The Contribution of Increased Equity to the Estimated Social Benefits from a Transfer Program: An Illustration from Progresa/Oportunidades

Most impact evaluations of Conditional Cash Transfers (CCTs) and Unconditional Cash Transfers (UCTs) focus on the returns to increased human capital investments that will be reaped largely or exclusively in the future (e.g., when current children have increased productivities as adults). But the objectives of these programs are not only to increase human capital investments with implications for future levels and distributions of income but also to alleviate current poverty and reduce current inequality. The current distributional gains from such programs depend on the degree of inequality aversion in the social welfare function. Simulations show that, for a range of inequality aversion parameters, the welfare gains from current redistribution for the Mexican PROGRESA CCT program can be as large, or possibly much larger, than the estimated present discounted value of future earnings from human capital investments in lower and upper secondary schooling. These, moreover, are underestimates of the gains from redistribution because, in addition to current gains, such gains will be augmented in the future through the distribution of the returns on the human capital investments induced by cash transfer programs. Therefore, to fully evaluate such programs, it is critical to incorporate the distributional gains, not only the impacts on human capital investments.

Most impact evaluations of Conditional Cash Transfers (CCTs) and Unconditional Cash Transfers (UCTs) focus on the returns to increased human capital investments that will be reaped largely or exclusively in the future (e.g., when current children have increased productivities as adults). But the objectives of these programs are not only to increase human capital investments with implications for future levels and distributions of income but also to alleviate current poverty and reduce current inequality. The current distributional gains from such programs depend on the degree of inequality aversion in the social welfare function. Simulations show that, for a range of inequality aversion parameters, the welfare gains from current redistribution for the Mexican PROGRESA CCT program can be as large, or possibly much larger, than the estimated present discounted value of future earnings from human capital investments in lower and upper secondary schooling. These, moreover, are underestimates of the gains from redistribution because, in addition to current gains, such gains will be augmented in the future through the distribution of the returns on the human capital investments induced by cash transfer programs. Therefore, to fully evaluate such programs, it is critical to incorporate the distributional gains, not only the impacts on human capital investments.
Transfer programs in low-and middle-income countries have increased appreciably in the last decade. By 2010, between 0.75 and 1.0 billion people in these countries were recipients of conditional and unconditional cash support, including over 60 million people in Brazil, 30 million in Mexico, and nine million in Ethiopia (DFID, 2011). Many of these programs, particularly conditional cash transfer (CCT) programs, are expected to create human capital.
Others, such as public works [workfare], construct physical assets as well as target income to low-income households, which indirectly may increase human capital investments (Mani et al. 2014). Many of these programs are designed to address both current poverty and future income growth and poverty (Levy 2006, Alderman andYemtsov 2014). They combine efficiency and equity motives because poorer households are more likely to face capital, information, and insurance market imperfections that limit their investments below levels that would be implied by efficiency (Das, Do, and Özler 2005, Behrman and Skoufias 2010, Blank 2002. While there are numerous studies that evaluate the impact of such programs on human and physical capital and others that assess the targeting effectiveness of transfers and, thus, their contribution to poverty reduction, attempts to combine these two objectives to indicate the overall effectiveness of transfer programs are limited by the absence of a common metric. Take, for example, education. A range of studies have reported the impact of transfer programs on schooling (Baird et al. 2014, Behrman 2009, Behrman, Parker, and Todd 2013, Fiszbein and Schady 2009, Orazem and King 2008. Often the estimated increased schooling from a given level of transfer is compared with the impact of equal value alternative investments in the sector, thus providing a cost-effectiveness ranking. 1 Alternatively, benefits can be converted into the expected impact on the present discounted value of lifetime earnings (assuming individual earnings are the only impact of policy interest) and compared to the present discounted value of costs (Behrman, Parker, and Todd 2011, BPT in the remainder of this paper).
