Son Preferences

A relation of particular interest to the present investigation is the one between son preferences and the total number of births a woman experiences in her lifetime. From a theoretical point of view Ben-Porath and Welch (1976) argue that the sex mix of children is something determining the quality of children within a quality/quantity framework à la Becker (1960). Past studies have documented the presence of son preferences in India (Bhalotra and Cochrane, 2010; Das Gupta et al., 2003) and – as mentioned in the previous section – these preferences appear to be particularly pronounced in UP. Furthermore and as mentioned above, descriptive evidence suggests these preferences to be present in the sample under consideration. The present analysis employs a strategy similar to the one used by Angrist and Evans (1998) to capture the effect of son preferences on fertility. The authors employ a dummy variable for the first two children having the same sex; the base case being one son and one daughter, irrespective of the birth order. In contrast to this, the present analysis defines three indicator variables. The first takes the value 1 if a couple has more surviving sons than daughters, the second if all children are male and the third if all are female. The base

category in the case at hand is that the couple has either an equal number of sons and daughters or more daughters than sons.

There are alternative measures of empirically modelling the sex mix of a woman’s offspring. An often employed strategy is to use the male to female ratio of offspring (Yount et al., 2000, for instance). This approach, however, has an important drawback. There are good reasons to believe the effect of the offspring’s sex mix to have a non-linear effect on fertility. Past studies have documented that parents are adverse to sex mixes consisting exclusively of one gender – either male or female (Angrist and Evans, 1998, for instance). Consequently, the effect of a child’s sex on fertility will depend on the sex mix of its older siblings. For example, the birth of a daughter is likely to decrease fertility if she is born into a household with an exclusively male offspring. By contrast, a female birth might increase fertility if the child is born into a household with an equal number of boys and girls. The use of three indicator variables enables the researcher to account for this particularity whereas a single ratio cannot. A further alternative is to employ indicator variables for all male and female sex mixes and a ratio of boys to girls for intermediate gender compositions. A drawback of this approach is that the values that the last variable takes depend on the parity of the woman. In other words: if the woman has two children, the ratio can take the value of ½, if she has three the values of 1/3 and 2/3, if she has four the values of ¼, ½ and ¾ and so on. The values of the indicator variable, by contrast, will be independent of the parity.

One way to determine which empirical strategy to adopt is to investigate how well the three alternatives fit the data. For this a dynamic probit is estimated three times. In the first run, son preferences are captured by the three indicator variables outlined above. In the second run, the same concept is measured via an index and in the third via

two indicator variables (one for an all male and one for an all female gender composition) and a ratio. The maximised log likelihood value of the former model is the largest14 – an indication that the three indicator variables produce a better fit compared to the two alternatives mentioned above.

A further alternative of modelling the sex mix of a woman’s offspring is to employ the number of sons alive at each parity. This strategy produces a better fit compared to the three indicator variables outlined above.15 The drawback of this approach, however, is that it does not allow the researcher to differentiate between the effect of, for instance, exclusively male or mixed male-female offspring. For this reason, this strategy is not pursued further.

An important issue in this context is child survival. The theoretical literature stresses that parents decide on the total number of surviving children (Becker, 1960; 1972). The death of one child will, therefore, prompt the birth of another. Similarly “excess children” will receive disproportionately little resources, which will decrease their survival chances. Mortality rates in India are not negligible. Since children belonging to mothers in the sample were born at different points in time, they were subject to varying survival rates. For the whole of India, the under-5 mortality rate in 1980 was 152 deaths per 1,000 live births. This figure decreases over time: in 1990, it was 117, in 2000, 91 and in 2005, 77 deaths per 1,000 live births.16 For UP, in particular, the DHS17 (2005/2006) reports under-5 and infant mortality rates of 96 and 73 deaths per 1,000 births respectively.18 To take account of this, the present analysis considers the sex mix

14_{The maximised log likelihood value for the model with the three indicator variables is -5,797.86, for the}

model with a single ratio -6,028.30 and with a ratio and two dummy variables for exclusively male and female offspring -5,851.16.

15_{The maximised log likelihood value for the model with the number of surviving sons is -5,712.92}

compared to -5,797.86 of the model with the three indicator variables.

16

Source: World Bank, Development Indicators, 2010. http://data.worldbank.org/

17 _{The DHS (2005/2006) is the overarching report encompassing the NFHS-3.}

of surviving children rather than the gender composition of previous births. Children, who died before the conception of the subsequent child, are, therefore, not considered here. The NFHS-3 provides information about the survival of all children born per woman. This was used to derive the total number of surviving children.

