The Dynamics of Son Preference, Technology Diffusion, and Fertility Decline Underlying Distorted Sex Ratios at Birth: A Simulation Approach

From a theoretical standpoint, the steep rise in SRBs and child sex ratios across Asia and the Caucasus despite rapid modernization and development posed a severe challenge to demographic and social theory (Chung and Das Gupta 2007a; Croll 2000). The same modernization forces that made women educated and economically productive and ensured other forms of social insurance for parents were implicitly assumed to erode the norms of son preference as well. Parents would no longer want children for extra labor, income, or social status (Croll 2000:109)—factors that were thought to underpin son preference in pretransitional societies. Moreover, low fertility would combine with greater industrialization and urbanization to shift families away from the extended patrilineal form—in which sons are imperative for family continuity—toward nuclear forms with more equitable sex roles (Goode 1963). However, contrary to theoretical expectations, even as levels of fertility steadily declined in the 1980s and 1990s across South Korea, China, and India, distorted SRBs seemed to suggest that son preference persisted.

A number of significant studies have noted that indicators of stated son preference, measured in different ways, appeared to decline even as sex ratios worsened (Bhat and Zavier 2003; Bongaarts 2013; Chung and Das Gupta 2007a). In attempting to reconcile these ostensibly paradoxical trends, these studies acknowledged the role of the diffusion of prenatal sex determination technology and fertility decline in contributing to masculine sex ratios amidst declining son preference. These studies, however, did not explicitly model the interplay of these preferences with technology diffusion and fertility decline at the individual-level and link them with macro-level SRB trajectories, nor did they attempt to quantify the micro-level behaviors underpinning macro-level patterns. This study highlights and extends insights on the micro-level underpinnings of SRB trajectories.

Guilmoto (2009) provided a valuable theoretical framework of the micro-level factors underpinning macro-level SRB distortions. The recent rise in SRBs across Asia, he argued, “resembles a diffusion process similar to that sometimes claimed to be characteristic of a fertility decline” (Guilmoto 2009:524). By likening the shape of the SRB transition to the fertility decline, Guilmoto adapted the well-known “ready, willing, and able” (RWA) approach, which Coale (1973) originally used to account for the European fertility decline in the nineteenth century, to the practice of sex selection. Within this framework, sex-determination technology can be conceptualized as “the key innovation that permits couples to resort to sex-selection in a context characterized by declining fertility and entrenched son preference” (Guilmoto 2009:524).

The practice of sex-selection from the actor or individual’s perspective can be seen as the outcome of three conditions being met: (1) willingness to consider sex selection because of the persistence of cultural norms that reinforce the value of male offspring; (2) ability to seek sex selection given the availability of relatively affordable and accurate prenatal sex-determination technology and relatively liberal abortion legislation; and (3) readiness to practice sex selection as a consequence of the fertility squeeze wherein individuals wish to reconcile their sex preferences with a small total family size. The idea of readiness gains importance as fertility declines with the diffusion of norms toward smaller families wherein prenatal sex selection becomes preferable to additional births as the means to realize son preference.

In the same study, Guilmoto speculated whether South Korean SRB trajectories may be a manifestation of an archetypal transition cycle involving three phases: (1) a rise; (2) a leveling off; and (3) a decline and eventual return to normal levels that may eventually come about across other parts of Asia where similar SRB distortions have been observed. Although the return to normal levels suggestive of a completed transition has been observed only in South Korea, the first (steep rise) and second (leveling off) phases have also been observed in other SRB trajectories, such as those of China and India.

What are the levels and trends of the three micro-level preconditions (willingness, ability, and readiness) that explain distinct phases of the SRB transition? The plausible levels of these three preconditions that inform the shape of the trajectories in these two phases and scenarios for their likely projection into the third phase requires a formalization of each of the three conditions within a flexible, dynamic model. The microsimulation model enables us to simulate the differing rates of change across each of these dimensions at the individual-level to approximate macro-level trajectories.

Individual-based simulation techniques—a term used to describe both microsimulation and agent-based modeling approaches—have been actively used to model demographic processes, such as kinship structures and kinship resources (Wachter 1997; Zagheni 2011), marriage (Billari et al. 2007; Grow and Van Bavel 2015), and the transition to parenthood (Aparicio Diaz et al. 2011; Winkler-Dworak et al. 2015). Although both approaches take individuals as the unit of analysis and use computer algorithms (Monte Carlo methods) to determine individual transition between states or the adoption of behavioral rules, the different goals and data requirements of the two simulation approaches have often been used to classify them separately (Zagheni 2015).