In both these examples, however, the impact on the current distribution of consumption is ignored. It is hard to argue that society does not value the poverty reduction or the increased equity resulting from a transfer given that society chooses to use resources to administer the targeting of such programs to the poor. Indeed, Alesina, Tella, and MacCulloch (2004) provide 1. Dhaliwal et al. (2013) present a variation of this approach, assigning the transfer from PROGRESA as a cost in a cost-effectiveness comparison of diverse schooling investments but excluding all but a single type of benefit as an outcome due to the challenges of aggregation of distinct categories of benefits. To no surprise, it appears costly to achieve the results studied. survey data that shows that even well-off individuals have a lower tendency to report themselves happy when inequality is high. If the values of increased equity or reduced poverty are policy goals, then standard benefit-cost estimates are presumably lower bounds for the true benefit-cost ratios of multi-objective policy packages that are directed towards current distributional goals as well as enhanced investments. 2 This point is often acknowledged; Blank (2002) provides a crisp theoretical model that places the efficiency and equity gains of transfers in a simple framework that illuminates efficiency and equity tradeoffs. But few studies of the human capital and other investments from transfers actually offer quantitative assessments.
Is looking only at the investment potential of a transfer program a minor underestimation, one that could, perhaps, be ignored when prioritizing investments? While the distributional social benefit cannot be directly measured, leaving it out of any assessment implicitly assumes that the social value of redistribution is zero, a tacit assumption that is hard to defend in the context of targeted transfer programs. To illustrate the range for the possible contribution of increased consumption of low-income households to the total impact of a well-known CCT program, Mexico's PROGRESA, 3 the current paper estimates social benefits under different assumed degrees of social inequality aversion using an explicit social welfare function. In particular, we construct a grid of the total benefits from the PROGRESA transfers that are conditional on attending lower or upper secondary school, including the social value of increased consumption by the poor under different assumed values for a parameter that measures social welfare of different outcomes given distributional weights. Because the benefits from current consumption are immediate while the benefits from human capital investments accrue after a number of years, the relative contribution from redistribution to social welfare also depends, in part, on the discount rate. As this is also not directly observed, and there is some debate about the appropriate discount rate to use, the simulations are presented with redistribution parameters on one axis and discount rates on the other. Clearly, both matter since, if redistribution of current consumption has any value at all, the share of its contribution to total benefits is higher the larger the discount rate for future earnings impact of program-induced human capital investments.
2. The standard argument for separating equity from efficiency considerations in project evaluation, with the former being addressed in separate transfers, clearly does not apply to CCTs. 3. PROGRESA was subsequently renamed Oportunidades, and its successor is currently entitled Prospera. The data employed here cover the transition to Oportunidades. However, for convenience we use PROGRESA to convey both phases of the program in the period.
Our particular illustration is informative about a program that has been analyzed extensively from both the perspective of human capital improvements and distributional efficiency. Among the latter is a study by Coady and Skoufias (2004), which decomposes welfare gains from targeting and redistribution using different welfare weights. The results are presented in relative terms and one that is scale-neutral. Wodon et al. (2003) also compare the social welfare of PROGRESA relative to other programs using an index based on decomposition of the Gini index. No study that we know of, however, is designed to include the distributional benefits of PROGRESA together with the value of the gains in future productivity. Brent (2013) does attempt this task for a pilot program for orphans and vulnerable children in Kenya, offering an approach that includes both dimensions of the CCT programs in cost-benefit analysis using primary school enrollments as well as distribution of consumption. That particular example has a favorable outcome under reasonable assumptions about the implicit social welfare function, but the results are driven largely by the distribution component.
In contrast, the current study shows that even when the transfer program has an appreciable role in increasing human capital investments and thus anticipated future earnings, the value of achieving these goals is enhanced when equity considerations are made explicit. Thus, modeling the contribution to social welfare of transfers provides an additional perspective on the assessment of dual roles of a transfer program.

I. APPROACH
The simulation is based on an additive social welfare function in which social welfare W is summed over individual well-being, of the N individuals in the society.

1) 1;
An important characteristic of this welfare function is that a single distribution parameter, ε, indicates how society values inequality. A higher value of ε implies greater inequality aversion.
As ε → ∞, W becomes Rawlsian and the lowest individual wellbeing is at the core of social welfare as equity considerations dominate entirely. If ε = 0, W is utilitarian with no concern 5 about distribution. Figure 1 illustrates these possibilities. The straight isowelfare line is for ε = 0.
