# A microsimulation model of fertility, childbearing, and child well-being

1. McCourt School of Public Policy, United States
2. Child Trends, United States
Research article
Cite this article as: A. Thomas, Q. Karpilow, K. Welti, J. Manlove, E. Cook; 2017; A microsimulation model of fertility, childbearing, and child well-being; International Journal of Microsimulation; 10(2); 3-85. doi: 10.34196/ijm.00156

## Abstract

The topic of family structure features prominently in social policy debates in the United States. This paper details the architecture of FamilyScape 3.0, a microsimulation tool that models a wide variety of real-world behaviours and outcomes related to family formation and child well-being. We describe FamilyScape’s procedures for simulating sexual activity, contraceptive behaviour, female fecundity, contraceptive efficacy, pregnancy and pregnancy outcomes, and maternal and child outcomes. We present an extensive set of simulation results demonstrating that the model realistically simulates of each of these dynamics. Most importantly, we show that FamilyScape closely approximates real-world rates of contraceptive failure, pregnancy, childbearing, and abortion. We conclude by briefly discussing the model’s potential to inform a range of policy debates.

## 1. Introduction

Nearly half of all pregnancies in the United States are unintended (Finer & Zolna, 2016), and more than 40% of all births are to unwed mothers (Martin, Hamilton, Osterman, Curtin, & Mathews, 2015). Research has shown that these features of the family-formation landscape have implications for a number of important child and family outcomes. For example, children in single-parent families are nearly four times as likely as children in married-parent families to fall below the federal poverty line (Vespa, Lewis, & Kreider, 2013). Nonmarital childbearing has also been found to have a negative impact on family earnings and a positive impact on welfare recipiency, especially among minority women (Bronars & Grogger, 1994). In addition, more than 90% of abortions are the result of pregnancies that were unintended (Thomas, 2012a), and studies have shown that previous reductions in unintended pregnancy raised female college attendance and graduation rates (Hock, 2007), increased the number of women seeking graduate degrees (Goldin & Katz, 2002), and boosted women’s earnings (Bailey, Hersbein, & Miller, 2012).

In part because of their far-reaching implications, family-formation dynamics have assumed a prominent place on the American policy agenda. For example, a recent report by a bipartisan group of policy experts highlights the importance of reducing the number of unintended and nonmarital births and argues that expanded access to contraception may help to achieve these objectives (AEI/Brookings Working Group on Poverty and Opportunity, 2015). Similarly, as a component of its Healthy People 2020 public health campaign, the Department of Health and Human Services (DHHS) seeks to increase proportion of births that are intended by ten percent over a ten-year period (Office of Population Affairs, 2010). A much-debated guideline issued by DHHS during its implementation of President Barack Obama’s signature health-care initiative, the Patient Protection and Affordable Care Act (ACA), requires that employer-sponsored health plans offer coverage for a wide range of family planning services without cost sharing (Sonfield, 2011). Such initiatives are often met with resistance by policy-makers and advocates who argue that the subsidization of family planning providers effectively increases funding for abortion services (Thomas, 2012a).

There are few tools available to the research community that allow for rigorous ex-ante evaluation of the likely impacts of policies and programs designed to affect family-formation outcomes in the United States.1 One of the only such tools is the FamilyScape microsimulation model, which simulates the key antecedents of pregnancy (sexual activity, contraceptive use, and female fecundity) and many of its most important outcomes (e.g., childbearing within and outside of marriage, children’s chances of being born into poverty, and abortion). The model readily lends itself to policy simulations, since any of its behavioural inputs can easily be changed under the assumption that a given intervention has a particular effect on individual behaviour. For instance, if one believes that a policy will have a particular effect on (say) the share of sexually active women who rely on condoms, it is straightforward to alter women’s baseline probabilities of condom use in order to estimate the impacts of this behavioural change on (for example) the incidences of pregnancy, childbearing, and abortion.2 FamilyScape has been used to simulate the effects of policies such as a national evidence-based sex education program targeted on at-risk youth, an expansion in states’ Medicaid family planning programs, and interventions designed to increase condom use. The results of these simulations are documented in numerous papers and reports, including Karpilow, Manlove, Sawhill, and Thomas (2013), Manlove, Cook, Karpilow, Thomas, and Fish (2014), Sawhill, Thomas, and Monea (2010) and Thomas (2012a, 2012b, 2014).

Earlier versions of FamilyScape explicitly modelled the formation and dissolution of opposite-sex relationships. The model’s relationship formation modules were designed to ensure that women in marital and nonmarital relationships were paired with men whose demographic characteristics were similar to their own (Thomas & Monea, 2009; Thomas, Karpilow, & Gold, 2013). However, due in large part to the fact that the relevant real-world data provide much less information on the contraceptive histories of men than of women, these earlier versions of the model did not directly condition relationship formation on contraceptive use. In other words, when a given woman’s partner was selected from among the pool of eligible men, the matching process did not account for the contraceptive method(s, if any) being used by that woman or by her potential male partners. Also important is the fact that, while women were allowed to switch contraceptive methods over the course of the simulation, the data constraints described above precluded us from explicitly simulating contraceptive switching among men.

In order to circumvent these data limitations, we have developed a new version of the model, FamilyScape 3.0, for which the simulation population is comprised solely of women. We developed all of the model’s simulation parameters using real-world data that reflect women’s self-reported histories of sexual activity, contraceptive use (including the use of male-controlled methods), and fertility outcomes. FamilyScape 3.0 might therefore be described as a “single-sex” model, given that the simulation population includes only women, and since the model’s parameters are based solely on women’s self-reports.3 One could alternatively think of the new version of FamilyScape as a “couple-level” model that accounts for both male and female sexual and contraceptive behaviours, but that uses women as the analytical focal point for the simulation of those behaviours. As a result of these changes to FamilyScape’s architecture, the new version of the model produces rates of contraceptive failure and switching for both female-controlled and male-controlled methods that are very closely aligned with their corresponding real-world benchmarks. We would also note that, whereas earlier versions of the model accounted for only a small number of child outcomes, FamilyScape 3.0 simulates a wider variety of outcomes for newborn children and their mothers. In addition, the new version of FamilyScape is the first iteration of the model to replicate precisely the real-world distribution of sexual activity across months, and it is parameterized using more recent data than was the case for previous iterations of the model.

FamilyScape 3.0 (henceforth, “FamilyScape”) was developed by researchers at Georgetown University, Child Trends, and The Brookings Institution. FamilyScape was programmed using the Stata statistical software package, release 13 (StataCorp, 2013).4 The technical aspects of the model’s simulation structure are described in detail in Thomas and Karpilow (2015). Our purpose here is fourfold. First, we outline FamilyScape’s architecture in broad strokes. Second, we extensively benchmark the model’s simulation results. Third, we provide detail on our methods for estimating FamilyScape’s simulation parameters. And fourth, we offer some thoughts about the model’s potential to produce information that may be useful to policy-makers and practitioners seeking to improve child and family well-being by affecting family-formation outcomes.

