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Poverty weighted measures of social welfare change
0305~750WXX$3.00 + 0.00
World Lkvelopmm~. Vol. 16. No. X, pp. XYO-001, 1088. Printed in Great Britain.
0
Poverty Weighted Measures Social Welfare Change
lY88 Perganion
Press plc
of
LARRY SAWERS Americun University, Washington, DC Summary. - This paper treats the index of social welfare change developed by Ahluwalia and Chenery. Some discussions of the methodology of this index conclude that the rate of change in GNP is a flawed measure of change in social welfare since it is biased against the poor. It is argued on the contrary that this conclusion is based on an improperly specified opportunity cost of favoring one income group over another in the design of development policy.
Growing interest in the distribution of the gains and losses from economic development led economists in the 1970s to construct new measures of social welfare which reflect changes in the distribution of income. One widely noted attempt to develop a measure of changes in social welfare that explicitly incorporates distributional concerns was first described in a paper by Ahluwalia and Chenery.’ They define an index of social welfare change
G =
~ gj I
Wi
i=
where g is the growth rate of income of n-tile i and w is the weight assigned to that n-tile. In the words of Gary Fields, “The Ahluwalia-Chenery index has received considerable attention as a means of combining growth and distribution in a single index.“2 Todaro, for example, has an extended treatment of this index in his discussion of poverty and development.’ By assigning the appropriate weights to the different n-tiles, social planners can measure changes in social welfare which explicitly take account of the distribution of income. If a planner were, for example, interested only in the income gains of the poorest group in society, a weight of 1 could be given to the poorest n-tile and a weight of 0 could be assigned all other ntiles. If all groups were to be given equal importance, then equal weights could be assigned (for example, 0.2 if the data were organized into quintiles). The arithmetic of the index is such that G equals the growth rate in gross national product (GNP) when the weights are the percen-
tage share of GNP of the respective n-tiles. Hence, these GNP shares are called GNP weights. To use the illustration provided by Ahluwalia and Chenery, if the most affluent quintile received 53% of the country’s income, its weight in determining the percentage change in GNP would be 0.53. The next quintile receives 22% of the country’s income and its weight is 0.22 and so on for each quintile. In short, as Gary Fields puts it, “a given percentage increase in income of the rich receives more weight than the same percentage increase in income of the poor. For those observers who wish to make welfare judgements favoring income gains among the goor, the GNP weights are not very appealing.” Fair enough, but a statement by Ahluwalia and Chenery is more problematic. They argue, “The combined share of the top 40% of the population amounts to about three-quarters of the total GNP. Thus the rate of growth of GNP measures essentially the income growth of the upper 40% and is not much affected by what happens to the income of the remaining 60% of the population.“5 Todaro builds on Ahluwalia and Chenery’s imprecise and misleading statement and makes an outright error. He argues, “using the measure of GNP growth as an index of improvement in social welfare and development accords to each income group a ‘welfare valuation’ that corresponds to their respective income shares. . It follows that the best way to maximize social welfare growth is to maximize the rate of growth of the incomes of the rich while neglecting the poor!“” A numerical illustration may elucidate the confusion. Row 1 of Table 1 indicates the percentage share in national income of each quintile of the XYY
900
WORLD
DEVELOPMENT
First quintilc
quintile
1. Share in GNP (GNP weights)
53%
22%
2. Income when GNP = $1 billion
$53Om
$22Om
Second
Third quintile
Fourth quint&
Fifth quintilc
Total
7%
5 ‘%,
100%
$13Om
$7Om
$SOm
0.7%
O.S’%
I .i’%,
$1 .OOOm
3. Increase in&x using
in if g, = 10% GNP weights
5 .3“X,
2.2%
1.3%
4. Income gain when g, = 10%
$53m
$22m
$13m
$7m
$Sm
$ 1OOm
5. Percentage gain in income from $53 million
10’1/”
2>.l’Y 0
40.8%
75.7%
106%
2(X.5”/”
in index if $S3m income gain
5 .3‘X
5 .3‘X,
s ,3‘%
5.3X
5.3’)/0
26.5’)0
10%
6. Increase
income
Row 2 shows the distribuif GNP equals $1 billion. Let us presume a 10% increase in income for each quintile. The GNP weights in determining G, the index of change in social welfare, are the income shares of each quintile found in Row 1. A 10% increase in income for the poorest quintile produces a 0.5% (10% times S%) rise in G but a 10% income gain for the top quintile produces a 5.3% (10% times 53%) increase in G. But note the numbers in Row 4 which gives the absolute increase in income from a 10% gain for each quintile. The reason that the richest quintile has the greatest impact on the index of social welfare change is because a 10% increase in their income amounts to $53 million. over 10 times the $5 million that the lowest quintile receives from their 10% gain.’ But if each quintile were to receive the same absolute amount of income gain, then the increase in G is affected equally by each income group. Row 5 is the percentage increase in income when each quintile receives an increase of $53 million. The top quintile’s percentage increase is still 10% and when weighted by its share in national income contributes to a 5.3% increase in G. But the lowest quintile’s income rises by 106% when it receives $53 million. This 106% weighted by the quintile’s share in national income of 5% leads to the same 5.3% increase in G that was true for the top quintile. Therefore the statement that growth in GNP is sensitive only to income gains of the upper quintiles makes sense only when income gains within quintiles are measured in percentage terms. If income gains are measured in absolute amounts, tion
distribution.