Microsimulation models rely on empirical transition rates and have been predominantly used for predictive purposes. Agent-based models are concerned with showing the emergence of interesting macro-level patterns from the behavioral rules of individual agents. In contrast to microsimulation approaches, agent-based models often tend to model interaction between agents and the environment, adaptation to stimuli, and other types of social learning or feedback effects. Despite their different classification, Bijak et al. (2013) and Zagheni (2015) have noted that the distinction between the two approaches, at least with respect to demographic applications, is not always clear-cut. Agent-based models in demography often include empirical transition rates to model fertility and mortality, and microsimulation models often include behavioral rules and feedback mechanisms. Our model borrows from both approaches and attempts to show how complex macro-level SRB trajectories can emerge from simple micro-level driving forces, and attempts to indirectly estimate these.

The model⁴ comprises individual agents who each have an identity number (id), age (x), sex (s), cohort (c), son preference (sp), parity (p), sons (so), technology access (tech), and abortions (ab). Table 1 lists agents’ state variables and their values. The model is initialized as a one-sex model with initial female agents; however, as we model male as well as female births, the model becomes two-sex from the first time-step onward.

An agent’s identity number, sex, and cohort are assigned to the agent at birth and remain the same throughout the life course. Parity (p) corresponds to the current parity of the female agent. Sons (so) refer to her number of sons. Access to technology (tech) is a Boolean variable that takes a true or false value depending on whether an agent has access to prenatal sex-determination technology. Abortion (ab) indicates how many sex-selective abortions a female agent has over her life course. An agent’s age, parity, son preference, sons, access to technology, and abortion values are time-varying and are updated at each time-step in the model.

To approximate the initial parity distribution of South Korean women from 1980 onward, we initialized the model 35 years earlier in 1945 to allow all women in reproductive ages (15+) to complete their fertility careers by 1980 and have their children belong to the starting population of 1980. Using UN WPP data, we approximate the South Korean population structure of 1945 and start a simulation in which individuals die and reproduce according to their age-specific death and fertility rates for each year (United Nations 2013).⁵ The abortion procedure is not modeled prior to 1980. The resulting population structure obtained in 1980 is very close to the population structure of South Korea reported in UN WPP, and the minor differences that persist are likely attributable to migration dynamics that are not modeled in our initialization procedure.

The model contains two procedures for agents: (1) aging and (2) reproduction, both of which are carried out at each time-step (tick) in the model. Each tick corresponds to one year. At each tick, an agent ages by one year, and time moves forward by one year. The model uses sex- and age-specific mortality rates until age 50 from UN WPP to model aging (United Nations 2013). Because we focus on reproductive behavior, all female and male agents who survive are removed from the simulation at age 50. By simulating male agents until age 50, we can account for child and young adult mortality for males, which may have an impact on a woman’s reproductive behavior, as we describe later. If a woman were to lose her son during childhood, she might then be able to attempt to have a son again.

The reproduction procedure models conception and birth for female agents. The risk of childbirth h _i (x _i , t) for each female agent i is determined by the age-specific (x _i ) fertility rates for that period (t) from UN WPP (\( {h}_i^{*}\left({x}_i,t\right) \)), her son preference (sp _i ), and her current number of sons (so _i ). The sex of the birth is determined at the point of conception by a probability of 0.5122 for male births and 0.4878 for female births, which corresponds to an SRB of 105.⁶ We model sex-differential birth-stopping behavior; and as our model moves in time and technology becomes available, we model the opportunity for female agents to have sex-selective abortions. Details of how these behaviors are modeled in our agents are described in the next section.

We calibrate the model for South Korea by seeking to match the shape and levels of model-generated SRB trajectories with UN WPP estimates of the same for the period, 1980–2010 (United Nations 2013). We find the combination of parameters that minimize the average yearly error (model fit measure, or root mean squared error (RMSE)) between the simulated SRB trajectories and UN estimates of South Korean SRBs. The model fit measure can be expressed as follows:

Low values of the RMSE model fit measure indicate better fit with smaller average yearly errors between model-generated SRBs and UN SRB estimates. We also attempt to calibrate model-generated TFR levels to UN WPP estimates of the same because the model-generated TFR forms an important part of the readiness condition, as shown in Eq. (4).