## 2. Overview of the model

FamilyScape is a static microsimulation model that reproduces real-world family-formation behaviours and outcomes in the United States as observed between 2006 and 2010.5 Its parameters were developed through extensive analysis of a wide range of real-world data sources, although most parameters were estimated using the 2006 – 2010 cycle of the National Survey of Family Growth (NSFG). FamilyScape has a daily periodicity, which is to say that each increment in analysis time corresponds to a single day. Behaviours and outcomes are simulated at the individual level and are then aggregated to produce population-wide estimates for various phenomena of interest. The women in the model’s simulation population are heterogeneous: each of them is assigned a set of demographic characteristics that help to govern the various actions that they will take over the course of the simulation. More specifically, the model’s simulation population is nationally representative of women who are of childbearing age with respect to marital status, age, race, educational attainment, and socioeconomic status (SES), and simulated behaviours and outcomes are allowed to vary across these demographic dimensions.6

As is the case in the real world, women within the simulation behave autonomously and sometimes inconsistently. For example, some women in the simulation population are more likely than others to use a particular method of contraception, but women may also switch methods over the course of the simulation. Each of FamilyScape’s inputs (sexual activity, contraceptive behaviour, and so forth) is simulated so as to ensure that distributions of the resulting behaviours are consistent with benchmarks that were produced from extensive analysis of several different data sources. We then validate the model by comparing its outputs (rates of pregnancy among women who rely on various types of contraception, the incidence of childbearing within and outside of marriage, the frequency of abortion, etc.) to their real-world equivalents. As is discussed below, FamilyScape generally performs quite well in this regard.7

Figure 1 diagrams FamilyScape’s overall structure and delineates the various stages of the simulation. During the first simulation stage, the model is populated with a nationally representative group of women who are assigned a set of behavioural attributes that vary as a function of their demographic characteristics. In the second stage, sexual activity (or a lack thereof) is simulated, and contraceptive use (or a lack thereof) is modelled among women who have sex. In the third stage, some sexually active women become pregnant, and each pregnancy eventually results in a birth, an abortion, or a fatal loss. In the model’s fourth and final stage, we simulate a variety of different outcomes for newborn children and their mothers. Because behaviours and outcomes are simulated on a daily basis, they may or may not occur anew on each new day. Thus, a woman who does not have sex today may do so tomorrow; a sexually active woman who will not become pregnant tomorrow may conceive on the day after; and so forth. Figure 1 therefore only illustrates the broad contours of the simulation’s four stages. The next four subsections describe each stage in greater detail.

Figure 1

### 2.1 Stage I: initialization of the simulation

Our simulations rely heavily on estimates derived from the 2006 – 2010 NSFG, which contains a nationally representative sample of individuals who are between 15 and 44 years of age (National Center for Health Statistics [NCHS], 2011). The NSFG collects information on respondents’ pregnancy and childbearing histories, sexual activity, contraceptive use, and a variety of other correlates of fertility, family formation, and child well-being (Lepowski, Mosher, Davis, Groves, & van Hoewyk, 2010). This survey is used extensively by scholars and practitioners to study topics related to reproductive, maternal, and infant health in the United States and by policy-makers to guide programmatic decisions with bearing on these outcomes (NCHS, 2016). The 2006 – 2010 cycle of the NSFG is a continuously fielded cross-section, which is to say that different nationally representative cross-sections are sampled in each year of the survey cycle (Lepowski et al., 2010).

While the NSFG surveys both men and women, recall that we rely exclusively on women’s responses to develop FamilyScape’s parameters. As a result, the model’s simulation population contains only women. Crucially, however, female NSFG sample members are asked for information on their use of female-controlled and male-controlled contraceptive methods. More specifically, women are asked for information on the contraceptive method or methods (female-controlled and male-controlled) that they have relied upon during each month for a period of up to four years (NCHS, 2011).8 Thus, although the NSFG is a cross-sectional survey, it provides rich retrospective data on women’s contraceptive histories. Male NSFG respondents are not asked to provide such detailed information on their past contraceptive use. As such, we would be unable realistically to model patterns of contraceptive switching for male-controlled methods if we were to rely on the self-reports of male NSFG sample members. Moreover, because reliance on men’s self-reports of contraceptive use would render us unable to model realistic patterns of male-controlled contraceptive switching, we would also be unable to condition changes in relationship formation and dissolution on the methods used by one’s (existing or potential) partner as the time passes. As previously discussed, these considerations constitute two of the primary limitations of earlier versions of the model and are the reason why men are not included in the simulation population for FamilyScape 3.0.

We would also emphasize that, while men are not included in FamilyScape’s simulation population, male behaviour is a crucial component of the model’s architecture. This is because we used women’s reports of their sexual histories with their male partners, and of the methods that their partners used, when developing the model’s sexual-activity and contraceptive-use parameters. Given that we do not explicitly simulate marital and nonmarital relationship formation and dissolution, one might argue that FamilyScape 3.0 is only a partial equilibrium model. On the other hand, relationship formation is, from the standpoint of our simulation, simply a means to an end: our ultimate goal is to model accurately the frequency of intercourse and the methods used during intercourse. As is discussed later, FamilyScape produces simulated distributions of heterosexual coital frequency, contraceptive use (at the couple level, including both male-controlled and female-controlled methods), and contraceptive switching (again, at the couple level) that are well-matched to their real-world counterparts.

We begin the simulation process by using the NSFG’s sampling weights to extract a group of 20,000 female respondents for inclusion in the simulation population.9 As we import individual observations from the NSFG into the simulation population, we retain information on each respondent’s marital status, age, race, educational attainment, and SES. We operationalize SES using a measure of maternal educational attainment (i.e., the attainment of the mothers of the members of the simulation population).10 We usually simulate variation in FamilyScape’s behavioural inputs and key outcomes according to each of these characteristics.

We considered the possibility of incorporating other covariates into the simulation, but we ultimately decided not to do so for three reasons. First, the model already contains more than a thousand input parameters, and we wanted to achieve a measure of modelling parsimony. Adding more covariates to the model would substantially increase the number of parameters that we would be required to estimate. Second, the general consensus among the experts advising us during the early stages of the FamilyScape project was that the characteristics listed above were the most important for us to include on substantive and policy grounds. And third, most of the other variables that have been found to be closely linked to family formation behaviours are time-varying. For example, contraceptive use varies according to income-to-needs status (Frost & Darroch, 2008; Jones, Mosher, & Daniels, 2012) and insurance status (Jones et al., 2012; Mosher, Jones, & Abma, 2015). Because FamilyScape is a static model, we limit our set of covariates to attributes that remain fixed over time.11 Thus, we do not include time-varying characteristics of this sort in the simulation.

