International Migration and the Education of Children: Evidence from Lima, Peru

Abstract

The issue of whether emigration has consequences for the education of children who remain behind in the country of origin occupies an increasingly prominent place in the agendas of both scholars and policy makers. The conventional wisdom is that the emigration of family members may benefit children by relaxing budget constraints through remittances that can be used to cover educational expenses. However, the empirical evidence on the overall effect of migration is inconclusive. This is due in part to a substantive emphasis on remittances in the literature, as well as the inability of some studies to deal satisfactorily with the endogeneity of household migration decisions in comparing outcomes across migrant and non-migrant households. Using Peruvian data from the Latin American Migration Project (LAMP), we apply an innovative instrumental variable technique to evaluate the overall effect of migration on educational attainment and schooling disruption among the children of immigrants. In contrast to conventional wisdom, our results suggest that a higher household risk of immigration has deleterious consequences for the education of children who remain behind.

Appendix: Survival Analysis

The survivorship function (S) is defined as follows:

$$ S\left( t \right) = { \Pr }(T_{m} > t) $$

(3)

where t denotes time and T _m denotes the time at which first migration occurs. Moreover, the hazard function or rate, denoted as λ, is defined as the rate at which migration occurs at time t conditional on survival until or later than time t:

$$ \lambda \left( t \right) = \mathop {\lim }\limits_{{{{\Updelta}}t \to 0}} {\frac{{{ \Pr }\left( {t < T_{m} < t + dt|T_{m} > t} \right)}}{{{{\Updelta}}t}}} = {\frac{f(t)}{S(t)}} = {\frac{{S^{\prime } (t)}}{S(t)}} $$

where f(t) is T _m ’s probability density function. Related to the hazard rate is the cumulative hazard function, Λ, which is obtained by integrating λ(t) over time:

$$ \Uplambda \left( t \right) = - \ln S(t) $$

Parametric proportional hazard models assert that the hazard rate for the jth subject is:

$$ \lambda \left( {t |x_{j} } \right) = \lambda_{0} \left( t \right)e^{{\left( {x_{j} \beta_{j} } \right)}} $$

(4)

where λ₀(t), the baseline hazard function, is parameterized, x _j is a vector containing k characteristics of individual j, and the coefficients β _j are obtained from the data. To parameterize λ ₀(t), we need to assign a specific probability distribution to the survival function in Eq. 3. To get a better idea of how the survival function for first migration behaves in the our sample, we arrived at a non-parametric maximum-likelihood estimate of S(t) using the Kaplan–Meier estimator, $\hat{S}(t)$:

$$ \hat{S}\left( t \right) = \mathop \prod \limits_{{t_{i} < t}} {\frac{{n_{i} - d_{i} }}{{n_{i} }}} $$

where n _i is just the number of survivors just prior to time t _i and d _i is the number of deaths at time t _i . After analyzing the Kaplan–Meier migration survivorship function for the household (figure available on request), the Weibull distribution was best suited to describe the pattern of first migration occurrence with the survivorship function S(t) = exp(−t ^p) and a hazard function which allows the hazard to grow as the household ages:

$$ \lambda \left( t \right) = pt^{p - 1} $$

(5)

Our parameterization yields $\lambda_{0} (t) = pt^{p - 1} \exp (a)$, where a is an extra parameter to estimate and p is the shape parameter for the Weibull distribution. The exponentiated coefficients β _x in Eq. 4 are the hazard ratios, which give us the relative hazard faced by a subject who has a certain characteristic denoted by x _k .