The following example might help to clarify the role child death plays in the construction of the sex mix variables. A woman with two sons gives birth to a girl. After this birth the individual will be in her fourth parity and must decide whether or not to opt for a further birth. In the absence of any deaths, the sex mix of this mother would be denoted as her having more boys than girls. Now suppose the girl dies. In this case, the woman is still regarded as in her fourth parity because she has given birth three times. The sex mix of her offspring, however, is reclassified to her having only two sons. The dead child, therefore, is disregarded for the construction of the three indicator variables employed in the present analysis. It is, however, counted as an extra parity.

As mentioned before, the interrelationships between child mortality and fertility behaviour are well documented (Maglat, 1990; Benefo and Schultz, 1992; for instance) and these relations should be accounted for when modelling lifetime fertility decisions. Consequently, it becomes important to control for such occurrences when modelling fertility decisions. The present analysis defines an indicator variable to capture the death of a child in a family. This variable takes the value of one at parity p if the child at parity p-1 died before the birth of the subsequent child. For example: if a woman’s third child (parity 4) died, the indicator variable for child death will take the value of one at parity 5 for the respective woman.

The percentages of the three explanatory variables of interest are given in Columns [2] to [4] of Table 1.2. The values for the indicator variable for the couple having more sons than daughters vary considerably from one birth to the other. For odd number of

children the values lie around 50%. For the first, third and fifth child the relevant values are 52%, 52% and 50%. By contrast, the percentages for an even number of surviving children lie around the one-third mark. For the second, fourth and sixth child, for instance, the numbers are 28%, 32% and 35%. The reason for this being that the odds of having the same amount of sons and daughters or more daughters than sons are obviously higher for even number of children. Notice that the variation in the values for this variable increases as the birth order increases. This is due to smaller sample sizes. In contrast to this, the percentages for all children being male and female decrease with the number of children. 52% of firstborn children are boys. The relevant percentages for 2, 3 and 4 children are 28%, 15% and 7%. The corresponding figures for an exclusively female offspring are 23%, 12% and 5%.

The fact that the sex of the first child is virtually randomly assigned has prompted many to give the coefficient on this variable – in the context of a labour supply framework, for instance – a causal interpretation. A possible reason for doubting the exogeneity of the sex of the first child is the presence of sex selective abortions, which give the parents a degree of control over the sex of the first child (Bhalotra and Cochrane, 2010). Foetal sex determination technology has caused such behaviour to become more and more frequent in India (Patel, 1989). It is possible to test for the presence of such practices by examining the sex ratio at birth. The natural sex ratio at birth is 105 boys per 100 girls.19

A possible way of testing for sex selective abortions is to investigate the gender composition of live births. Table 1.3. reports the sample percentages of all male and female births20 alongside the percentages predicted by the natural rate outlined above.21

19

For a general discussion on the natural sex ratio see Trivers and Willard (1973).

20_{Note: In contrast to the explanatory variables, these numbers reflect births irrespective of whether or}

At a first glance, the frequencies in the sample under consideration and the predicted rates are very similar. They rarely differ by more than one percentage point. The largest differences can be found for the first parity where the difference between the predicted and actual percentage is 1.1%. Furthermore, for no instance could the null hypothesis of equality of means be rejected. This can be seen as evidence against the presence of sex selective abortions for the sample under consideration. A possible reason for this is the following: women under consideration were born between 1956 and 1966. At the moment these individuals were giving birth, ultrasound facilities were not widespread and discovering the sex of the child before its birth was, consequently, difficult.

1.5.

Econometric Model

The empirical model analyses the probability of a woman experiencing a further birth at each parity within a dynamic Probit framework. This specification has previously been employed in a variety of different contexts. Previous applications comprise infant mortality (Arulampalam and Bhalotra, 2006), self-reported health status (Contoyannis et al., 2004), unemployment duration (Arulampalam et al., 2000) and unemployment and low pay dynamics (Stewart, 2007). This is – to our knowledge – the first application of this model to an investigation of the effect son preferences can have on fertility.

A woman’s unobserved propensity to give birth at parity j is modelled as y *ij = ′ s ij−1γ+xijβ+αi+uij (1.1)

Where s′_ij−1is a vector modelling the sex mix of surviving children, xij a vector of exogenous covariates,

β

and

γ

the associated coefficient vectors,

α

i the unobserved, mother-level heterogeneity and uij the parity specific error term. The uij are assumed to be independent of the

α

i, which in turn are assumed to be invariant across parities. In

21_{These sex compositions have been chosen since same sex offspring is likely to produce the strongest}

the present case j=1,…,K denotes the woman’s parity. Women with no children are denoted as j=1. As mentioned above, s′_ij−1consists of three binary indicators; the first takes the value 1 if the woman’s surviving offspring consists of more boys than girls. The second and third take the value of 1 if the surviving children the woman gave birth to are all male or female.

