Child Sponsorship and Educational Aspirations

The puzzle: Returns to education are positive and significant — yet educational attainment remains very low

• Average years of schooling for adults \(>24\) in Oaxaca and Chiapas: 7.5 and 7.2 years (barely above primary)
• Significant returns to higher education exist even for rural populations

Standard explanation: external constraints

• Income, distance to schools, poor health

Compassion International: Third largest child sponsorship program worldwide

• Sponsors \(\approx\) 2.2 million children across 29 countries
• Faith-based NGO; collaborates with local churches
• In Mexico: 33,360 children in \(>185\) centers

Duration: Average 9.3 years of sponsorship (\(\approx\) 4,000 hrs of organized activities)

Program components:

• In-kind income transfers: school supplies, uniforms, healthcare
• After-school program: 5–6 hrs/week (socio-emotional development, academic tutoring)
• Letter exchanges with sponsor: broadens career horizons
• Catastrophic health insurance; access to nurses and doctors

Material support:

• School supplies and uniforms
• Food and basic goods
• Catastrophic health insurance
• Access to affiliated nurses and doctors

Educational support:

• Academic tutoring (in after-school program)
• Spiritual and values-based education

Socio-emotional development:

• Classes emphasizing self-efficacy, self-esteem, social trust
• Structured extracurricular activities
• Letter exchanges with international sponsors

Multi-stage targeting procedure:

1. Identify most economically deprived communities in the poorest regions
2. Partner with a local church to implement the program
3. Church staff identify households with greatest need
4. Household selects specific child; eligibility criteria apply

Eligibility criteria:

• Lives within 30 min walk of a CI center
• Not already receiving sponsorship from another organization
• Household has \(\leq 3\) already-sponsored children
• Age \(\leq 9\) when starting sponsorship (lower priority given closer to 9)

Survey design:

• June – August 2017
• Southern Mexican states: Oaxaca and Chiapas (some of the poorest in Mexico)
• 8 rural communities: 4 with active CI project, 4 comparable controls
• CI sites chosen randomly; each matched to a nearby control community with similar educational and healthcare infrastructure

Survey subjects:

• Sponsored children + next oldest/youngest sibling (ages 10–18)
• Non-sponsored: random household sampling within CI communities
• Control communities: every other household, ages 10–18

From the survey data, for each individual \(i\) and education level \(\ell\):

\[\mathbb{E}[\ln(Y^{\ell}_i)] = \int_{y^\ell_{\min,i}}^{y^\ell_{\max,i}} \ln(y)\, f_{Y^\ell_i}(y)\, dy\]

This is computed directly from the individual’s stated \(y^\ell_{\min}\), \(y^\ell_{\max}\), and the probability question that pins the triangular distribution.

Perceived return to education level \(\ell\):

\[\rho^\ell_i = \mathbb{E}[\ln(Y^\ell_i)] - \mathbb{E}[\ln(Y^{\ell-1}_i)]\]

Used directly as a control variable in the outcome equations.

Reading the figure:

• Both HS and Univ distributions are right-skewed — consistent with log-normal income
• Distribution modes closely match census medians (vertical lines)
• Substantial heterogeneity: wide right tail — some children are very optimistic
• Sponsored and non-sponsored distributions largely overlap

Naive comparison is biased:

• Sponsored children differ from non-sponsored in observable and unobservable ways
• E.g., more motivated families may seek sponsorship; CI targets the most vulnerable
• Raw difference in aspirations \(\neq\) causal effect of CI

Standard IV approach (LATE):

• Identifies effect only for compliers
• Assumes \(\alpha_1 = \alpha_0\) (no selection on gains)
• Misses heterogeneity in treatment effects

Exclusion restrictions: \(\mathit{Agep}\) dummies

• \(\mathit{Agep} = 1\) if child was \(p\) years old when CI arrived in the village (\(p \in \{6,7,8\}\))
• Omitted category: age 9 or older (too old to be eligible)
• Intuition: younger children when CI arrived \(\Rightarrow\) higher probability of being sponsored — but age-at-arrival should not directly affect current aspiration

Other controls: Asset index (wealth), Protestant (church attendance), CI site dummy

Regressors \(X_i = (1,\, \rho_{HE,i},\, \mathit{Dist}_i,\, \tilde{X}_i)\):

• \(\rho_{HE,i}\): perceived returns to higher education — enters as extra variable (in Model 2)
• \(\mathit{Dist}_i\): distance to nearest university (km) — access proxy
• \(\tilde{X}_i\): gender, asset index, parental education, Prospera dummy

