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P R W P 7940
Conditionality as Targeting?
Participation and Distributional Eects
of Conditional Cash Transfers
Carlos Rodríguez-Castelán
Poverty and Equity Global Practice Group
January 2017
WPS7940
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Abstract
e Policy Research Working Paper Series disseminates the ndings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the ndings out quickly, even if the presentations are less than fully polished. e papers carry the
names of the authors and should be cited accordingly. e ndings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. ey do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its aliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
P R W P 7940
is paper is a product of the Poverty and Equity Global Practice Group. It is part of a larger eort by the World Bank to
provide open access to its research and make a contribution to development policy discussions around the world. Policy
Research Working Papers are also posted on the Web at http://econ.worldbank.org. e author may be contacted at
crodriguezc@worldbank.org.
Conditional cash transfer programs, whereby transfers to
households are conditional on school attendance or health
checkups, have become a widespread policy tool. ey
are viewed as a means of immediate poverty alleviation
through the cash payments, and as a foundation of long-
term poverty reduction through the emphasis on human
capital formation. Because targeted transfers are usually
conditioned on the consumption of normal goods, richer
eligible households are more likely to consume more edu-
cational and health care opportunities than poorer ones.
us, the eligible poorest households may benet least from
conditional cash transfers even to the extent that they may
not participate at all. If conditionality is conceptualized as
a cost at the margin, it may be leading poor households
to opt out. is paper proposes a framework to model
household decision making on participation (or not) in
cash transfer programs depending on whether a condition-
ality exists. e paper outlines the optimal size of the cash
transfer such that a xed government budget maximizes
the poverty reduction. e paper also shows that uncon-
ditional cash transfers may be preferable over conditional
cash transfers if a government has a suciently high degree
of poverty aversion, that is, if, beyond the poverty head-
count, the government cares about how poor the poor are
or the distance of the poorest among the poor below the
poverty line. is basic argument carries over from income
poverty to education poverty. e framework can be useful
in shaping the recent discussion on the merits of univer-
sal benets over conditional transfers in reducing poverty.
Conditionality as Targeting? Participation and Distributional
Effects of Conditional Cash Transfers
Carlos Rodríguez-Castelán‡
JEL Classification: H21, H31, H41, I32,
Key words: Cash Transfers, Provision of Welfare Programs, Poverty, Household decision making
‡ Senior Economist. World Bank. E-mail: crodriguezc@worldbank.org. The author is especially grateful to Ravi Kanbur
for numerous discussions, revisions, and insightful comments. This version of the paper has benefited from comments by
Margaret E. Grosh, Samantha Lach and Luis-Felipe Lopez-Calva. An earlier version of this paper under the title of
“Participation of the Poorest and Distributional Effects of Conditional Cash Transfers” was presented at the 2011
American Economic Association Annual Meeting, and benefited from helpful comments and suggestions from Kaushik
Basu, Peter Brummund, Joerg Ohmstedt, Eswar S. Prasad, Jeffrey T. Prince, Mario Ramirez Basora, David E. Sahn, Liliana
Sousa, and Russell Toth, as well as seminar participants at the Brookings Institution, the International Food Policy
Research Institute, and the Development Workshop at Cornell University. The findings, interpretations, and conclusions
in this paper are entirely those of the author. They do not necessarily represent the views of the World Bank Group, its
Executive Directors, or the countries they represent.
2
1. Introduction
Recent evidence on the lack of a long-term impact of conditional cash transfer (CCT) programs represents an
invitation to researchers to reopen the door on our understanding of the functioning of these schemes and the
cases in which they may (or may not) operate most effectively. The objective of CCTs is usually twofold:
immediate poverty alleviation through cash benefits and long-term poverty reduction through human capital
formation. Programs such as Prospera (formerly Oportunidades) in Mexico, Bolsa Família in Brazil, and Familias en
Acción in Colombia transfer cash to households conditional on the fulfillment of certain requirements by the
child and parents, notably, school enrollment and periodic health and nutrition checkups. An extensive body
of literature evaluating CCT interventions has found significant positive effects of participation on household
use of educational and health services, while concurrently reducing poverty and child labor.1 CCTs are found
to have reduced current consumption or income poverty significantly, though the evidence linking final
outcomes in health and education (beyond increased enrollment and health visits), such as cognitive
development and child height, is more split (Fiszbein and Schady 2009).
Notwithstanding this evidence, recent studies are beginning to cast doubt on how significant the
benefits of CCTs are over the long term. Araujo, Bosch, and Schady (2016) look at the 10-year effects of
Ecuador’s Bono de Desarrollo Humano Program. Their findings suggest a modest increase in the probability that
young women graduated from secondary school (2–3 percentage points); yet, they do not find evidence that
the program’s cash transfers had an impact on attending tertiary education institutions or on the probability of
working.In Cambodia, Filmer and Schady (2014) evaluate the medium-term impact of a scholarship program
three years after it had ended. While they find an impact on completion rates (0.6 more years of schooling),
they find no evidence of an effect of the program on test achievement, earnings, or employment or on the
probability of teenage pregnancy or marriage.Evidence from Mexico is more mixed. Behrman et al. (2009)
compare the effects of differential exposure to Oportunidades on rural teenagers receiving transfers for 5.5 years
relative to teenagers receiving them for 4.0 years. While the study finds 0.2 additional years of schooling among
students in the treatment group (those with 1.5 years longer exposure); there is no evidence of an effect on
achievement tests. The program is found to have a negative effect on labor market participation among boys.2
Results also show a decline in migration rates among boys (6 percent less likely to migrate than the control
group). Additional research on the subject based on nonexperimental evidence in Behrman, Parker and Todd
1 See, for example, Attanasio et al. (2005); Behrman, Sengupta, and Todd (2005); Bourguignon, Ferreira, and Leite
(2003); Cardoso and Souza (2003); De Janvry and Sadoulet (2006); Glewwe and Olinto (2004); León and Younger
(2007); Maluccio and Flores (2005); Schady and Araujo (2008); Schultz (2004); Todd and Wolpin (2006).
2 As discussed in the study, the effect of the program is ambiguous for the stage of the life cycle considered. The effect
of schooling that substitutes for work appears to dominate the opposite effect, that is, once school is finished, the
increase in human capital should lead to higher employment and wages.
3
(2011) indicates a decline in the rate of work among younger boys, no impact on the labor participation of older
boys, and positive impacts of the program on work among older girls.
Other long term results are more encouraging for CCTs. For instance, Barham, Macours, and Maluccio
(2014) look at Nicaragua’s Red de Protección Social on educational attainment a decade after the program began.
The study exploits the randomized phasing of the program to estimate the differential effect of the access of
two treatment groups and considering individuals who had stopped receiving the transfer seven years earlier. It
finds that boys who had received a transfer in early childhood (benefitting more intensely from the education
transfer) had about 0.3 years more years of completed education, scored 0.2 standard deviations higher, and
showed higher earnings from seasonal migration reflected in a 10–30 percent higher monthly off-farm income
relative to the late treatment group. To assess the concern that CCTs may discourage work, Banerjee et al.
(2015) reanalyze the results of randomized assessments of seven CCTs worldwide to study their effect on labor
supply. Their analysis finds no systematic evidence that there is an undesirable effect on the propensity to work
nor on the number of hours worked. Moreover, Banerjee et al. (2016) find proof of long-term (and growing)
effects of an antipoverty program that includes an asset transfer in West Bengal, India, based on data from
three survey waves. Over five years after having stopped receiving benefits, according to the study, households
present increased consumption (25 percent), higher food security, more assets, higher earnings, and more
financial stability than the control group. Mental and physical health indicators also show an improvement
relative to nonbeneficiaries.
