Abstract

Since the advent of prenatal sex-determination technologies in the mid-1980s, India has experienced an increasingly male-biased sex ratio at birth, presumably from sex-selective abortions. Abortions lengthen birth intervals, but we know little about how birth spacing has changed or the effects of these changes. I show that, although the overall length of birth intervals increased from 1970 to the mid-2010s, well-educated women with no sons had the most substantial lengthening, as well as the most male-biased sex ratios. Furthermore, most of these changes took place immediately after the introduction of prenatal sex-determination technologies. Consequently, some women without sons now have longer birth intervals than those with sons, reversing India's traditional spacing pattern. Women with low education continue short birth spacing when they have no sons, with only limited evidence of male-biased sex ratios. Because of the rapid lengthening of birth intervals, period fertility rates substantially overestimated how fast cohort fertility fell. Moreover, predicted cohort fertility is still 10%–20% above the period fertility rate. If the lengthening of birth intervals arises from repeated abortions, the associated short pregnancy spacing may counteract any positive effects of longer birth spacing. There is, however, no evidence of this effect on infant mortality. Judging from sex ratios, sex-selective abortion use is not declining.

Introduction

India has experienced many positive changes over the past four decades: the economy has grown substantially, real wages have more than doubled, educational attainment has increased for males and females, and the total fertility rate (TFR) has fallen to 2.2 children (Bosworth and Collins 2008; Dharmalingam et al. 2014; International Institute for Population Sciences and ICF 2017; Klasen and Pieters 2015). However, during this period, India also witnessed the advent of sex selection—the selective abortion of female fetuses based on prenatal sex determination—with the introduction of ultrasound in the mid-1980s. In combination with a strong, continued preference for sons, the result was a dramatic increase in the male–female ratio at birth (Arnold et al. 2002; Das Gupta and Bhat 1997; Guilmoto 2012; Jayachandran 2017; Pörtner 2015; Retherford and Roy 2003).

The main question I address here is how birth spacing responded to these changes, especially the spread of sex selection. The motivation is twofold. First, past research has failed to appreciate that the use of sex-selective abortions could substantially increase birth spacing, given that it takes six months or more after an abortion to reach the same point in the next pregnancy. Second, other major societal changes, such as women's greater educational attainment, higher household income, and a low and declining female labor force participation, all likely influence birth spacing. The combination of the apparent increasing use of sex selection and societal changes can significantly impact birth spacing, but we know little about how much.

Studying birth spacing contributes to our understanding of fertility decisions, but equally important, birth spacing also affects the reliability of our fertility measures and may affect mortality. Therefore, I address two additional questions. First, did changes in birth spacing lead us to overestimate the decline in cohort fertility? With longer spacing, mothers will be older at each parity, and this tempo effect makes period fertility measures, such as TFR, downward-biased estimates of cohort fertility (Bongaarts 1999; Hotz et al. 1997; Ní Bhrolcháin 2011). Hence, a rapidly expanding use of sex selection could make the TFR—our most used fertility measure—fall substantially faster than cohort fertility. In this case, households' fertility may be higher than generally accepted.

Second, what is the relationship between infant mortality and the changes in birth spacing and sex selection? In India, birth intervals have traditionally been short for women with no or few sons, contributing to girls' higher mortality risk (Bhalotra and van Soest 2008; Jayachandran and Kuziemko 2011; Jayachandran and Pande 2017; Maitra and Pal 2008; Whitworth and Stephenson 2002). Longer birth spacing may, therefore, reduce mortality through, for example, diminished sibling competition (Conde-Agudelo et al. 2012; Molitoris et al. 2019). However, if the spacing between births lengthens because of sex-selective abortions, the spacing between pregnancies may still be very short. Short pregnancy spacing may lead to worse child outcomes because of maternal nutritional depletion and insufficient time to recover from the previous pregnancy. Hence, children born after a long birth interval punctuated by multiple abortions may not see the same benefits as children born after a long interval not punctuated by abortions.

To investigate how birth spacing has changed, I use a competing risk hazard model with two exit states: the birth of a girl or the birth of a boy. I apply the model to Hindu women's birth histories between 1972 and 2016 using data from the four National Family and Health Surveys (NFHS). The primary outcomes I examine are the 25th, 50th, and 75th percentile birth interval durations; the sex ratio at birth; and the likelihood of giving birth. I estimate the model across four periods to capture the changing access and legality of sex selection. The key explanatory variables are maternal education, the sex of previous children, and the area of residence.

The empirical model allows me to predict cohort fertility. To examine whether tempo effects bias our standard fertility measures, I compare the predicted cohort fertility with fertility calculated from age-specific fertility rates. I also use the same data to study how infant mortality changed with birth spacing and the increasing use of sex selection. The key explanatory variables remain the same, except for the addition of birth spacing and the sex of the index child.

There are three main results. First, birth intervals lengthened over the four decades, with the lengthening being longer the higher the parity, the more educated the woman, and the higher the percentile of the birth interval duration. Well-educated women with no sons had the most substantial lengthening of birth intervals and the most male-biased sex ratios—both likely arising from sex-selective abortions. Consequently, some women with no sons now have longer birth intervals than those with sons, reversing India's traditional spacing pattern. Women with low education continued to have short spacing when they have no sons, with only limited evidence of male-biased sex ratios. The likelihood of a very short birth interval changed little across most groups.