Our calibration strategy proceeds as follows: we run the model on an exploratory Latin hypercube sample comprising 224 design points. One simulation was run at 180 of the 224 design points, and five repetitions were performed at 44 randomly chosen points in the sample, totaling 400 simulation runs ((180 × 1) + (44 × 5)).¹¹ Each design point corresponds to a unique combination of the six model parameters. These design points range over the minimum and maximum values for the parameters listed in Table 2. From this sample of points, we interpolate across all possible combinations of the parameter space (total of 548,856 design points) using a regression metamodel, and explore the sensitivity of the model to different regions of the parameter space that give us good fit (for more details, see the upcoming section Sensitivity Analysis and Online Resource 1). Regions where the simulated SRB trajectories match UN estimates for South Korea well (with low model fit or RMSE values) indicate early (low ϕ) and steady technology diffusion (ρ values between 0.5 to 0.6) as well as a strong readiness to abort (σ values upward of 1.7 combined with smaller values of β in the region of 0.2). SRB fit is expectedly less sensitive to α and γ. We run the simulation at a combination of levels varying the ability and readiness parameters, as shown in Fig. 3. In panel a of the figure, we vary ability parameters ρ and ϕ across their range while holding σ = 1.7 and β = 0.2; and in panel b, we vary readiness parameters σ and β while holding ρ = 0.5 and ϕ = 7.

Data on son preference from South Korean fertility surveys indicate that stated son preference declined from 48 % in 1985 to 26 % in 1994; over the same time, South Korean SRBs rose from around 108 to 114, and fertility declined around 2.1 to 1.6. It is interesting to note that son preference levels appear to be relatively low (approximately 30 % of the population stating “must have son”) as SRBs reached their peak in 1990.

Figure 4 shows model-generated SRB and fertility trajectories with 95 % empirical confidence interval bands that best match UN WPP SRB trajectories, which are shown in the background in gray.¹²

The dotted-dashed SRB curve in Fig. 4 shows five-year moving averages of SRBs averaged across 240 simulation runs with an initial population of 1,000,000 individuals, with the following parameter values: γ = 0.20, α = 0.075, ρ = 0.5, ϕ = 7, σ = 1.7, and β = 0.2. Increasing β to levels closer to 0.25 allows us to match the peak better but at the expense of worsening the fit for the period 1998 onward, thereby worsening the average yearly error between the simulated and UN SRB estimates. Our simulated fit, while capturing the general shape and SRB levels well, does not capture the drastic turnaround toward normalization that occurred in the mid-2000s. The dynamic trajectories and associated parameters of willingness (son preference), ability (technology access), and readiness (abortion probabilities as a function of the fertility squeeze) that underlie the simulated SRB curve reported in Fig. 4 are shown in Fig. 5. The technological diffusion trajectories indicate saturation by the mid-1990s, with the steepest rise in the 1980s, combined with an increase in the probabilities to abort in the mid-1980s that lead to the rise in the SRB, even as son preference continued to decline throughout the period.

A son preference intensity parameter of γ = 0.20 and birth risk adjustment of α = 0.075 allow us to match Korean fertility trajectories over the period with the prevailing levels of son preference very well. How much did the practice of sex-selective abortion hasten the fertility decline in South Korea? To answer this question, we adopted a counterfactual strategy assuming that no sex-selective abortion was practiced (σ = 0 and β = 0), keeping all other parameters constant at the levels used to generate the SRB distortions. The solid black line shows TFR levels assuming that no sex-selective abortion had been practiced. When SRBs peaked at the end of the 1980s and early 1990s, the TFR levels in the no sex-selective abortion scenario are about 2.5 % to 3.5 % higher than with sex-selective abortion. The difference in TFR levels between the two scenarios is greatest between the years 1990 and 1995 when it was at 0.05, which can be interpreted as 5 births per 100 mothers of childbearing age. For 1990 when SRBs peaked, in the absence of sex-selective abortion, simulations suggest that the TFR would have been approximately 1.65 instead of 1.60.