A related though different question to that of long-term impact is how efficient CCTs are in
comparison with other unconditional programs. While this area has yet to be more profoundly studied, recent
empirical research has started to shed some light. Baird et al. (2013) analyze data from 35 studies in 75 reports
to compare the effectiveness of CCTs relative to UCTs in terms of schooling outcomes. Their review suggests
that both CCTs and unconditional cash transfers (UCTs) increase the probability of enrollment and attendance,
though the effects on test scores are moderate at best. Differentiating between intensity of conditioning, their
analysis indicates that interventions that are explicitly conditional and monitor and penalize noncompliance
have a larger impact than programs with no conditions or that have some conditions with minimum
enforcement and monitoring. Özler, Baird, and McIntosh (2016) look at the sustained (medium-term) effects
of a two-year CCT program compared with a UCT program among young women and adolescent girls in
Malawi.3 The study finds declines in HIV prevalence, teenage pregnancy and early marriage among the UCT
group, unlike the CCT group, however these effects dissipated after the cessation of the unconditional grants.
Conditionality, they conclude, could be limiting the social protection aspect of CCTs, even if it appears to be
more effective in achieving behavioral change. The study also finds that children born to UCT beneficiaries
3 While the conditional transfer is based on attendance, recipients only need to show up to obtain the unconditional one.
4
during the program had higher height-for-age z-scores at follow-up. This study also concludes that although
CCTs offered to out-of-school females at baseline produced an increase in educational achievement and
sustained reduction in the total number of births, it caused no gains in health, labor market outcomes and
empowerment. On the basis of a large randomized experiment in Morocco, Benhassine et al. (2015) find that
a small UCT, explicitly labeled to be used for education, had a substantial effect on school participation, but
that adding conditionality led to (small) negative effects. A “nudge,” the authors argue, may be enough to
encourage human capital investment without the need for conditionality, which can lead to exclusion, while the
lower administrative costs of UCTs make them more cost-effective than conditional ones. In a different kind
of program, Dutta et al. (2014) look at the conditionality within India’s 2005 National Rural Employment
Guarantee Act, which promises minimum wage employment to all rural households. The study finds that one
of the reasons the program could be falling short of its potential on poverty reduction in Bihar (in addition to
unmet demand for work) is that participation in the scheme is “far from costless” for workers. Individuals
report a trade-off whereby they have to let go of other income-generating activities to participate in the scheme’s
work.
From the economic theory perspective any “condition” represents a constraint to both individual
behavior and social welfare. CCTs make monetary benefits conditional on the consumption of normal goods,
which implies program-eligible richer households are more likely to make use of more education and health
services than poorer households. If the social planner chooses a costly condition to receive a cash transfer, the
poorest eligible households may opt out of the program because they might face more difficulty meeting such
a condition relative to the less poor eligible households. The poorest households, in this way, may benefit least
from CCTs, even potentially resulting in the poorest not participating at all.
This paper examines the extent to which household income plays a role in a family’s decision to
participate in a CCT program. Knowledge of the nature of the household’s decision to enroll in CCTs can have
implications for public policy. Particularly, a better understanding of the determinants of CCT enrollment could
help increase participation rates among the poorest households, thereby boosting the effectiveness of public
spending and improving the progressivity of CCTs.
The paper presents a partial equilibrium model to analyze the decisions of the poorest households to
participate in CCT programs.4 Following the optimal income tax literature and previous studies on household
decisions to enroll in CCT programs, the paper assumes that the income distribution in a given economy already
captures the difference in labor productivity across all households.5 Furthermore, the analysis assumes the
4 Taking the overall transfer budget as given.
5 See Akerlof (1978), Arrow (1971), Besley and Coate (1991), Mirrless (1971), Stiglitz (1982). On dropouts in CCT
interventions, see Alvarez, Devoto, and Winters (2008); on food stamp schemes, see Clarkson (1976); and on housing
allowance programs, see Cronin (1982), Kennedy and MacMillian (1979).
5
government can identify each household’s income level, such that there is a critical income level at which eligible
households are indifferent whether to participate or not participate in CCT programs to attain the socially
optimal quantity condition. In particular, any household with an income level that is strictly less than such a
critical income level will not enroll in the program.
To investigate the budgetary efficiencies underlying the analysis, this paper follows the notion of a cash
benefit known as “guaranteed minimum income” to propose an optimal design for a CCT program.6 The
analysis shows that, if the government can compensate only what is needed to persuade each household to
demand exactly the socially optimal quantity of the conditioned good (say, education), all households would
participate in the program. The spending inefficiency in such a scenario would be lower with respect to an
intervention contemplating a flat monetary transfer to all households, though such an optimal intervention has
key shortcomings, not the least of which would be the administrative complexities in execution.
Could UCTs be superior to CCTs if the objective of the government is to minimize income poverty
measures given a fixed budget? In the last section of the analysis, this paper identifies conditions under which
CCTs dominate UCTs and vice-versa.7 Specifically, it shows that UCTs could be preferred over CCTs if a
government has a sufficiently high degree of poverty aversion, that is, if beyond the poverty headcount, it cares
about how poor the poor are or how far away from the poverty line the poorest among the poor are living and,
thus, about the distributional effects of CCTs on these indicators. On the other hand, it could be argued that
the ultimate objective of CCT programs is not only short-term poverty alleviation but also the long-term benefit
provided by increased consumption of a particular merit good, such as education. In this sense, the paper shows
that the analysis and results carry over broadly for “education poverty.”
The remainder of this paper is organized as follows. Section 2 presents a brief literature review of
studies analyzing household decisions to participate in poverty reduction programs. Section 3 develops a model
of household decision making to define an optimal cash transfer scheme such that a fixed government budget
maximizes poverty reduction. This section also identifies the conditions under which conditional transfer
schemes dominate unconditional ones and vice-versa, considering poverty measures that account for the
intensity and severity of poverty. Finally, section 4 discusses policy ideas related to the dialogue on universal
benefits and offers concluding remarks.
6 This analysis is similar to the one presented by de Janvry and Sadoulet (2006), although their analysis focuses on
maximizing the gain in enrollment over the population instead of maximizing poverty reduction.
7 The idea of making meaningful comparisons among redistributive schemes has been noted previously. Blackorby and
Donaldson (1988), for example, analyze Pareto efficiency under incomplete information for cash and in-kind transfers.
Besley and Kanbur (1988) compare the poverty alleviation effects of marginal and inframarginal subsidies. Besley and
Coate (1992) analyze incentive arguments to compare workfare and welfare programs to alleviate poverty. Currie and
Gahvari (2008) contrast transfers in-cash and in-kind, concluding that paternalism and interdependent preferences are
leading explanations for the existence of in-kind transfer programs. Cunha (2014) compares measured consumption and
health outcomes under both in-kind food and in-cash transfers.
6
2. Literature review
Studies on the determinants of participation in antipoverty programs have typically focused on public works
programs. There is strong empirical evidence confirming a negative relationship between household wealth and
participation in these programs (see, for example, Chirwa, Zgovu, and Mvula 2002; Gaiha 1996; Jalan and
Ravallion 1999). But this negative association is driven by the design of the workfare programs, which were
aimed at facilitating the self-selection of unemployed workers from usually poorer families.