Moving along an isowelfare curve from an equal distribution with xi = xj at point a to a very unequal distribution with xi << xj at point b has no impact on social welfare for this function with ε = 0. In this extreme case, the distribution of individual welfare is irrelevant in the sense that it does not affect social welfare, which is identical along the linear isowelfare curves. At the other extreme, with ε → ∞, the welfare function is L-shaped. If one starts with equal distribution at point a' and increases either xi or xj, there is no impact on welfare. 4 All that matters is the wellbeing of the worst-off member of society, for which reason this welfare function is called Rawlsian. At this extreme, distribution is everything in the sense that the only way to increase social welfare is to improve the consumption of the unit with the lowest wellbeing. In between these two extremes are an infinite number of possible isowelfare curves. Those that are closer to the L-shaped extreme by being fairly sharply curved weigh equality much more than those that are closer to the linear extreme by having little curvature.
This welfare function also has the property that the ratio of marginal social utility of two individuals is the reciprocal of the ratio of their wellbeing raised to the power of the distribution parameter, ε. 5

2)
This expression indicates again that if ε = 0 then there is no difference in the marginal social utility with different distributions between the ith and jth individual; and, thus, society places no value on redistribution. If the ith individual is poorer than the jth, and thus xj/xi is greater than one, then for all values of ε > 0, social welfare increases at a faster rate with an increase of wellbeing for the ith individual than an equal increase in wellbeing for the jth. As ε increases, the social gain of redistribution from richer to poorer individuals also increases. 4. We have assumed symmetry around the 45 0 line so the corner of the isowelfare curve is on this line. One could allow asymmetry (what Behrman, Pollak, and Taubman 1982 call "unequal concern" because welfare weights are such that, for the same consumption level, some families are weighted more heavily in the welfare function than others), but this complication would not add much to our analysis.
5. Squire and van der Tak (1975) start with equation 2 and integrate back to get equation 1. Equation 2, however, is also a property of an alternative social welfare function, as used by Behrman and Birdsall (1988). Equation 2 also makes it apparent that the overall origin of this social welfare function stems from the convexity of utility under constant relative risk aversion as acknowledged in Atkinson (1970).
Equation 2 has been applied to various studies of taxation and redistribution (Deaton 1997, Coady and Skoufias 2004, Coady and Harris 2004. These studies often compare the relative outcomes of different taxation instruments and do not present their result in terms of a dollar metric that can be combined with the investment returns of a transfer program, which is our objective. Indeed, equation 1 is not anchored in a manner conducive to direct comparisons. The value of aggregate welfare is asymptotic at 1, approaching infinity from below and negative infinity from above. That is, the value of W becomes negative if ε > 1, a parameter value that is often explored in the literature (Deaton 1997, Olken 2007, Coady and Skoufias 2004. Therefore, direct comparisons of W are meaningful for a given value of ε but not for changing values of ε. This study, however, is not attempting to measure aggregate welfare but only the sum of marginal changes relative to the change at a reference value, δW/δxj. To do this, we require a few additional assumptions. First, we focus on equation 2, aggregating weighted marginal changes attributable to the program. Consistent with much of the literature, we use per capita consumption or expenditures as the measure of individual wellbeing (Deaton 1997). However, in order to make direct comparisons of changes in W when the value of ɛ varies, we need to calibrate the calculations. We first set xj to mean per capita consumption. 6 However, many studies based on equation 1 focus on relative income inequality and do not require a cardinal value as is necessary here in order to sum changes in welfare with the present discounted value of increased earnings. We thus also set δW/δxj = 1. If this simulation achieves our objective of opening up a line of inquiry, the sensitivity to alterative measurement approaches can be explored. We return to this issue briefly below.