Second, the period fertility rate substantially overestimated how fast cohort fertility fell in the 1990s and early 2000s as spacing initially increased. Although the two have lately been converging, the predicted cohort fertility is still 10%–20% higher than the period fertility rate. Furthermore, predicted cohort fertility is still at or above replacement level for all but the most highly educated urban women.

Finally, infant mortality has declined substantially over time for all groups, but fastest for the less educated, who are now close to the level of the most highly educated women. However, mortality is still inversely related to education level, especially for very short birth intervals. There is no evidence that repeated sex-selective abortions are associated with higher mortality for the next child born.

Conceptual Framework

To establish a conceptual framework for understanding changes in birth spacing, I first introduce three potential explanations that link fertility and birth spacing decisions: economic conditions, investment in children, and son preference (Casterline and Odden 2016; Pörtner 2018). I then discuss why female education, area of residence, and sex composition are the principal factors in the empirical analyses and tie them to the three explanations.

The improvements in economic conditions—especially the doubling of real wages—are likely to affect fertility, although the direction is ambiguous; empirically, higher female wages reduce fertility, whereas higher male wages increase fertility (Hotz et al. 1997; Schultz 1997). According to economic theory, the substitution and income effects' relative strengths determine the effect of higher wages on fertility. The substitution effect captures that when wages increase, time becomes more expensive, leading people to work more and spend less time on non-wage-earning activities, such as children or leisure. The income effect captures that higher wages increase the available income, which leads people to spend more time on time-intensive activities and less time working. Because women spend substantially more time than men on child-rearing, the substitution effect dominates for women, while the income effect dominates for men. Higher female wages may also shorten birth spacing if having children requires mothers to curtail their economic activities. Shortening birth spacing allows parents to take advantage of economies of scale in child-rearing—for example, looking after two children requires less than double the time needed for one child (Hotz et al. 1997; Vijverberg 1982).

With higher returns to education and lower offspring mortality, parents are likely to reduce fertility and invest more in each child (Rosenzweig and Schultz 1982; Wolpin 1997). The higher return to education means a stronger incentive to invest in children's education, thereby increasing the cost of having children and lowering fertility. With lower expected mortality, parents need fewer births to reach the desired number of surviving children, which in turn allows parents to invest more in each child.

An increased desire to invest in children may also lengthen birth spacing. The clearest example of a positive effect of longer spacing is for health: very short spacing—approximately 24 months or less—leads to worse child health and mortality outcomes (Conde-Agudelo et al. 2012; Whitworth and Stephenson 2002). Whether longer spacing also improves human capital outcomes is more speculative, with mixed evidence for more developed countries and no evidence for less developed countries (Barclay and Kolk 2017; Buckles and Munnich 2012; Pettersson-Lidbom and Thoursie 2009; Powell and Steelman 1993; Zajonc 1976).

Stronger son preference has traditionally been associated with shorter spacing and worse health outcomes for daughters when there are no sons in the household (Jayachandran and Kuziemko 2011; Whitworth and Stephenson 2002). Although son preference increases average fertility only marginally, differential stopping behavior means that girls tend to end up in larger families, resulting in fewer resources per child (Barcellos et al. 2014; Basu and De Jong 2010; Clark 2000; Repetto 1972). However, with the advent of sex selection, stronger son preference may lead to longer spacing because each sex-selective abortion adds 6–12 months to the length of the birth interval. After an abortion, a woman's uterus typically needs at least two menstrual cycles—approximately two months—to recover or the subsequent risk of spontaneous abortion increases substantially (Zhou et al. 2000). Once conception can be attempted, the waiting time to conception is likely 1–6 months. Finally, sex-determination tests are reliable only from three months of gestation. Hence, it takes at least six months before the couple is at the same point in the next pregnancy as they were in the prior pregnancy when they decided to abort.

The closest available proxies in the data for capturing the explanations linking fertility and birth spacing are the sex composition of previous children, mothers' education, and the area of residence. The remainder of this section discusses how these three variables fit into the explanations and the predicted effects.

Sex composition proxies for son preference and the use of sex selection, which are both unobserved.1 In the absence of sons, sex selection appears to increase with lower desired fertility and higher parity (Jayachandran 2017; Pörtner 2015). Thus, for a given parity, birth intervals should lengthen substantially over time for women with no sons, for women with lower desired fertility, and for those with better access to sex selection.

Both higher female education and urbanization are associated with lower fertility and increased use of sex selection—and, therefore, likely also with changes in birth spacing (Das Gupta and Bhat 1997; Pörtner 2015; Retherford and Roy 2003). The lower fertility results from the higher cost of children and lower child mortality risk.2 The greater use of sex selection comes partly from the lower fertility and partly from higher income and better access to health care facilities. Furthermore, female education and urbanization are representative of the tremendous changes being observed in India. Figure 1 illustrates the substantial increase in female education in the rural and urban populations, and the urban proportion of the population nearly doubled from 18% in 1960 to 35% in 2019 (United Nations 2019).

Even though the higher potential wages associated with increased education should shorten birth spacing and lower fertility, the low and declining female labor force participation suggests that there is little economic incentive to space children closer together. Even as women's education increased, their labor force participation stagnated or decreased, and it is now one of the lowest outside the Middle East (Afridi et al. 2018; Bhargava 2018; Chatterjee et al. 2018; Fletcher et al. 2017; Klasen and Pieters 2015). The decline in female labor force participation appears to be driven by a combination of a relatively small expansion in the sectors in which women work and the income effect from rapidly increasing male wages and education dominating the substitution effect from higher female wages (Bhargava 2018; Klasen and Pieters 2015). The income effect can dominate because not only do men have a higher average level of education than women, they are also paid more for a given level of education, and the returns to education increase with education in India (Agrawal 2011). Hence, a given increase in male education will result in a larger increase in income than a similar increase in female education.