Given that FamilyScape accounts for a relatively modest number of individual attributes, the regressions that estimate the model’s parameters generally have limited predictive power (see Appendix A). However, as is documented throughout this paper, FamilyScape nonetheless closely matches a multitude of important real-world benchmarks. For instance, the model realistically simulates the rate at which women have sex; the frequency with which sexually active women use contraception; the types of male-controlled and female-controlled contraceptive methods that they use; the number of women who switch onto and off of various methods; the frequency with which women using various forms of contraception (or none at all) become pregnant; the share of pregnancies that result in live births, abortions, and fatal losses; the typical gestation periods for each of these pregnancy outcomes; and the rate at which newborn children and their mothers experience a variety of adverse economic and health outcomes.

Table 1 shows the categorical specifications that were chosen for each of the demographic characteristics that are included in the simulation. We selected these specifications either based on the results of econometric analyses or because we were compelled to do so by the limitations of the data available to us.12

Table 1

Because we use the NSFG’s sampling weights to extract observations, the demographic characteristics of FamilyScape’s simulation population should match closely the weighted characteristics of the sample from which it was drawn. As shown in Table 2, this is in fact the case.13

Table 2

At the outset of the simulation, each woman in the simulation population is assigned a set of probabilities that are subsequently used to model various aspects of her behaviour (e.g. the use of a particular contraceptive method or methods). Most of these probabilities vary as a function of women’s demographic attributes – and, in all instances in which that is true, they are derived based on the results of regression models that were estimated using real-world data. Some regressions include behavioural controls in addition to demographic covariates, as detailed below. When an individual has to make a decision about whether to take a particular action, we randomly select a number from a uniform (0,1) distribution, and the woman engages in the behaviour in question if that draw falls below the relevant probability. If a choice must be made from among more than two options, we model the relevant decision as a series of binary choices. As an example, for a choice with three options, we first model whether women choose option one (as opposed to options two or three). Among women who do not choose the first option, we then model the choice between options two and three. This approach is functionally equivalent to the modelling of simultaneous choices from among all available options, but it is easier to implement in practice.

Given FamilyScape’s heavy reliance on random variation, no two runs of the model are exactly alike. We therefore report simulation results using data that are averaged over multiple runs of the model. Our objective is to perform enough simulation runs to prevent outliers from exercising undue influence over average measures of FamilyScape’s aggregate outcomes across runs. We concluded after a series of exploratory analyses that, when the model is run about 100 distinct times, distributions of its results are consistently unimodal and roughly symmetric. Thus, all results reported in this paper are from 100 one-year simulation runs.

We would also note that no single dataset contains the breadth of information necessary to estimate the entire model’s many input parameters. Thus, once women are imported from the NSFG’s sample into the simulation population, we use data from a variety of different sources to develop the various parameters that govern their behaviour. For reasons of internal consistency, we parameterize the model using data from 2006 – 2010 whenever possible. When data from these years are not available, we use information from the closest available year. We use 2006 – 2010 data because these are the most recent years for which NSFG files were available when FamilyScape 3.0 was being developed. After we completed work on the current version of FamilyScape, a new cycle of NSFG data for 2011 – 2013 was released. However, detailed pregnancy-rate estimates have not yet been published for this recent period, which is to say that there would not be sufficient external benchmarks to allow us thoroughly to validate the model’s results if it were parameterized using this new cycle of the NSFG. Thus, the current version of FamilyScape was developed using data from the most recent time period for which the model’s results can be externally validated.

### 2.2 Stage II: sexual and contraceptive behaviour

The parameters for FamilyScape’s sexual behaviour modules were developed using real-world data on sexual activity across months (these data reflect the number of months over the course of a year during which a woman was sexually active) and coital frequency within months (these data reflect the number of days on which a woman had intercourse during a sexually active month).14 FamilyScape’s process for simulating sexual behaviour is thus comprised of two steps. First, we identify the months (if any) during which a given woman will be sexually active over the course of a given year of analysis time. And second, we identify the specific days on which she will have sex during a month when she is sexually active. Because the married and unmarried populations have fundamentally different distributions of coital frequency, we develop the model’s sexual behaviour parameters separately for these two groups (indeed, for almost all components of the simulation, we estimate parameters separately for married and unmarried women; as a result, we usually benchmark the model’s results separately for these two groups).

Regarding the first of the two steps described above, our analysis of data from the NSFG suggests that, over the course of a year, many women have sex at least once per month, others have no sex, and the remainder fall in between these two extremes.15 Women in the latter group are distributed relatively evenly across months. We therefore place each woman in the simulation population into one of three “annual sexual activity” categories: “highly active,” “moderately active,” or “inactive.” We use the results of analyses of the NSFG to vary women’s chances of being placed into each of these three groups as a function of their demographic characteristics. Women who are assigned to the “highly active” category are sexually active during each month of a year within the simulation; women in the “inactive” category are sexually inactive for the entire year; and women in the “moderately active” category are randomly assigned to be sexually active for between one and eleven months. Figures 2 and 3 report annual distributions of across-month sexual activity for unmarried and married women in the NSFG and in FamilyScape’s simulation population. As is shown in these figures, the simulated and real-world distributions of annual sexual activity are qualitatively similar to one another.

Figure 2
Figure 3

Among women in the NSFG who are sexually active during a given month, the within-month distribution of coital frequency is similar to the above-described distribution of sexual activity across months. In other words, sexually active women can readily be grouped into “high,” “moderate,” and “low” categories with respect to their within-month coital frequency. In order to develop the model’s parameters governing coital frequency during a sexually active month, we therefore use NSFG-derived parameters to assign women to one of three different groups, again as a function of their demographic characteristics.16 We also vary a woman’s chances of falling into each of these groups as a function of her annual sexual activity type. We then calibrate the model to ensure that: a) women in the “high” coital-frequency category have intercourse more often than women in the “moderate” coital-frequency category; b) women in the “moderate” coital-frequency category have intercourse more often than women in the “low” coital-frequency category; and c) the simulation produces a realistic distribution of overall within-month coital frequency. Figure 4 compares the cumulative distribution of within-month coital frequency among unmarried NSFG respondents with the equivalent distribution from a series of FamilyScape simulation runs. Figure 5 shows the same comparison for married women.17 These figures include data on women who have no sex during a given month as a means of further validating the model’s capacity to simulate sexual inactivity. For both groups, the simulated and real-world distributions of within-month coital frequency are quite comparable.

Figure 4
Figure 5

We now describe the model’s procedures for simulating contraceptive behaviour. At the start of a simulation run, members of FamilyScape’s simulation population are assigned to the use of a particular female-controlled and/or male-controlled method (or to the use of no method at all) according to their demographic and behavioural characteristics. We assign women to initial contraceptive categories using data on method use among female NSFG respondents. More specifically, we use contraceptive calendar data on method use during the first month of the past year in which NSFG respondents report that they were sexually active and were not pregnant (we also allow women to switch methods over the course of the simulation using an approach detailed below).