The vector xij comprises socio-economic factors pertaining to the woman and her partner. The first category comprises the caste of the woman and is measured by two indicator variables, which take the value 1 if the woman belongs to a scheduled caste or any other backward caste. The base category here is the woman belonging to one of the four castes. The woman’s religion is captured by a dummy variable for her being of Muslim faith (base category: Hindu). A woman’s education has been identified as a major determinant of fertility and is measured via an indicator variable for whether the woman has completed primary education. Finally, women are divided into various age cohorts, which are identified via indicator variables. Educational achievements vary considerably between men and women. Male education is on average higher and is measured via two dummy variables, one for the partner having achieved completed primary and one for secondary education. Relations between husband and wife can be captured by looking at the age difference between the spouses. For this, an indicator variable is defined, which takes the value 1 if husband and wife are five or more years apart. Furthermore, the indicator variable for the presence of child death outlined above is included as a covariate.

In this framework, every woman will contribute multiple observations to the analysis: one for every birth she experiences with the addition of one observation accounting for the first parity – in this state the woman has not experienced a birth. The resulting dataset is an unbalanced panel where every woman contributes a minimum of

one and a maximum of K observations, where K is the parity of the woman – the number of children she gave birth to plus 1. A woman with a total of three births in her lifetime, for instance, will contribute four observations. The advantage of this data structure is that it allows the sex mix of surviving children to vary from parity to parity. In practice, the value of this variable is allowed to change from one observation to the next. If the first two children born to a couple are male, the indicator variable for all children being male takes the value 1 for the first and second parity. If the couple’s subsequent child is female, however, the value of this indicator variable will take the value 0 for the third parity.

The dependent variable consists of a binary indicator taking the value 1 if the woman experienced a birth at parity j

yij =1[yij*>0] (1.2)

where yij* indicates the woman’s unobserved propensity to experience a birth at parity j. Consequently, every woman will have a series of 1s followed by a 0 once she stops childbearing at parity K. Note, the number of binary indicators per woman is K. In the example laid out above – a woman with three children – the vector for the dependent variable will have four elements. For the first three rows, the dependent variable will take the value of one, indicating that the couple decided to have a further child three times at parities one, two and three. In the last row, this variable will take the value zero, denoting that the parents decided to stop childbearing at parity three.

A problem for the present analysis is that ui1 is likely to be correlated with the mother-level unobserved heterogeneity,

α

i. In other words: for the first period the error term is likely to be correlated with unobserved characteristics of the mother. A possible

way to account for this is to condition decisions taken after the birth of the first child on the first birth. In the present case the equation for the first birth is specified as

1

1* i i i

i z u

y = ′

λ

+

θα

+ (1.3)

where zi is a vector of exogenous covariates, which contains the same elements as xij with the addition of a number of instruments for the first equation and

θ

the parameter on the mother-level unobserved heterogeneity. This coefficient captures the correlation between the initial coefficient and the subsequent equations. A test of

θ

=0, therefore, will be a test of the exogeneity of the first parity.

In the present case, the vector zi contains all the aforementioned variables with the addition of the woman’s age at marriage. This variable constitutes the instrument for the initial conditions equation and is assumed to influence a woman’s first birth. This influence might stem from biological as well as from social factors. A woman’s age at marriage often coincides with the beginning of her reproductive life. From a biological perspective, the older the woman is, the less fertile she is likely to be. An advanced age at marriage, therefore, should decrease the chances of a woman having any offspring. From a social perspective, the age at which a woman marries might determine her say in the household as women, who marry younger, may have less bargaining power. As a consequence, such individuals will be less able to influence decisions regarding childbearing and the main decision-maker on whether or not the couple should have a child will be the husband. Since men are less likely to internalise the full costs of childbirth they are more likely to wish to become a parent. Hence both biological and social factors point towards a negative relationship between a relatively advanced age at marriage and the probability of the first birth.

An alternative instrument for the initial conditions equation is the age difference between the spouses. The assumption behind this exclusion restriction is similar to the one behind the woman’s age at marriage. Women, who are considerably younger than their husbands, are assumed to have little say within the household. The argument for this to be the case is strong and has been employed in the literature on female autonomy (Abadian, 1996, for instance). Nonetheless, the woman’s age at marriage appears to be a preferable instrument. This variable – like the age difference between the spouses – is likely to affect a woman’s bargaining power within the household. In addition to this concept, however, the age at marriage also captured biological concerns regarding the woman’s fertility – older women are considerably less fertile. The fact that the woman’s age at marriage captures biological as well as sociological factors and the alternative

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