Policy Research Working Paper 7940

Conditionality as Targeting?

Participation and Distributional Effects of Conditional Cash Transfers

Carlos Rodríguez-Castelán

Poverty and Equity Global Practice GroupJanuary 2017

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Abstract

The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

Policy Research Working Paper 7940

This paper is a product of the Poverty and Equity Global Practice Group. It is part of a larger effort 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. The 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. They 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. Thus, the eligible poorest households may benefit 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. This paper proposes a framework to model

household decision making on participation (or not) in cash transfer programs depending on whether a condition-ality exists. The paper outlines the optimal size of the cash transfer such that a fixed government budget maximizes the poverty reduction. The paper also shows that uncon-ditional cash transfers may be preferable over conditional cash transfers if a government has a sufficiently 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. This basic argument carries over from income poverty to education poverty. The framework can be useful in shaping the recent discussion on the merits of univer-sal benefits 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.

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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 Proteccion 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.

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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.

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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, 1x (education) and 2x (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 1x

of the good 1x , 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 ix 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 1x 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 1x than the socially optimal condition, 1x , before the CCT program was introduced, and,

because it is assumed that good 1x is a normal good, it will consume more of good 1x 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 1x by type II (dashed line) households was below the condition

1x , but, after the introduction of the CCT program, its consumption of good 1x 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 1x . Two factors are combined such that a type III household does not receive the transfer: (1) it has a

weak preference over the good 1x , and (2) the transfer size may not be large enough for this type of household

to meet the socially optimal condition 1x .

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

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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 yz be the poverty line induced from an implicit eligibility

line Az 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 ix 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 1x prior to the implementation of the program was higher than the condition 1x , 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 1x can be defined as y~ . Therefore,

if the household’s income level iy 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 1x prior to the implementation of the

transfer program was lower than the condition 1x , but, because they enroll in the program once it is available,

their after-transfer consumption of good 1x will be greater than or equal to the condition 1x . In particular,

the critical pretransfer value of income associated with the pivot household is defined as y , that is, if the

household’s income level iy is greater than or equal to y , then the CCT intervention induces a level of private

investment in the conditioned good 1x that 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 iy between yyi ˆ0 . In

particular, given a transfer of size t , these households are not able to achieve at least a demand level of 1x of

good 1x , 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:

),,,( 2121 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 1ix and 2ix are normal goods and denote the

demand for schooling and the consumption of a composite good, respectively. The parameters 1ia and 2ia

represent the parents’ preferences for schooling and all other goods.

The parents maximize iU subject to the budget constraint, as follows:

iii yxpxp 2211 2

where iy denotes household i ’s income, 1p represents the cost of schooling, and 2p is the price of the

composite good. Assuming an interior optimum, combining the first-order conditions leaves

.

/,,,

/,,,

2

1

22111

12111 pp

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 *1ix that is increasing

in income and parents’ preferences and decreasing in the relative price of schooling, as follows:

).,,,( 211*1 paayxx iiii 4

Now assume that household i is offered a cash transfer it , conditional upon consuming a schooling

quantity greater than or equal to 1x (determined by the government, and usually requiring a monthly attendance

rate of 85 percent of school days). The parents maximize equation iU subject to a new budget constraint, as

follows:

iii yxpxp 2211 if 1*1 xxi 5

iiii tyxpxp 2211 if .1*1 xxi 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*1 iiiii 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 *iV , is greater than zero.14 This difference depends on the pretransfer income, iy , the expected cash

transfer, it , the relative price of schooling, ip , and other characteristics that might independently affect

participation, iX (for example, economic status and parental preferences). Thus

iiiii XptyVV ,,,* , 8

                                                            14 Where *

iV is a continuous but unobservable response variable often defined in the literature as a latent utility

function.