Even with decreasing female labor force participation, we may still observe an association between higher maternal education and lower fertility and increased use of sex selection, provided that higher schooling of mothers enhances their children's human capital, as suggested by Behrman et al. (1999). As argued above, a higher return to education leads to lower fertility and more investment in each child. Therefore, in a situation where the labor market return to education increases proportionally more for males than for females, the households have an incentive to lower fertility and increase sex selection, and at the same time invest more in boys. One of these potential investments is a more educated mother. That is, households desire better educated mothers, not for their higher potential income but rather for their ability to produce better educated sons. The implication is that the usual policy recommendation of increased female education may not affect the use of sex selection unless there is a concurrent increase in the relative return to female education in the labor market.

Finally, the process of “Sanskritization” implies that as lower-caste females gain access to education, they adopt higher-caste norms, such as stronger son preference and a retraction from the formal labor market (Srinivas 1956). The declining female labor force participation suggests that this process is still operating (Abraham 2013; Chatterjee et al. 2018). Thus, we are unlikely to see substantial changes in how women with a given education level behave even as access to education expands.

In summary, with substantial increases in husbands' income and declining female labor force participation, I expect to see longer birth spacing over time, independent of education levels. Furthermore, birth spacing likely increases the most among the more highly educated, as their household income increases the most and because of their presumptive use of sex selection. “Sanskritization” implies that the changing composition of more highly educated women will not substantially alter their use of sex selection.

Methods

Estimation Strategy

The empirical analysis has three parts. First, I document the changes in birth spacing over time and how the introduction of sex selection influenced birth spacing. Second, I compare period fertility estimates with predicted cohort fertility using the birth spacing estimates. Finally, I examine how birth intervals affected infant mortality and whether the apparent increase in sex selection influenced mortality.

In this setting, there are two problems with using the standard approach in the birth spacing literature, which is a proportional hazard model with the birth of a child as the single exit.3 First and foremost, the use of sex selection means that the sex of the next child is no longer random and that the birth intervals ending with the birth of a boy will, on average, be longer than the birth intervals ending with the birth of a girl. I use a competing risk setup that captures both the nonrandomness of the birth outcome and the differential spacing.4

Second, even without sex selection, it is unlikely that such characteristics as previous births' sex composition have the same effects throughout the entire birth interval. The proportional hazard model requires that an individual's hazard is a fixed proportion of the hazard for any other individual. Nonconstant effects violate that assumption and, thus, the results from a proportional hazard model would be biased. The proportionality assumption is especially problematic for higher order birth intervals because there are substantial differences across groups in the likelihood of progressing to the next birth and how soon couples want their next child if they are going to have one (Bhalotra and van Soest 2008; Whitworth and Stephenson 2002). The introduction of prenatal sex determination exacerbates any bias from the proportionality assumption for two reasons. First, different groups have different levels of sex-selective abortion use and, thereby, birth spacing. Second, within a birth interval, a household's use of sex selection may vary, and that means that the effects of covariates vary as well. Therefore, I use a nonproportional hazard specification that allows the shape of the hazard function to vary across groups. Furthermore, the combination of a nonproportional specification and a flexible baseline hazard mitigates the potential effects of unobserved heterogeneity (Dolton and von der Klaauw 1995).

The model is a discrete-time, nonproportional, competing risk hazard model with two exit states: either a boy or a girl is born. The unit of analysis is a spell—the period from one parity birth to the following birth or censoring. For estimation purposes, the spells begin nine months after the previous birth because this is the earliest we should expect to observe a new birth. Censoring can happen for three reasons: the survey takes place, sterilization of the woman or her husband, or because there are too few births for the method to work.

For each woman, i = 1, . . . , n, the starting point for a spell is time t = 1, and the spell continues until time ti, when either a birth or censoring of the spell occurs. The time of censoring is assumed to be independent of the hazard rate, as is standard in the literature. The two exit states are the birth of a boy, j = 1, or a girl, j = 2. The discrete-time hazard rate hijt is
hijt=exp(Dj(t)+αjtZit+βjXi)1+l=12exp(Dl(t)+αltZit+βlXi) for j=1,2,
(1)
where Dj(t) is the piecewise constant baseline hazard for outcome j, captured by dummy variables and the associated coefficients,
Dj(t)=γj1D1+γj2D2+. . .+γjTDT,
(2)

with Dm = 1 if t = m and zero otherwise. This approach to modeling the baseline hazard is flexible and does not restrict the baseline hazard unnecessarily. Z is the nonproportional part, which includes the interactions between Dj(t) and a set of explanatory variables, as well as the interactions of those variables. The remaining explanatory variables, X, enter proportionally.

Equation (1) is equivalent to the logistic hazard model and has the same likelihood function as the multinomial logit model (Allison 1982; Jenkins 1995). Hence, by splitting spells into smaller intervals—here equal to three months—and treating them as observations, I can estimate the model using a standard multinomial logit model. I use the model to predict birth interval lengths, parity progression probabilities, and the sex ratio rather than present coefficients because the interpretation of competing risk model coefficients is challenging (Thomas 1996). The predicted parity progression probability is the likelihood of giving birth by the imposed censoring based on standard survival curve calculations averaged across all women in a given sample.