With respect to female-controlled methods, we simulate the use of three different categories of contraception: long-acting reversible contraceptive methods (LARC); other hormonal methods such as the pill, patch, or ring (PPR); and female sterilization.18 With respect to male-controlled methods, we simulate the use of condoms and male sterilization.19 We also allow for the possibility that a woman will not use any female- or male-controlled methods. Indeed, a nontrivial number of women are noncontraceptors in the NSFG, and therefore also within FamilyScape’s simulation population. For contraceptive categories that contain several different methods, FamilyScape’s estimates of contraceptive efficacy represent a weighted average of the relevant methods’ efficacies. Because we use women’s self-reports on their own (female-controlled) methods and their partners’ (male-controlled) methods, we are able to model dual-method use at the couple level. In other words, some women are assigned to the use of PPR methods and condoms; others are assigned to use LARC methods and no male-controlled method; others are assigned to use condoms and no female-controlled method; and so forth.

As we do for sexual behaviour, we use the results of NSFG-based regressions to vary women’s chances of assuming a given contraceptive type according to their demographic characteristics. We also vary contraceptive choice as a function of annual sexual activity type and within-month coital frequency type. Thus, if women who report having relatively more (or less) intercourse in our real-world data also report being relatively more (or less) likely to use a particular type of contraception (or not to use any contraception at all), that dynamic is captured in our estimation of this module’s parameters. Table 3 compares distributions of initial contraceptive method use among female NSFG respondents and members of FamilyScape’s simulation population. The estimates reported in this table reflect the choice of methods among women who are sexually active and are not pregnant. These results confirm that FamilyScape produces distributions of couple-level contraceptive use that are closely matched to the relevant benchmarks from the NSFG.

Table 3

As the simulation progresses, noncontracepting women are allowed to begin using contraception, and contracepting women are allowed to discontinue contraceptive use or to switch methods.20 Women are allowed to begin (or to discontinue) the use of both female- and male-controlled methods. Because FamilyScape’s simulation population functions as a fixed cohort, and since some demographic groups in the real world (and therefore also in the simulation) are more likely than others to adopt certain switching patterns, different contraceptive categories would ultimately become absorbing states for different demographic groups if we were to allow the model to run in perpetuity after the contraceptive switching module was activated. Over the course of a single simulated year, however, such changes mirror realistic developments in female contraceptive behaviours within the simulation population. For this reason, we only activate FamilyScape’s contraceptive switching module for a single year of analysis time. More precisely, we first allow all other behaviours and outcomes (e.g., sexual activity, pregnancy, and childbearing) to reach steady states, and we then allow contraceptive switching to occur over a 365-day window during which we also record data on all simulation outputs of interest (e.g., births, abortions, etc.). All of our reported simulation results reflect outcomes as measured over this one-year period of analysis time.

Contraceptive switching is simulated on a monthly basis. Women are allowed to change contraceptive types multiple times over the course of a year, but they are only considered to be eligible for method switching during months in which they are sexually active and not pregnant. It is also important to note that many women in the real world (and therefore also in the simulation population) do not switch contraceptive types at all: a large share of women using LARC methods will continue to do so throughout the year; many noncontraceptors will not begin using contraception; and so forth.

FamilyScape’s switching module is parameterized using results from four different sets of regression models, each of which is estimated using the 2006 – 2010 NSFG: a) discrete-time hazard models predicting the probability that a woman will switch methods for the first time during a given twelve-month segment; b) hazard models predicting the probability of a “higher-order” contraceptive switch among women who have already switched methods at least once during the twelve-month segment; c) logistic regressions that predict the contraceptive type assumed by a woman who switches methods for the first time; and d) logistic regressions that predict the contraceptive type assumed by a woman who has engaged in a higher-order method switch. Switching probabilities and method selection after a switch vary according to a woman’s demographic attributes, the contraceptive method(s, or lack thereof) that she had previously been using, and whether she was pregnant in the previous month. Higher-order switching behaviours also vary according to the number of previous contraceptive switches.

Tables 4 and 5 allow for an assessment of FamilyScape’s ability to simulate realistic switching behaviours. Both tables report, for women in each origin contraceptive category, the across-month distribution of method choice over a period of twelve months starting with the month in which the origin method was identified. Real-world benchmarks were estimated using the NSFG, and simulated estimates were produced using microdata taken from the year of analysis time during which the model’s switching module was activated. Table 4 reports switching estimates for unmarried women, and Table 5 reports the same for married women. For instance, the second row of data in each panel of Table 4 reports estimates of switching behaviours among unmarried women whose origin contraceptive type was “No Female-Controlled Method & Condom.” Within the simulation, women in this origin category spend an average of 3.9% of months during the focal year in the “No Female-Controlled Method & No Male-Controlled Method” category. The corresponding estimate is 3.6% for our NSFG sample. More broadly, the results reported in these tables demonstrate that FamilyScape’s simulated switching patterns are generally analogous to their real-world equivalents.21

Table 4
Table 5

The reader should bear in mind that, within the context of FamilyScape’s architecture, the concept of contraceptive consistency is distinct from the concept of contraceptive switching. As an example, a woman who is considered to be a pill user during every month of a given year (i.e., a woman who does not switch methods over the course of the year) might also be an inconsistent contraceptor (if she misses a certain number of pills per month). In order directly to simulate inconsistency of contraceptive use, we would require two pieces of information that we do not have. First, we would need data on the distribution of the consistency of method use. For instance, we would require information on the proportion of oral contraceptors who miss one pill per month, the proportion who miss two pills per month, and so forth. And second, we would require evidence on the relationship between each method’s efficacy and the consistency with which it is used. For example, we would require information on the decline in the efficacy of oral contraception when one pill is missed, the further decline in efficacy when two pills are missed, and so forth. We would require similar information in order to simulate variation in the correctness of contraceptive use (i.e., the extent to which methods such as condoms are used as intended).

Such data do not exist. We have therefore chosen not to attempt directly to integrate these dynamics into FamilyScape. Rather, we capture much of the variation in the consistency and correctness of contraceptive use by allowing the efficacies of the methods incorporated into the simulation to vary across demographic groups. There are in fact substantial demographic differences in many methods’ efficacy levels. Much of this variation occurs across marital-status and age categories. For instance, we estimate that the single-act contraceptive failure rate for PPR methods is about 35% lower among married women over the age of 30 than among unmarried women under 30. We assume that this sort of variation reflects demographic differences in the consistency and correctness of method use among women who fall into different contraceptive categories. Under this assumption, FamilyScape accounts for a portion of the heterogeneity that exists in the consistency and correctness with which various methods are used. FamilyScape’s contraceptive efficacy module is described in more detail in the next subsection.