  15

where *iV is not directly observed, and one only observes the final decision of participation, iV , which is an

indicator variable equal to 1 if the household participates in the CCT program and zero if it does not, therefore:

iV

1 if 0* iV

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 1x 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 2x 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

1 21),(

aEiaE

iEii p

yayaypv

10

2

1 11),(

a

iaii p

xtyxypv

11

where Eiy denotes 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

.1

21

21 11

21

ai

a

aaEi xtyx

aay

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 , in terms of equivalent income, as follows:

tyaxxvyaxv Eiiiii 11

*11

*1 ˆ

.ˆ tyy 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 Eiyax 11 into (12) generates the threshold level of income that

represents the cutoff between participation and nonparticipation in the CCT, as follows:

0ˆ1

1 ta

xy , .10 1 a 14

Then, household i ’s demand for schooling in terms of the threshold level of income is

*1ix

iya1 if t

a

xyi

1

1

15

ii tya 1 if .1

1 ta

xyi

Figure 5 depicts the Engel curve of schooling ( 1x ) for all households eligible to enroll in a CCT

program. The relevant eligibility line is assumed to be equivalent to the poverty line yz , so that the Engel curve

is restricted to the interval of the income distribution yF that lies between yz,0 .15 Also, figure 5 portrays

                                                            15The eligibility line yz defined over the income space is induced from an implicit eligibility line Az defined 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 . 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:

Ey

y if t

a

xyi

1

1

16

ty if .1

1 ta

xyi

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 yz . The poverty ratio in the economy is defined as follows:

I

qdyyfP

yz

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

rdyyfQ

yz

y

0 )( , 18

where r is the number of poor households with income greater than the critical value of income, y .

Because both 0Q and 1/ xyf are continuous in y and 1x and because both taxy )/(ˆ 11

and yz are continuous in 1x , both have continuous derivatives for tax 110 . Then, using the Leibniz

integral rule for tax 110 , gives

01

ˆ)(

ˆ

ˆ 1

0

ˆ 11

0

1

0

1

0

ay

Qdyyf

xxd

yd

y

Q

xd

dz

z

Q

xd

dQ yz

y

y

y

19

because 0ˆ/0 yQ and 01 a . 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 1x , defined as 1x , and (b) a poverty line yz 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 1x , while the complement 212 aBB is spent by households to consume good 2x .

  20

As shown in figure 6, the government’s budget has an upper bound defined by yza

x

1

1 , that is, if

yza

x

1

1 , all poor households participate in the CCT program and attain or exceed the socially optimal

condition 1x . 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 1b (the dark-

shaded area) of budget is efficiently allocated to attain the socially optimal condition 1x , while fraction 2b

(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 1b 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 yzax )/( 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

Ey

a

x

1

1 1

1

a

xyE

20

0 1

1

a

xyE

where the optimal transfer *it , also defined as a function of each household i equivalent income

Ey

a

x

1

1,0max if 11 xxi , represents the difference in terms of money between the socially optimal

quantity 1x and each household’s current demand of the conditioned good 1x .

From 20 , the budgetary cost * of the optimal CCTs schedule *t is given as follows:

  22

dyyfya

xdyyft

a

x

i

a

x

i

1

1

1

1

0 1

1*

0

** 21

Ey

a

xJ

1

1* 22 ,

where J is the number of households that have a current demand of the conditioned good 1x below the socially

optimal quantity 1x and where

Ey

a

x

1

1 is the following:

1

1

1

1

0

0 1

1

1

1

a

x

a

x

iE

dyyf

dyyfya

x

ya

x, 23

the mean income gap in terms of equivalent income to attain the socially optimal condition 1x .

Alternatively, from (16), the budgetary cost of the flat CCTs schedule t is

dyyftyz

xy

i1ˆ

~ 24

tI ~ 25 ,

where I is the number of households that have an equivalent income above the critical value of income

1ˆ xy , but lower than the poverty line yz , 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 1x . 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 ) is a function of the size of the flat transfer

t .

Figure 7 depicts Engel curves in the conditioned good 1x 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 1x 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 1a equivalent to the taste parameter of good 1x . 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 . 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 yzx ,, 1 . For instance, assuming that income distribution is uniformly distributed within

the interval y,0 , then

~

*

dyyftyz

xy

i1ˆ

dyyfya

xa

x

i

1

1

0 1

1

yz

ta

xyyt

1

1

1

1

1

0

2

1

1

2

1 a

x

yy

a

x

y

t

a

xzt y

1

1

2

)/( 211 ax

.

