Directory UMM :Data Elmu:jurnal:S:Socio-Economic Planning Sciences:Vol34.Issue1.Mar2000:

Socio-Economic Planning Sciences 34 (2000) 51±67
www.elsevier.com/locate/orms

Ecient provision of child quality of life in less developed
countries: conventional development indexes versus a
programming approach to development indexes
Raymond Raab a,*, Pradeep Kotamraju b, Stephen Haag c
a

Department of Economics, University of Minnesota-Duluth, Duluth, MN 55812, USA
b
Minnesota State Colleges and Universities System, St. Paul, MN 55101, USA
c
Daniels College of Business, University of Denver, Denver, CO 80208, USA

Abstract
Using a linear programming approach, we establish a child quality of life (CQL) index by evaluating
the ability of a less developed country (LDC) to maximize speci®c child development goals subject to
minimizing speci®c resource availability indicators. This approach Ð which ranks LDCs from the most
robustly ecient to the most robustly inecient in their ability to maximize goals while minimizing
resource utilization Ð avoids using equal or subjective weights employed in conventional ranking

schemes. The ranking of the 38 LDCs yields unexpected results and suggests a very di€erent way of
measuring and evaluating development policy. # 2000 Elsevier Science Ltd. All rights reserved.
Keywords: DEA; Development indexes; Child quality of life

1. Introduction
Early development literature from the 1950s and 1960s generally treated rising per capita
income as the central measure of economic development. Pioneering work by Kuznets [1] in
the 1950s pointed to an inverted U-shaped relationship between per capita income and income
inequality. By relating a country's per capita level of income to its income share of the top
20% of the population, Kuznets showed that if low-income developing countries strive to
achieve higher rates of per capita gross domestic product (GDP), they would inevitably face

* Corresponding author. Tel.: +1-218-726-7284; fax:+1-218-726-6509.
0038-0121/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 3 8 - 0 1 2 1 ( 9 9 ) 0 0 0 1 3 - 0

52

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

growing income inequality. Subsequent studies have attempted to test the validity of the
Kuznets curve. Ahluwalia [2], Anand and Kanbur [3], and others noted that the expected
inverse relation between rising GDP per capita and an income inequality measure seemed to
disappear under more stringent multivariate statistical tests. Anand and Ravallion [4] showed
that, when the extent of poverty and the level of public expenditures on basic services were
included as explanatory variables, the presumed causal relationship between social indicators
and per capita income disappeared.
However, the pendulum is swinging back with more recent studies by Ram [5] and Jha [6]
showing a trade-o€ between growth and equity. Jha uses more recent estimates of income
distribution obtained from the 1994 World Bank Social Indicators of Development database
and attempts to validate the Kuznets curve. He ®nds that the trade-o€ between growth and
equity holds, particularly when income growth rate and schooling variables are included in the
regression. Ram [5] experiments with di€erent functional forms and argues that a regression
equation in which the constant term is constrained to zero increases the precision of the
estimates and provides stronger support for the Kuznets hypothesis. The debate about the
validity of the Kuznets curve is still ongoing as evidenced by the interchange between
Ravallion [7] and the rejoinder by Ram [8].
In the past two decades, development specialists have increasingly recognized that pure
economic indicators Ð such as GDP per capita or even income distribution measures such as
the Gini coecients Ð do not suciently indicate overall welfare in a country. If the role of

pure economic variables as indicators of welfare has become less clear, similarly, the debate
continues about which social indicator best represents destitution and well-being [9]. Beginning
with the World Bank's ``Basic Needs Approach'' in the early 1970s, to the United Nations
Development Program (UNDP) Human Development Reports (HDRs), a range of social
indicators has been combined with pure economic indicators in an e€ort to capture a country's
quality of life in a single index.
The Human Development Index (HDI), is, as presented annually in the UNDP Human
Development Report (see [10] for instance), one such index and by far the most widely used.
Nevertheless, the HDI remains controversial. Some have gone so far as to label the HDI as a
statistical artifact with limited policy value. Implicit in the HDI is the notion that it measures a
country's quality of life better than a pure economic indicator such as per capita GDP.
Ravallion [11] argues that the HDRs, by their undue concentration on the HDI, spend a
considerable emphasis on distinguishing between ``good'' and ``bad'' growth and thus do not
give sucient consideration to the overall growth and policy choices that favor high growth.
Luchters and Menkho€ [12] are particularly critical of the transformation of GDP values
into human development values. They argue that the HDI income component is not sensitive
to how income is denominated; that poor intertemporal comparisons are made when income is
rising; and that income measures do not seem to follow the concept of diminishing marginal
returns. From our perspective, the HDI can be criticized because the changes in output values
occur without recognizing the changes in the resource base from which these outputs are

derived. In this regard, Data Envelopment Analysis (DEA) is able to measure the eciency of
countries in delivering a higher quality of life by explicitly emphasizing that output levels are
accounted for by varying resource commitments.
More recently, Dasgupta and Weale [13] employed the Borda Rule (that is, ranks based on