### 2.3 Stage III: pregnancy and pregnancy outcomes

As is the case in the real world, a woman’s chance of becoming pregnant after having sex during the simulation depends on her level of fecundity (i.e., her probability of conceiving from a single act of unprotected intercourse) and on the effectiveness of the contraceptive method(s, if any) that she and her partner using. FamilyScape allows for variation in a woman’s fecundity as a function of her age and the day in her menstrual cycle. Thus, as the simulation advances from one day to the next, it also updates each woman’s menstrual calendar and modifies her (age-adjusted) fecundity level accordingly. We assign age-and-day-specific fecundity values based on our synthesis of the results of several published clinical studies. We rely primarily on Royston’s (1982) results for this purpose because his model has the unique benefit of allowing the probability of pregnancy to vary simultaneously as a function of the woman’s age and her menstrual calendar. Royston estimates parameters for the following equation:

(1) $P{\left(Conception\right)}_{i,t}=\left({\chi }_{0}-{\chi }_{1}*\left[{A}_{i}-\overline{A}\right]\right)*{\alpha }_{t},$

where P(conception)i,t is the probability that individual i will conceive if she has unprotected sex on day t; Ai is the age of individual i; Ā is the mean age of all of the women in the author’s sample; χ0 and χ1 are econometrically estimated parameters that capture the age-dependent likelihood of fertilization; and αt is a vector of generic probabilities of ovular fertilization that vary by the day in the menstrual cycle.22 Royston derived his estimates using data on a sample of women aged 20–39 (Barrett & Marshall, 1969; Royston, 1982). However, given that the women in FamilyScape’s simulation population are between the ages 15 and 44, we use the results of a number of other clinical studies to adjust the imputed fecundity levels assigned to women in the tails of FamilyScape’s age distribution (Dunson, Colombo, & Baird, 2002; Lass et al., 1998; Leridon, 2004).23

As previously discussed, we simulate variation in the consistency and correctness of contraceptive use by modelling variation across demographic groups in the risk of pregnancy that is associated with the use of a given method.24 We calculate a method’s failure rate as follows. Assume that a woman’s fecundity level is given by the constant f, and assume that she has intercourse n times over a one-year period. Thus, the woman’s probability of avoiding pregnancy from a single act of intercourse is (1-f), her probability of avoiding pregnancy over n acts of intercourse can be assumed to be (1-f)n, and her risk of experiencing a pregnancy over n acts of intercourse is (1 – (1-f)n). Now assume that the woman in question uses a contraceptive method that reduces her risk of pregnancy by 95% each time she has sex. We define this method’s “single-act failure rate” to be (1-.95) = .05. According to this formulation, the woman’s single-act conception probability is now .05*f, and her conception probability over n acts of intercourse is (1 – (1-(.05*f))n).

More generally, one can think of a method’s single-act failure rate, c, as one minus its “efficacy rate”, where contraceptive efficacy in this context is defined as the proportional reduction in the risk of pregnancy at a given act of intercourse that is achieved by the use of that method. Although we allow for demographic variation in most methods’ single-act failure rates, we make the simplifying assumption that failure rates are homogenous within groups. Our approach thus yields the following generalized equation:

(2) $P{\left(\mathrm{Pregnant}\right)}_{i,j}=\left(1-{\left[1-\left({c}_{i,j}*{f}_{i,j}\right)\right]}^{{n}_{i,j}}\right),$

where P(Pregnant)i,j is the monthly probability of experiencing a pregnancy for women who are in demographic subgroup i and are using method j; fi,j gives the mean fecundity level (averaged across all relevant ages and all days in the menstrual cycle) for women in demographic group i who use method j; ni,j gives the average monthly coital frequency among women in demographic group i who use method j; and ci,j gives the contraceptive failure rate experienced by women in demographic group i who use method j. We then re-state Equation 2 as follows in order to solve for ci,j

(3) ${c}_{i,j}=\frac{1-{\left(1-P{\left(\mathrm{Pregnent}\right)}_{i,j}\right)}^{\frac{1}{{n}_{i,j}}}}{{f}_{i,j}}$

We perform separate calculations for each distinct combination of i and j. In other words, we develop demographically specific single-act failure-rate estimates for each possible combination of female- and male-controlled methods. For example, we separately calculate dual-method failure rates for women who use a PPR method and condoms and single-method failure rates for women who use a PPR method and no male-controlled method. The only exception to this rule is sterilization: we make the simplifying assumption that the risk of pregnancy is completely eliminated for any woman who is sterilized or whose partner is sterilized.

We estimate ni,j using data on the monthly coital frequencies of women in the 2006 – 2010 NSFG who fall into each demographic-contraceptive-method subgroup. We produce demographically specific estimates of fi,j, by: a) using our adjusted Royston equations to calculate a single fecundity estimate, averaged across all days in the menstrual cycle, for each woman in the NSFG; and b) using these estimates to calculate a mean fecundity level for each demographic-contraceptive-method group. We estimate P(Pregnant)i,j in two stages. First, we use the NSFG to estimate the monthly pregnancy rates of women falling into each demographic subgroup. And second, because abortions have been found to be substantially underreported in the NSFG (Jones & Kost, 2007), we correct our NSFG-based estimates of method-specific pregnancy rates for abortion underreporting. Our corrections rely on data taken from Jones, Darroch, and Henshaw (2002) and Jones and Jerman (2014).25 After developing demographically specific estimates of ni,j, fi,j, and P(Pregnant)i,j, we plug these quantities into Equation 3 in order to calculate a single-act contraceptive failure rate for each demographic-contraceptive-method subgroup. We then calculate a woman’s single-act conception probability at a given act of intercourse by taking the product of her (day-and-age-specific) natural fecundity level and the single-act failure rate of the contraceptive method(s, if any) that she is using.

Having described the way in which FamilyScape simulates the occurrence of pregnancy, we next benchmark the model’s simulated annual contraceptive failure rates among women who use various forms of birth control. The best available real-world estimates of method-specific pregnancy rates are reported by Trussell (2011), who calculates the probability of experiencing a pregnancy within a year of typical use of a given method. We calculate weighted averages of these method-specific pregnancy probabilities in order to produce estimates for broad contraceptive groupings that are comparable to FamilyScape’s contraceptive categories. The weights used in these calculations reflect the relative shares of women who use each method included within a given contraceptive category. We employ contraceptive-use data reported in Jones et al. (2012) to develop these weights.

Table 6 compares FamilyScape’s simulated method-specific annual pregnancy probabilities to our real-world benchmarks. Because Trussell’s estimates are not disaggregated by marital status (or by any other demographic characteristic), we report simulated method-specific pregnancy rates for all women, without respect to marital status. Note that we report simulated and real-world estimates for women not using any contraception. There is wide variation in real-world estimates of risk of pregnancy among noncontraceptors. For example, Trussell (2011) concludes that women currently using reversible contraception would have an 85% probability of becoming pregnant if they were to discontinue use of their methods but leave their behaviour otherwise unchanged. However, other research suggests that the annual pregnancy rate is 46% among women who abandon contraception and are not seeking pregnancy (Vaughan, Trussell, Kost, & Jones, 2008). Thus, we report a range of 46% to 85% as the real-world benchmark for the “no-method” group. For male and female sterilization, LARC methods, PPR methods, and condoms, the simulated and real-world estimates reported in Table 6 are very similar to each other. The simulated annual pregnancy probability for women in the “no-method” group is roughly equidistant of the two real-world benchmarks for this category. In sum, FamilyScape closely approximates annual real-world, method-specific contraceptive failure rates.