More recently, a number of empirical studies have argued that poverty is associated with a higher
probability of participating in CCTs. Heinrich (2007) presents evidence of the positive effects of Argentina’s
Becas Estudiantiles CCT program on student outcomes. In the first-stage regression of this paper, the author
finds that students in households with a per capita income below a certain threshold (Arg$45 per month) were
significantly more likely to participate. However, after controlling for an index of basic needs, the author finds
that students in households with lower per capita incomes were less likely to participate in the CCT program, a
result that is in line with the framework outlined in this paper.8 In a related study, Oosterbeek, Ponce, and
Schady (2008) analyze the impact of Ecuador’s Bono de Desarrolo Humano CCT program on school enrollment.
They report the results of a regression of actual treatment status on background characteristics and find that
poorer people are more likely to receive the transfer. These authors incorporate a third-degree polynomial of
the poverty index in the children’s outcome estimation, but they only use the linear poverty index in the
regression of actual treatment.
Two studies using the Urban Evaluation Survey (Encelurb) of Mexico’s Oportunidades CCT program
investigate the extent to which the urban component of Oportunidades affects children’s outcomes and
household consumption. Angelucci and Attanasio (2009) estimate a linear probability model of program
participation among eligible households in treatment areas that incorporates second-degree polynomials for the
poverty level as well as household income and consumption variables. They find that a household in the 75th
percentile of the poverty distribution is 69 percent more likely to be a program participant than a household in
the 25th percentile. They also conclude that participation is inversely related to both consumption and income.
In addition to data on household income, consumption, and poverty level, their model includes information
on transitory shocks and the local availability of schools and health centers. However, their model has some
data limitations because it does not include key determinants of household decisions to participate in
Oportunidades, such as proxies for the relative price of schooling, parental preferences, and the opportunity costs
of participating. Although their results do not directly support the outline presented in this paper, they conclude
8 Heinrich (2007) constructed an index of need using 20 measures from base data that include: dependents, household
head occupation, whether household head is pregnant, type of home/tenancy/living conditions, distance to school, years
of education of all household members, student hours worked outside/inside home, student age-grade difference, illness
or disability, and household income.
7
that the observed low participation rate in the urban component of Oportunidades may derive from self-selection
caused by both insufficient information and inadequate financial incentives and that “further research to
estimate the relative importance of these determinants is needed.” Finally, it is unclear why their participation
model includes in the same regression measures of poverty level, food and nonfood consumption and income,
instead of estimating different models using each of these measures of household well-being.
In the other study that uses the urban component of Oportunidades, Behrman et al. (2012) estimate a
first-stage discrete choice model of participation. Their results show that key correlates of poverty, such as dirt
floor in the home and walls or ceilings made of provisional materials or the need for certain assets, increase the
probability of participation in Oportunidades. However, besides having access to a rich set of household and
community characteristics, their model neither concentrates the information into one sole poverty index nor
incorporates any second- or third-degree polynomials of household wealth. In addition, their participation
model does not control for the costs of schooling and school and teacher quality variables.
Closer to the model outlined in this paper are the results of Alvarez, Devoto, and Winters (2008) and
González-Flores, Heracleous, and Winters (2012) who, using discrete duration models, show a u-shaped
relationship between the probability of dropping out of Oportunidades and a poverty index score (puntaje).
Alvarez, Devoto, and Winters (2008) find that the likelihood that a household will leave Oportunidades in rural
areas is the highest among relatively wealthier recipients; it declines at diminishing rates as wealth decreases,
and it increases again at the poorer end of the distribution. Correspondingly, González-Flores, Heracleous, and
Winters (2012) study the determinants of the probability of dropping out from Oportunidades in urban areas. In
line with the framework outlined in this paper, they show that the poorest recipients, those below the 70th
percentile of the poverty index score distribution, are more likely to drop out.
The analysis in this paper contributes to the literature by providing a formal framework to model the
decision of households to participate in cash transfer programs contingent on whether there is a conditionality
on the consumption of normal goods (typically, education and health) to receive the transfer. This paper also
outlines an optimal cash transfer scheme if the government has a fixed budget and a poverty alleviation goal.
Furthermore, this paper also outlines cases where, according to a government’s degree of aversion to poverty—
if, beyond the poverty headcount, it cares about the depth of poverty and the distribution of poverty among
the poor, unconditional cash transfers could be superior to conditional ones and vice-versa. As discussed in
more detail in section 4, this framework can be helpful in framing the growing dialogue on universal benefit
approaches relative to conditional transfers.
8
3. A simple model to understand the distributional effects of cash transfers
To investigate the distributional effects of cash transfers and their broader policy implications, this section
proposes a model representing household decision making on participation in cash transfer programs. It then
describes a simple model to outline the characteristics of an optimal transfer scheme using a fixed government
budget. Finally, it presents conditions under which CCTs dominate UCTs and vice-versa on the basis of several
commonly used poverty measures that take into account the intensity and severity of poverty.
3.1 The structure of household decision making
The benchmark case
Before developing the model, this section illustrates the potential drawbacks of the conditionality of cash
transfers in terms of participation in these schemes if the condition is assigned to a normal good. Figure 1
depicts the impact of a CCT program in any given household. It assumes that a household can consume two
goods, 1
x (education) and 2
x (composite good). The household’s budget constraint prior to the
implementation of the CCT program is represented by line AB, while the after-CCT program budget constraint
is characterized by ACDE. Under this new budget constraint, if a household consumes at least a quantity 1
x
of the good 1
x, it receives a positive transfer, otherwise such a household does not receive the monetary
transfer and remains on its original budget constraint.9
This benchmark case also assumes that the household is a rational utility maximizer and, so, accepts a
CCT if and only if it is made better off than it would be if it rejects the offer. The household’s preferences can
be represented by a concave utility function
21,xxU , which also strictly increases in i
x for
2,1i. It also
assumes heterogeneous preferences such that various types of households can be identified with different sets
of indifference curves.
9 In the vast majority of the currently implemented CCT programs, the condition 1
x on schooling requires the child to
attend school a minimum of 85 percent of the time.
9
Figure 1. CCT programs and different types of households
Three representative types of households are identified in figure 1. Type I (solid line) already demanded
more of good 1
x than the socially optimal condition, 1
x, before the CCT program was introduced, and,
because it is assumed that good 1
x is a normal good, it will consume more of good 1
x after it receives the
cash transfer. Therefore, for type I households, a CCT represents an inframarginal transfer of income. In
contrast, the pre-intervention demand for good 1
x by type II (dashed line) households was below the condition
1
x, but, after the introduction of the CCT program, its consumption of good 1
x is greater than the optimal
quantity. Finally, type III (thin line) does not participate in the CCT program and demands the same quantities
of good 1
x. Two factors are combined such that a type III household does not receive the transfer: (1) it has a
weak preference over the good 1
x, and (2) the transfer size may not be large enough for this type of household
to meet the socially optimal condition 1
x.
Most of the studies on CCT programs use this benchmark case as their structural model to explain
why the level of investment in the conditioned good for some households is too low compared with the true
10
private optimal of the households.10 In particular, some studies associate no participation or dropouts from
CCT programs with weak preferences for the conditioned good.11 However, a problem in estimating the
reduced form of this benchmark case is the validity of the assumption that no-participation in the CCT program
is a function of the underlying difference in the preferences of the targeted households; and, although this is a
plausible explanation, the preferences of households that are eligible to receive the cash transfer (poor
households) may in reality be quite similar within the cohort. In contrast, the approach proposed here assumes
that no-participation in CCTs is a function of the income distribution within the targeted group.
In the partial equilibrium analysis, first, let us assume that the income distribution in the economy
already captures the difference in labor productivity across all households. In addition, such a cumulative
distribution function of household income,
yF , is induced uniquely by an underlying asset distribution
AF =
0dttf .12 Therefore, the economy’s income distribution
yF lies between ],0[ y where
y
represents the income of the richest household. Let y
z be the poverty line induced from an implicit eligibility
line A
z in the asset space, such that all those households with yi zy are eligible to participate in the CCT
program.13 Second, assume that all households share the same concave utility function
21,xxU that is strictly
increasing in i
x for
2,1i.