We present two sets of counterfactual scenarios to show how SRB trajectories respond to different assumptions about willingness, readiness, and ability. First, we compare how SRB trajectories would have looked had son preference (willingness) been constant (1) at 1980 levels of 50 %, and (2) at 100 %. We keep technology diffusion early and steady at the same parameters as in Fig. 4 (ϕ = 7 and ρ = 0.5) along with strong readiness parameters of σ = 1.7 and β = 0.2. We compare these against the simulated SRB trajectories presented in Fig. 4. All three SRB trajectories are shown in Fig. 6.¹³

In both constant scenarios, SRB trajectories stabilize at high levels by the early 1990s and do not show a turnaround. If son preference is kept at 1980 levels, SRBs stabilize at levels of 120; and in the 100 % scenario, they stabilize at very high levels of 145—levels that have not been observed in national-level SRB trajectories anywhere.

In the second set of scenarios, we modify assumptions about ability and readiness. These are shown in Fig. 7, which assumes that (1) technology availability stays constant at 50 % throughout the simulation (ρ = 0 and ϕ = 0, and σ = 1.7 and β = 0.2); and (2) that the fertility squeeze felt by individuals is less intense, leading to a lower readiness to abort with no parity 0 abortion (σ is reduced to 1 instead of 1.7 in Fig. 4; and β is reduced to 0 instead of 0.2, with ρ = 0.5 and ϕ = 7). In Scenario 1, the rise in SRB levels is triggered by increasing readiness to abort induced by the fertility squeeze, but SRB levels start high in 1980 and don’t capture the shape between 1980 and 1990 well. In Scenario 2, SRB levels remain much lower, reaching a peak of 110 instead of 113–114 when σ and β are higher in the best-fit simulated trajectories.

How much of the variance of model outcomes is accounted for by different parameters? We address this issue by sensitivity analysis of three model outcomes: (1) the model fit or RMSE measure, which is the average yearly error for 1980–2010 between simulated and UN estimates of South Korean SRB trajectories (see Eq. (5)); (2) the South Korean SRB for 1990, when the SRB peaks according to UN estimates; and (3) the maximum SRB level reached by the model. We estimate regression metamodels on data generated by the simulation model.¹⁴ These models separately take each of the three outcomes of interest as the dependent variable, with the parameter values as the predictor variables in the regression model. Regression metamodeling for simulation models is widely used in the sensitivity analysis of simulation models (Kleijnen 1995; Santner et al. 2003) and has been used in agent-based modeling applications in demography (Grow and Van Bavel 2015). After finding a well-fitted metamodel for each outcome, we perform an analysis of variance (ANOVA) of the regression metamodel to assess how much of the model variance is accounted for by each parameter (Santner et al. 2003: chapter 7). The variance explained by each parameter as well as selected, statistically significant (p < .05) higher-order terms and interactions from the ANOVA decompositions are reported in Table 3. Further sensitivity analysis results are reported in Online Resource 1.

Nearly one-half of the variance (44.3 %) in the model fit or RMSE measure can be accounted for by the inflection point for the onset of technology diffusion (ϕ), the quadratic term involving the speed of technology diffusion (ρ), and the interaction of the two technology diffusion parameters. This finding indicates that the shape of the South Korean SRB trajectory, including the rise and turnaround, is especially sensitive to the ability parameters. The interaction terms involving the readiness parameters (σ and β) account for 8 % of the variance, and interaction terms involving γ (the son preference intensity parameter), account for about 7 % of the variance of the model fit measure. Technology diffusion parameters also account for the greatest fraction of the variation in the levels of the South Korean SRB in 1990 (about 47 %, including first-order, second-order, and interaction terms), followed by the readiness parameters of β and σ, which account for about 26 %. The maximum SRB levels reached in the model is most sensitive to the readiness parameters (σ and β), which together account for nearly 50 % of the variation in this outcome. The son preference–intensity parameter γ also accounts for a sizable proportion of the variation in the maximum SRB outcome, although it is more important in its role in interactions with other parameters for the other two outcomes. This result is plausible given that α and γ do not have direct effects on the SRB but effects that are mediated through the TFR in the model.

The regression metamodels incorporating linear, quadratic, and interaction terms for each of the three outcomes capture a sufficiently high fraction of the variance in the output. For the model fit measure, the best-fit metamodel captures 78 % of the model variance (residual variance 22.06 %). The best-fit regression metamodel with the maximum SRB reached in the model as the outcome captures a similar proportion of the variance (79.11 %; residual variance 20.89 %), whereas the metamodel with the South Korean SRB in 1990 captures 87.02 % of the variance (residual variance 12.98 %).¹⁵