Methodology, Instrument and Data

3.1 Methodology

To estimate the impact of the number on the education of children we follow Rosenzweig and Wolpin (1980) by estimating the following empirical model

E= α + α₁n + Xα₂ + ε
n= β + β₁z + Xβ₂ + μ

E is the education variable, n is the number of children z is the instrument to control for the endogeneity of n and X is a vector of individual, household and community characteristics. The error terms å and µ are, by implication, correlated. The implied subscripts are omitted for clarity. As shown in Rosenzweig and Wolpin (1980) this model is derived from the quantity-quality tradeoff framework originally introduced in Becker and Lewis (1973).

Estimating (1) with OLS will result in a biased and inconsistent estimate if indeed n is endogenous. We, therefore, test for the endogeneity of n in (1). If n is endogenous, we use as instruments, the sex of the first two children. The validity of this instrument is explained in the next section. Since we use cross-section data where heteroscedasticity is commonly present, we also test for heteroscedasticity and apply the GMM estimation³ if it exists.

The dependent variable we use in this paper is the proportion of school-age children that are attending school. Most other studies, except for Rosenzweig and Wolpin (1980) and Lee (2004), used individual outcomes⁴. A household outcome variable, rather an individualistic outcome, would be closer to the spirit of the Becker and Lewis (1973) framework. An individualistic schooling variable, by implication, adds the assumption of independence of the decision for each child in the same household, which the Becker and Lewis (1973) framework did not consider. Rosenzweig and Wolpin (1980) used an age-standardized aggregate of the years of education of the children in the household. Lee (2004), on the other hand, used household expenditures on education.

The estimation strategy is as follows. We first establish the endogeneity of the number of children using the sex of the first two children as instruments following Angrist and Evans (1998). We do this by various tests available in the ivreg2 Stata routine described in Baum et al. (2003). We also check the relevance of the instruments by checking the first stage regression results, particularly, the partial R2 for the instruments and check if we have a weak instrument problem (Bound, Jaeger and Baker, 1995). We also test for the presence of heteroscedasticity in the data because this is common in cross-section data. When endogeneity is established, it is well known that the OLS estimate will be biased and inconsistent and the 2SLS or GMM estimates would provide a consistent estimate and in the case of the GMM, an efficient estimate as well. When heteroscedasticity is present, GMM would provide a more efficient estimate. When a weak instrument is indicated, we present LIML estimates that are found to be more robust than the GMM in this case (Stock, Wright and Yogo, 2002). Finally, in the case of using a separate both male and both female instruments we check the overidentifying restrictions test results. This, of course, cannot be done when using the same sex as an instrument as the system is exactly identified.

It is worth noting that given that we are dealing with proportions data, Greene (2003) shows that this can be treated as separate responses for each individual child given common household explanatory variables, i.e., these are essentially replications of individual school attendance decisions within the household. Under this framework, the model can be estimated using the grouped probit using the bprobit routine in Stata. Since this is essentially a probit routine, the endogeneity of the number of children equation is corrected by estimating a two-stage probit using the sex of the first two children as instruments using the proposals discussed in Rivers and Vuong (1988). But then again, we are back to assuming independence of the decision for each individual child in a household, even if we consider that they are grouped.

Finally, to provide estimates of the varying impact of the number of children by socioeconomic class, models that include the interaction of the number of children and the per capita income quintile dummy variables are estimated. The differential impact across socioeconomic classes will be estimated by the sum of the coefficient of the base category and the coefficient of the corresponding interaction term. The estimator that we deem to give the most reliable estimate in the average equation is used here.

3.2 Balanced Sex-Mix as an Instrument

There are not too many instruments that one can find for the number children in household models. Most of the likely candidates such the household income, education of the parents or age of marriage are also related to the dependent variable of interest such as labor force participation of parents, savings or education of children, rendering these inappropriate as instruments. Recent research using US data such as Angrist and Evans (1998) has used the hypothesis that families prefer to have balanced sex-mix of children as an instrument for the number of children. The Philippines is one of the countries in Asia where a balanced sex-mix are found to have prevailed in contrast to countries in South and Eastern Asia where indications for son preference are often found (Wongboonsin and Ruffolo, 1995). Early literature that confirms the preference for a balanced sex-mix in the Philippines is found in Stinner and Mader (1975). The other instruments that are available are limited by their applicability only in very specific circumstances. The occurrence of twins also has been used as an instrument again using US data first in Rosenzweig and Wolpin (1980a) and in subsequent studies such as Angrist and Evans (1998). A much more recent applications were for the US (Vere 2005), for Romania (Glick, Marini and Sahn, 2005) and for Norway (Black et al, 2004). Son-preference in the Republic of Korea was also used as an instrument for fertility, for instance in Lee (2004). Finally, another instrument would be an exogenous policy change that could affect child bearing. Quian (2004), for instance, used the relaxation of the one-child policy in the People’s Republic of China that allows rural households to have another child if the first child is a girl. Viitanen (2003), on the other hand, used the large-scale giving out of vouchers for privately provided childcare in Finland.