For birth interval lengths, I estimate a set of percentile durations. I first calculate for each woman when there is a given percentage chance that she will have a given birth, conditional on the probability of giving birth in the spell. For example, with an 80% parity progression probability, the median birth interval is the predicted number of months before a woman passes the 60% mark on her survival curve. I then add nine months to account for the start of the spell. The reported statistic is the average of a given percentile interval across all women in a sample using the individual progression probabilities as weights.

The predicted sex ratio is the weighted average of individual predicted sex ratios, using parity progression probabilities as weights. To find the individual sex ratio, I estimate the percentage of births that are boys at t, conditional on not having had a child before t. Weighting the percentage of boys with the likelihood of exiting the spell with a birth across all t gives the predicted percentage of boys over the entire spell for an individual.5

Data

The data come from the four rounds of the NFHS collected in 1992–1993, 1998–1999, 2005– 2006, and 2015–2016. The survey samples are large, covering 89,777; 90,303; 124,385; and 699,686 women, respectively. NFHS-1 and NFHS-2 surveyed only ever-married women, while the two later surveys included never-married women.

I first discuss sample restrictions and their motivations, and then introduce the potential issue of underreporting of female births and the imposed censoring of birth intervals. Next, I discuss how the analyses are split by periods to capture the introduction and changing legality of prenatal sex determination. Finally, I introduce the explanatory variables, split by whether they enter as proportional or nonproportional variables.

I focus on three spells, starting from the first birth and ending with the fourth birth. I exclude the interval from marriage to the first birth because many are imputed, as well as the higher order intervals because few women had five or more births, especially among the more highly educated.

I restrict the sample to Hindus for two reasons. First, Hindus are the largest population group—about 80% of India's population. Second, the literature shows that son preference and sex selection vary substantially between Hindus and the second-largest group, Muslims. Combining them and assuming that the baseline hazard is the same would lead to biased results. Because of space constraints and the relatively small number of observations once split by education and periods, I do not provide separate results for Muslims or any remaining groups, such as Sikhs, Jains, and Christians.

Finally, I exclude visitors and women in any of the following categories: never-married, no gauna (marriage consummation ceremony) yet, married more than once, divorced, not living with husband, inconsistent age at marriage, or missing education information. The same goes for women who reported either at least one multiple birth, giving birth before age 12, a birth before marriage, or an interval between births of less than nine months.

In addition to the large number of women surveyed and the long period covered, a significant benefit of the NFHS over other surveys is that enumerators pay careful attention to the spacing between births and probe for “missed” births. For India, the main concern is the underreporting of deceased children, especially a systematic recall error in which respondents' likelihood of reporting the birth of a deceased child depends on the sex of that child. Unreported deceased children inflate the length of birth intervals and, with declining mortality, make changes over time appear too small. In the online appendix, I provide a detailed analysis of systematic recall error, which shows that recall error depends heavily on how long ago a woman was married. Consequently, I drop women who were married for 22 years or more.6

To ensure that there are enough births for the method to work, I censor spells at 96 months (eight years) after a woman can first give birth, equivalent to 105 months after the birth of the prior child. Less than 1% of observed births occur after the cutoff. The final sample consists of 395,695 women, with 815,360 births of parity one through four.

Direct information on sex selection is not available, so I compare periods based on the changes in access and legality of prenatal sex determination in India. Abortion has been legal in India since 1971. Reports of sex determination appeared around 1982–1983, and the number of clinics offering sex selection quickly increased (Bhat 2006; Grover and Vijayvergiya 2006; Sudha and Rajan 1999). In 1994, the Prenatal Diagnostic Techniques Act made determining and communicating the sex of a fetus illegal.7 Although the use of sex selection continued to increase even after 1994, we may have passed a turning point in its use in the mid-2000s (Bongaarts 2013; Das Gupta et al. 2009; Diamond-Smith and Bishai 2015; Kumar and Sathyanarayana 2012).

I examine four periods: 1972–1984, 1985–1994, 1995–2004, and 2005–2016. The first covers the period before sex selection became available, and the second covers from when sex selection became available until the Prenatal Diagnostic Techniques Act. I have split the period from 1995 to 2016 to enable me to determine whether there was support for the literature's hypothesized reversal in child sex ratios and son preference in India. The allocation of spells into periods is determined by when conception—and, therefore, decisions on sex selection—can begin. Hence, some spells cover two periods, which may bias downward the differences between the periods. Most sterilizations take place soon after giving birth. These spells, therefore, do not show up in the samples used. Furthermore, sterilization depends strongly on prior children's sex composition: the fewer boys, the lower the probability of sterilization. The effect is to bias downward the differences in parity progression probabilities.

I divide the explanatory variables into two groups—nonproportional and proportional. The first group consists of characteristics shown in the literature to affect the spacing choice and the use of sex selection: mother's education, sex composition of previous children, and area of residence. To minimize any potential bias from including proportional variables, I estimate separate models for each birth interval, education group, and period combination, rather than including education as a variable. Education levels are divided into no education, 1–7 years, 8–11 years, and 12 and more years; the latter two correspond to having completed primary and secondary school, respectively.8 To ensure that the results are comparable with the literature on fertility and mortality in India, I follow the NFHS reports, except that I combine the less than five years and 5–7 years of schooling completed and the 8–9 and 10–11 years of schooling completed to ensure sufficient cell sizes. Finally, I capture sex composition with dummy variables for the possible combinations, ignoring the ordering of births.9 Area of residence is a dummy variable for living in an urban area.