of income
hy quintile
GNP is equally sensitive to income gains at all levels of the income distribution. It is clear that Ahluwalia and Chenery understand this despite their imprecise statement quoted earlier. The issue is not the arithmetic of the index, on which all agree, but instead on whether, as Ahluwalia, Chenery and Todaro have implicitly assumed, income gain measured in percentage terms is likely to capture the opportunity cost of augmenting income in alternative quintiles. My argument is that absolute changes are the appropriate reference point for the purpose at hand and that use of percentage measures of income gain lead to thoroughly fallacious conclusions. My point can perhaps best be illustrated by referring to Todaro’s statement that the best way to maximize growth in GNP is to maximize the income gains of the most affluent. Given his well known sympathies for the poor, it is clear that Todaro is not using the word “best” to mean preferred, but to mean easiest. However this substitution of words does not eliminate the error. Todaro is correct only if equal (or nearly so) percentage gains in income within alternative quintiles appropriately express in some meaningful sense the trade-offs facing the planner whose task it is to find the best or easiest way to maximize GNP growth. Percentage change does reflect the impact on each income group from that group’s point of view, but is unlikely to shed any light on the opportunity costs of favoring one income group over another in the design of development policy. Put another way, it would be a bizarre development policy indeed which offered the choice of a 10% gain in income for either the first quintile or the fifth quintile of the income distri-
POVERTY
WEIGHTED
MEASURES
bution. What conceivable investment would produce, to use the numbers from the above illustration, $53 million for the rich or $5 million for the poor with the same resource cost in either instance?* In other words, from a development planner’s point of view, the appropriate index of social welfare change is
G*
=-
i=l
GNP where gi is the absolute gain in income for the ith n-tile, not the percentage gain as in the Ahluwalia and Chenery index. The GNP weights for this index are 1 for each n-tile. This index in a straightforward fashion reflects the opportunity
OF SOCIAL
WELFARE
CHANGE
901
costs of manipulating the distributional impact of development policy and does not encourage the sophism criticized above. Greater concern with distribution was one of the more salutary advances made by development economics in the 1970s. With greater concern for distribution must come better ways to measure it. Ahluwalia and Chenery’s index is a step forward. The growth rate in GNP as an indicator of change in social welfare is flawed for many reasons including its failure to reflect the distributional impact of growth. But its flaws do not include an insensitivity to the income gains of the bottom 60% of the population or a bias against the poor. And Todaro’s conclusion that the best (or easiest) way to maximize growth in GNP is to ignore the poor - has been shown to be unfounded.
NOTES 1.
Ahluwalia and Chenery (1974).
2.
Fields
3.
Todaro
4.
Fields
(1980), (1985), (1980),
p. 175. pp.
161-165.
p. 24.
5. Ahluwalia and Chenery (1974), p. 40. This true if income growth is measured in percentage than dollar terms. As I argue below, measuring gains in percentage terms is inappropriate context. 6.
Todaro
(1985),
7. As Todaro (1985, p. 162) puts it, “a 1% growth in the income of the top quintile carries over 10 times the weight of a 1% growth in the lowest quintile because it implies an absolute increment that is 10 times larger.” His next sentence draws the incorrect conclusion found in the previous quotation.
is only rather income in this
p. 162.
8. It is, of course, possible or even probable that the dollar gain in GNP from any project would vary, perhaps substantially, depending on which income group received the net benefits. For instance, those in one income group may save and invest a larger share of their income gains than another group. But neither this nor any other argument about the way an economy functions is invoked by these authors.
REFERENCES Ahluwalia, Montek S., and Hollis Chenery, “The economic framework,” in Chencry et al.. Redistribution with Growth (London: Oxford University Press, 1974), Chap. 2.
Fields, Gary, Poverty, Inequality, and Development (Cambridge: Cambridge University Press, 1980). Todaro, Michael, Economic Development in the Third World (New York: Longman, 1985).