In the case of the balanced sex-mix hypothesis, the fact that families do not have control over the sex of their children makes same sex for the first two children virtually a random assignment. As argued in Angrist and Evans (1998) using same sex as an instrument will allow a causal interpretation. It should be noted, however, that the downside of this instrument is that it will render families that have less than two children unusable for analysis. While this maybe a serious problem in low fertility areas, this may not be in the case of the Philippines where the average number of children exceeds four.

To check the validity of this instrument, Table 7 [ PDF 129KB | 12 page ] provides a cross tabulation of the average proportion of families that have additional children and the average number of number of children by sex of their first two children for 24,000 families that have two or more children using the APIS 2002 dataset. The table shows that 67.4% families that had one male and one female for their first two children had another child, while 71.8% had another child when they have the same sex for their first two children or a difference of more than 4%. In terms of average number of children, this is 3.49 as against 3.61 or an average difference of a little over 0.12 children. These average differences are statistically significant under conventional levels of significance. Comparing this with Table 3 and Table 5 in Angrist and Evans (1998) one can observe several differences. The difference in the proportion of families having a third child for the two groups of families is smaller and the standard error is larger. In the case of the difference in the average number of children, the difference is larger, but so is the standard error. This is not unexpected given the larger family size in the Philippines and the expected larger dispersion of the distribution. Consequently, the implied t statistics in Table 7 [ PDF 129KB | 12 page ] are not as large as those in Angrist and Evans (1998), indicating that discrimination generated from the same-sex instrument may not be as strong as that obtained using US data.

3.3 Data Sources

The data on individual and household characteristics and location characteristics were taken from the 2002 Annual Poverty Indicator Survey (APIS). The APIS is a rider survey to the July round of the quarterly Labor Force Survey (LFS) conducted by the National Statistics Office (NSO). The 2002 round is the third of the APIS series conducted by the NSO. The other two were conducted in 1998 and 1999. It provides basic demographic information on all members of the household as well as household amenities. Income and expenditure for the past 6 month period preceding the survey are also gathered. All monetary values such as wage and non-wage income are deflated using provincial consumer price indices compiled by the Price Division of the NSO. This is done to control for inter-provincial price variability. The unemployment rate is computed as the domain level average unemployment rate using APIS data.

3.4 Descriptive Statistics

Table 1 [ PDF 91.9KB | 5 pages ] provides the attendance rates by per capita income quintile and number of children of the total school-aged children (6-24) and also grouped into age groups corresponding to the elementary (6-12), secondary (13-16) and tertiary (17-24) levels. The disparity in school attendance proportion is not very clear in the total school age category but becomes more apparent as one goes up the education ladder. For instance, for the 6-24 age group, attendance proportion for the poorest is 74.2% while for the richest this is 76.8%. For the elementary level the corresponding attendance proportions are 89.6% for the poorest and 99.3% for the richest or about a10-percentage point difference. But for the tertiary level, the attendance proportion is 28.3% for the poorest but 54.7% for the richest or about a 26-percentage point difference.

By number of children, the enrollment proportion appears to increase up to about 4 children then starts to go down as one goes to households with more children although this is not true for the elementary school age group. The initial rise for the secondary and tertiary group has to allow for the fact that smaller households may contain both young families that do not have yet children in this age category and old families whose children may no longer be with their parents. With this consideration in mind, one observes that the decline in school participation is mild as one moves from small households to large households. This can be explained the well-known attitude of Filipino parents to always keep their children in school as long as possible. This is main explanation of the relative high attendance rates one finds in the Philippines given its per capita income. De Dios (1993) succinctly describe this Filipino trait in the following statement: “Makapagpatapos (to let a son/daughter graduate) is still the standard by which successful parenting is measured; the stereotype of good parents, bordering caricature, is still those who scrimp and save to send their children to school and to college.”

Table 2 [ PDF 91.9KB | 5 pages ] provides the descriptive statistics of the variables used in the estimation. The average number of children is about 3.5. The average number of years of education is slightly higher for mothers at 9.2 than for fathers at 9.0. This is not a surprising in the Philippine case. The proportion of barangays with an elementary school is about 76%, while those with a secondary school is substantially lower at 24%.

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Comment(s)

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1. grace quimpan
   (posted 26 August 2005 / 02:10:47 PM)
   
   Yes your right! but how will they will go to school if their parents has no job to afford their school finances. Some parents are working but the salary they get is not enough even for their food.