The costs of the program include both transfers per se and administration costs, which on average were 10.6 pesos for every 100 pesos transferred in the first four years of the program (Caldés et al. 2006). This, however, included targeting of beneficiaries as well as external evaluation. Marginal costs by the fourth year dropped to only 5.4 pesos per 100, of which 11% was for identification and incorporation of beneficiaries and 6% was for external evaluation. We assume that these marginal costs are the costs in the year of the study and will be part of the 6. Alternatively, one can calibrate based on median per capita expenditures as in Olken (2007). Coady and Skoufias (2004) calibrate on the mean income for the poorest quintile. Atkinson and Brandolini (2010) use per capita income in their study of global inequality. 7 financing needs in the year corresponding to the consumption survey. 7 We also need to consider financing of transfers themselves. In the standard benefit-cost literature in the absence of distributional weights, transfers are not considered either a cost or a benefit as they are assumed merely to shift resources and not actually use them. Once one considers distributional weights for beneficiaries, one needs to consider these for financing as well. Few, if any, taxation systems are free of economic distortions. While the issue of how different taxation policies affect the relative net social value of a transfer program is important (Coady and Harris 2004), it is an issue for which we do not have anything to add to the literature. Nevertheless, we do take the distributional impact of revenue into account by modeling the program in a manner that offsets the transfers paid out and administration with revenues (so that the net resources available to the economy are unchanged). In particular, we assume that the program is financed out of general taxation with the consumption of each individual's resources reduced by his or her share of the total taxation bill. However, we also assume that the program is financed by a reallocation of current revenue, and thus total revenue is not affected. Therefore, there is no additional deadweight loss from additional taxation. for impact evaluations of both PROGRESA and Oportunidades; although most of those studies use pre-and post-implementation surveys, they do not have a national representation that allows for the study of the distribution of benefits and taxation over the full population that is undertaken here.
For the current study, the transfer received by these recipients was based on the allocation formula reported in BPT (see table 1) rather than the amount reported per individual in the survey data. We assume that the monthly support for secondary school students was provided for only ten months of the year in accord with the academic year.
Taking our measure of current welfare as current consumption, it is not necessarily the case that consumption (x) increases on a one-for-one basis with a unit of transfer (t). We assume that δxi/δti = δxi/δyi * δyi/δti where yi is incremental expenditures. While the former derivative is likely close to one (by construction in this study) 9 , δyi/δti < 1 in most cases because labor allocation will be affected by a transfer due to the substitution effect coming from the change in the price of schooling whenever the transfer includes conditionality. Thus, the increment of income from the transfer will be somewhat offset by reduced labor earnings (Blank 2002).
The Mexican Family Life Survey reports consumption after the distribution of PROGRESA.
To derive an estimate of what consumption would have been in the absence of the program, we subtract the net per capita transfer (vi), from observed consumption, wherein net transfer is the transfer to all families with eligible individuals in lower or upper secondary school minus assumed labor reallocation to schooling as well as the household's share in the taxes necessary to fund the program. BPT report that male PROGRESA recipients aged 12 to 16 reduced their labor by 28.6%. Thus, we subtracted 28.6% of the average of labor earnings of males in that same age bracket who were not in school and also in the poorest quartile of the population-roughly the share of population that was targeted in PROGRESA at the time-from the estimated transfer received by the families of similar males who were in school. 10 Taxation is assumed to come from the Value Added Tax (VAT) and is based on the household's share of total taxable 9. Thus, we are ruling out many forms of savings although we recognize that this is a simplification from behavior (Gertler, Martinez, and Rubio-Codina 2012).
10. This assumes that the labor reallocation is due to the reallocation of current income and current consumption to investment in schooling that leads to the future earnings estimated by BPT. To the degree that the change in labor is partially increased leisure-outside the welfare measure used here-the overall welfare gain for PROGRESA beneficiaries is somewhat underestimated in our procedure. consumption with the non-exempt categories based on Davila and Levy (2010). As indicated, the aggregate taxation is set equal to the aggregate value of the transfer.
While most households do not receive a transfer for lower and upper secondary school students-even those that receive PROGRESA support based on compliance with other conditions may not have a student in the appropriate age bracket-all do pay a share of taxation.
There is, thus, a marginal welfare gain or loss for each household from this component of the program.