The second group of variables consists of those expected to have an approximately proportional effect on the hazard. These include the mother's age when the spell begins, the household's land ownership, and whether the household belongs to a scheduled tribe or caste. Descriptive statistics are presented in the online appendix.

Results

How Birth Spacing Changed

The first question I address is how birth spacing responded to the significant changes in India. I begin with a broad outline of how parity progression probabilities and sex ratios have changed over time and by group, and then use these findings to separately discuss the changes in birth spacing for women who do not appear to use sex selection and for those who do.

Figures 27 present the 25th, 50th, and 75th percentile birth interval durations in months, the sex ratio, and the probability of having a next birth (parity progression) for each spell by education level and area of residence.10 The sex ratio graphs also show the natural sex ratio, approximately 51.2% boys (Jacobsen et al. 1999; Pörtner 2015). The underlying values with bootstrapped standard errors and tests for statistically significant differences across sex compositions are available in the online appendix.

The parity progression and sex ratio graphs show two broad trends. First, in line with the falling TFR, the likelihood of a next birth decreased over time, falling more rapidly the more educated the mother and the higher the parity. Within a given spell and period, parity progressions were lower in urban areas than in rural ones, if at least one son was present, and the more educated the mother.

Second, sex ratios of next births became more male-dominated for women with no prior sons, indicating the spread of sex selection. The percentage of boys increased more quickly the higher the education and parity. There were no clear trends for the other sex compositions. Within a given spell and period combination and in the absence of a son, sex ratios were higher with increased mother's education and parity. Sex ratios were also higher in urban areas than in rural ones. Some women with one son also showed an unnaturally high percentage of boys, although the decline in fertility makes these estimates noisy.

When Sex Selection Is Less Used

To separate the effects of the introduction of sex selection and the other changes in India, I first discuss how the lengths of birth intervals have changed in situations in which, based on sex ratios, there appears to be less sex selection. The group broadly covers women with no education, regardless of their children's sex composition, and women with any education who already have one or two sons.

Despite the apparent lower level of sex selection, son preference was still evident with the shortest spacing when women had only daughters. Notably, for those who appeared the least likely to use sex selection, (i.e., rural women with no education), birth spacing was almost uniformly significantly longer when at least one son was present than if no son was present (see Figure 2). Furthermore, the difference in birth interval length across sex compositions grew over time as spacing when sons were present became longer.

A remarkably high proportion of birth intervals were still very short. For all but the most educated women, 25% or more had their second and third child within 24 months of the previous birth. These intervals were substantially below the 24 months between pregnancies that the WHO recommends. Even with the more substantial lengthening of birth intervals for higher parities, the 25th percentile duration was still around 24 months for the fourth spell for women with less than eight years of education (see Figure 3 and Figure 4). Median birth interval lengths also increased relatively little, only 3–6 months over the four decades, compared with around 3.5 months per decade in other countries with declining fertility (Casterline and Odden 2016; Rutstein 2011).11 The result was that most of the median birth interval durations were still at 36 months or less, with the shortest being only 29 months.

Birth intervals appeared to lengthen the most for women who were the least likely to work. For example, from lowest to highest education, the average duration of third-spell birth intervals for urban women with one son and one daughter increased by 2.7, 3.4, 5.8, and 1.8 months over the four decades.12 Hence, women with the lowest labor force participation—those with 8–11 years of education—also saw the largest increases in average spacing, possibly driven by the substantial improvement in household income for this group from economic growth (see Figure 5 and Figure 6).

The most substantial changes occurred in the 75th percentile birth interval durations, where the more the parity progression probabilities declined, the more the birth interval lengthened. For example, the probability of a fourth birth for urban women with 8–11 years of education and two sons and one daughter declined by almost 40 percentage points as the 75th percentile birth interval length increased by 22 months (see Figure 6). In comparison, for rural women with no education and a boy as their first child, the probability of a third birth declined by fewer than six percentage points, while the birth interval increased by only slightly more than two months (see Figure 2).

These results are in line with research showing that falling fertility is associated with a lengthening of particularly the longer birth intervals, although why is still an unresolved question (Casterline and Odden 2016). The case of the most highly educated urban women who already had a son is an exception to this trend: the probability of a third birth declined rapidly, but the birth interval lengths changed little (see Figure 7). These women had access to modern contraceptives and were more adept at using traditional contraceptive methods (Rosenzweig and Schultz 1989). Hence, it is possible that the lengthening of birth intervals with falling fertility seen in prior research arose because unintended births became a relatively larger proportion of the total number of births for a given parity, and such births can occur at any time.

Sex Selection and Birth Spacing

A clear illustration of how the combination of son preference and the introduction of sex selection affected birth spacing comes from the third spell for the most highly educated urban women. With two daughters and no sons, almost 80% of the third births were boys, and the 75th percentile birth interval length was close to 70 months, an increase of almost 21 months over the four decades (see Figure 7). This interval went from being statistically significantly shorter than the intervals with at least one son to being a statistically significant 13 months longer. Even more striking, most of the change took place right at the introduction of sex selection. The 75th percentile birth interval with two daughters increased from 48 months to 64 months in a decade, while the other sex compositions showed a slight decrease from around 55 months to 54 months. These birth spacing changes may even understate the impact because this particular group appeared to have had access to sex selection even before it became widespread, as shown by the unequal sex ratio for the 1972–1984 period for women with two daughters. The apparent use of sex selection also affected the 25th and median birth interval lengths. For the most highly educated urban women with two daughters, the 25th percentile birth interval length increased by six months, or 23%, while the median percentile birth interval length increased by 15 months (43%).