From these assumptions, one can identify three cases among those households eligible for the CCT
program. Case 1, illustrated in figure 2, includes all those households with a sufficiently large income such that
their demand for good 1
x prior to the implementation of the program was higher than the condition 1
x, and
this demand increases after the cash transfer program is introduced. In particular, the pretransfer income
threshold associated with the consumption of the socially optimal condition 1
x can be defined as y
~
. Therefore,
if the household’s income level i
y lies between yi zyy
~
, then the CCT program has an inframarginal
effect on household behavior. In contrast, figure 3 describes the case for those households that belong to an
10 The true private optimal is defined counterfactually by the absence of misguided beliefs, intrahousehold principal-
agent problems, or hyperbolic discounting.
11 Among some of the explanations of weak preferences for the conditioned good are (a) incomplete information,
(b) imperfect and persistent private information about the nature of certain investments or about the expected returns,
(c) conflicts of interest within the household that may result in incomplete altruism (parental decisions that are not fully
consistent with what the child would have chosen herself, if fully rational), and (d) the unreasonably high opportunity
costs of conditionality.
12 Most CCT programs base their eligibility criteria on data on household assets (see Sahn and Stifel 2003).
13 For instance, according to the general rules of operation of Opordunidades, besides the presence of a child of school age
in the household, eligibility depends on a cutoff value of a poverty index based on an asset valuation, so the eligibility
line will be the same as the poverty line.
11
interval of the income distribution such that their demand for good 1
x prior to the implementation of the
transfer program was lower than the condition 1
x, but, because they enroll in the program once it is available,
their after-transfer consumption of good 1
x will be greater than or equal to the condition 1
x. In particular,
the critical pretransfer value of income associated with the pivot household is defined as y
ˆ, that is, if the
household’s income level i
y is greater than or equal to y
ˆ, then the CCT intervention induces a level of private
investment in the conditioned good 1
xthat is greater than or equal to the social optimum.
Figure 2. Inframarginal effect on the demand of the conditioned good by a poor household
Figure 3. The effect of a CCT on investment in the conditioned good by a poor household
12
Finally, figure 4 represents the case on nonparticipation in the CCT program. Case 3 thus characterizes
the situation of the poorest households in the economy, those with income i
y between yyiˆ
0 . In
particular, given a transfer of size
t
, these households are not able to achieve at least a demand level of 1
x of
good 1
x, and they therefore do not participate in the program.
Figure 4. The effect of a CCT on investment in the conditioned good by one of the poorest households
13
Next, this paper describes the basic household utility maximization problem when a CCT program is
introduced. First, it assumes that the size of the cash transfer
t
is exogenous to the model; then, in section 3.4,
it solves for the equilibrium size of the monetary transfer given a fixed government budget.
The household model parameters
If utility maximization holds, a household must participate in the CCT program if the utility associated with
receiving the cash transfer, minus the cost of fulfilling the condition, is greater than the utility derived from
nonparticipation. To help in providing a discrete dependent variable model, let us consider a single period
model of a parent’s investment in education. For the purposes of this study, consider a representative child and
so ignore issues of intrahousehold inequality in education. Parents are treated as individuals in that they are
assumed to maximize a single utility function and face a budget constraint based on their joint income. The
preferences of the parents in household i are represented by a utility function, as follows:
),,,( 21
21 iiiii aaxxUU
1
where )(U is a quasi-concave and continuous function representing a strongly monotonic preference relation
defined on the consumption of the bundle ),( 21 ii xx , so that 1i
x and 2i
x are normal goods and denote the
demand for schooling and the consumption of a composite good, respectively. The parameters 1
i
a and 2
i
a
represent the parents’ preferences for schooling and all other goods.
The parents maximize i
U subject to the budget constraint, as follows:
iii yxpxp 2211
2
where i
y denotes household i’s income, 1
p represents the cost of schooling, and 2
p is the price of the
composite good. Assuming an interior optimum, combining the first-order conditions leaves
.
/,,, /,,,
2
1
22111
12
1
11 p
p
p
xaaxxU
xaaxxU
iiiii
iiiii
3
Equation (3) establishes that household i’s marginal rate of substitution between schooling and the
composite good must be equal to the relative price of schooling,
p
.
14
After solving for household i’s demand for schooling, one can obtain a function *
1
i
x that is increasing
in income and parents’ preferences and decreasing in the relative price of schooling, as follows:
).,,,( 211
*
1paayxx iiii
4
Now assume that household i is offered a cash transfer i
t, conditional upon consuming a schooling
quantity greater than or equal to 1
x (determined by the government, and usually requiring a monthly attendance
rate of 85 percent of school days). The parents maximize equation i
Usubject to a new budget constraint, as
follows:
iii yxpxp 2211 if
1
*
1xxi
5
iiii tyxpxp 2211 if
.
1
*
1xxi
6
So, if household i’s demand for schooling exceeds the minimum required by the CCT program rules,
the new demand for schooling will be an increasing function of the transfer, as follows:
).,,,,( 211
*
1iiiii tpaayxx
7
Thus, the decision of the parents in household i to send their child to school in response to the
conditional transfer depends on the utility derived from participation. Parents in household i choose to
enroll in the CCT program if the difference between the utility of participation and nonparticipation, defined
as *
i
V, is greater than zero.14 This difference depends on the pretransfer income, i
y, the expected cash
transfer, i
t, the relative price of schooling, i
p, and other characteristics that might independently affect
participation, i
X(for example, economic status and parental preferences). Thus
iiiii XptyVV ,,,
* ,
8
14 Where *
i
V is a continuous but unobservable response variable often defined in the literature as a latent utility
function.
15
where *
i
V is not directly observed, and one only observes the final decision of participation, i
V
, which is an
indicator variable equal to 1 if the household participates in the CCT program and zero if it does not, therefore:
i
V
1 if 0
* i
V
9
0 .otherwise
Assume that the utility of the parents in household i discussed above is represented by a log-linear
utility function. Then, the expenditure on schooling if the household demands an amount of education that is
greater, or equal to, the CCT schooling condition 1
x is 11
*
1/)( pyax ii , that is, a constant fraction of wealth
given any cost of schooling. The expenditure in schooling if the condition is met becomes
11
*
1/)( ptyax ii , that is, a constant proportion of the income, plus the flat transfer for any cost of
schooling.
Following King (1983), one can solve for the equivalent income function of the CCT scheme to identify
the threshold value that defines whether or not the parental demand for schooling exceeds the CCT schooling
condition so that the cash transfer is provided (or not). First, normalize to 1 the cost of schooling; the price of
good 2
x is then defined as p. Compare the indirect utility functions of the expenditure minimizing commodity
bundle that provides the same level of utility as the utility received from the subsidized commodity bundle, as
follows:
2
12
1
),(
a
E
i
a
E
i
E
ii p
ya
yaypv
10
2
11
1
),(
a
i
a
ii p
xty
xypv
11
where E
i
ydenotes equivalent income. Equalizing (10) and (11) gives way to the equivalent income function of
household i, which is the value of income at which the CCT schooling condition generates the same utility as
the actual income level, as follows:
16
.
121
21 11
21
a
i
a
aa
E
ixtyx
aa
y
12
The threshold value of income that determines the participation decision of the poor
Consider the nonparticipating choice as the reference point for the definition of the threshold value of wealth,
y
ˆ, in terms of equivalent income, as follows:
tyaxxvyaxv E
iiiii 11
*
11
*
1ˆ .