World Lkvelopmm~. Vol. 16. No. X, pp. XYO-001, 1088. Printed in Great Britain.
0
Poverty Weighted Measures Social Welfare Change
lY88 Perganion
Press plc
of
LARRY SAWERS Americun University, Washington, DC Summary. - This paper treats the index of social welfare change developed by Ahluwalia and Chenery. Some discussions of the methodology of this index conclude that the rate of change in GNP is a flawed measure of change in social welfare since it is biased against the poor. It is argued on the contrary that this conclusion is based on an improperly specified opportunity cost of favoring one income group over another in the design of development policy.
Growing interest in the distribution of the gains and losses from economic development led economists in the 1970s to construct new measures of social welfare which reflect changes in the distribution of income. One widely noted attempt to develop a measure of changes in social welfare that explicitly incorporates distributional concerns was first described in a paper by Ahluwalia and Chenery.’ They define an index of social welfare change
G =
~ gj I
Wi
i=
where g is the growth rate of income of n-tile i and w is the weight assigned to that n-tile. In the words of Gary Fields, “The Ahluwalia-Chenery index has received considerable attention as a means of combining growth and distribution in a single index.“2 Todaro, for example, has an extended treatment of this index in his discussion of poverty and development.’ By assigning the appropriate weights to the different n-tiles, social planners can measure changes in social welfare which explicitly take account of the distribution of income. If a planner were, for example, interested only in the income gains of the poorest group in society, a weight of 1 could be given to the poorest n-tile and a weight of 0 could be assigned all other ntiles. If all groups were to be given equal importance, then equal weights could be assigned (for example, 0.2 if the data were organized into quintiles). The arithmetic of the index is such that G equals the growth rate in gross national product (GNP) when the weights are the percen-
tage share of GNP of the respective n-tiles. Hence, these GNP shares are called GNP weights. To use the illustration provided by Ahluwalia and Chenery, if the most affluent quintile received 53% of the country’s income, its weight in determining the percentage change in GNP would be 0.53. The next quintile receives 22% of the country’s income and its weight is 0.22 and so on for each quintile. In short, as Gary Fields puts it, “a given percentage increase in income of the rich receives more weight than the same percentage increase in income of the poor. For those observers who wish to make welfare judgements favoring income gains among the goor, the GNP weights are not very appealing.” Fair enough, but a statement by Ahluwalia and Chenery is more problematic. They argue, “The combined share of the top 40% of the population amounts to about three-quarters of the total GNP. Thus the rate of growth of GNP measures essentially the income growth of the upper 40% and is not much affected by what happens to the income of the remaining 60% of the population.“5 Todaro builds on Ahluwalia and Chenery’s imprecise and misleading statement and makes an outright error. He argues, “using the measure of GNP growth as an index of improvement in social welfare and development accords to each income group a ‘welfare valuation’ that corresponds to their respective income shares. . It follows that the best way to maximize social welfare growth is to maximize the rate of growth of the incomes of the rich while neglecting the poor!“” A numerical illustration may elucidate the confusion. Row 1 of Table 1 indicates the percentage share in national income of each quintile of the XYY
900
WORLD
DEVELOPMENT
First quintilc
quintile
1. Share in GNP (GNP weights)
53%
22%
2. Income when GNP = $1 billion
$53Om
$22Om
Second
Third quintile
Fourth quint&
Fifth quintilc
Total
7%
5 ‘%,
100%
$13Om
$7Om
$SOm
0.7%
O.S’%
I .i’%,
$1 .OOOm
3. Increase in&x using
in if g, = 10% GNP weights
5 .3“X,
2.2%
1.3%
4. Income gain when g, = 10%
$53m
$22m
$13m
$7m
$Sm
$ 1OOm
5. Percentage gain in income from $53 million
10’1/”
2>.l’Y 0
40.8%
75.7%
106%
2(X.5”/”
in index if $S3m income gain
5 .3‘X
5 .3‘X,
s ,3‘%
5.3X
5.3’)/0
26.5’)0
10%
6. Increase
income
Row 2 shows the distribuif GNP equals $1 billion. Let us presume a 10% increase in income for each quintile. The GNP weights in determining G, the index of change in social welfare, are the income shares of each quintile found in Row 1. A 10% increase in income for the poorest quintile produces a 0.5% (10% times S%) rise in G but a 10% income gain for the top quintile produces a 5.3% (10% times 53%) increase in G. But note the numbers in Row 4 which gives the absolute increase in income from a 10% gain for each quintile. The reason that the richest quintile has the greatest impact on the index of social welfare change is because a 10% increase in their income amounts to $53 million. over 10 times the $5 million that the lowest quintile receives from their 10% gain.’ But if each quintile were to receive the same absolute amount of income gain, then the increase in G is affected equally by each income group. Row 5 is the percentage increase in income when each quintile receives an increase of $53 million. The top quintile’s percentage increase is still 10% and when weighted by its share in national income contributes to a 5.3% increase in G. But the lowest quintile’s income rises by 106% when it receives $53 million. This 106% weighted by the quintile’s share in national income of 5% leads to the same 5.3% increase in G that was true for the top quintile. Therefore the statement that growth in GNP is sensitive only to income gains of the upper quintiles makes sense only when income gains within quintiles are measured in percentage terms. If income gains are measured in absolute amounts, tion
distribution.