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

53

the sum of individual factor ranks) to rank order general well-being among the world's poorest
countries. Following the approach of Dasgupta and Weal [13], Kotamraju [14] constructed a
separate child quality of life (CQL) ranking for 22 less developed countries (LDCs). Kotamraju
also developed a similar Borda Rule ranking for the 38 LDCs used in this study.
Unlike the traditional ranking approach to establishing a CQL index, the current research
uses DEA to measure and rank the relative technical eciency by which 38 LDCs provide for
childrens' future potential for, and quality of, life. Signi®cant social, cultural, and economic
factors are treated as resources to be eciently rationed in order to maximize survivability,
youth physical development, and literacy. The DEA approach ranks development eciency by
evaluating the extent to which each LDC minimizes input components or conditions (the
resources to be eciently rationed) and maximizes outputs or goals (survivability, youth

physical development, and literacy). This approach is unique in that each LDC is allowed to
select the particular set of importance weights or coecients (for the inputs and outputs) that
allows the LDC to achieve its maximum CQL ranking. In short, a unique best production or
transformation relationship can (and usually does) exist for each individual LDC. While
conventional ranking schemes employ either equal, ®xed, or regression weights (thus implying
a single function for all cases), DEA allows each particular LDC to choose the set of weights
that maximizes its eciency in the face of the remaining LDCs, where the latter are
constrained to employ that ``best'' set of weights.
There are several ways to measure the welfare of children. Often this is done with a single
measure with the most common being the rate of child mortality. United Nations International
Education Fund (UNICEF) [15] thus uses the under-®ve mortality rate as a measure for child
welfare and ranks countries accordingly. In addition to the UNICEF measure, Kotamraju [14]
added youth literacy rates and the percentage of children a€ected by chronic malnutrition. This
CQL ranking procedure is comprised of these three equally weighted components. Other
factors Ð as we present in this study Ð are also related to CQL. These include per capita real
domestic product, population per doctor, female literacy rate, and female average age at ®rst
marriage.
The current paper rede®nes the relationship between the above variables into an input±
output or transformation paradigm. Three outputs or goals describe actual and potential child
quality of life and are represented by (1) the under-®ve survival rate, (2) the lack of severe

malnutrition, and (3) youth literacy rate. Inputs, resources, or conditions that determine actual
or potential CQL can be represented by (1) per capita real domestic product, (2) female
literacy rate, (3) females average age at ®rst marriage, and (4) population per doctor. This
speci®cation of a transformation function leads to conclusions very di€erent from those
generated by contemporary ranking methodologies. We assert that many of the socio-economic
indicators comprising well-known development indexes can be pro®tably rede®ned into
resources to be minimized and goals to be maximized. In our proposed model, these inputs are
thought to in¯uence the future quality of life Ð which is represented by outputs Ð of a
developing country. This unique view of development indicators leads to a very di€erent and
more policy-oriented view of national development achievements.
It is interesting to note that an input±output transformation function is not even a necessary
assumption to construct an index of rankings. A DEA-based CQL index could be constructed
by maximizing indicators (variables) that would lead to a higher index ranking, and minimizing

54

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

those indicators (variables) that are inversely related to the index ranking. The advantage of
this procedure vs. the Borda Rule, or other ®xed weight schemes, is that the linear

programming weights or coecients are explicitly chosen to maximize the individual country's
ranking. With the DEA approach, weights are not equal nor subjectively selected, but are
instead chosen by an optimization criterion. However, by formulating a reasonable
transformation function, as we have with the CQL index, policy and program initiatives that
maximize outputs, i.e., move the lowest ranking countries to higher ranks in the most ecient
way, can be made more easily. A detailed account of the additive DEA model and the
sensitivity analysis employed to rank the LDCs is presented in Appendix A.1 The following
section summarizes the model measuring the eciency of child quality of life and describes the
data set employed. We then present the ranking of the LDCs' eciency in improving CQL and
discuss the usefulness of this approach.

2. The model and data
To evaluate the eciency in providing improved levels of childrens' well-being, a
determination must be made of those cultural conditions and resource components (inputs) to
be minimized and those CQL goal components (outputs) to be maximized. The ®rst goal
indicator to be maximized is the under-®ve survival rate. International organizations usually
express the under-®ve mortality rate (U5MR) as the percentage of children who die before
reaching the age of ®ve. Hence, a DEA variable to maximized, SURVIVE, is de®ned as 100%
minus U5MR; that is, the percentage of children who live beyond the age of ®ve.2
The second goal indicator to be maximized is the extent to which children thrive physically

through the avoidance of malnutrition. The extent of malnutrition (STUNTING) is measured
as the percentage of children under ®ve who are at least two standard deviations below the
height-age norm. The DEA variable to be maximized, THRIVE, is thus de®ned as 100%
minus STUNTING. (After surveying the athropometric literature, Dasgupta [9] concluded that
any damage done to children occurs in the very early years (before the age of three) and
``growth failure in early childhood. . .predicts functional impairment in adults''.)
The third goal indicator to be maximized is the youth literacy rate (YLR); that is, the
percentage of literate children in the population age group 15±19. These goals Ð SURVIVE,
THRIVE, and YLR Ð di€er from the traditional income-centered approach that seeks to
either maximize per capita income or minimize income inequality. In contrast, Anand and
Ravallion [4] emphasize the human development approach to these goals, which `` . . .focuses on
the (capabilities) of people Ð the lives they lead Ð not the detached objects they possess''.
With respect to the input side of the transformation relationship, a whole host of economic
1
The additive model of DEA is uniquely appropriate to formulate indexes since it is neither input-oriented nor
output-oriented only. Rather, the additive model simultaneously minimizes resources (inputs) while maximizing
goals (outputs).
2
In the context of DEA, it makes little di€erence if SURVIVE is speci®ed as an output to be maximized or, alternatively, if U5MR is speci®ed as an input to be minimized. Even in a production model where pollution e‚uents
represent ``negative'' outputs, they can be treated as competitive inputs, and therefore minimized.