Not surprisingly, given these changes, the third spell for the most highly educated women shows the clearest reversal in the spacing pattern: the birth intervals with two daughters were consistently statistically significantly longer than the intervals with one or two sons, no matter the percentile used. A similar reversal, although more muted, occurred for the third spell for urban women with 1–7 years of education (see Figure 4), and for both urban and rural women with 8–11 years of education (see Figure 5 and Figure 6).

Did the predictions of declining use of sex selection come true? There is no clear evidence for or against a reversal in the use of sex selection, with some cases showing increases in sex ratios between the last two periods, others little change, and some a decline. The most highly educated women are again a good illustration. The sex ratio for women with two daughters continued to increase over the last two periods, but the likelihood of a third birth declined. Furthermore, if the first child was a girl, the sex ratio for the second birth dropped slightly, as did the probability of having a second birth. However, there are also cases where there was no abatement in the increasing use of sex selection. For example, for rural women with 1–7 years of education, the sex ratios in the absence of daughters continued to increase while the likelihood of an additional birth remained high (see Figure 3).

Overall, over the four decades, birth intervals lengthened with improving economic conditions and falling fertility. These increases were larger with higher parity and higher percentile measure. Furthermore, when there was little evidence of the use of sex selection, it appears that the women least likely to work were also those with the most substantial increases in birth interval lengths.

The most substantial increases in birth spacing appear, however, to originate from the use of sex selection. The most highly educated women with two daughters and no sons had the most biased sex ratio and the most significant increase in birth interval lengths. Over the four decades, the median birth interval length for this group increased by almost 15 months. Even more striking, the 75th percentile birth interval length increased by a staggering 21 months, most of that within a decade of the introduction of sex selection.

What Happened to Fertility?

The tempo effect from longer birth intervals means that the TFR may underestimate cohort fertility. The next question I address is, therefore, to what extent did the changes bias the fertility estimates for India? To this end, I compare fertility based on a variation of the TFR with predicted cohort fertility from the hazard model. Table 1 shows the two fertility measures by area of residence and education.

The fertility rate follows the same procedure as in the Demographic and Health Survey reports: I use the births from 36 months to 1 month before the survey month to calculate age-specific fertility rates for five-year age-groups and then sum the age-specific fertility rates multiplied by five (Croft et al. 2018). However, because the hazard model predictions use only births up to parity four, I use the same set of births for the fertility rate and label it the “four-parity” fertility rate. Hence, the presented fertility rates are not directly comparable to those in the NFHS reports.

Because NFHS-1 was conducted after the introduction of sex selection, I cannot calculate a fertility rate in precisely the same manner for a period before sex selection was widely available. Instead, I calculate the fertility rates for women aged 15–39 five years before the survey month, again using the number of births three years before. This rate is shown as “1987–1988” in the table. Given the relatively low number of births to women aged 40–45, this approach provides the best estimate of the fertility rate when sex selection still was not widespread.

To predict cohort fertility using the hazard models, I estimate the parity progression probability for each spell. Because parity progression depends on the sex composition of prior children, I estimate the probability for each sex composition and weigh the probabilities with the likelihood of the sex compositions. The survey rounds do not coincide directly with the periods used for the hazard model. Therefore, I compare the model results for 1972–1984, 1985–1994, 1995–2004, and 2005–2016 with NFHS rounds 1–4, respectively.

I include the spell from marriage to first birth, despite the problems in capturing the exact timing of marriages because the estimated progression probabilities should not be affected by this problem. I begin with the age of marriage for each woman and predict the likelihood of progressing to each parity, assuming three-year increases in age between births. Shorter assumed increases in age lead to slightly higher predicted fertility. Sterilizations were not incorporated into the hazard model because most occur immediately after giving birth. To compensate, I estimate the probability of sterilization using a logit model and use that to scale down the parity progression probability when predicting cohort fertility.

Consistent with an increased bias in the period fertility rate from tempo effects when the age of marriage and the length of birth intervals increase, the absolute bias was least in the first and the last period and highest in the middle two periods. Hence, the fertility rate declined too fast from the mid-1980s to the century's end. Only recently, as the rate of increase for the birth interval lengths has slowed, have the two fertility measures begun to converge. Even with the convergence, the predicted 2005–2016 cohort fertility was still above the 1992–1993 fertility rate for every group, except for urban women with no education. Furthermore, the predicted cohort fertility remained at least 10%–20% higher than the fertility rate for the last period. Only women with no education in the first period showed little difference between the two fertility measures, a situation in which fertility was high and spacing was very short and likely unchanged for an extended period.

Another indication of how tempo effects bias the fertility rate is that the fertility rate increases for some groups. For example, for urban women with 8–11 years of education, the fertility rates were 1.84, 1.81, and 1.87 over the last three surveys. This pattern likely arises from the stabilization of the age of first birth and the spacing between births.

Finally, even with the declines in fertility, the predicted cohort fertility mostly remains above replacement. Only for urban women with 12 or more years of education was the predicted cohort fertility clearly below 2.1 children. Even then, cohort fertility was still more than 0.3 children higher than the fertility rate estimate of 1.5. Furthermore, the predicted cohort fertility numbers are likely too low because I use only the first four births and births before the imposed 105-month censoring of birth interval durations.