ˆtyy E
i
13
Because the demand for schooling at the critical value of income is precisely the demand for schooling
at the CCT schooling condition, plugging E
i
yax 11 into (12) generates the threshold level of income that
represents the cutoff between participation and nonparticipation in the CCT, as follows:
0
ˆ
1
1 t
a
x
y, .10 1 a
14
Then, household i’s demand for schooling in terms of the threshold level of income is
*
1i
x
i
ya1 if t
a
x
yi
1
1
15
ii tya
1 if .
1
1t
a
x
yi
Figure 5 depicts the Engel curve of schooling ( 1
x) for all households eligible to enroll in a CCT
program. The relevant eligibility line is assumed to be equivalent to the poverty line y
z, so that the Engel curve
is restricted to the interval of the income distribution
yF that lies between
y
z,0 .15 Also, figure 5 portrays
15The eligibility line y
z defined over the income space is induced from an implicit eligibility line A
zdefined in the asset
distribution. Most of the screening mechanisms of CCT programs give an important weight in their eligibility criteria to
indicators derived by factor analysis on household assets. According to Sahn and Stifel (2003), such asset-based
indicators are considered valid predictors of poverty and represent an alternative to the standard use of expenditures in
17
both the pretransfer income associated with the CCT schooling condition, y
~
, and the threshold level of
income, y
ˆ. Thus, a poor household i with an income level greater or equal to the critical value of income will
participate in the program and will move from its original Engel curve to a higher curve.
defining well-being. This is particularly applicable to poor regions where there is limited capacity to collect consumption,
expenditure, and price data.
18
Figure 5. Engel curve of the conditioned good-space for eligible poor households before and after the
introduction of a CCTs program
From (14) and (15), it is possible to define the equivalent income distribution in terms of the income
distribution, the expected cash transfer, the CCT schooling condition and the parental preferences for schooling
(figure 5), as follows:
E
y
y
if t
a
x
yi
1
1
16
ty if .
1
1t
a
x
yi
Participation rate among the poorest eligible households
Assume a continuous income distribution that lies between ),0[ with an associated density function )(yf
and a poverty line defined by y
z. The poverty ratio in the economy is defined as follows:
I
q
dyyfP
y
z
0
0)( ,
17
19
where q is the number of poor households, and
I
is the total number of households in the economy.
Moreover, using the threshold condition from (14) shows that the participation rate in the CCT program among
eligible poor households in the economy is defined as follows:
q
r
dyyfQ
y
z
y
ˆ
0)( ,
18
where
r
is the number of poor households with income greater than the critical value of income, y
ˆ.
Because both 0
Q and
1
/xyf are continuous in y and 1
x and because both taxy )/(
ˆ11
and y
z are continuous in 1
x, both have continuous derivatives for tax 11
0 . Then, using the Leibniz
integral rule for tax 11
0 , gives
0
1
ˆ
)(
ˆ
ˆ1
0
ˆ11
0
1
0
1
0
ay
Q
dyyf
xxd
yd
y
Q
xd
dz
z
Q
xd
dQ y
z
y
y
y
19
because 0
ˆ
/
0 yQ and 0
1a. This result implies that, given a condition on the consumption of a normal
good (education) and assuming a fixed budget, the government has to impose a sufficiently low CCT schooling
condition to grant the transfer to increase the participation rates of the poorest households.
3.2 The government’s budget constraint
In the previous section, two interesting parameters were incorporated into the household decision-making
problem: (a) a socially optimal quantity of good 1
x, defined as 1
x, and (b) a poverty line y
z defined by income,
such that households with an income yi zy are eligible to participate in the CCT program. Next, assume
that the government has a fixed budget that is entirely allocated to the CCT program. Given household
preferences, a share 11 aB of the government’s budget would be allocated to consume the conditioned
good 1
x, while the complement 212 aBB is spent by households to consume good 2
x.
20
As shown in figure 6, the government’s budget has an upper bound defined by y
z
a
x
1
1, that is, if
y
z
a
x
1
1, all poor households participate in the CCT program and attain or exceed the socially optimal
condition 1
x. In contrast, has a lower-bound on zero.16 Hence, a key assumption in this paper is that the
CCT
t
has a maximum at
1
1
a
x. Also, from figure 6, it is possible to observe that only fraction 1
b(the dark-
shaded area) of budget is efficiently allocated to attain the socially optimal condition 1
x, while fraction 2
b
(the light-shaded area) is used in excess of the condition. Next, this paper describes how this result is relevant
for characterizing an optimal transfer schedule that induces all eligible recipients of the CCTs to participate in
the program. In short, to incentivize all the targeted households to demand exactly the social optimum, the
government would require a budget of size 1
b rather than one of size .
Figure 6. Upper bound of the budget such that all poor households participate and receive the CCT
16 Ignore the cases y
zax )/( 11 and 0 , because the problem becomes trivial otherwise.
21
3.3. The optimal conditional cash transfer scheme
A fixed budget is a realistic assumption for those developing countries that have implemented CCT programs
because their available fiscal resources are limited and have a high opportunity cost. In particular, the
opportunity cost of increasing the available budget for transfer interventions would deteriorate public
investment in other programs, which are also essential for economic growth (such as education, health care,
employment, infrastructure, and sustainable development). Given modest real increases in poverty reduction
funds in developing countries, an optimal CCT scheme aimed at minimizing poverty, subject to a fixed budget
and to the attainment of the socially optimal quantity of the conditioned good, would be a powerful tool for
policy makers.
Following the notion of a guaranteed minimum income, first used in England in 1795 (Salanié 2002),
to design an optimal CCT scheme, the policy maker would like to act as a discriminatory monopsonist. Consider
the extreme case in which the policy maker can make a separate bargain with all eligible households,
compensating them only with what is needed to persuade each to accept the transfer and demand exactly the
socially optimal quantity
x
of the conditioned good (perfect discriminatory monopsonist). In the case of the
proportional expenditure system, the optimal CCTs schedule *
t can be described as follows:
*
t
E
y
a
x
1
1
1
1
a
x
yE
20
0 1
1
a
x
yE
where the optimal transfer *
i
t, also defined as a function of each household i equivalent income
E
y
a
x
1
1
,0max if 11 xxi, represents the difference in terms of money between the socially optimal
quantity 1
x and each household’s current demand of the conditioned good 1
x.
From
20 , the budgetary cost *
of the optimal CCTs schedule *
t is given as follows:
22
dyyfy
a
x
dyyft
a
x
i
a
x
i
1
1
1
1
01
1
*
0
**
21
E
y
a
x
J
1
1
*
22 ,
where
J
is the number of households that have a current demand of the conditioned good 1
x below the socially
optimal quantity 1
x and where
E
y
a
x
1
1 is the following:
1
1
1
1
0
01
1
1
1
a
x
a
x
i
E
dyyf
dyyfy
a
x
y
a
x,
23
the mean income gap in terms of equivalent income to attain the socially optimal condition 1
x.
Alternatively, from (16), the budgetary cost of the flat CCTs schedule
t
is
dyyft
y
z
xy
i
1
ˆ
~
24
tI
~
25 ,
where
I
is the number of households that have an equivalent income above the critical value of income
1
ˆxy , but lower than the poverty line y
z, and
t
is the flat cash transfer.