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

55

and social factors can act as resources that in¯uence the previously identi®ed goals. First,
income is recognized as a key variable. It expands capabilities directly through a greater
command over material resources and leads to a lowering of poverty. Rising incomes and a
more equal distribution of income should include improvements in the direct provision of
public services. Higher average incomes are tied directly to the ®nancing of these public
services. Anand and Ravallion [4] argue that higher incomes must be directed towards the poor
in the form of increased public services. Thus, in the DEA framework, income is seen as an
input into the development process that improves the potential of LDCs' children. In this
study, per capita real gross domestic product (GDPCAP) is the income variable utilized and is
de®ned in purchasing parity dollars.
For the second and third resource components, we look to the capabilities of women who
are expected to raise children's welfare. According to the development literature, an
improvement in the economic status of women increases income-earning capabilities of the
individual and the family [16,17]. In addition, with the reduction of gender inequalities at
home, the social status for women in society should also improve [18]. Hence, social and

cultural conditions are expected to raise the welfare of children. The two variables chosen here
as inputs for these considerations were female literacy rate (FEMLIT), which is the percentage
of adult women who are literate, and female average age at ®rst marriage (FIRMAR).
Finally, avoiding morbidity and undernourishment are necessary for living well. And, so, for
children, a critical factor in their survival is avoiding hunger and disease. Moreover, as
Dasgupta [9] explained, better health `` . . . is in great part a matter of medical application.
These considerations form the basis of the claim that in poor countries attention needs to be
given to public health''. Therefore, to account for health inputs we use doctor per person
(DOCPOP), which indicates doctor availability per capita.
With these inputs to be minimized and outputs to be maximized, the form of the proposed
model is given as follows:
Inputs (minimize resource use or conditions):
. per capita real domestic product (GDPCAP)
. female literacy rate (FEMLIT)
. female average age at ®rst marriage (FIRMAR)
. doctor per capita (DOCPOP)
Outputs (maximize outputs or goals):
. under-®ve survival rate (SURVIVE)
. 100% minus STUNTING (THRIVE)
. youth literacy rate (YLR).

Extensive missing cases for these seven variables limited the population to 38 LDCs. The data
on STUNTING (used to derive THRIVE), YLR, GDPCAP, DOCPOP, FEMLIT, and
FIRMAR were obtained from the Human Development Report [10]. The State of the World's
Children [15] contained data for U5MR (used to derive SURVIVE). Table 1 shows the data
for the 38 LDCs on which the DEA was performed.
Based on these inputs to be minimized and outputs to be maximized, our model
demonstrates that child welfare improvements should depend not only on material inputs, but

56

Table 1
Child quality of life dataa
Three outputs

Four inputs

Country
THRIVE
(100% minus
STUNTING)

YLR
(Youth
literacy
rate)

GDPCAP
(Per capita
real domestic
product)

FEMLIT
(Female
literacy
rate)

FIRMAR
(Female average
age at
®rst marriage)

DOCPOP
(Reciprocal of
population
per doctor)

83.1
93.9
98.1
77.5
86.3
86.7
87.4
96.7
80.0
95.7
94.2
81.1
97.3
81.9
95.4
97.9
97.9
90.9
98.3
91.2
93.8
95.4
92.4
91.5
98.2
96.3
97.6
94.1
86.6
87.4

68
87
93
66
61
35
57
72
41
93
77
66
59
40
79
61
82
66
86
69
45
55
74
68
92
78
84
83
40
35

37
88
100
67
88
46
77
99
90
97
95
65
93
80
97
96
94
80
82
81
79
96
94
65
97
96
99
96
50
66

949
3011
2979
572
1016
872
1646
3986
744
6169
3579
657
1990
625
2345
2405
4237
2348
15178
1484
3253
2303
2404
1988
4542
5918
5916
2790
1862
1072

12
46
99
24
51
22
43
91
65
90
56
37
62
40
70
84
86
38
67
60
43
90
82
34
93
85
96
88
21
34

21.3
21.0
25.2
18.1
19.3
16.7
17.5
22.7
19.4
21.2
24.3
21.2
22.4
20.8
22.6
24.1
20.4
21.3
22.9
20.4
19.7
22.4
20.5
21.3
22.7
20.6
22.4
22.1
19.8
18.7

0.000098
0.000429
0.000490
0.000043
0.000049
0.000145
0.000082
0.000159
0.000140
0.001429
0.000463
0.000013
0.000990
0.000048
0.001163
0.000181
0.000813
0.000210
0.001450
0.000139
0.000339
0.000152
0.000565
0.001299
0.001042
0.000806
0.001961
0.000685
0.000340
0.000397