Mortality and the Changing Birth Spacing

The final question I address is whether there is an association between infant mortality and increases in birth spacing related to the introduction of sex selection. Starting with the sample used for estimating birth spacing, I select children born more than 12 months before the survey month. I restrict the analyses to parities two and three because of the small number of births and deaths at parity four.

The dependent variable is whether the child died within the first 12 months of life. The main set of explanatory variables consists of dummy variables for the spacing from the prior birth. The birth interval duration dummy variables cover 12-month periods, starting nine months after the prior birth, until the 57-month dummy variable, which covers until 105 months after the prior birth. I use dummy variables for the sex of the index child and the sex composition of the prior children. The birth spacing dummy variables, the sex of the index child, and the sex composition dummy variables are all interacted. Because the actual number of abortions is unobserved, the interactions between the sex composition of prior children and the sex of the index child serve as proxies for the use of sex selection. The other explanatory variables are the same as described earlier, and estimations are done separately by education level and parity.

I estimate the probability of infant mortality using a logit model. Figure 8 and Figure 9 show the predicted probability of the second child dying within the first year by the possible combinations of index child sex, sex composition of prior children, and birth spacing, with all other variables at their average values.13 To improve legibility, the graphs do not show confidence intervals.

An important caveat is that the estimations do not address potential selection problems. For example, suppose women who have difficulties conceiving or carrying a pregnancy to term also have a higher mortality risk for their offspring. In that case, a spurious correlation between long birth spacing and mortality may arise (Kozuki and Walker 2013). Unfortunately, methods to address selection, such as family fixed effects, do not work well when the number of births is as low as it is here for more highly educated women (Kozuki and Walker 2013; Molitoris et al. 2019). However, the fixed-effects and linear probability results did not deviate substantially in prior research.

There has been substantial convergence in mortality risk across groups over time. For intervals of 21 months or longer, there is now little difference across the education groups, with even the no education group showing an infant mortality risk below 5%. Very short birth intervals still exhibit a higher mortality risk, although the effect declines with education level. The mortality risk is 3%–4% for the most highly educated women, whereas women with no education still show a risk that is close to 10%. Despite the prior findings of differential mortality by sex, there is little evidence that girls have substantially higher mortality risk. There is some weak evidence that a boy born after a girl has a lower mortality risk in the earliest periods; however, this difference disappears with the general decline in mortality risk.

Although there is concern that multiple abortions might increase mortality risk by shortening the interval between pregnancies, I found no evidence for this effect. Suppose repeated sex-selective abortions lead to a higher mortality risk for the child eventually born. In that case, boys born after a girl (the solid lines in Figure 8 and Figure 9) should have an increased risk with longer spacing for the two highest education groups in the last two periods. However, there are no apparent consistent differences between these groups and the other potential combinations. The same holds for the third spell.

The raw numbers for women with the most uneven sex ratio also suggest that even with a very high apparent use of sex selection, there is no impact on mortality. A total of 1,004 women with 12 or more years of education and no sons at the start of the third spell in the last period had a third child, of which 685 were boys. Of these boys, only six died within the first year of life. Half of those who died were born in the 9- to 32-month interval, and none died in the 57-month or greater interval.

Discussion and Conclusions

The main question I addressed is how birth spacing responded to the significant demographic and socioeconomic changes in India between 1972 and 2016, particularly the spread of sex selection. I also examined two related questions. First, did changes in birth spacing lead to an overestimation of the decline in cohort fertility? Second, what is the relationship between infant mortality and the changes in birth spacing and sex selection?

The most substantial lengthening of birth intervals occurred among the most highly educated women, likely because of substantial use of sex selection combined with falling fertility. Consider, for example, women with 12 or more years of education who had two daughters. As the sex ratio reached almost 80% boys for the third birth, the expected median birth interval length increased by almost 15 months, and the 75th percentile interval length increased by 21 months. Most of the lengthening in the long intervals came immediately after the introduction of sex selection in India.

For some groups, the lengthening in birth intervals with the introduction of sex selection was, in fact, so substantial that it led to a reversal of the traditional spacing pattern:in the absence of sons, these groups now show statistically significantly longer—rather than shorter—birth intervals than if there is at least one son. The women who are the least likely to use sex selection, as indicated by their sex ratios at birth, still show the traditional spacing pattern with short spacing in the absence of sons. Son preference also continues to be evident in fertility decisions. Fertility has declined in all groups, but the likelihood of having an additional child still depends strongly on the number of sons, with women with no sons having the highest parity progression probabilities.

Birth intervals also lengthened in cases when sex selection appears to be less used. However, in comparison with other countries with similar declines in fertility, the median spacing increases were smaller at 3–6 months over the period. Most of the median intervals when sex ratios were close to normal were still short at 36 months or less. Furthermore, many women still have very short birth intervals: more than 25% of women have their next child within 24 months of the previous birth in many cases.

Despite predictions that the use of sex selection would decline, there is no clear evidence of this. The most likely users of sex selection continue to show substantial male-biased sex ratios, although there may be some leveling off. More concerning, however, are the increasingly male-biased sex ratios seen among women with low education, which suggests that the use of sex selection appears to be spreading as fertility declines.

The increases in spacing make the total fertility rate a more biased measure of cohort fertility. This bias was most prominent early in the spread of access to sex selection, when the fertility rate was up to one child lower than the predicted cohort fertility. However, this bias is still present, with the predicted cohort fertility 10%–20% higher than the fertility rate. The most highly educated urban women are the only group for whom the predicted cohort fertility is below replacement, at 1.8 children.