Whether the budgetary cost of the optimal CCTs schedule
*
t described in
23 is greater or less than
the budgetary cost of the flat CCTs schedule
t
from
25 will depend on the size of the flat transfer chosen
by the policy maker and the relative position of the poverty line with respect to the monetary value of the
condition 1
x. Up to this point, this paper has taken the size of the flat transfer
t
as exogenously given, but it
23
deals below with the issue of an endogenous transfer because the number of households that participate in the
flat CCT program
I
(and therefore the critical value of income y
ˆ) is a function of the size of the flat transfer
t
.
Figure 7 depicts Engel curves in the conditioned good 1
x space for eligible poor households under
both the optimal CCT scheme (solid line) and the flat CCT program (dashed line). On the one hand, the
Engel curve for the optimal CCTs schedule is described by the value of the socially optimal quantity 1
x until
the income level reaches yyi
~
(the cutoff point at which the effect of the CCTs is inframarginal), and, for
yyi
~
, then it has a slope 1
a equivalent to the taste parameter of good 1
x. On the other hand, the Engel
curve for the flat CCTs schedule is the same as illustrated in figure 5.
Figure 7. Engel curves in the conditioned good space for eligible poor households under the flat CCT
program and the optimal CCT program
Figure 8 identifies the budgetary cost of both transfer schemes in the equivalent income space. For
the optimal CCT scheme, the required government budget ( 321
*sss ) is represented by the area
below the socially optimal quantity, divided by the test parameter, on top of the original income distribution
yyE. For the case of the flat CCT scheme, the budgetary cost ( 43
~
ss ) is described by the gap
between the after-transfer income distribution and the original income distribution for those eligible
households with an income greater than or equal to the critical value y
ˆ. The fact that only a fraction of the
24
fixed budget is common between the optimal CCT scheme and the standard flat CCT program is an
indication of the latent spending inefficiency and unequal distribution of the latter.
Figure 8. Budgetary cost of the flat CCT program and the optimal CCT program
Now, whether the budget required to operate the standard flat transfer scheme is greater, equal, or
lower than the corresponding budget needed to run the optimal transfer scheme depends upon the government
choice of the triple
y
zx ,, 1
. For instance, assuming that income distribution is uniformly distributed within
the interval
y,0 , then
~
*
dyyft
y
z
xy
i
1
ˆ
dyyfy
a
x
a
x
i
1
1
01
1
y
z
t
a
x
y
y
t
1
1
1
1
1
0
2
1
12
1a
x
y
y
a
x
y
t
a
x
zt y
1
1
2)/( 2
11 ax .
25
Moreover, assuming the policy maker chooses a poverty line and a socially optimal quantity such that
1
1
a
x
zy, the above expression can be reduced to
t
2
y
z,
that is, if the size of the flat transfer is greater than the poverty line, multiplied by a factor that is less than one
(that is, 2/1 ), then the budgetary cost of the flat CCT program will be greater than the budgetary cost of
the optimal CCT program.
In sum, if the policy maker is able to discriminate between two or more groups of households, total
participation in the CCT program will be greater, while spending inefficiency may be lower in comparison with
an intervention with a flat monetary transfer to all households. Greater distributional impact is also to be
expected under the optimal CCT scheme. The main shortcoming of the optimal intervention, however, lies in
the manifest administrative difficulty in field execution. This is mainly because of asymmetries in the collection
of data on household income and expenditures and because of the complexity of perfect discrimination in
reality. In contrast, as proven by several empirical studies, flat CCT programs are much easier to implement.
Also, given a fixed budget, it may be difficult to incorporate the poorest of the poor into the optimal program
because they are precisely the households that will require a larger than average transfer. Finally, as noted for
the guaranteed minimum income scheme, this type of optimal intervention may have large disincentive effects
on labor supply and might encourage recipients to evade the system by pursuing informal jobs or by
understating their income and expenditures. Taking into account these critiques to the optimal CCT scheme,
this paper discusses alternative poverty alleviation instruments below based on third-degree discrimination (that
is, whereby discrimination is possible between groups of households (poor and extreme poor, or urban and
rural), but, within each cohort, the transfer is equal).
3.4 The equilibrium transfer size
Up to this point, the size of the transfer has been treated as exogenous. However, given a fixed budget, the
equilibrium transfer size would depend on the total number of beneficiary families. It is thus a share of the
threshold value of income, which is a function of the transfer size.
Before implementing a standard CCT scheme, the policy maker must choose a poverty line, y
z, a CCT
schooling condition, 1
x, and a fixed budget to operate the program, , which is characterized by the triple
26
,, 1
xzy that uniquely determines the threshold value of income and the participation rate in the CCT
program.17
Let a cash transfer
,
ˆ
,yzt y be a function of the critical value of income defined in (14), and,
conversely, define the threshold level of income,
txy ,
ˆ1, as a function of the cash transfer of size
t
. Then,
,
ˆ
,yzt y should be treated as a fixed amount equal to
, such that (14) becomes
.,
ˆ
1
1
1
a
x
xy
26
For tractability, consider a uniform income distribution for all eligible poor households on the interval
],0[ y
z, with
y
zyyF /
ˆ
)
ˆ
( and 1)(
y
zF . Combining both )
ˆ
(yF and )( y
zF with a fixed budget , the
number of poor households q, and the threshold value of income defined in (26), it is possible to solve for
:
1
1
)]
ˆ
()([
a
x
zq
z
yFzFq
y
y
y
.0
1
1
2
q
z
a
x
zy
y
27
Thus, the equilibrium threshold value of income, y
ˆ, is obtained by substituting the
that solves (27)
into (26), and, subsequently, the equilibrium transfer size is
.4
2
1
2
1
,,
ˆ2
1
2
1
1
1
1
1
q
z
a
x
z
a
x
zxzt y
yyy
28
From (28), the following comparative static results are calculated:
17 It is assumed that the government’s budget has an upper bound at 11 /)( azx y
and a lower bound at zero;
otherwise, the problem becomes trivial. This implies that the cash transfer cannot exceed an amount 11 /ax ; otherwise,
all poor households will participate in the program and would no longer be under the poverty line.
27
,0
ˆ
y
z
t
29
,0
ˆ
1
x
t
30
.0
ˆ
t
31
Holding everything else constant, the relationship in (29) predicts a decline in the equilibrium size of
the transfer as the government expands the eligibility criteria for the program. The logic behind this result is
that a larger pool of potential recipients will reduce the average size of the subsidy, given a fixed budget. The
result from (30) implies an increase in the equilibrium transfer size as the government chooses a higher CCT
schooling condition to grant the subsidy. It is reasonable to assume that, given a fixed budget, a greater number
of eligible poor households would fall short of the mandatory education requirement if the policy maker raises
the CCT schooling condition. Because schooling is a normal good, the average transfer size will be larger among
those poor households still demanding a quantity of schooling greater than the CCT schooling condition.
Finally, as expected, the association in (31) shows that the equilibrium transfer size is an increasing function of
government spending.
Measuring poverty
Next, we follow the Foster-Greer-Thorbecke (1984) index (FGT index), which consists of a class of poverty
measures that satisfy both the monotonicity and transfer axioms proposed by Sen (1976) and the
decomposability property, to conduct meaningful comparisons between a CCT program and a UCT scheme.
The FGT index (also known as the
P measure) can aggregate information on poor households below certain
income threshold conditions. It also represents several commonly used poverty metrics that take into account
the intensity and severity of poverty, and it has the property of subgroup decomposability.
The FGT index estimates the weighted sum of the poverty gap ratios of a group of observations under
an arbitrary poverty line and includes a parameter
that measures the sensitivity of the income distribution
within those observations. Assuming a continuous income distribution that lies between
,0 , the FGT index
can be represented as
28
dyyf
z
yz
P
y
z
y
iy )(
0
, .0
32
The FGT index represented in (32) groups several commonly used poverty indicators as special cases.