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

Sudan
Algeria
Jamaica
Mali
Ghana
Bangladesh
Cameroon
Thailand
Zambia
Venezuela
Tunisia
Rwanda
Mainland China
Burundi
Jordan
Sri Lanka
Colombia
Morocco
Kuwait
Zimbabwe
Iran
Philippines
Dominican Republic
Egypt
Costa Rica
Mexico
Uruguay
Paraguay
Pakistan
India

SURVIVE
(100% minus
U5MR)

Table 1 (continued )
Three outputs

Four inputs

Country

a

THRIVE
(100% minus
STUNTING)

87.4
97.0
97.9
90.3
91.8
81.2
90.8
93.3

49
76
90
57
61
46
42
85

YLR
(Youth
literacy
rate)
94
95
98
96
95
78
67
92

GDPCAP
(Per capita
real domestic
product)
1572
3317
5099
2622
3074
1215
2576
4718

FEMLIT
(Female
literacy
rate)

FIRMAR
(Female average
age at
®rst marriage)

DOCPOP
(Reciprocal of
population
per doctor)

71
88
93
79
84
78
47
80

22.1
21.2
23.6
22.7
22.1
18.7
20.5
22.6

0.000654
0.001000
0.000813
0.000962
0.001220
0.000156
0.000459
0.000926

Sources: UNICEF [15], SURVIVE from Appendix Table 1, UNDP [10], THRIVE from Table 11, YLR and FEMLIT from Table 5, GDPCAP
from Table 1, FIRMAR from Table 8, and DOCPOP from Table 12.

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

Bolivia
Panama
Chile
Peru
Ecuador
Nigeria
Guatemala
Brazil

SURVIVE
(100% minus
U5MR)

57

58

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

other social and health resources as well. Material inputs to a child's upbringing can be
represented by the variable GDPCAP. Social and cultural factors like FEMLIT and FIRMAR
are responsible for lowering child mortality and illiteracy. Similarly, the necessary health
resources can be partially proxied by DOCPOP and also in¯uence survivability, physical
thriving, and literacy. Within the DEA context then, an ecient country has comparable
material, social, and health resources (to other countries) but better utilizes those resources to
produce greater survivability, physical thriving, and literacy. Conversely, an ecient country
may similarly be viewed as having comparable outputs of survivability, physical thriving, and
literacy, but generally produces those levels of outputs with less material, social, and health
resources.

3. Rankings of LDCs' eciency
Table 2 arrays the stability index values and yields stability index rankings from 1
(representing the most robustly ecient LDC) to 38 (representing the most robustly inecient
LDC). It also gives the overall ranking based on the Borda Rule constructed in Kotamraju
[14]. A casual viewing of the results does not indicate any obvious patterns amongst the
outcomes. The Spearman rank correlation was ÿ0.024 but not statistically signi®cant at any
level. Comparing CQL rankings using DEA weights and Borda rankings using equal weights,
even with identical goals (outputs), resulted in an expected negative correlation. This is to be
expected because LDCs with few resources and comparable outputs, when contrasted to LDCs
with larger resource bases, are judged to be more ecient. But, from the Borda ranking, these
LDCs appear to have somewhat less child development since no comparison to the resource
base is made (see also Breu and Raab [19]).3 Hence, the Borda Rule appears to rank the
absolute CQL, while the DEA index ranks the relative eciency in delivering CQL.
By organizing LDCs into ®ve continents and/or regions, a Kruskal±Wallis test statistic
(H=17.61) rejected that the ®ve groups came from the same population at the 0.01 level (Chisquare critical value=13.28). Based upon these results, one could conclude that statistically
signi®cant di€erences exist in the robustness of eciency classi®cations across these geographic
groupings. By computing pairwise di€erences in average stability index ranks using Dunn's
procedure of the Kruskal±Wallis rank test for di€erences in pairs of medians [21], only two
signi®cant comparisons existed at the ®ve percent level of signi®cance. Sub-Saharan African
LDCs appeared more robustly ecient relative to South American and to Central American
LDCs, which appeared as the most robustly inecient.
Table 3 displays the comparison of outputs and inputs for Sub-Saharan Africa versus South
America and Central America. In general, South American output means are somewhat higher
(SURVIVE by nearly 13%, THRIVE by 33%, and YLR by almost 30%), while resource
means are considerably higher (GDPCAP by 306%, FIRMAR by 9%, FEMLIT by 87%, and
3

A U.S. News and World Report [20] ®xed-weight ranking of the quality of institutions of higher learning when
correlated to a DEA ratio model ranking, resulted in a signi®cant negative correlation. The di€erence exists because
a DEA ranking is an eciency ranking, while the U.S. News ranking is a quality ranking.

