Methodology, the Instrument and Data

3.1 Methodology

To determine the impact of the number of children in the household on the labor supply and earnings of parents we estimate these relationships by recognizing the endogeneity of the number of children. The importance of recognizing the endogeneity of children in the labor supply and earnings equation of parents has been highlighted in the previous section. We follow Angrist and Evans (1998) in assuming a balanced sex-mix and using same sex of the first two-births as the instrument. The validity of this instrument for the number of children is explained after a discussion of the empirical specification.

While it would have been desirable to include labor hours, the data that we use does not have this information. For labor supply, therefore, we only estimate an equation for the labor force participation of parents.

Labor Force Participation of Parents. The labor force participation rate equation we estimate is the following model:

(1) l = α₀ + α₁w₁ + α₂y + α₃n + Xα₄ + ε
(2) n = β₀ + β₁z + Xβ₃ + μ

Equation (1) is a typical labor supply equation where l is the labor force participation of the parent, w is wage, Y is other (non-wage) income received by the household, n is the number of children, and X is the set of control variables and e the disturbance term. The vector X would usually include age and education.

The estimation methodology is as follows. Since (1) is a dichotomous choice model, we will use a probit form to estimate the model. But the endogeneity of n will result in a biased estimate. We therefore test for the endogeneity of n using the suggestions in Rivers and Vuong (1988). They proposed a two-stage probit where the estimated error from the first-stage regression is added as an explanatory variable in the second-stage probit regression to obtain a consistent estimate. The pointed out that the coefficient of the error term will constitute a test for the endogeneity of n. Rivers and Vuong (1988) indicated that adjustment is needed for the variance-covariance matrix in the second stage probit to get asymptotically correct errors. Bollen, Guilkey and Mroz (1995) however, established through Monte Carlo simulations that results are not readily affected by using the asymptotically correct standard errors². Another method is the use of efficient³ full-information maximum likelihood (FIML) estimation of the two equations, directly testing the significance of the correlation between the error terms in the number of children equation and the labor force participation equation. Both of these methods are used to establish the endogeneity of the number of children variable in the labor force participation equation. If n is found to be endogenous we will use the estimation that will give us more a precise (higher significance) estimate for the variable of interest - the number of children, otherwise, we use the simple probit results.

Earnings of Parents. Similarly, to determine the impact of the number of children on their parents’ wage earnings we estimate an augmented Mincerian equation of the following form

(3) ln w = α₀ + α₁age + α₂age² + α₃educ + α₄n + Xα + ε
(4) n = β₀ + β₁z + Xβ₃ + μ

The estimation used the standard Mincerian equation for estimating the earnings of parents with the number of children and location dummies added. This is essentially adopted from Angrist and Evans (1998). We instrument for n using the sex of the firsttwo births as explained in the next section. In addition, w may not be observed for those who did not work requiring adjustment for the censoring.

The estimation methodology is similar to the one described above except that the second stage regression in this model is censored. Since the earnings will be zero both for the non-wage workers and the non-workers, Tobit estimation is used to take account of the censoring in the earnings equation. We test for the endogeneity of n in the earnings equation. Smith and Blundell (1986) suggested a two-stage Tobit to determine the endogeneity of the variable in the structure described above. Specifically, the estimated error term from the first-stage regression is added as a variable in the earnings equation to arrive at a consistent estimate. A significant coefficient for the estimated error term implies endogeneity of n. If the n is found to be endogenous, we use the results of the two-stage Tobit estimation. Otherwise, we use the simple Tobit estimation results.

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 128.2KB | 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 128.2KB | 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 2 [ PDF 128.2KB | 12 page ] shows the proportion of mothers and fathers working by per capita income quintile and by number of children. The proportion of mothers working shows that more mothers in higher income households work both for all types of work and for paid work. The opposite appears to be true for fathers. One way to explain the difference is that richer households are able to pay for house help freeing them to participate in the labor market and still contribute to household income. This may not be the case for mothers from poorer households. There is no clear explanation for the lower labor force participation of fathers from richer household, except perhaps that they may be earning more from other sources. In terms of number of children, as expected, mothers with smaller number of children work more. The same is true for fathers. It is also noteworthy that unpaid work (the difference between all types of work and paid work) is about 20 percent for mothers. Table 3 [ PDF 128.2KB | 12 page ] 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 than fathers, at 9.2 versus 9.0, respectively. This is not a surprising phenomenon in the case of the Philippines. About 50% of the households have children below usual primary school age (6 years).

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