Why \(\rho_{HE}\) matters:

• Tests whether subjective expectations about returns shape aspirations
• Jensen (2010), Nguyen (2008): information about returns can shift schooling choices
• If \(\beta^1_2\) or \(\beta^0_2\) significant: subjective beliefs drive aspirations
• If not: other factors (internal constraints, income, social context) dominate

What this allows:

• Non-zero correlation between \(U_{Si}\) and \(U_{ji}\): \(\mathrm{Cov}(U_S, U_1) = \alpha_1\), \(\mathrm{Cov}(U_S, U_0) = \alpha_0\)
• Selection on unobserved gains: \(\alpha_1 \neq \alpha_0\)
• Recovers joint distribution of \((U_S, U_1, U_0)\) under normality

Normalization: \(\mathrm{Var}(\theta_i) = \mathrm{Var}(\varepsilon_{ji}) = 1\;\forall i\)

Average Treatment Effect (ATE):

\[\mathrm{ATE}(x) = \Phi\!\left(\frac{x\hat{\beta}_1}{\sqrt{1+\hat{\alpha}_1^2}}\right) - \Phi\!\left(\frac{x\hat{\beta}_0}{\sqrt{1+\hat{\alpha}_0^2}}\right)\]

Average over all children with characteristics \(x\)

Average Treatment on Treated (ATT):

\[\mathrm{ATT}(x, S=1) = \frac{1}{F_{U_S}(z\hat{\gamma})} \left[F_{U_S, U_1}(\cdot) - F_{U_S, U_0}(\cdot)\right]\]

Average only over sponsored children

Marginal Treatment Effect (MTE):

\[\begin{aligned} \mathrm{MTE}(x, u_S) &= \Pr(Y_1=1 \mid X=x, U_S=u_S) \\ &\quad - \Pr(Y_0=1 \mid X=x, U_S=u_S) \end{aligned}\]

Effect for children at the margin of selection \(u_S\)

Average treatment effect on the treated (ATT):

• Model 1: CI’s estimated ATT \(\approx\) 17 percentage points increase in aspiration probability
• Model 2 (with \(\rho_{HE}\)): \(\approx\) 20 percentage points
• Direction consistent with prior CI studies
• Not statistically significant — large standard errors due to small sample + bootstrap

How to interpret imprecision:

• Coefficients estimated via MLE with integration — inherently noisier than OLS
• Results should be read as suggestive evidence, not definitive

Reading the MTE curve:

• \(u_S\) = unobserved resistance to selection
• Low \(u_S\): children most likely to be selected into CI
• High \(u_S\): children least likely to be selected

Pattern: MTE declines in \(u_S\)

• Sponsored children exhibit higher sponsorship effect
• Positive correlation between selection and treatment effect

Key finding from MTE:

\[\mathrm{Cov}(U_S, U_1) = \alpha_1 > 0\]

Children who are more likely to be selected are also those who benefit more from sponsorship

Policy implication for CI:

• Aid agencies often face efficiency vs. equity trade-off: targeting most-vulnerable \(\neq\) targeting those with highest gains
• CI does not face this trade-off in this context: the most vulnerable also benefit the most
• Reassuring for CI’s targeting strategy

Result: \(\rho_{HE}\) (perceived returns to higher education) is not statistically significant in either the sponsored or non-sponsored outcome equations (Model 2)

Two possible interpretations:

1. Children age 12–15 are too young to integrate income beliefs into long-run plans — other factors dominate (external constraints, identity, social context)
2. Low levels of education in rural communities make higher education aspirationally unrealistic, even with accurate income beliefs

Aspirations (outcome equation):

• Being male \(\Rightarrow\) lower aspiration for higher education
• Non-sponsored: marginal effect of being male \(\approx -0.12\) (significant)
• Sponsored: same sign, not significant

Income expectations (Table 2):

• Females expect \(\approx\) 50% lower income than males at high-school level
• Gender gap exists even among 12–15 year olds
• Females have higher aspirations despite expecting lower income — gap is not explained by income beliefs

For child sponsorship programs:

• Holistic programs that combine material support with socio-emotional development appear well-positioned to shift aspirations
• Emphasize short-term attainable goals alongside long-run aspirations — realistic milestones may be more actionable than abstract future income
• School attendance requirements (even informal) may be a valuable design feature

For gender equity:

• Gender gap in income expectations starts early (ages 12–15)
• Information interventions about female returns may be insufficient — structural constraints and identity formation play a larger role at this age
• Programs should address gender-specific barriers explicitly