59

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

POPDOC [the reciprocal of DOCPOP] by ÿ95%). The negative sign on the POPDOC means
implies that South American countries have more doctors per population unit. Similarly,
comparison of the descriptive statistics for Sub-Saharan African versus Central American
output means and input means yields similar ®ndings. Thus, Central American output means
are somewhat higher (SURVIVE by over 14%, THRIVE by almost 33%, and YLR by 24%),

Table 2
Stability index rankings
DEA rank

Borda rank

Country

Continent/Region

Stability index value (y )

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38

29
15
1
30
27
38
28
6
31
5
14
32
19
34
7
13
9
23
8
22
26
18
17
24
2
10
4
11
37
36
24
12
3
21
20
34
33
16

Sudan
Algeria
Jamaica
Mali
Ghana
Bangladesh
Cameroon
Thailand
Zambia
Venezuela
Tunisia
Rwanda
Mainland China
Burundi
Jordan
Sri Lanka
Colombia
Morocco
Kuwait
Zimbabwe
Iran
Philippines
Dominican Republic
Egypt
Costa Rica
Mexico
Uruguay
Paraguay
Pakistan
India
Bolivia
Panama
Chile
Peru
Ecuador
Nigeria
Guatemala
Brazil

Sub-Sahara Africa
North Africa
Central America
Sub-Sahara Africa
Sub-Sahara Africa
Asia
Sub-Sahara Africa
Asia
Sub-Sahara Africa
South America
North Africa
Sub-Sahara Africa
Asia
Sub-Sahara Africa
Middle East
Asia
South America
North Africa
Middle East
Sub-Sahara Africa
Middle East
Asia
Central America
North Africa
Central America
Central America
South America
South America
Asia
Asia
South America
Central America
South America
South America
South America
Sub-Sahara Africa
Central America
South America

0.1469
0.1209
0.1001
0.0898
0.0732
0.0669
0.0660
0.0625
0.0521
0.0421
0.0407
0.0367
0.0349
0.0316
0.0281
0.0270
0.0234
0.0228
0.0222
0.0191
0.0154
0.0133
0.0125
0.0122
0.0112
0.0106
0.0087
0.0052
0.0047
0.0041
0.0036
0.0028
ÿ0.0004
ÿ0.0122
ÿ0.0174
ÿ0.0282
ÿ0.0284
ÿ0.0334

60

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

Table 3
Descriptive statistics for outputs and inputs (Sub-Sahara Africa vs South America and Central America)
Region/Continent
Sub-Sahara Africa
Means (1)
Std. Dev.
C.V.a
South America
Means (2)
Std. Dev.
C.V.a
Percent Di€erence in Means (1)±(2)
Central America
Means (3)
Std. Dev.
C.V.a
Percent Di€erence in Means (1)±(3)
a

SURVIVE

THRIVE

YLR

82.3
5.9
5.0

57.1
11.7
20.5

73.7
16.0
21.6

94.0
3.7
3.9
12.8

76.0
15.9
20.9
33.1

95.5
3.1
3.3
14.2

75.8
18.5
24.4
32.8

GDPCAP

FIRMAR

FEMLIT

POPDOC

990
388
39

19.7
1.4
7.1

45.6
20.5
40.0

20,339
21,515
106

95.7
2.0
2.1
29.7

4022
1592
39.6
306.3

22.1
0.9
4.1
9.0

85.2
7.7
9.4
86.8

1067
341
32.0
ÿ94.7

91.5
12.8
13.3
24.2

3623
1357
37.5
266.0

20.7
1.3
6.2
5.1

71.5
24.6
34.5
56.8

1358
504
37.2
ÿ93.3

Note: C.V.=coecient of variation.

while resources are considerably higher (GDPCAP by 266%, FIRMAR by 5%, FEMLIT by
57%, and POPDOC [reciprocal of DOCPOP] by ÿ93%). Note that the standard deviation and
the resulting coecients of variation in the material and physical inputs suggest di€ering
resource endowments, even between countries of a particular continent. Notwithstanding some
of these large di€erences that make policy generalizations dicult, the general pattern of
eciency rankings between Sub-Saharan Africa compared to South America and compared to
Central America appear valid.
On a more intuitive level, we o€er the following explanation. Given the much higher
resource levels of South American and Central American LDCs, they are more ``inecient'' in
delivering the desired outputs. In other words, despite their higher resource levels, South
American and Central American countries are not doing a signi®cantly better job in taking
care of their children than are Sub-Saharan African countries, who have comparable, if not
somewhat smaller, levels of output (survivability, youth physical development, and youth
literacy rates). Conversely, from the African point of view, a higher general level of deprivation
requires subsistence countries to allocate, albeit at a very productive level, a signi®cantly higher
proportion of their resources towards improving the lives of children in order to achieve a
minimally accepted output. Hence, Sub-Saharan African countries are more ``ecient'' in
fostering CQL.
A major problem faced in this paper is the lack of complete and comparable data at a point
in time for an extensive set of countries. Only very recently has a concerted e€ort been made
to collect such data for policy analysis. To arrive at a more policy-based CQL index, other
policy inputs such as government expenditures Ð particularly those relating to the raising of
health and literacy levels of poor children Ð should be included over the proxy variables

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

61

included in our model. In addition, discretionary inputs such as female labor force
participation rate may be built into the development of an improved CQL index. Finally, other
policy-induced changes such as trade patterns, along with more autonomous ones such as
weather, may be considered signi®cant conditioning factors of a more comprehensive CQL
index [22].
Another problem exists when rankings are used as a production-policy paradigm, rather
than a simple index composed of directly and inversely related indicators. A data problem
appears because several inputs, especially domestic income and per capita doctors, are macro
variables, which can account for goals and outcomes other than CQL. For example, doctors
per capita may not be the critical input in improving health outcomes for LDCs (as many
might believe). Mass immunizations and community health programs may thus be more
ecient in the poorest of LDCs and data for such inputs need to be included. Proportion of
median family income directly related to child care and per capita pediatricians or doctors
devoted to child health care outcomes might be more acceptable inputs. Despite the limited set
of variables used for developing the CQL index, our model begs for the inclusion of these
additional variables to improve policies regarding child quality of life. However, the paucity of
accurate data, even at the macro level, suggests that such re®nements are unlikely until the
importance of such discretionary inputs is recognized.