In particular, if 0
, this index becomes the headcount ratio. This metric represents the number of
households under the poverty line, although it fails to capture the extent to which each household income falls
below the poverty line. If 1
, the index becomes the income gap ratio for the mean poor income. This ratio
measures the shortfall of poor households, on average, with respect to the poverty line. However, the income
gap ratio is not sensitive to the distribution of incomes among the poor. If 2
, the FGT index becomes
the square income gap ratio. This index computes the severity of poverty more accurately because it represents
the square income gap ratio for the mean poor income. In this form, the index incorporates information on
both poverty and income inequality among poor households. Higher order classes of poverty indicators can be
derived as
becomes larger. Finally, as
, the FGT family of poverty measures tends to a Rawlsian
social welfare function, that is, the index depends only on the welfare of the poorest household in the
population.
3.5 Conditional versus unconditional cash transfers
To conduct the comparison of the distributional effects for different levels of poverty aversion of a CCT
program with respect to a UCT intervention, we focus on schooling as the conditioned good. Particularly, we
are interested in calculating the optimal conditioning of schooling, *
1
x, that minimizes the
P measure, subject
to a fixed budget of size and the equilibrium transfer size defined in (28). This is to address the question
about whether UCTs may be superior to CCTs if the objective of the government is to minimize income
poverty for different measures of aversion to the severity of poverty (that is, for different values of parameter
0
).
Consider the problem
dyyf
z
yz
P
y
z
E
EE
x)(min
0
0
1
33
29
..
t
s
2
1
2
1
1
1
1
14
2
1
2
1
,,
ˆ
q
z
a
x
z
a
x
zxzt y
yyy ,
where E
z is the poverty line in the equivalent income space.
If 0
and there is a uniform distribution of income among all eligible poor households on the
interval ],0[ y
z, such that
yyy ztztzF /
ˆ
)
ˆ
( , the problem (33) becomes
tz
x
y
dyyfP
ˆ
0
0
0)(min
1
.
ˆ
min 0
0
1
y
y
xz
tz
P
34
Taking the derivative of the poverty headcount ratio with respect to the CCT schooling condition
yields
.0
ˆ
1
11
0
x
t
zx
P
y
35
Partially differentiating the equilibrium transfer size with respect to the CCT schooling condition yields
.0
4
1
ˆ
2
1
2
1
1
1
1
1
q
z
a
x
z
a
x
z
x
t
y
y
y
36
Combining (35) and (36), the optimal CCT schooling condition that minimizes the poverty headcount
ratio, 0
P, is
.
1
*
1y
zax
37
For comparison, consider a UCT scheme that transfers a cash benefit of size m to all eligible poor
households. Given (37), we can compare the effect on the poverty headcount ratio of CCTs with respect to
UCTs, as follows:
30
dyyf
tz
y
ˆ
0
⋛
dyyf
my
z
0
t ⋛
.m
38
A UCT is a special case of a CCT if the threshold value of income that determines participation is
equal to zero. However, in the current example, the critical value of income is strictly positive (that is,
0
ˆ
ˆ tzy
y
), and so the conditional monetary benefit,
t
ˆ
, is strictly greater than the unconditional subsidy,
m
, which implies that the poverty headcount ratio under a CCT program (
CCT
P
,0
) will be strictly smaller than
the corresponding poverty headcount ratio under a UCT intervention (
UCT
P
,0
). In other words, if the objective
of the government is to minimize the poverty headcount ratio (that is,
0
), then CCTs are superior to
UCTs. This result is illustrated in figure 9.
Figure 9: CCTs versus UCTs (income poverty headcount ratio)
For the case of
1
(poverty income gap ratio,
1
P), problem (33) becomes
.)(min
ˆ
0
1
0
1
dyyf
z
yz
P
tz
E
EE
x
y
39
31
Taking the derivative of the poverty income gap ratio with respect to the CCT schooling condition
yields
.
ˆ
1
1
ˆ
1
1
1
11
1
t
a
x
zx
t
zx
P
E
y
40
By substituting the equilibrium transfer described in (28) and the partial derivative of the equilibrium
transfer with respect to the CCT condition of schooling in (36) into expression (40), the optimal CCT schooling
condition that minimizes 1
P becomes
.
ˆ
1
*
1tax
41
From (41), the threshold value of income that determines participation is equal to zero at the optimal
education condition, which implies that a CCT program is equivalent to a UCT scheme, and thus their
corresponding transfer sizes are equivalent (that is, m
t
). Moreover, the condition tax ˆ
1
*
1 is not binding
because public schooling is assumed to be a normal good and all eligible poor families receiving the transfer
attain or exceed such a condition (that is, poor families allocate a fraction 10 1 a to spending in education).
In terms of the poverty income gap ratio, if the policy maker sets a condition of schooling strictly greater than
the proportion 1
a of the cash transfer, the reduction of the poverty income gap ratio will always be larger under
a UCT scheme ( UCT
P,1 ) relative to a CCT intervention ( CCT
P,1 ). In general, if the government’s objective is to
minimize the poverty income gap ratio (that is, 1
), then UCTs would dominate CCTs.
As illustrated in figure 10. the government’s budget that is not used effectively to achieve the schooling
condition under CCTs is defined by the area of the triangle
taxzt yˆ
/2/
ˆ11 , and correspondingly, under
a UCT scheme, it is characterized by the area
maxzm y 11 /2/ . Then, because m
t
, it is better in
this particular setting to transfer cash unconditionally.
In general, the result for 1
holds true for any 1
, that is, UCTs would be preferred over CCTs
if a government’s poverty aversion is sufficiently high. Moreover, these basic arguments carry over from income
poverty to education poverty (see the appendix). In particular, figures A.1 and A.2 show that UCTs would also
be preferable with a sufficiently high degree of education poverty aversion (
P for 1
), that is, if the policy
maker’s objective is to minimize measures of education expenditure (and schooling) poverty that are more
distributionally sensitive than the headcount ratio, a UCT program should be implemented.
32
Figure 10: CCTs versus UCTs (poverty income gap ratio)
4. Conclusions and policy discussion
Few studies have focused on how imposing conditions on cash transfer programs, which are based on the
consumption of normal goods (such as a minimum consumption of education and health care), can impact the
decision of the poor to participate. The poorest households may not be able to afford to consume more
education or health services. If conditionality is converted into a monetary dimension and thus a cost, it could
make, at the margin, the poorest households opt out.
18
The poorest households, in this sense, may be benefiting
the least from CCTs, even to the extent that they may not participate at all. To look into this concern, this paper
develops a partial equilibrium model representing household decision making to enroll (or not) in a CCT
program given a conditionality. The solution to the problem of the equilibrium transfer size and its
corresponding critical value of income characterizes the cutoff point between participation and
nonparticipation. Any household with an income level strictly below such a critical value will not participate in
the program.
18
Conditionality implies transaction costs, such as the cost of transportation to pick up the transfer at the municipality
office, which, particularly in rural areas, can be nontrivial. These transaction costs are in addition to the opportunity cost
of forgone employment.
33
Furthermore, this paper studies the potential distributional effects (participation rates among the
eligible poor population) of CCTs relative to UCTs by means of setting up a government fixed budget problem
for different degrees of poverty aversion. Comparing the distributional effect of a CCT program with respect
to an unconditional one shows that the latter would be favored over CCTs under a sufficiently high degree of
poverty aversion, that is, if beyond the headcount ratio, the governments care about the depth of poverty (the
income gap ratio), and, in general, any measure of poverty that is more distributionally sensitive (that is, for any
1
in the FGT index), UCTs will be preferred over conditional transfers. This paper also shows how these
basic arguments carry over from income poverty to education poverty.