Table 6

After a woman in the simulation becomes pregnant, her simulated pregnancy will eventually result in a live birth, an abortion, or a fatal loss. We use information from the National Center for Health Statistics’ 2008 National Vital Statistics System (NVSS), the Guttmacher Institute’s 2008 Abortion Provider Survey, and the 2006 – 2010 NSFG to assign an outcome to each new pregnancy as a function of the woman’s demographic characteristics.26 Figure 6 compares simulated and real-world data on the shares of pregnancies to unmarried women that result in live births, induced abortions, and fatal losses. Figure 7 presents the same comparison for pregnancies to married women. For both groups, FamilyScape produces realistic pregnancy-outcome distributions.

Figure 6
Figure 7

Although a woman within the simulation may continue to have sex while she is pregnant, she cannot become pregnant again for the duration of her pregnancy or during an interval of simulated post-pregnancy infertility. We synthesize information from several different sources to develop the model’s parameters governing the lengths of the gestation periods and post-pregnancy infertility intervals for each pregnancy outcome.27

We now turn to a comparison of aggregate simulated and real-world pregnancy, birth, and abortion rates. Table 7 reports annual simulated and real-world pregnancy and pregnancy-outcome rates per 1,000 women aged 15 to 39. Estimates are disaggregated by marital status and age. The top panel of the table displays averaged results from 100 runs of the model. The bottom panel presents real-world pregnancy and pregnancy-outcome benchmarks from 2008 as measured using the data described above. The greyed rows at the bottom of each panel report aggregate pregnancy, birth, and abortion rates among married and unmarried women. Aggregate simulated pregnancy and birth rates for unmarried women are within about 2% of their real-world targets, and the simulated unmarried abortion rate is within about 4% of its corresponding benchmark. Among married women, the simulated pregnancy rate is within about 3% of its target, and simulated and real-world birth rates are nearly identical. The simulated rate of abortion among married women is, in proportional terms, somewhat further away from its real-world benchmark, but this difference is small in absolute terms (.7 abortions per 1,000 married women) because the married abortion rate is so low. On the whole, then, these results demonstrate that FamilyScape is able to replicate with considerable precision a number of important aggregate real-world benchmarks among both married and unmarried women.

Table 7

Many of FamilyScape’s demographically disaggregated estimates are also well-matched to their real-world equivalents. Among unmarried women in their twenties, for example, the simulated rates of pregnancy, birth, and abortion are all quite close to their targets. For other subgroups, however, the model’s simulated results are further removed from their corresponding benchmarks. This dynamic is the most pronounced for comparatively small groups (e.g., married teenagers and unmarried women in their thirties) and for outcomes that occur with very low frequency within a given subpopulation (in particular, age-specific abortion rates among married women).28 This general result is to be expected, given that the demands placed upon the relevant data become increasingly difficult to meet for increasingly small groups and/or or for outcomes that are increasingly rare. It is, however, noteworthy that the simulated teenage pregnancy rate (79.5 pregnancies per 1,000 teenaged girls) is not far off from its real-world benchmark (72.5 pregnancies per 1,000 teens).

We have also found that the model over-simulates pregnancies to a noticeably greater degree among women in their forties than among women under 40. This suggests that the age-based decline in fecundity within FamilyScape may be too gradual for this group. Thus, and since the literature is particularly sparse with respect to the shape of the age-fecundity profile for women over 40, we have chosen not to include results for this age range when we report findings from FamilyScape’s policy simulations. Hence the fact that Table 7 focuses only on pregnancies and pregnancy outcomes among women aged 15 to 39. Taken as a whole, these results suggest that it is more appropriate to use FamilyScape to perform policy simulations targeted on broad groups (teenagers and unmarried women, for example) than to target narrowly defined demographic subpopulations. For these larger groups, FamilyScape’s simulated fertility outcomes are sufficiently realistic to allow for credible and informative policy analyses.

Recall that we report simulation results using data that are aggregated over 100 distinct simulation runs so as to ensure that average measures of the model’s outcomes across runs are not influenced unduly by outliers. Figure 8 reports the distribution of simulated pregnancy rates among unmarried women across 100 runs of the model, and Figure 9 reports the same for married women. For both groups, the pregnancy-rate distribution across runs is unimodal and roughly symmetric.

Figure 8
Figure 9

### 2.4 Stage IV: maternal and child outcomes

FamilyScape models a number of different maternal and child outcomes for each simulated birth. For instance, because we record the marital status of each woman in the simulation, we also automatically track the structures of the families – specifically, whether they are married-parent or single-parent – into which children are born. For each live birth, the model also assigns a poverty status to the newborn child as a function of the mother’s demographic characteristics. FamilyScape’s child poverty module is parameterized using data from the March 2009 Current Population Survey, which contains income information for calendar year 2008.

We model several additional maternal and child outcomes using 2008 NVSS data. Given that being born at low birth weight is predictive of later health problems such as asthma, diabetes, and heart disease (Johnson & Schoeni, 2011), we model the probability that a newborn child will weigh less than 2,500 grams at birth. Evidence also suggests that children are more likely to experience a variety of negative outcomes if their mothers smoke or experience hypertension or diabetes during pregnancy (Gilland, Li, & Peters., 2001; Kim, Vohr, & Oh, 1996: Yessoufou & Moutairou, 2011). We therefore simulate maternal smoking, maternal hypertension, and maternal diabetes for pregnancies that will ultimately result in births. We use the results of NVSS-based regressions to vary women’s probabilities of experiencing these outcomes as a function of their demographic attributes.

Table 8 compares simulated and real-world estimates for each of these outcomes except family structure, which is benchmarked in Table 7. For all outcomes, FamilyScape produces simulated results that are similar to their real-world benchmarks.

Table 8

## 3. Parameter estimation

As previously discussed, we assign most of FamilyScape’s behavioural parameters to members of the simulation population using the results of regression analyses that were estimated using real-world data. Each of these regression models includes as covariates some or all of the demographic characteristics enumerated in Table 1. Many regressions also include controls for certain behavioural attributes. For example, when we estimate regressions models for the purpose of assigning an initial contraceptive type to each member of the simulation population, we control for annual sexual activity type and within-month coital frequency type. Likewise, we model the probability of contraceptive switching as a function of whether the woman was pregnant in the previous month and of her initial contraceptive type (i.e., the contraceptive type assigned to her at the outset of the simulation). For a woman who switches methods multiple times, we additionally condition the probability of “higher-order” switching on her most recent contraceptive type and on the number of times that she has switched methods during the current year.