4. Summary and conclusion
A CQL index for 38 LDCs, for which data exist, is developed and subsequently employed
using a programming approach. A transformation relationship establishes the goals to be
maximized Ð such as promoting child survival, avoiding failure to thrive, and raising child
literacy Ð subject to resource-availability indicators (output per capita, doctors per capita) and
conditioning variables (female literacy rate and female age at ®rst marriage) which are to be
minimized. This approach better distinguishes between inputs and outputs and avoids using
equal or subjective weights as employed in more conventional rankings of various economic
and social development indexes. It allows a particular LDC to choose an optimum set of
weights, i.e., one that maximize its eciency robustness. A sensitivity analysis not only allows
the ranking of inecient LDCs, but also measures and ranks ``robustly'' ecient LDCs that
comprise the eciency frontier. By focusing on eciency in the provision of CQL policy, and
not the absolute level of CQL as might be included in, say, a Borda ranking, Sub-Saharan
African LDCs are evaluated as more robustly ecient, while South American and Central
American LDCs are found to be as more robustly inecient. This counter-intuitive result may
occur because South American and Central American countries, with signi®cantly more
resources, do not achieve comparably higher child development goals.
Subjective or ®xed weighted indexes measuring only outputs do yield some information
suitable for policy planning. But, this is only ``half the picture''. The eciency approach used
in this study considers the e€ective use of policy initiatives by emphasizing outcomes relative to
the resource base employed and focuses on the e€ectiveness of these inputs. The obvious
diculty in implementing this model, as presented, underscores the necessity of gathering
information on critical policy variables, especially on the input side.

62

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

Acknowledgements
The authors wish to thank Jean Jacobson for her editing assistance and Tabitha Schmidt for
the computations.
Appendix A
A1. Data Envelopment Analysis
Data Envelopment Analysis (DEA) can be used to evaluate the relative technical eciency
of transforming a set of inputs or resources to produce a set of multiple outputs. As a linear
programming implementation of Farrell's [23] notion of technical eciency, DEA is an
``extremal'' approach to eciency evaluation. In particular, an ecient frontier is constructed
that is composed of LDCs that either (1) use as little input as possible to produce a given level
of output, or (2) produce as much output as possible from a given level of input consumption.4
Those LDCs meeting one of the above criteria comprise the ecient frontier and are
technically ecient, while those LDCs not on the ecient frontier are technically inecient
(enveloped by the ecient LDCs).
The original model of DEA, known as the ratio or CCR model [24], has been joined by
other DEA models [25,26,33], including the additive model [27], the model of interest in this
research. To rank order the LDCs from most robustly ecient to most robustly inecient
using the additive model of DEA, we employ a two-step process. In the ®rst step, the technical
eciency status (ecient or inecient) for each LDC is determined by solving a linear
program for each LDC. This ®rst step serves only to categorize LDCs as either ecient or
inecient. In the second step, di€erent linear programs are solved for the ecient and
inecient LDCs. With respect to a particular ecient LDC, the linear program yields a
measure of its eciency ``robustness''; with respect to a particular inecient LDC, the linear
program yields a measure of its ineciency ``robustness''. These robustness measures then
comprise the index for rank ordering the LDCs. Below, we describe these two steps in greater
detail.
In the additive DEA model, the observed input consumption and output production for a
number of LDCs are measured. They are referred to as an LDC's component vector. All
component vectors for the LDCs under scrutiny are combined to form the empirical
production possibility set (PE):
)
(
n
n
X
X
…1†
mi …Y Ti , X Ti †; mi ˆ 1, mi e0:
PE ˆ …Y T , X T † ˆ
iˆ1

iˆ1

where i represents the general index of i = 1,. . . , 38 LDCs and (Y Tj , X Tj ) is the transposed
vector of outputs and inputs, respectively, for LDCj.
4

Within the general DEA context, the entities or organizations under scrutiny are termed decision making units or
DMUs. Our focus in this study is on evaluating the eciency of less developed countries or LDCs; therefore, in this
appendix we substitute LDC for the more general DEA term, DMU.

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

63

Fig. 1. A hypothetical production possibility set and its frontier.

