population
falls between that for the urban and that for the rural. These elasticities
suggest that the results can be affected by imposing a constraint on rural-to-
urban cross-subsidization.
This article describes the search for Dalton-improving reforms. When the
method is applied to the energy sector of Indonesia, which is characterized by
high gasoline taxes and high kerosene subsidies, we find that efficiency concerns
alone suggest that the distortionary gasoline tax and kerosene subsidy should
both be lowered. But when distributional concerns are considered, we see that
the given structure of energy taxes is more reasonable. Indeed, the analysis sug-
gests that, given the structure of demand for different energy products, equity
could be improved further by reducing the gasoline tax, increasing the subsidy
to kerosene, and imposing a tax on electricity (to achieve revenue neutrality).
These conclusions are robust to changes in the relevant parameters representing
the Indonesian economy.
APPENDIX. THE COMPUTABLE GENERAL EQUILIBRIUM MODEL
The Indonesian CGE model used to derive the estimates of the marginal effi-
ciency cost of public funds is one of a class of models that have been applied to
issues of trade strategy, income distribution, and structural change in develop-
ing countries. Such models simulate the operation of a market system in which
prices, wages, and the exchange rate vary in order to equate supply and demand
for goods, labor, and foreign exchange. A variety of substitution mechanisms
are specified among labor types, between capital and labor, between value added
and intermediate inputs, between imports and domestic goods, and between
Yitzhaki and Lewis 561
exports and domestic sales—all occurring in response to variations in relative
prices.
The CGE model contains twenty-six productive sectors. The structure of the
energy and environment sector includes seven separate fuel sectors (coal, diesel,
fuel oil, gasoline, high-speed diesel oil, kerosene, and natural gas) and three
others that are related to energy supply and demand (electricity and gas, lique-
fied natural gas, and oil). Of the remaining sectors, two are agricultural, three
are services, and the others are industrial. There are seven primary factors of
production (two types of agricultural labor, three types of industrial labor, capi-
tal, and land), four household categories, and three groups borrowing externally
(the government, public enterprises, and the private sector), with separate ex-
ternal debt accounts for each. Labor supply in each category is assumed to be
fixed. Investment is set equal to total savings, determined by applying fixed
saving rates to household and government income. In keeping with the focus on
energy, we expanded the modeling of energy supply and demand interactions.
The model includes the possibility of extensive interfuel substitution and speci-
fication of more elaborate market-clearing mechanisms for the energy products
in order to reflect the endogenous fuel taxes or subsidies created by the system
of government-administered retail fuel prices.
Although there are a variety of different tax instruments in the model, the
simulations carried out for this article involve changes only in the sectoral con-
sumption tax levied on domestic consumption (including both domestically pro-
duced and imported goods). In each case the experiment involves raising the
sectoral tax by 5 percentage points from its initial value. The static revenue
impact is calculated as 5 percent of the base-period value of consumption. The
equilibrium impact is the overall change in government revenue after the model
is solved and all markets clear following the tax change. Although estimates of
revenue change depend on the parameterization of the CGE model, what is im-
portant for the Dalton-improving calculations is the relative magnitudes of the
marginal efficiency cost of public funds for each commodity. Given the CGE
model structure, different plausible parameter choices are unlikely to affect the
ranking or relative magnitudes of these costs.
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