of income
hy quintile
GNP is equally sensitive to income gains at all levels of the income distribution. It is clear that Ahluwalia and Chenery understand this despite their imprecise statement quoted earlier. The issue is not the arithmetic of the index, on which all agree, but instead on whether, as Ahluwalia, Chenery and Todaro have implicitly assumed, income gain measured in percentage terms is likely to capture the opportunity cost of augmenting income in alternative quintiles. My argument is that absolute changes are the appropriate reference point for the purpose at hand and that use of percentage measures of income gain lead to thoroughly fallacious conclusions. My point can perhaps best be illustrated by referring to Todaro’s statement that the best way to maximize growth in GNP is to maximize the income gains of the most affluent. Given his well known sympathies for the poor, it is clear that Todaro is not using the word “best” to mean preferred, but to mean easiest. However this substitution of words does not eliminate the error. Todaro is correct only if equal (or nearly so) percentage gains in income within alternative quintiles appropriately express in some meaningful sense the trade-offs facing the planner whose task it is to find the best or easiest way to maximize GNP growth. Percentage change does reflect the impact on each income group from that group’s point of view, but is unlikely to shed any light on the opportunity costs of favoring one income group over another in the design of development policy. Put another way, it would be a bizarre development policy indeed which offered the choice of a 10% gain in income for either the first quintile or the fifth quintile of the income distri-
POVERTY
WEIGHTED
MEASURES
bution. What conceivable investment would produce, to use the numbers from the above illustration, $53 million for the rich or $5 million for the poor with the same resource cost in either instance?* In other words, from a development planner’s point of view, the appropriate index of social welfare change is
G*
=-
i=l
GNP where gi is the absolute gain in income for the ith n-tile, not the percentage gain as in the Ahluwalia and Chenery index. The GNP weights for this index are 1 for each n-tile. This index in a straightforward fashion reflects the opportunity
OF SOCIAL
WELFARE
CHANGE
901
costs of manipulating the distributional impact of development policy and does not encourage the sophism criticized above. Greater concern with distribution was one of the more salutary advances made by development economics in the 1970s. With greater concern for distribution must come better ways to measure it. Ahluwalia and Chenery’s index is a step forward. The growth rate in GNP as an indicator of change in social welfare is flawed for many reasons including its failure to reflect the distributional impact of growth. But its flaws do not include an insensitivity to the income gains of the bottom 60% of the population or a bias against the poor. And Todaro’s conclusion that the best (or easiest) way to maximize growth in GNP is to ignore the poor - has been shown to be unfounded.
NOTES 1.
Ahluwalia and Chenery (1974).
2.
Fields
3.
Todaro
4.
Fields
(1980), (1985), (1980),
p. 175. pp.
161-165.
p. 24.
5. Ahluwalia and Chenery (1974), p. 40. This true if income growth is measured in percentage than dollar terms. As I argue below, measuring gains in percentage terms is inappropriate context. 6.
Todaro
(1985),
7. As Todaro (1985, p. 162) puts it, “a 1% growth in the income of the top quintile carries over 10 times the weight of a 1% growth in the lowest quintile because it implies an absolute increment that is 10 times larger.” His next sentence draws the incorrect conclusion found in the previous quotation.
is only rather income in this
p. 162.
8. It is, of course, possible or even probable that the dollar gain in GNP from any project would vary, perhaps substantially, depending on which income group received the net benefits. For instance, those in one income group may save and invest a larger share of their income gains than another group. But neither this nor any other argument about the way an economy functions is invoked by these authors.
REFERENCES Ahluwalia, Montek S., and Hollis Chenery, “The economic framework,” in Chencry et al.. Redistribution with Growth (London: Oxford University Press, 1974), Chap. 2.
Fields, Gary, Poverty, Inequality, and Development (Cambridge: Cambridge University Press, 1980). Todaro, Michael, Economic Development in the Third World (New York: Longman, 1985).