In theory, the social welfare function is based on individual wellbeing, and different individuals in a household may have different weights in the social welfare function. However, as the aggregation is additively separable in the absence of different individual weights, the summation is unaffected by utilizing changes in household consumption, although the weights themselves are based on per capita expenditures. The total distributional benefit, D is obtained where vi is net transfer to N individuals in society and change in consumption is assumed to be equal to this net transfer. As the welfare weights, (xj/xi) ε , depend on the level of consumption, we take the average of pre-and post-PROGRESA distributions. That is, xi = ½(xi 0 + xi 1 ) where the superscripts 0, 1 indicate pre-and post-program consumption.
Unfortunately, of course, the underlying social welfare function is not directly observable.
Not only is the parameter ε not derived from observations, the underlying functional form used in this study is not the only plausible candidate for modeling the social policy objectives of the government. For example, it is not necessarily the case that the government's objective in means testing is redistribution per se as implied in this study, but poverty reduction-in which case ε = 0 for all households above the poverty line. Coady and Skoufias (2004) use such an approach to assess alternative targeting strategies for PROGRESA and also employ equation 2 for deriving the social valuation of increased income. Little and Mirrlees (1994) report that, while myriad attempts to ascertain the value of distribution from governments' revealed preferences were attempted by World Bank staff in the 1970s, few were applied and interest rapidly waned. Behrman and Birdsall (1988) present such a study designed to uncover the revealed social preference based on investments in schooling in Brazil and find the estimated value for ε to be 0.68. This is close to the value for ε of 0.57, at which the benefits begin to exceed the costs for the Kenyan CCT studied by Brent (2013). While, below we report the results of the study using a range of values for Є, we confine some of the sensitivity analyses to results with a value of 0.7 for clarity. Table 2 reports the present value of the increased schooling from the component of PROGRESA for lower and upper secondary school based on BPT and using a range of plausible discount values. 11 BPT, however, focused only on labor market returns for males. As there is substantial evidence that education enhances both labor returns for females (Alderman and King 1998) as well as non-labor market returns often at equal or greater rates (Schultz 2002) we assume that the discounted future benefits do not differ by gender. As the gains in schooling are based on participation in the program for six years, these have been divided by six and multiplied by the number of beneficiaries in the sample in order to compare with the annual distributional benefits.

III. RESULTS
In principle, with neither welfare weights on transfers nor taxes, when ε = 0 a fully paid-for program should have no distributional benefits or losses. However, there is an estimated reallocation of labor into time spent in school that reduces current consumption in PROGRESA households. In some studies this might be considered a cost; indeed, it is likely that households view this as an opportunity cost when deciding on their schooling investments. However, as the reduction in current consumption does influence the estimated distribution when ε > 0, for parallel purposes the implication of reduced consumption is also included in the estimates of the distributional benefits when ε = 0. The distributional benefits at various values of ε are reported in figure 2a. Figure 2b presents the total peso value of the program including both distributional gains and net present value (NPV) of human capital for the entire sample in the MxFLS. Our goal is not to scale this result for the entire national investment in the program but to illustrate the relative contribution of increased current consumption of low-income households. Thus, the proportion 11. Equation 1 imposes a lower bound on any discount rate that is consistent with the rate of income growth when ɛ > 0. This is because the marginal contribution of future income to welfare declines as income grows at a rate that is determined by ɛ. This is additional to pure time preference. However, since BPT do not base the estimated returns to schooling on any assumed growth in productivity, this bound does not apply to this study. of the total benefits that is attributable to the long-term increase of worker productivity is presented in figure 2c. When ε = 0.7, there are appreciable distributional benefits from current consumption even with a relatively high weight placed on future productivity, that is, when the discount rate is low. With this distribution parameter, when the discount rate rises from 3% to 5%, the share of benefits attributed to future earnings drops from 84 percent of total benefits to 69 percent. When ε = 1, future gains in productivity amount to about two-thirds of the total at 3% discount rate and decline to about a half when discount rate is 5% as illustrated in figure 2c; at higher values for ε the human capital component becomes a negligible portion of the total.