Table 9 provides a summary of the covariates included in each set of regression equations. In addition, the table reports the number of unique outcomes that are modelled by each set of regressions and the number of equations required to model those outcomes. For instance, there are three possible outcomes for a given pregnancy (i.e., each pregnancy will result in a birth, an abortion, or a fatal loss), and we use two equations to model these three outcomes. One regression models the probability that a given pregnancy will result in an abortion; a second regression models the probability that the pregnancy will result in a birth given that it did not result in an abortion; and the residual probability reflects the likelihood that the pregnancy will result in a fatal loss. As is indicated in the table, we estimate separate regression equations for married and unmarried women for each outcome.29 The table also describes the functional form for each set of regressions. As an example, we use the results of hazard models to simulate contraceptive method switching (this approach allows the probability of switching to vary as a function of analysis time), and we use the results of logistic regression models to simulate the choice of contraception among women who switch methods.30 In Appendix A, we report results for all of the regressions used to estimate FamilyScape’s parameters.

Table 9
Table 10

A smaller number of FamilyScape’s parameters were generated using an approach other than regression-based estimation. For instance, a fecundity level is imputed to each member of the simulation population on each day by plugging her age and the day in her menstrual cycle into one of several equations that we developed by synthesizing the results of a number of different clinical studies that were previously referenced.31 Similarly, a woman is assigned a contraceptive failure rate as a function of the method(s, if any) that she is using, her age, and her marital status. More specifically, we estimate subgroup failure rates by plugging the characteristics of each contraception-age-marital-status group (e.g., that group’s monthly pregnancy rate and average monthly coital frequency) into Equation 3, which was developed specifically for the purpose of modelling single-act contraceptive failure rates within FamilyScape’s simulation framework.32 Table 10 briefly describes the estimation approach that was used to develop each of FamilyScape’s nonregression-based parameters. The table also reports the demographic and/or behavioural dimensions along which these parameters vary. As an example, a pregnancy’s gestation period varies only according to the pregnancy’s outcome (e.g., a birth will have a notably longer gestation period than will an abortion or a fatal loss).33

## 4. Discussion

FamilyScape 3.0 successfully reproduces real-world variation in the most important proximate antecedents of pregnancy, including sexual activity, contraceptive behaviour, and female fecundity. Perhaps most importantly, the model generates aggregate rates of contraceptive failure, pregnancy, birth, abortion, and maternal and child outcomes that closely match their real-world equivalents. Data from numerous sources are integrated into the model’s simulation structure in order to ensure that these behaviours and outcomes vary realistically according to marital status, age, race, educational attainment, and SES.

FamilyScape also has important limitations. Our results suggest that the model is better suited to analyses that focus on broadly defined groups (for example, unmarried women) than to analyses that focus on more narrowly defined groups (for example, young unmarried nonwhite women). Also important is the fact that FamilyScape only accounts for a limited number of individual attributes. However, given the precision with which the model replicates real-world fertility outcomes at the aggregate level for both married and unmarried women, we believe that it holds considerable promise as a policy analysis tool.

We intend to use FamilyScape to project the impacts of a variety of different policy interventions. To the extent that external estimates are available regarding policies’ effects on sexual and contraceptive behaviours, the model can be used to project the implications of these behavioural impacts for rates of pregnancy, childbearing, abortion, child poverty, low birth weight, and so forth. For example, in the wake of the ACA’s implementation, researchers will undoubtedly estimate its impacts on contraceptive behaviour. FamilyScape can then be used to study the implications of these behavioural changes for a range of different outcomes. As another example, several recent studies have shown that rates of unintended pregnancy can be dramatically reduced by increasing access to LARC methods (Harper et al., 2015; Ricketts, Klingler, & Schwalberg, 2014; Winner et al., 2012). This body of evidence has led some researchers to conclude that future reductions in unintended pregnancy may require expanded use of LARC methods (Peipert, Madden, Allsworth, & Secura; Secura, 2013). We plan to use FamilyScape to test this hypothesis by assessing the extent to which pregnancy rates could be reduced via increases in the use of other forms of contraception, such as condoms and PPR methods. More broadly, our expectation is that FamilyScape will be used to answer a host of important policy questions, especially given that considerations of family structure feature so prominently in contemporary social policy debates in the United States.

## A. Parameter-estimation regressions

The tables below report results for each of the regressions used to estimate FamilyScape’s parameters pertaining to annual sexual activity, within-month coital frequency, initial contraceptive assignment, contraceptive switching, pregnancy outcomes, and birth outcomes.1 We would note that, due to small sample sizes and/or limited variation in our data, we are occasionally unable to estimate models that contain a full set of covariates. For instance, only eleven married women in our NSFG data are initially assigned to the “LARC & Condom” contraceptive category. As a result, we are unable to include all of our demographic controls in the initial contraceptive assignment regression that models married women’s probability of falling into this category. We therefore control only for age in this regression specification (see Table A.4). In all such cases, our goal was to extract as much information as possible from our data while still allowing for reliable estimation of our regression models.2

Table A1
Table A2
Table A3
Table A4
Table A5
Table A6
Table A7
Table A8
Table A9
Table A10
Table A11
Table A12
Table A13

## B. Description of familyscape’s simulation process

The FamilyScape simulation process consists of the following three steps, each of which is discussed further below:

I. Create a simulation population

II. Specify and execute FamilyScape simulations (i.e., baseline or policy-intervention)

III. Analyse FamilyScape simulation output

### B.1 Create Simulation Population

Before FamilyScape simulations can be performed, a simulation population must be created by randomly sampling observations with replacement from the female respondent file of the 2006 – 2010 NSFG. A given simulation population can be replicated by using the same random seed number each time that a sample is extracted. Recall that FamilyScape incorporates randomness into its simulation of behaviours and outcomes (e.g., a woman who has sex becomes pregnant if a random draw from a uniform (0,1) distribution falls below some specified threshold that is based on her fecundity and the efficacy of the contraceptive methods used during intercourse). As such, simulated output (e.g., annual pregnancy rates) will vary from run to run. Users can increase the precision of FamilyScape estimates (i.e., reduce the influence of random variation of simulation results across runs) by augmenting the size of the simulation population.3 An increase in precision might be desirable when simulating relatively small behavioural changes (e.g., a 5 percent increase in condom use) whose effects on (say) pregnancy rates are at risk of being drowned out by random variation across simulation runs. The trade-off here is that any increase in the size of the simulation population dataset will also increase (1) the runtime of FamilyScape simulations and (2) the required data storage capacity.

### B.2 Specify and Execute FamilyScape Simulation

Once a simulation population has been created, simulations can be performed for that population. FamilyScape has the capacity to execute two types of simulations: (1) baseline (i.e., pre-intervention) simulations, and (2) simulations that change behaviours related to contraception, including contraceptive use, contraceptive switching, and contraceptive efficacy. FamilyScape is programmed such that it can easily accommodate a variety of contraceptive interventions for a plethora of demographic subgroups. Importantly, however, simulation data should only be analysed for days 1081 through 1446. This is because (1) time must pass before FamilyScape’s simulated behaviours and outcomes (e.g., pregnancy rates) reach a steady state; and (2) members of the simulation population are only allowed to switch contraceptive methods starting on day 1081. Because FamilyScape’s switching parameters are only able to model switching patterns over the course of a single year, the focal year spans from day 1081 to day 1446.

