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The Dynamics of Son Preference, Technology Diffusion, and Fertility Decline Underlying Distorted Sex Ratios at Birth: A Simulation Approach [1]
['Kashyap', 'Kashyap Demogr.Mpg.De', 'Max Planck Institute For Demographic Research', 'Rostock', 'Nuffield College', 'Department Of Sociology', 'University Of Oxford', 'Oxford', 'United Kingdom', 'Villavicencio']
Date: 2016-10-04
Microsimulation and Agent-Based Models
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.
State Variables
The modelFootnote 4 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.
Table 1 Agent’s state variables Full size table
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.
Initialization
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).Footnote 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.
Procedures
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.Footnote 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.
Modeling Reproductive Behaviors
Sex Selection: Ready, Willing, and Able (RWA)
The model formalizes the RWA framework to the practice of prenatal sex selection as presented in Guilmoto (2009). A woman’s decision to practice sex selection is the outcome of three processes that are modeled as probabilities, in this order: (1) whether she has a son preference (willing), (2) whether she has access to technology (able), and (3) whether she feels a fertility squeeze to restrict her total family size while realizing her son preference (ready). Figure 1 illustrates how each simulation step proceeds.
Fig. 1 Diagram of each simulation step Full size image
Son Preference (Willingness)
Son preference (sp i ) is assigned as follows: agents have either no preference for male offspring (sp i = 0) or a desire for one male offspring (sp i = 1). Only women in their reproductive ages have a son preference. Those who have son preference (sp i = 1) practice DSB: that is, they have higher fertility rates than those who do not or have met their son preference (see the following section on DSB).
For South Korea, we approximate an individual’s probability of having son preference as time-varying, using data from a question that asks women whether they feel that they must have a son.Footnote 7 We rely on time trends in proportions stating they must have a son, as reported in Chung and Das Gupta (2007b). Given that we are modeling a dichotomous proportion that is bounded between 0 and 1, we fit a logistic regression (Eq. (1)) with one predictor variable (δ t ) and an intercept term (δ 0 ) to obtain yearly probabilities of son preference for the period between 1980 and 2050. Figure 2 shows the observed and fitted son preference trends from Eq. (1).Footnote 8
$$ sp(t)=\frac{e^{\updelta_0 + {\updelta}_t}}{1+{e}^{\updelta_0 + {\updelta}_t}}. $$ (1)
Fig. 2 Proportion with son preference: South Korea, 1980–2050. Observed values from Chung and Das Gupta (2007b) Full size image
We choose to assign son preference dichotomously because we believe this effectively captures the way individuals experience son preference, by finding it imperative to bear a son. This measure also allows for easy interpretation for how much son preference exists in a population. Although some individuals—particularly among older cohorts—may desire more than one son, the desire for several sons likely reflects the indirect influence of higher mortality conditions where bearing at least two sons might be considered a strategy to ensure at least one survived into adulthood. By simulating mortality dynamics for males until age 50, this feedback effect of high mortality levels on fertility behavior is accounted for in the model as mentioned in the earlier section on procedures.
Differential Stopping Behavior
Differential stopping behavior (DSB) is a common manifestation of son preference (Arnold et al. 1998; Clark 2000; Larsen et al. 1998; Retherford and Roy 2003). In the model, female agents with unmet son preference have a higher fertility risk, expressed as a deviation from the standard fertility schedule \( {h}_i^{*}\left({x}_i,t\right) \) by a proportional expansion factor (1 + γ).
$$ {h}_i\left({x}_i,t\right)=\left\{\begin{array}{ll}{h}^{*}\left({x}_i,t\right)\hfill & \mathrm{if}\ s{p}_i(t)=0,\hfill \\ {}{h}^{*}\left({x}_i,t\right)\times \left(1+\upgamma \right)\hfill & \mathrm{if}\ s{o}_i(t)<s{p}_i(t),\hfill \\ {}{h}^{*}\left({x}_i,t\right)\times \left(1 - \upalpha \right)\hfill & \mathrm{if}\ s{o}_i(t)\ge s{p}_i(t)\ \mathrm{and}\ s{p}_i(t)
e 0.\hfill \end{array}\right. $$ (2)
As Eq. (2) shows, if the current number of sons so i (t) of female agent i is less than her son preference sp i (t), her period age-specific rate is multiplied by a factor of (1 + γ), where γ may be conceptualized as a son preference–intensity parameter. For example, γ = 0.2 implies that a woman with unmet son preference experiences a fertility risk that is 20 % higher than the period age-specific schedule that normally determines her risk for childbearing. A higher value of γ indicates a higher intensity of son preference through its impact on fertility behavior.