To determine the technical eciency status (ecient or inecient) for a given LDC, its
component vector is compared to PE. If no component vector in PE, observed or hypothetical,
can be found that strictly dominates the tested LDC, then the LDC is said to be technically
ecient. Those LDCs for which a component vector can be found in PE that strictly
dominates are said to be technically inecient. Fig. 1 provides a graphical depiction of a set of
LDCs for a single-input, single-output example. From Fig. 1, LDCs Nos.1, 2, and 3 would be
technically ecient, while LDCs Nos.4, 5, 6, and 7 would be technically inecient. Segments
12 and 23 comprise the ecient frontier.
Mathematically, the test for the technical eciency status of LDCj is achieved by solving the
following linear program:
ÿ
‡
min …ÿeT Dÿ1
ÿ eT Dxÿ1
 s †
y s

s:t: Yl ÿ s‡ ˆ Yj
Xl ‡ sÿ ˆ Xj
eT lE1
l, s‡ , sÿ e0

…2†

where Y and X represent the matrices of the outputs and inputs, respectively; and s + and s ÿ
denote the shortfall in production and excess consumption slacks, respectively. The eT vector is
the sum vector, guaranteeing a convex combination or scalar multiple (less than one) of the
LDCs under scrutiny.5 As the additive model is not units invariant, we note that Y and X are
5

The conventional additive model forces the ls to sum to unity (eTl=1), guaranteeing that the ecient frontier is
constructed of a convex combination of input and output levels. This constraint predetermines that an LDC with a
unique minimum of any input must lie on the ecient frontier, regardless of how little output it may produce. By
relaxing the lambda constraint as above (eTl E 1), a particular LDC, even if it has a minimum of a given input, can
be inecient. See Haag, Jaska, and Semple [28].

64

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

ÿ1
transformed by component averages in the objective function (D ÿ1
y- , D x- ) to assure common
6
results regardless of the units of measure chosen for each component.
Again, the execution of (2) for each LDC serves only to categorize the LDCs as technically
ecient or technically inecient. That is, the execution of (2) for each LDC does not yield a
set of measures that can be used to construct a rank ordering. To develop a rank ordering of
most robustly ecient to most robustly inecient LDCs, one additional linear program must
be executed for each LDC, with the result yielding an 1-norm measure of the minimum
distance to a Pareto optimum point (ecient frontier).
Charnes et al. [25,29] developed a sensitivity analysis technique based on the 1-norm
measure of a vector. It de®nes the necessary simultaneous perturbations to the component
vector of a given LDC that cause it to move to a state of ``virtual'' eciency. Virtual eciency
is de®ned as a point on the ecient frontier where (1) any minuscule detrimental perturbation
(increase in inputs and/or decrease in outputs) will cause an ecient LDC to become
inecient, or (2) any minuscule favorable perturbation (decrease in inputs and/or increase in
outputs) will cause an inecient LDC to become ecient.
For an ecient LDC, the 1-norm measure (herein termed stability index) de®nes the largest
``cell'' in which all simultaneous detrimental perturbations to the input and output components
will not cause a change in the eciency status from technically ecient to technically inecient
[32]. As such, the larger the stability index, the more robustly ecient the LDC is said to be.
Those ecient LDCs with small stability indices will thus become technically inecient with
smaller detrimental perturbations than those ecient LDCs with larger stability indices.
Mathematically, the stability index for an ecient LDC (LDCj) is determined by solving the
following linear program:

min y
s:t:

Y …E† l ÿ s‡ ‡ yd0 ˆ Yj
X …E† l ‡ sÿ ÿ ydI ˆ Xj
eT l ˆ 1
l, s‡ , sÿ , ye0

…3†

where y represents the stability index. The matrix of outputs and inputs are represented by
Y (E) and X (E), respectively, with the component vector for ecient LDCj omitted. Finally, d0
and d1 are given by d T0 and d T1=(1,1, . . .,1), which cause y to simultaneously increase inputs
6

Haag, Jaska, and Semple [28] ®rst introduced the notion of pre-scaling the data by component averages to create
a units invariant model. See Haag and Jaska [30] for a complete numerical analysis and explanation. See Lovell and
Pastor [31] for an alternative pre-scaling technique that must be used when the data contain zero (0) and/or negative
values.

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

65

Fig. 2. Dashed line within stability cell represents the y measure for LDC No. 2.

and decrease outputs as the linear program determines the optimal solution. Fig. 2 provides a
graphical depiction of the 1-norm measure (stability cell) for ecient LDC No. 2.
For an inecient LDC, the stability index de®nes the largest ``cell'' in which all simultaneous
favorable perturbations to the input and output components will not cause a change in the
eciency status from technically inecient to technically ecient. As such, the larger the stability
index for an inecient LDC the more robustly inecient the LDC would be. An inecient LDC
with a large stability index thus rests a greater distance from the ecient frontier than does an
inecient LDC with a smaller stability index. Mathematically, the stability index for an inecient
LDC (LDCj) is determined by solving the following linear program:
max y
s:t:

Yl ÿ s‡ ÿ yd0 ˆ Yj
Xl ‡ sÿ ‡ ydI ˆ Xj
eT l ˆ 1
l, s‡ , sÿ , yr0

Fig. 3. Dashed line within stability cell represents the y measure for LDC No. 7.

…4†

66

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

where all notations are de®ned in the prior formulations. Observe that y simultaneously
decreases inputs and increases outputs as the linear program determines the optimal solution.
Fig. 3 provides a graphical depiction of the 1-norm measure (stability cell) for inecient LDC
No. 7.
Once the stability index is known for each LDC, the LDCs can be ranked from most
robustly technically ecient to most robustly technically inecient. To do so, the stability
indices for inecient LDCs are ®rst negated. Then, the LDCs can be rank ordered from
highest to lowest based on their stability index values.