While PROGRESA is targeted to roughly a quarter of the population, there is a social welfare gain for transfers to all households when the transfer they receive exceeds their share of taxation since the welfare function is continuous in consumption over the population. Thus, under the assumption that the welfare weight is based on equation 2 with the reference consumption, xj, at mean per capita expenditure, what is commonly called a program leakage does not necessarily preclude net distributional gains depending on the share of beneficiaries in any expenditure category and the share of the costs assigned to them. This effect is illustrated in table 3 for ε = 0.7. A third of the PROGRESA recipient households have expenditures between the 25 th percentile and the mean consumption and 12% actually have consumption per capita higher than the mean (this consumption category represents less than half the households since, as is commonly observed, expenditures are skewed upwards and the mean is above the median). The transfer to all of the 413 PROGRESA secondary-school transfer recipient households in the MxFLS leads to net increases of social welfare for these households-that is, none pay more taxes for this program than they receive as benefits-although the social welfare gain per peso spent by the government is less than one for the better-off recipients while it is about two for the poorest quartile. Given that the tax needed to finance the program is distributed among the entire population in this simulation according to the share of consumption subject to the VAT, the payments lead to a net social welfare loss for the entire population above the 25th percentile of expenditures per capita, that is, for both recipients and non-recipients in that group.
In figure 3 we take the illustration one step further by considering an additional distribution issue, the distribution of deadweight costs over the population. Often the cost of the funds for an investment is based on the cost of servicing a loan. In the public finance literature, it is generally argued that the revenue for loan repayment ultimately comes from taxes and incurs distortion of 12 economic behavior. Estimates of the marginal social cost of public funds typically run in the range of 20 to 25% of the revenue (Auriol andWarlters 2012, Harberger 1997). If this cost is neutrally distributed over the population, or if no welfare value is placed on distribution, the cost can be put into the denominator of a benefit-cost ratio or netted out as a lump sum from total benefits. If the deadweight costs are not borne equally over the population, such an approach slightly distorts the welfare benefits. The estimates in figure 3 assume that the aggregate deadweight loss is 25% of the tax revenue and the share of the loss is proportional to the earnings of the household (here proxied by consumption).
Finally, our choice of setting δW/δxj = 1 at mean consumption has an implication for distribution; as the mean is higher than the median, the transfer program will appear to provide more distribution using the mean rather than the median. To ascertain the degree that the results are sensitive to this assumption, we re-estimated the main results using the median for xj (see the figures in the annex). When the discount rate is 0.05 and ε = 0.7, the estimated social welfare value of the component of PROGRESA transfers attributed to distribution using a benchmark set at median expenditures declines by 21% and the share of total benefits from increased human capital rises from 69% of the total to 74%. By construction, the relative decline is larger when the distribution parameter is larger. The differences are not major relative to the overall patterns observed.

IV. DISCUSSION
Governments, including that of Mexico, devote substantial resources to means testing or otherwise targeting transfer programs. They clearly value increased consumption of the poor in and of itself as well as any contribution the transfers may make to increased investment in human capital (Levy 2006). The results here indicate that, under a range of plausible social welfare weights and discount rates, this redistribution can account for a high share of the total social benefits of the transfers. Total benefits have also increased appreciable since the 2002 MxFLS survey. There were 2.5 times as many beneficiaries in Prospera in 2015 than were covered in 2002, not including individuals who had been assisted by Programa de Apoyo Alimentario and 13 were shifted to Prospera. 12 While this program expansion should have a significant impact on the value of redistribution when ε >0, the share of total benefits from redistribution and from human capital investments cannot be ascertained with the data available.
The study has also concentrated on only a subset of PROGRESA recipients, those who received a transfer conditional on attending lower and upper secondary school. Additional families with younger children benefited from the program, all of whom would contribute to distributional gains using equation 2. However, the present discounted productivity gains from increased schooling-given the high rates of primary school enrollment existing in Mexico prior to the introduction of the program-are likely to be a relatively small share of the total. If almost all the effects of the transfers to primary school age children are distributional, we underestimate the share of distributional gains in our simulations. PROGRESA also targeted nutritional investments for young children. However, the gains depend on the targeting of an additional supplement (Behrman and Hoddinott 2005), and valuing the nutritional gains depend on a range of additional assumptions on the impact of nutrition on schooling outcomes (Alderman, Behrman, and Puett 2017). Thus, illustrating the contribution of this component of PROGRESA adds to the complexity of exposition and yet would reiterate the main point of this illustration.