When son-preferring female agents bear a son, their birth risk is adjusted down by a factor of (1 − α), indicating a reduced risk from the standard fertility schedule \( {h}_i^{*}\left({x}_i,t\right) \). Standard period age-specific rates h *(x i , t) apply to female agents with no son preference (sp i (t) = 0).
Access to Technology (Ability)
We use the logistic diffusion model, widely used to describe the diffusion of new technologies, to model an individual’s ability or probability of gaining access to technology (Geroski 2000).
$$ Ability(t)=\frac{e^{\uprho \left(t - \upphi \right)}}{1+{e}^{\uprho \left(t - \upphi \right)}}. $$ (3)
In Eq. (3), Ability(t) simulates an individual’s probability of getting access to technology, which increases as a function of time (t), where t corresponds to the time-step in the simulation (t = 0, 1, 2, . . . , 30 for a 30-year simulation covering the period 1980–2010), ρ determines the slope or rate of increase, and ϕ is the inflection point of the logistic diffusion curve. At the population level, Ability(t) can be interpreted as the proportion of individuals at a particular time-step gaining access to prenatal sex-determination technology. At each time-step, Ability(t) is recalculated, and a random number from a uniform distribution for each individual is redrawn, which when less than Ability(t) sets the state variable tech i (t) = true for that individual.
Fertility Decline (Readiness)
As fertility falls, norms surrounding smaller families become more entrenched. Individuals are likely to desire smaller families; and if means are available to allow them to realize their son preference with small family size, they are likely to do so. This is the motivating idea to generate an individual’s probability (readiness) to abort. Guilmoto (2009) described the readiness to abort as strongly related to the fertility squeeze felt by couples planning the size and composition of their families. From a modeling perspective, this fertility squeeze can be viewed as a form of social pressure that is closely related to prevailing total fertility levels and determines an individual’s readiness to abort. This readiness to abort is likely higher when fertility levels are lower, couples feel a greater squeeze or pressure to reconcile their son preference at lower parities than when average family size is higher, and proceeding to higher parities is not out of step with prevailing total fertility norms.
Equation (4) shows how we model readiness to sex-selectively abort. A woman is ready only if she has unmet son preference (willing) and she has access to technology (able): that is, if sp i (t) > so i (t), and tech i (t) = true. Hence, if these two conditions are met,
$$ Readines{s}_i(t)=\left\{\begin{array}{cc}\hfill \min \left\{1,\frac{\upbeta}{\mathrm{TFR}\left(t - 1\right)}\right\}\hfill & \hfill \mathrm{if}\ {p}_i(t)=0,\hfill \\ {}\hfill \min \left\{1,\frac{p_i(t)\times \upsigma}{\mathrm{TFR}\left(t - 1\right)}\right\}\hfill & \hfill \mathrm{if}\ {p}_i(t)>0,\hfill \end{array}\right. $$ (4)
where p i (t) denotes the parity of agent i at time t. Because Readiness i (t) is a probability to abort, it is bounded between 0 and 1.
An agent’s readiness to abort depends on her (1) current parity (p i (t)) at the beginning of the period; (2) prevailing, model-generatedFootnote 9 fertility levels, TFR(t − 1); and (3) two parameters σ (if p i (t) > 0) and β (if p i (t) = 0).Footnote 10 In Eq. (4), the ratio of the agent’s current parity and prevailing fertility levels is conceptualized as determining the extent of her fertility squeeze. When fertility levels are higher—for example, at a TFR of 3 children per woman—a woman with unmet son preference and access to technology has a 0.33 × σ probability to abort as she transitions from first to second parity compared with a woman who transitions from first to second parity when total fertility levels have fallen to 2.5 and the probability is 0.4 × σ. The parameter σ allows us to assess the impact of the fertility squeeze by scaling it up or down on SRB trajectories when calibrating the model. It also allows us to account for the possibility that even if the fertility squeeze may be present in a population, there might be other counteracting forces—such as religious or cultural taboos against the practice of abortion, or punitive measures against sex-selective abortion—that may not allow for the full extent of the fertility squeeze to be felt. Conversely, higher σ values indicate a greater intensity of the fertility squeeze.
Indeed, in some situations, particularly as fertility becomes very low, we may expect some women to abort at the lowest possible parity: that is, parity 0 or before the transition to first birth. Although abortions before the first birth may become more frequent as fertility falls, these events tend to be more rare than higher-parity abortions (Guilmoto 2009:533). We therefore model parity 0 abortions as a function of prevailing fertility levels but subject to their own parameter β than higher-parity abortions, which are controlled by the parameter σ. Table 2 lists the relevant parameters that control the three factors in the model: son preference, fertility decline, and technology availability. The range listed in the table refers to theoretically plausible values for each parameter over which we analyze model behavior.
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[1] Url:
https://link.springer.com/article/10.1007/s13524-016-0500-z
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