References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]

[15]
[16]
[17]
[18]

[19]
[20]
[21]
[22]

Kuznets S. Economic growth and income inequality. Amer Econ Rev 1995;45:1±28.
Ahluwalia MS. Inequality, poverty and development. J Devel Econ 1976;3(4):307±42.
Anand S, Kanbur R. Income inequality: A critique. J Devel Econ 1993;43(1):19±43.
Anand S, Ravallion M. Human development in poor countries: On the role of private incomes and public services. J Econ Perspect 1993;7(1):133±50 Winter.
Ram R. Economic development and income inequality: An overlooked regression constraint. Econ Devel Cult
Change 1995;43(2):425±34.
Jha SK. The Kuznets curve: A reassessment. World Development 1996;24(4):773±80.
Ravallion M. A comment on Rati Ram's test of the Kuznets hypothesis. Econ Devel Cult Change
1997;46(1):191±5.
Ram R. Reply to the comment on Rati Ram's test of the Kuznets hypothesis. Econ Devel Cult Change
1997;46(1):191±5.
Dasgupta P. In: An inquiry into well-being and destitution. New York, NY: Oxford University Press, 1993. p.
85±95.
Human Development Report. United Nations Development Program (UNDP), Oxford University Press, New
Delhi, India 1993.
Ravallion M. Good and bad growth: The human development reports. World Development 1997;25(5):631±8.
Luchters G, Menkho€ L. Human development as statistical artifact. World Development 1996;24(8):1385±92.
Dasgupta P, Weale M. On measuring the quality of life. World Development 1992;20:119±31.
Kotamraju P. Child quality of life: a rank correlation analysis for selected issues developing countries and
selected developed countries. Paper presented at Association of Indian Economic Studies Meetings, Boston,
Massachusetts, January 3±5 1994.
United Nations International Education Fund (UNICEF). The state of the world's children. New York:
Oxford University Press, 1993.
Dwyer D, Bruce J, editors. Introduction. A home divided: Women and income in the third world. Stanford,
CA:Stanford University Press, 1988. p. 1±8.
Sen AK. Capability and well-being. In: Nussbaum MC, Sen A, editors. The quality of life. New York:
Clarendon Paperbacks, Oxford University Press, 1993.
Folbre N. The black four of hearts: toward a new paradigm of household economics. In: Dwyer D, Bruce J,
editors. Introduction. A home divided: Women and income in the third world. Stanford, CA:Stanford
University Press, 1988.
Breu TM, Raab RL. Eciency and perceived quality of the nation's liberal arts colleges: An application of
data envelopment analysis to higher education. Socio-Econ Plann Sci 1994;28(1):33±45.
U.S. News and World Report. American's best colleges. June 5 1992.
Berenson M, Levine D. In: Basic business statistics, 6th ed. Englewood Cli€s, NJ: Prentice-Hall, 1996. p. 549±
50.
Ghura D. Macro policies, external forces and economic growth in Sub-Saharan Africa. Econ Devel Cult
Change 1995;43(2).

R. Raab et al. / Socio-Economic Planning Sciences 34 (2000) 51±67

67

[23] Farrell MJ. The measurement of productive eciency. J Royal Statist Soc Ser A 1957;120(3):253±90.
[24] Charnes A, Cooper WW, Rhodes E. Measuring the eciency of decision making units. Eur J Opr Res
1978;2:429±44.
[25] Charnes A, Haag S, Jaska P, Semple J. Sensitivity of eciency classi®cations in the additive model of data
envelopment analysis. Int J Sys Science 1992;23:789±98.
[26] Banker R, Charnes A, Cooper WW. Some models for estimating technical and scale eciencies in data envelopment analysis. Mgmt Sci 1984;30:1078±92.
[27] Charnes A, Cooper WW, Golany B, Seiford L, Stutz J. Foundations of data envelopment analysis for ParetoKoopmans ecient empirical production functions. J Econometrics 1985;30:91±107.
[28] Haag S, Jaska P, Semple J. Assessing the relative eciency of agricultural production units in the Blackland
Prairie, Texas. Applied Economics 1992;24:559±65.
[29] Charnes A, Rousseau J, Semple J. Sensitivity and stability of eciency classi®cations in data envelopment
analysis. J Productiv Anal 1996;7:5±18.
[30] Haag S, Jaska P. Interpreting ineciency ratings: an application of bank branch operating eciencies.
Managerial and Decision Econ 1995;16(1):7±14.
[31] Lovell CAK, Pastor JT. Units invariant and translation invariant DEA models. Operations Research Letters
1995;18:147±51.
[32] Haag J, Haag S, Levin I. Augmenting the analysis of ®nancial statements with technical stability indices in data
envelopment analysis. Financial Management Association Annual Meeting, Toronto, Canada 1993.
[33] Charnes A, Cooper WW, Seiford L, Stutz J. A multiplicative model for eciency analysis. Socio-Econ Plann
Sc 1982;6:223±4.