  25

Moreover, assuming the policy maker chooses a poverty line and a socially optimal quantity such that

1

1

a

xzy , the above expression can be reduced to

t

2yz

,

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, yz , a CCT

schooling condition, 1x , and a fixed budget to operate the program, , which is characterized by the triple

  26

,, 1xzy 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 ,ˆ 1 , 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

.,ˆ1

11

a

xxy 26

For tractability, consider a uniform income distribution for all eligible poor households on the interval

],0[ yz , with yzyyF /ˆ)ˆ( and 1)( yzF . Combining both )ˆ( yF and )( yzF 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

xzq

z

yFzFqy

y

y

.01

12

q

z

a

xz yy 27

Thus, the equilibrium threshold value of income, y , is obtained by substituting the that solves (27)

into (26), and, subsequently, the equilibrium transfer size is

.42

1

2

1,,ˆ

2

12

1

1

1

11

q

z

a

xz

a

xzxzt 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

,0ˆ

yz

t 29

,0ˆ

1

x

t

30

.0ˆ

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

dyyfz

yzP

yz

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,*1x , 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

dyyfz

yzP

yz

E

EE

x)(min

001

33

  29

..ts 2

12

1

1

1

11 4

2

1

2

1,,ˆ

q

z

a

xz

a

xzxzt y

yyy ,

where Ez 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[ yz , such that yyy ztztzF /ˆ)ˆ( , the problem (33) becomes

tz

x

y

dyyfP

ˆ

0

00

)(min1

.ˆ

min 001

y

y

x z

tzP 34

Taking the derivative of the poverty headcount ratio with respect to the CCT schooling condition

yields

.0ˆ1

11

0

x

t

zx

P

y

35

Partially differentiating the equilibrium transfer size with respect to the CCT schooling condition yields

.0

4

1ˆ

2

12

1

1

1

1

1

q

z

a

xz

a

xz

x

t

yy

y

36

Combining (35) and (36), the optimal CCT schooling condition that minimizes the poverty headcount

ratio, 0P , is

.1*1 yzax 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

dyyftz y

ˆ

0

⋛ dyyfmyz

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,

0ˆˆ tzy y ), and so the conditional monetary benefit, t , is strictly greater than the unconditional subsidy,

m , which implies that the poverty headcount ratio under a CCT program ( CCTP ,0 ) will be strictly smaller than

the corresponding poverty headcount ratio under a UCT intervention ( UCTP ,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, 1P), problem (33) becomes

.)(min

ˆ

0

101

dyyf

z

yzP

tz

E

EE

x

y

39

  31

Taking the derivative of the poverty income gap ratio with respect to the CCT schooling condition

yields

.ˆ11

ˆ1

1

1

11

1

ta

x

zx

t

zx

PE

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 1P becomes

.1*1 tax 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, mt ). Moreover, the condition tax ˆ1

*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 1a of the cash transfer, the reduction of the poverty income gap ratio will always be larger under

a UCT scheme ( UCTP,1 ) relative to a CCT intervention ( CCTP,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/ˆ

11 , and correspondingly, under

a UCT scheme, it is characterized by the area maxzm y 11 /2/ . Then, because mt , 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:

Ex1  

 1x ,  taxx 111  

1.B  

tx 1 ,  taxx 111 , 

where Ex denotes 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

1x is the CCT schooling condition; the parameter 1a 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 *1x that minimizes the

1,xP measure for

education expenditure, subject to a fixed budget of size and the equilibrium transfer defined in (26). Consider

the problem

11

0 1

1,

0)(min

1

1

1

11

dxxfza

xzaP

yza

Ex

EEx

xx

  2.B  

  39

..ts   2

12

1

1

1

11 4

2

1

2

1,,ˆ

q

z

a

xz

a

xzxzt y

yyy ,   

where Exz 1

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, yza1 ),

1,0 xP , is

yzax 1*1   3.B  

Because the CCT of size t 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 xP , is 

tax ˆ1

*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 ˆ1

*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)