Methods

The primary source of data for the analysis is the 2003–04 Nepal Living Standards Survey (NLSS), a nationally representative multi-purpose household survey conducted by Nepal's Central Bureau of Statistics with assistance from the World Bank. Designed to assess living standards of the Nepalese population, the questionnaire includes questions regarding consumption, income, assets, housing, education, health, fertility, migration and employment, among other topics. The survey follows the Living Standards Measurement Survey (LSMS) methodology developed by the World Bank and applied in more than 50 developing countries. The LSMS data have been used extensively in previous studies to investigate the determinants of fertility and contraceptive use in developing countries (Bhushan & Oliver, Reference Bhushan, Oliver, Grosh and Glewwe2000). The 2001 Population Census of Nepal provided the basis for the survey's sampling frame. Further details on the sampling strategy and questionnaire can be found in World Bank (2006).

To test Caldwell's mass-schooling hypothesis, it is important to measure characteristics of the schooling environment when each woman was a child. Possible measures of the schooling environment include the net enrolment ratio, the gross enrolment ratio and the attendance rate. As is the case in many developing countries, there is limited availability of these data because schooling data have not been systematically collected in Nepal until recently. The NLSS administered community questionnaires to collect information on the presence of schools and the number of years these schools have been open, but using these data would be problematic since the NLSS was not designed to be representative at the district level. Two other possible sources of data are the National Population Census of Nepal and the Statistical Yearbook of Nepal, both published by the Government of Nepal. Neither of these sources contains systematic schooling information in every publication. However, the census conducted in 1971 included the total number of students in each district attending primary and secondary school that year (Government of Nepal, 1971), and the Statistical Yearbook of 2007 (Government of Nepal, 2007) contains the total number of students in each district attending primary school from 1994 to 2003 and the total number of students in each district attending secondary school from 1997 to 2003.

Each of the sources of schooling data, the Census and the Statistical Yearbook, presents advantages and limitations. The census has the advantage of providing information as far back as 1971. However, unfortunately, the 1981 census data do not include the number of current students (Government of Nepal, 1981). Data are available on the educational attainment of individuals, but this information is available only at the regional level, not the district level. The 1991 census data, on the other hand, do not include the number of students of all ages (Government of Nepal, 1991). Thus, the census data are clearly not comparable across years. The Statistical Yearbook, on the other hand, was more recently published, may be more reliable, but only presents information for more recent years.

Based on these data issues, two approaches are adopted. In the first, census data and mathematical interpolations are used to estimate the number of students attending primary and secondary schools in each of the years that these variables are missing, as described below. However, considering these data substantial limitations, one must be cautious about the results. Thus, in the second approach, the more concrete Statistical Yearbook data are used and the age of the mothers included in the estimations limited to 30 years or younger. As will be discussed later in this article, both procedures yield qualitatively similar results, providing robustness to the analysis.

Since population estimates are needed for public policy and managerial purposes and are made available on a regular but infrequent basis, such as censuses, which are conducted every 10 years, a wide variety of estimation techniques have been developed (Bryan, Reference Bryan, Siegel and Swanson2004). Intercensal estimates, which relate to estimates for a year in between two censuses, as in this paper's case, can be obtained either by mathematical interpolative techniques or by methods that require additional, sometimes called ‘symptomatic’, data (Bryan, Reference Bryan, Siegel and Swanson2004). One example of the latter is the Component Method, which uses data on birth, death and migration to estimate the population in between censuses. However, these kinds of data are often unavailable for geographical subdivisions, especially in undeveloped countries and for specific groups, such as the number of students. Besides, although evaluation studies show that mathematical methods are not very reliable for making post-censal population projections for geographical subdivisions, they are much more reliable when used to prepare intercensal estimates (Bryan, Reference Bryan, Siegel and Swanson2004). Thus, in this analysis, mathematical interpolation is used to impute school enrolment data for missing years.

Numerous mathematical interpolation methods are available, ranging from very simplistic to extremely complex ones. However, many of the most complex interpolative functions will generate estimates that are nearly identical to simple ones, minimizing the debate about which method to use (Bryan, Reference Bryan, Siegel and Swanson2004). Thus, the total number of students (of any age) enrolled in primary school in 1971 (from the Census) and in 1994 (from the Statistical Yearbook) is used to construct a district-level, annual series of estimates of the number of primary school students between these two dates using geometric interpolation. Specifically, the growth rate of primary students is computed using the formula:

$$r=[(number of primary students in 1994)/(number of primary students in 1971)]^{(1/23)}-1$$

, and, subsequently, the number of primary students in each year was estimated by:

$$(number of primary students in year t)=(number of primary students in 1971) (1+r)^{(t-1971)}, t=1972, 1973, \ldots , 1993$$

.

The same procedure is used to estimate the number of secondary students between 1971 and 1997. In addition, the censuses of 1971 and 2001 contain information on the age distribution of the population for each district and, also using geometric interpolation, a district-level annual series of population is constructed. Thus, the primary and secondary gross enrolment ratios could be estimated by dividing the number of individuals who are estimated to have been enrolled in school by the number of children who were of the corresponding school enrolment age.