### B.3 Analyse FamilyScape Output

After specifying and running a simulation with FamilyScape, the microdata produced by the simulation can be used to estimate the effects of a policy intervention on a given measure of interest. For example, suppose that the user is interested in estimating the effects of increasing LARC use on the pregnancy rate among unmarried women. To perform this analysis, she would:

A. Run a baseline specification of FamilyScape and compute a pre-intervention pregnancy rate for unmarried women using microdata produced by these runs;

B. Run an intervention specification of FamilyScape (e.g., one in which LARC use is increased by 10%) and compute a post-intervention pregnancy rate for unmarried women using the microdata produced by these runs; and

C. Compare simulated pre- and post-intervention pregnancy rates in order to estimate the effect of the intervention on nonmarital pregnancies.

Post-simulation analysis of FamilyScape output requires not only merging micro-level datasets across days in a simulation run (e.g., to compute a change in pregnancy counts across individual members of the simulation population), but also averaging estimates across multiple runs (e.g., averaging pregnancy rates across runs to generate a final nonmarital pregnancy rate).

The model keeps track of abortions, miscarriages, live births, and maternal and newborn child outcomes. users can therefore perform the same set of calculations described above for (say) teenagers to compute pregnancy-outcome rates (e.g., teen birth rates, teen abortion rates, etc.). However, the reader may be wondering what analysis timeframe to use when tabulating pregnancy outcomes, since pregnancies take time to resolve into births, abortions, and miscarriages. In particular, many pregnancies that occur between days 1081 and 1446 will technically resolve in the subsequent year (i.e., beyond day 1446). For example, a pregnancy that occurs on day 1445 could result in a birth 9 months later. To circumvent this problem, FamilyScape determines the pregnancy outcome of each pregnancy (and, for simulated births, the corresponding maternal and child outcomes) on the day of the conception. Thus, if a woman becomes pregnant on day 1440, FamilyScape imputes to that pregnancy an outcome on day 1440, even though the resolution of the pregnancy will occur many days in the future. Consequently, FamilyScape is designed to count pregnancy and birth outcomes on the day of conception, rather than on the day of pregnancy resolution, thereby avoiding the timeframe complications outlined above.

## C. Pseudocode

FamilyScape 3.0 was created using release 13 of the Stata statistical software package (StataCorp, 2013). The pseudocode below provides a general overview of the coding approach used to implement each of FamilyScape’s modules.

### C.1 Procedures for Simulating Sexual Behaviour

The Assign Across Month Sexual Activity Type and Assign Within Month Coital Frequency Type programs are executed at the beginning of the simulation. The probabilities of falling into sexual activity type and coital frequency type categories vary according to the characteristics enumerated in Table 9. The parameters used to assign these probabilities are listed in Tables A.1 and A.2 in Appendix A. The Assign Sexually Active Months program is executed at the beginning of each year of analysis time. The Have Sex this Month and Assign Sexually Active Days programs are executed at the beginning of each month of analysis time. Finally, the Have Sex Today program is executed at the beginning of each day of analysis time.

Algorithm C.1
Algorithm C.2
Algorithm C.3
Algorithm C.4
Algorithm C.5
Algorithm C.6

### C.2 Procedures for Simulating Contraceptive Behaviour

The Assign Initial Contracptive Type program is executed at the beginning of the simulation. The probabilities of falling into FamilyScape’s contraceptive method categories vary according to the characteristics enumerated in Table 9. The parameters used to assign these probabilities are listed in Tables A.3 and A.4 in Appendix A. The Method Switching program is executed at the beginning of each month of analysis time after the first month in which the switching module is activated. First-time method switches and higher-order switches are simulated separately, but both processes follow the same basic procedures outlined below. The probabilities of first-time and higher-order switching, and the selection of methods after a contraceptive switch, vary according to characteristics that are again enumerated in Table 9. The parameters that govern switching behaviour are listed in Tables A.5A.11 in Appendix A. FamilyScape’s contraceptive method category variable is coded as follows:

(0) Female Sterilized/No Male-Controlled Method

(1) Female Not Sterilized/Male Sterilized

(2) LARC/Condom

(3) LARC/No Male-Controlled Method

(4) PPR/Condom

(5) PPR/No Male-Controlled Method

(6) No Female-Controlled Method/Condom

(7) No Method

Algorithm C.7
Algorithm C.8

### C.3 Procedures for Simulating the Occurrence of Pregnancy

All of the programs below are executed each time a woman has intercourse. The Assign Fecundity program models fecundity levels using an approach that is described in the main text. The Assign Contraceptive Failure Rate program incorporates a set of demographically specific contraceptive failure rates for each method category. The “infertileToday” term is a dummy variable set equal to one if a woman is in the midst of a period of post-pregnancy infertility (see the next section of this appendix for more information).

Algorithm C.9
Algorithm C.10
Algorithm C.11

### C.4 Procedures for Simulating Pregnancy and Birth Outcomes

The Assign Pregnancy Outcome Probabilities and Assign Birth Outcome Probabilities programs are executed at the beginning of the simulation. The probabilities that a pregnancy will result in a given outcome, and that various outcomes will obtain for a given birth, vary according to the characteristics enumerated in Table 9. The parameters used to assign these probabilities are listed in Tables A.12 and A.13 in Appendix A. The Assign Pregnancy Outcome and Assign Post Pregnancy Infertility Period programs are executed each time that a pregnancy occurs. Post pregnancy infertility periods encompass both a pregnancy’s gestation period and an interval of infertility that begins once the pregnancy has ended. Gestation periods and post pregnancy infertility intervals vary in length according to a pregnancy’s outcome. FamilyScape models a variety of birth outcomes; the generic code below is a general representation of the routines used to model each outcome. Birth outcomes are simulated each time that a birth occurs.

Algorithm C.12
Algorithm C.13
Algorithm C.14
Algorithm C.15
Algorithm C.16

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## Article and author information

### Author details

McCourt School of Public Policy, United States
2. #### Quentin Karpilow

Child Trends, United States
##### For correspondence
qkarpilow@childtrends.org
3. #### Kate Welti

Child Trends, United States
##### For correspondence
kwelti@childtrends.org
4. #### Jennifer Manlove

Child Trends, United States
##### For correspondence
jmanlove@childtrends.org
5. #### Elizabeth Cook

Child Trends, United States
##### For correspondence
ecook@childtrends.org

### Acknowledgements

We thank Isabel Sawhill, Scott Winship, Joshua Epstein, Ross Hammond, Kristin Moore, Kelleen Kaye, and James Trussell for their contributions to the development of the FamilyScape model, and we thank the journal’s editors and four anonymous referees for their constructive comments on earlier drafts of this manuscript. Thanks also to the JPB Foundation and Child Trends for their generous support of our work. And finally, we owe debts of gratitude to Alex Gold, Emily Monea, and Miles Parker for the roles that they played in the development of earlier versions of FamilyScape.

### Publication history

1. Version of Record published: August 31, 2017 (version 1)