There is ample margin for further research. The analysis here has been restricted to a proportional
expenditure system with homogeneous preferences. It would be useful to extend it to include general functional
forms for household utility functions and heterogeneous preferences. Also, in addition to UCTs, CCTs could
be compared with other, alternative redistributive interventions such as in-kind transfers or workfare programs.
Finally, further research could include general equilibrium analysis, which allows a solution of the optimal
income tax system that minimizes income poverty, conditional on the consumption of a minimum level of the
conditioned good. A first step to achieve this is to relax the assumption that the income distribution in the
economy already captures the difference in labor productivity across households.
The analysis in this paper calls for a more nuanced assessment of CCTs, beyond the mere comparison
with UCT programs. Indeed, the conditional-unconditional continuum described by Özler, in this way, can be
framed more broadly within the growing discussion on the virtues of universal benefits approaches.19 In fact,
the idea of a universal basic income based on citizenship has been making inroads on policy discussions in both
developing and developed countries.
For instance, in June 2016, Switzerland voted on a proposal to guarantee a universal basic income of
Sw F 2,500 monthly for every adult citizen and long-term resident.20 The proposal met with concerns—about
budgetary issues, labor market disincentives, and the undue attraction of immigration—and was ultimately
defeated in referendum by an overwhelming majority. Nevertheless, other developed economies, including
Canada, Finland, and the Netherlands, appear undeterred and are conducting experimental trials. In the
Netherlands, for instance, the city of Utrecht is planning a two-year pilot project. The monthly transfer of €960
19 See Berk Özler’s July/2013 blog post discussion on the continuum of CCTs/UCTs considering the dimensions of the
announcement, monitoring, and enforcement of programs: http://blogs.worldbank.org/impactevaluations/defining-
conditional-cash-transfer-programs-unconditional-mess.
20 http://www.bbc.com/news/world-europe-36454060.
34
for Dutch citizens already receiving government benefits would allow individuals to dedicate more time to
education, care, and volunteering, and to have a more flexible work schedule.21
Universal benefit schemes are also increasingly being considered in developing countries, particularly
comparing their effectiveness with that of conditioned and targeted transfers. A series of pilot initiatives on
UCTs in India’s Madhya Pradesh, led by the United Nations Children’s Fund, in partnership with the Self
Employed Women’s Association, found positive results in such a scheme (SEWA Bharat and UNICEF 2014).
The cash payment was given out monthly with no strings attached. The study shows that the transfer led to
increased spending on nutrition, health care, education, and productive assets. Moreover, the benefits of the
transfer appear to build on one another, for example, increased schooling led to a reduction in child labor, and
so on.
In a further step, several scholars have recently discussed the idea of an unconditional, universal income
for all citizens in India. In a July 2016 blog post, Debraj Ray discusses the pros (eliminating leaks because of
corruption, mistargeting, providing individuals with the liberty to make decisions about how to spend their
money) and cons (the magnitude of such a commitment, the question of indexing to the appropriate prices, the
effects of such a setup on long-term inequality) of a universal cash transfer that would substitute for the Indian
system of multiple transfers.22 Instead, he proposes a universal basic share of the country’s GDP, which would
allow starting small, would do away with indexing, and would provide the incentives for everyone to share in
the prosperity of the country, as well as to demand better tax collection. Other scholars, such as Abhijit
Banerjee, Pranab Bardhan, Maitreesh Ghatak, Kalle Moene, and T. N. Srinivasan have also joined in on the
discussion of universal benefits schemes in India.23 Questioning the view that careful targeting is always better,
Martin Ravallion has also recently discussed the advantages of a basic income guarantee, which might be more
cost-effective in reducing poverty than a program such as India’s National Rural Employment Guarantee
scheme.24
While evidence is incipient, this discussion is a reminder of the wide array of instruments available to
policy makers, certainly including, but not limited to CCTs. Depending on the policy objective, different
options, including cash transfers with no strings attached, may be more suitable. Given scarce resources, the
quest to find the most effective way to reach the poor, including the poorest among the poor, is far from over.
21 See http://borgenproject.org/netherlands-universal-benefits/ and
http://www.theatlantic.com/business/archive/2016/06/netherlands-utrecht-universal-basic-income-
experiment/487883/.
22 http://debrajray.blogspot.in/2016/07/the-universal-basic-share.html.
23 See Ideas for India’s e-symposium on universal basic income, featuring essays by these economists:
http://basicincome.org/news/2016/11/ideas-india-e-symposium-idea-universal-basic-income-indian-context/.
24 http://www.cgdev.org/blog/time-big-idea-developing-world.
35
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Appendix. The effect of cash transfers on education expenditure (and schooling): Conditional versus
unconditional cash
This appendix addresses the question: could UCTs be superior to CCTs if the objective of the government is
to minimize education expenditure (and schooling) poverty for different measures of the severity of poverty
(represented by the parameter 0 in the FGT Index)? In the subsequent analysis, because the relative price
of schooling was normalized to one, the value and distribution of education expenditure are equivalent to the
value and distribution of education for all poor families. This implies that the results of the comparison between
UCTs and CCTs for the distributional effects of education expenditure will hold true for the distributional
effects of the demand for schooling.
To compare the distributional effects of CCTs with respect to UCTs, we use the definition of the
threshold value of income described in (18) and the income distribution in terms of equivalent income in (20)
to define the equivalent education expenditure function of poor households, as follows:
E
x1
1
x,taxx 111
1.B
tx
1,taxx 111 ,
where E
xdenotes equivalent education expenditure, which is the value of spending in education that, with
the CCT schooling condition, gives the same utility as the actual education expenditure level,
x
, and where
1
x is the CCT schooling condition; the parameter 1
a denotes parental preferences for schooling, and t is the
cash transfer. Figure A.1 plots the correspondence in (B.1).
Next, we solve for the optimal condition of schooling *
1
x that minimizes the 1
,x
P
measure for
education expenditure, subject to a fixed budget of size and the equilibrium transfer defined in (26). Consider
the problem
11
01
1
,
0)(min 1
1
1
1
1
dxxf
za
xza
P
y
za
E
x
EE
x
x
x
2.B
39
..t
s
2
1
2
1
1
1
1
14
2
1
2
1
,,
ˆ
q
z
a
x
z
a
x
zxzt y
yyy ,
where E
x
z1 is the poverty line in the equivalent education expenditure space.
For 0
, the optimal schooling condition that minimizes the education expenditure poverty
headcount ratio (the number of households that fall short of the education expenditure poverty line, y
za1),
1
,0 x
P, is
y
zax 1
*
1
3.B
Because the CCT of size t
ˆ is greater than the UCT of size m, CCTs are superior to UCTs if the
objective is to minimize the education expenditure poverty headcount ratio (figure A.2).
For 1
, the optimal condition of schooling that minimizes the education expenditure gap ratio,
1
,0 x
P, is
tax ˆ
1
*
1
4.B
So, if the policy maker sets a condition of schooling strictly greater than the share of the transfer that
is used to demand schooling ( tax ˆ
1
*
1 ), the reduction of poverty in terms of the education expenditure gap
is superior under UCTs relative to CCTs. As in the case of income poverty, the result for 1
can be
generalized for any 1
. Therefore, UCTs are preferred with a sufficiently high degree of poverty aversion
to education poverty.
40
Appendix figures
Figure A.1: The equivalent education-expenditure function before and after the introduction of CCTs
Figure A.2: CCTs versus UCTs (poverty headcount ratio for education expenditure)