This method presents significant limitations. First, since multiple sources are used, the Census and Statistical Yearbook data should be comparable. Second, as in any mathematical interpolation, some assumptions must be made as to the trend of the population change (Bryan, Reference Bryan, Siegel and Swanson2004). Specifically, it is assumed that the population groups are growing exponentially at a constant rate during the study period, which, in this case, includes more than two decades. On the other hand, despite these limitations, this uses the scarce data available in the best possible way. Moreover, it should be pointed out that the main goal was not to precisely estimate the number of students in each year of the study period but to construct a proxy for the school environment across districts during those years. Thus, we are interested in the variability of these variables, not in their exact levels.

Given these data limitations, in the second approach the 1994 primary gross enrolment ratio and the 1997 secondary gross enrolment ratio, computed directly from the Statistical Yearbook, are used as proxies for school environment during the women's childhoods and, as mentioned above, the analysis limited to women 30 years and younger. The survey data from the NLSS contain information on 2946 rural ever-married women of reproductive age (from 15 to 45 years). The analysis is restricted to ever-married women because never-married women were not asked about their fertility history. However, as described next, the data are used to reconstruct the women's yearly birth histories from 5 years before the interview to the interview date, a total of 6 years. Thus, the total number of observations is 17,672 (current observations plus five lags; however, there were four observations in which the data on the number of living children seemed to contradict the data on children's educational level, leaving 17,672 observations). The list of variables and descriptive statistics are presented in Table 1.

Table 1.

Descriptive statistics of study sample, Nepal 2003–04

^a SLC, school leaving certificate.

The goal of the analysis is to estimate the determinants of fertility. Specifically, Schellekens' (Reference Schellekens2009) methodology is followed, which entails reconstructing the women's birth history for 5 years. This is possible since the NLSS data contain retrospective data on each woman's fertility history, including the date of birth of each child. The paper's main dependent variable, y_it, is binary and equal to one in year t if woman i gave birth between years t−1 and t. This variable is constructed for t=0 (interview date), −1, −2, −3 and −4 (4 years before the interview). For instance, this variable is equal to one in year t=−4 if the women had a baby between the years t=−5 and t=−4. One advantage of using Schellekens' (Reference Schellekens2009) method is that it is possible to run parity-specific regressions. For instance, it is possible to estimate, at time t, the probability of a woman who had a certain number of children alive in year t−1 giving birth to another child between the years t−1 and t. This is especially relevant since, as discussed in the next section, the results show that education has a larger effect among women of higher parities.

Given that the main dependent variable is discrete, the logit model of probability is used throughout. Specifically, denoting the probability that woman i gives birth between the years t−1 and t by:

$$\pi_{it}=Prob(y_{it}=1|{\bi x}_{it})=F({\bi x}^\prime_{it}{\bi \beta})$$

, where x_it is the vector of control variables, β is the vector of parameters to be estimated and F(.) is the cumulative logistic distribution. It is convenient to re-write this equation in terms of the log-odds that y_it=1:

(1)$$log [\pi_{it}/(1-\pi_{it})]=F^{-1}(\pi_{it})=\beta_0+x^prime_{it}\beta_1$$

, where β ₀ is a constant term and β₁ is the vector of all parameter but that of the constant. This general specification is modified to accommodate different assumptions regarding the possible inclusion of random effects and the variance–covariance structure of the data.

Independent variables that potentially change over time are also included in the model. For instance, the woman's and child's level of educational attainment and ages were obtained by backdating information from the year of the survey. It was possible to determine past education with a considerate degree of certainly since the data contain information regarding the mothers' and the children's past and current school enrolment, even if the children do not currently live at home.

Because the study's main interest is to assess the effects of education on fertility, the proxies for the schooling environment at the time the woman was a child, as described earlier, are among the independent variables of interest. When including these variables in the regression, it is important to point out that migration within rural areas is common in Nepal. In fact, the results from the NLSS suggest that more than 70% of women in rural Nepal had ever migrated across districts. To address this issue, women are linked to their schooling environment when they were children through the use of information collected on past migration. Specifically, if the woman had migrated to her current district after she was 10 years old, the information from the district of her previous residence was used.

The woman's level of education is also controlled for and, following Axinn & Barber (Reference Axinn and Barber2001), a dummy variable measuring whether the woman has any child that has ever attended school is included. In line with Caldwell's mass-schooling hypothesis, a mother may have less incentive to have children when she has learned the costs associated with education. The data also present information on the current availability of schools. Specifically, dummy variables corresponding to the distance between the respondent's home and the closest primary school are included.

Other determinants of parity have been studied in the literature and, to investigate the effects of mass education, it is important to control for them in the estimations to avoid omitted variable bias. The first one is the socioeconomic status of the woman. One approach is to include proxies for expenditure and employment. Information on household expenditure (monetary and non-monetary) and on the respondent's job market participation is available in the present data, but only their current levels. Thus, the previous values of these variables must be proxied by their current ones. Facing a similar challenge, Schellekens (Reference Schellekens2009) only included women's educational level. However, since this study's main research question is about the effect of education on fertility net of all other effects, this approach would not be appropriate. Since the longer the time period the more problematic this procedure, the robustness of the results is tested by including only three lags.