Tempo effects have been studied extensively (see, e.g., Bongaarts 1999). Still, to my knowledge, there are no other cases where there has been as substantial an increase in birth interval lengths and associated bias in fertility rates as for India. If interventions against sex selection are successful, it is conceivable that we might see increases in the TFR as birth spacing stabilizes or even shortens again.

There has been a substantial reduction in infant mortality over time, and the size of the reductions is inversely related to the mother's education. Hence, there is now little difference in mortality risk across education groups if the birth took place more than 21 months after the previous birth. Short birth spacing is still associated with higher mortality, although the effect is small for the most highly educated women. There is no evidence that repeated abortions in a birth interval are associated with higher infant mortality; boys born after long birth intervals to families with well-educated mothers, only daughters, and high predicted sex ratios—the combination of which suggests repeated sex-selective abortions—have no higher infant mortality than other children.

These results paint a less rosy picture of India's prospects for a continued reduction in population growth than generally accepted. With predicted cohort fertility still substantially higher than the period fertility rate, India's TFR will likely stabilize or even increase as birth intervals slow their lengthening. The more successful the attempts at combatting sex selection are, the more likely an increase in the TFR will be. Furthermore, the rapid decline in infant mortality risk, combined with likely future declines as the proportion of very short birth intervals falls, may also slow the reduction in population growth.

There are two crucial questions that future research should address. First, what is behind the improvements in girls' health status? Access to sex selection means that families with only daughters are less likely to have very short birth intervals, which may reduce sibling competition. Hence, better health outcomes for girls when sex selection is available could be an unintended side effect, rather than the result of girls becoming more valued, as is often assumed (Hu and Schlosser 2015). Comparison of prior children's outcomes across sex composition and the sex of the next child could be a way to understand why girls' health outcomes improve in the presence of sex selection.

Second, what is the relationship between female labor force participation and sex selection? Women may be staying out of the labor market precisely because sex selection makes them more likely to have a boy and increases the expected birth spacing. Better job opportunities for women could reduce the use of sex selection for two reasons. With improved economic opportunities, it becomes more expensive to be out of the labor market for long periods, and the differential in potential earnings between husband and wife would decline, making it relatively more attractive to invest in daughters' human capital. This approach could, however, be a double-edged sword. If better job opportunities further lower fertility, the use of sex selection may increase, everything else being equal. Understanding the trade-off between long-term benefits from improvements in women's labor force participation and short-term costs from potential increases in sex selection is of paramount importance.

Acknowledgments

I am grateful to Andrew Foster and Darryl Holman for discussions about the method. I owe thanks to Monica Das Gupta, Shelly Lundberg, Daniel Rees, David Ribar, Hendrik Wolff, three anonymous reviewers, and seminar participants at the University of Copenhagen, the University of Michigan, the University of Washington, the University of Aarhus, the fourth annual conference on Population, Reproductive Health, and Economic Development, and the Economic Demography Workshop for helpful suggestions and comments. I would also like to thank Nalina Varanasi for research assistance. Support for development of the method from the University of Washington Royalty Research Fund and the Development Research Group of the World Bank is gratefully acknowledged. The views and findings expressed here are those of the author and should not be attributed to the World Bank or any of its member countries. Partial support for this research came from a Eunice Kennedy Shriver National Institute of Child Health and Human Development research infrastructure grant (5R24HD042828) to the Center for Studies in Demography and Ecology at the University of Washington. The Stata code for this article is available at https://github.com/cportner/sexSelectionSpacing.

Notes

1

The surveys ask about the ideal number of sons and daughters, but these appear to be unreliable son preference indicators; more highly educated women simultaneously show declining son preference and increasing sex selection (Bhat and Zavier 2003; Pande and Astone 2007).

2

However, when holding parental education constant, children in Indian slums have worse health outcomes than children in rural areas (Pörtner and Su 2018).

3

See Sheps et al. (1970) and Newman and McCulloch (1984) for early discussions of why hazard models are the preferred way to deal with the censoring of birth intervals.

4

Merli and Raftery (2000) used a discrete hazard model to examine whether there was underreporting of births in rural China, although they estimated separate waiting time regressions for boys and girls.

5

Imagine T = 2. If 54% and 66% of the births are boys and the likelihood of giving birth is 20% and 40%, then the predicted sex ratio is 54×0.2+66×0.40.2+0.4 = 62% boys.

6

Recall error is likely behind the designation of the first two rounds of NFHS as being of “moderate quality” in an analysis of the quality of birth histories in DHS surveys and its impact on fertility estimates (Schoumaker 2014).

7

There is little evidence that the ban significantly affected sex ratios (Das Gupta 2019).

8

Although there are variations by state, elementary education in India consists of primary school covering grades one through five and upper primary—or middle school—covering grades six through eight. Similarly, secondary education covers grades nine and 10 for “secondary education” and 11 and 12 for “upper secondary.”

9

With sex selection, the composition of prior children is, in principle, endogenous. It is beyond the scope of this article to develop a method for dealing with this issue.

10

Results for urban women without education, rural women with 12 or more years of education, and the fourth spell for women with 12 or more years of education are presented in the online appendix because of relatively small samples.

11

The NFHS reports show median durations of closed birth intervals of approximately 31 months, which have barely changed over time, underscoring the importance of accounting for censoring when examining birth spacing.

12

For women with two sons, the numbers were 4.3, 6.3, 7.0, and 3.0, respectively. See the online appendix tables for the average birth interval durations.

13

The online appendix shows the corresponding graphs for the third child.

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