Thus, assessing a transfer program in terms of a single education (health) outcome-in effect asking "is the transfer the most cost-effective way to allocate the education (health) budget?"will provide a misleading answer compared to using the human capital improvements as one dimension of the answer to the question "is the program the best way to allocate the funds devoted to transfers given multiple objectives?" The current study has not explored the possibility that the investments in schooling not only raise future productivity but also increase future equity. That is, we estimate the value of changes in welfare during the investment period but not the present discounted value of all future changes in distribution. These future distributional benefits are likely to accrue from expansions of schooling. They could also stem from investments out of transfers as documented by Gertler,12. We are indebted to Citlalli Hernández Juárez who provided this calculation based on data from the Dirección General de Padrón y Liquidación de PROSPERA. Martinez, and Rubio-Codina (2012). 13 While conceivably future distributional gains stemming from PROGRESA would add an extra dimension to our results and would likely reinforce the contribution of the program to social welfare, these discounted future distributional gains likely would not qualitatively alter our main results.
We do, however, explore one additional distributional issue, that of UCTs compared to CCTs. While we do not have a counterfactual to indicate the impact of a UCT on schoolinglikely positive, even if smaller than the impact of a CCT (Baird et al. 2014)-we can indicate the distributional benefits of a UCT that provides total transfers similar to the transfers studied here.
A starting point would be to assume that every family with per capita income less than the 25th percentile and with a child between eight and 21 received an UCT. But, as a comparison with the distributional value of the CCT is most informative when the aggregated amount of transfer is the same, the per beneficiary transfer needs to be scaled back to have the total transfer budget This, however, is still an unrealistic comparison that favors redistribution benefits since it assumes perfect targeting when, in fact, only 54% of the households receiving PROGRESA schooling benefits in our sample were in the poorest expenditure quartile as indicated in table 3.
If we compute a scenario in which UCT benefits are distributed with the same probability of targeting errors as the CCT, then the social welfare value of the transfers is only two million pesos when ε = 0.7. As mentioned, we do not include a present discounted value (PDV) for the human capital component for UCTs as this is not available. Although this component is 13. Presumably, on average such investments are welfare-increasing for the household. However, their influence on future equity is less clear.
presumably positive, it is likely small since the per capita transfer covering a larger number of households would be smaller than in the CCT. Thus ignoring the schooling impact of a UCTand thus presenting a lower bound-we estimate that, at a 3% discount, the total social welfare value of the CCT would dominate the UCT at all values of ε. In contrast, when ε =0.7 and a 5% discount rate the two programs make more or less the same contribution. Thus, at this discount rate ε = 0.7 is a switching point; when the parameter is larger UCTs make a greater contribution to social welfare, and when the parameter is smaller the calculations favor a CCT.
We can also illustrate another switching point of potential interest. BPT estimate that the NPV for human capital investment is negative when the discount rate is 10% in their approach which tacitly assumes ε = 0.0. However, when ε > 0.24, the distribution benefits offset this negative NPV and the total social value of the program is positive.
Researchers apply substantial creativity and effort to minimizing biased assessments of the impact of transfers on human capital accumulation, employing a wide array of tools for impact evaluation that control for self-selection into a program or non-random placement of the program itself. The biases avoided, however, may be small in comparison to the error of implicitly limiting the value of the program to a single outcome. As indicated in this paper, under a range of plausible assumptions about Mexico's policy goals, the social value of redistribution can be as great, or greater, than the measured value of the increased productivity attributed to the program.
It is unlikely, however, that any consensus will be achieved on the precise value for this parameter. In addition, major policy choices may be sensitive to the value of the social discount rate. However, the fact that these parameters are hard to specify should not be a justification for avoiding sensitivity analysis on their implications for program design or policy choice. There may be major implications for public policy with regard, for example, to the choice between transfer programs and other programs directed towards increasing education.      Note: Relative shares calculated using the "PDV of benefits per grade of schooling" in table 2 and the total PDV of benefits including redistribution shown in figure A2.