The interdependencies between fertility and women's labour force participation and between fertility and income are well documented (Becker, Reference Becker and Becker1960, Reference Becker1965; Mincer, Reference Mincer1962; Willis, Reference Willis1973; Soares & Falcao, Reference Soares and Falcao2008; Matysiak, Reference Matysiak2009; Fang et al., Reference Fang, Eggleston, Rizzo and Zeckhauser2010). Thus Terza's et al. (Reference Terza, Basu and Rathouz2008) methodology was used to control for the endogeneity. While the traditional approach would be to use instrumental equations, Terza et al. (Reference Terza, Basu and Rathouz2008) showed that extending the techniques derived for linear models to non-linear ones, which are estimated in this analysis since the main dependent variable is discrete, produces inconsistent estimates. He proposed a simple and consistent alternative.

The first step is to estimate the reduced form of the equations of expenditure and job market participation. For identification purposes, the educational level of the parents of the respondent woman is included in both equations. While the expenditure equation is estimated by OLS, the job market participation is estimated using the logit model of probability. The Huber/White variance–covariance estimator is used in both regressions to control for the possibility of non-standard errors. The results are presented in the Appendix. Second, the estimates are used to predict the residuals in both models. Finally, the predicted residuals are included in the estimation of the main model of interest. The level of significance of the residuals' coefficients constitutes a test of the endogeneity of expenditure and job market participation.

The time series component of the data is likely to be temporally dependent. Thus, the number of years between the previous birth and t−1 is included as an independent variable for the cases where parity at t−1 is larger than zero. In addition, since fertility has fallen rapidly in Nepal, dummies for each time period are included. The existence of son preference, which is likely to be an important factor in Nepal, is also accounted for by controlling for the sex composition of previous children. Dummies for age groups, ethnicity, economic regions and ecologic zones are included to capture the effects of age and other unobserved factors.

Since women generally contribute more than one year to the analysis, it is important to investigate the possibility of unobserved heterogeneity between women before the results are interpreted. This possibility is examined by modifying equation (1) to:

(2)$$F^{-1}(\pi_{it}=\beta_0+x^\prime_{it}\beta_1+u_i$$

, where the intercept β ₀ is shared by all women while the random intercept u_i is specific to women i and follow a normal distribution with mean zero and variance σ²_u. The results are reported in Table 2, column 1. The estimated rho (intra-class correlation coefficient) is 1.22×10^–6 and the p-value of the likelihood test that rho is different from zero is 0.488. Thus, there is no evidence of unobserved heterogeneity between women that is not already accounted for by the covariates.

Table 2.

Logit model estimates of the probability of giving birth, Nepal 2003–04

***p<0.01; **p<0.05; *p<0.1.

A model is also estimated including a random intercept for each district (Table 2, column 2). The model being estimated is:

(3)$$F^{-1}(\pi _{ijt})=\gamma_0+{\bf x}^\prime_{it}{\bf \beta}_1+w_j$$

, where the intercept γ ₀ is shared by all districts and the random effect w_j∼N(0, σ ²_w) is specific to district j. In this case, the estimated rho is 0.0004 and the p-value of the likelihood test that rho is different from zero is 0.434. Thus, there is also no evidence of unobserved heterogeneity between communities. For completeness, a hybrid model containing both of the above-mentioned random intercepts is estimated, one for each women, one for each community, independently normally distributed and following the same distribution assumptions as before. The results, presented in column 3 of Table 2, also show no evidence of unobserved effects. The p-value of the likelihood test comparing the random effect model versus the logistic regression is 0.9864. Although this test is considered conservative (McLachlan & Basford, Reference McLachlan and Basford1988; Stram & Lee, Reference Stram and Lee1994), it is reported as a reference since the qualitative results do not change.

However, the random effects model assumes that the random components and the independent variables are uncorrelated. If this assumption is not satisfied, the estimations described above are invalid and there may be unobserved effects unaccounted for. Another possibility is to use the marginal model (also known as population-averaged panel-data model), which addresses the correlation structure explicitly. Specifically, a marginal model consists of two components: (i) a generalized linear model specifying the relationship between the response probability and the predictors; and (ii) a specification of the structure of the correlations between pairs of individuals in the same clusters, in this paper's case, districts and women (Steele, Reference Steele2009). The approach used by Miglioretti & Heagerty (Reference Miglioretti and Heagerty2007) is followed to estimate the marginal models by GEE and obtain confidence intervals that are still valid, even if there are multiple levels of clustering. Specifically, since cluster levels are nested (each women is in only one community), Miglioretti & Heagerty (Reference Miglioretti and Heagerty2007) show that the analysis requires only clustering on the top-level cluster and the use of the Huber/White variance estimation method (contact authors for details).