Demography and Family: A Microsimulation Strategy to Bridge the Gap

The study of the family has had a long and distinguished history in the demographic research tradition.[1] A central preoccupation of this early work was the development of methods to obtain information about family structures from basic demographic characteristics of populations. As a result of this work, we learned to adapt classic life table methods and stable population equations to estimate key measures of kinship.

More recently, improvements in computational power have allowed for more sophisticated microsimulation-based techniques that enable the modeling of demographic behaviors at the individual level. These techniques generate kinship projections at finer resolutions and often with great fidelity to empirical fact. In this post, I present a brief introduction to the theoretical relationship between demography and the family, and demonstrate how a microsimulation strategy can help us bridge the analytic gap between the two.


The Mechanical Relationship between Demography and the Family

Let’s begin by talking about the relationship between demography and the trajectory of family life. To do that, let’s imagine that we have an individual – Sally – represented by a life line. Now imagine that Sally has a child at age 20. At that moment, Sally has transitioned into the kinship relation that we call “parenthood.” Now imagine that Sally’s parents had a child when she was 10-years-old. At that moment, Sally transitions into the kinship relation that we call “siblinghood.”


Figure 1. Birth of family members trigger kinship transitions

What is worth noting in each of these cases is how the fertility, not only of the individual, but of related individuals, demarcates the transition points into and out-of different kinship relations. In addition, mortality too can initiate kinship transitions. For example, if Sally experiences the death of her last parent at age 50, she is an orphan from that point on – she has transitioned out of the “childhood” relation.


Figure 2. Death of family members trigger kinship transitions

This relationship between demography (birth and death) and kinship is a completely mechanical one; being in any given kinship relation at each age is perfectly determined by the timing of fertility and mortality events of the individual and her kin.

At the population level, this relationship holds at the margins. That is on average the timing of an individual’s kinship transitions are determined by age-specific rates of fertility and mortality of the population. Taking the family, rather than the individual, as our unit of observation we can further formalize this insight by noting two principal mechanisms by which demography shapes family: death constraints and life constraints.


Figure 3. Baseline age-profiles of mortality and fertility

Imagine, for example, a population with some baseline fertility and mortality. Under these demographic conditions, we might observe the following hypothetical family network:


Figure 4. Hypothetical family network at baseline

Here we see not just Sally, but her entire constellation of living relatives.[2] Now let us imagine that Sally’s family existed in a demographic regime where mortality was much higher and fertility much lower.



Figure 5. Demographic constraints operating on the family network

Under this scenario, we see that death has removed Sally’s aunt from the family network and, in some sense, has “severed” the network connection linking Sally to her uncle and cousin. Because it is a mortality (death) event that triggers this truncation of the family network, I call this a mechanism of death constraint. On the opposite end of the life course, we see that the reduction in fertility has led to a situation where Sally’s sibling was never born. This effectively removes the sibling node from Sally’s family network and forecloses the possibility of a future family tie between Sally and her sister-in-law or nephew. In this instance, because the lack of a fertility (birth) event triggers this truncation of the family network, I call this a mechanism of life constraint. Finally, because fertility and mortality work in different ways to delimit the boundaries of kinship (the former by determining the ever-existence of relatives and the latter by determining the current-existence of relatives), we expect both constraints of life and death to operate simultaneously within populations.

At this point, a skeptical observer might argue that these demographic constraints on kinship, while certainly plausible on paper, remain largely hypothetical, relying on a type of counterfactual thinking that we are not accustomed to or un-willing to entertain – what does it mean, for instance, to account for people who were never born? We will return to this important point, but first we attend to the question of measurement.

Data Limitations: The Challenge

If we are convinced that demography influences the shape and trajectory of family, the question remains: how can we formally investigate this linkage given a general dearth of good genealogical data? As one might expect, this is a rather difficult challenge to overcome. In fact, much of the early work by family demographers was devoted to developing clever ways to address exactly this issue. Today, as ever, the ideal solution is to make use of high-quality observational data wherever they may exist. For example, Kinsources, the International Social Survey Programme, and various national censuses all provide some measurements of family structure. However, there remain several limitations of these data that prevent more extensive investigations:

  1. Narrow samples. These data are often only collected for small and specially-defined groups of people, preventing generalization to larger populations.
  2. Cross sectional data collection. These data are often period “snapshots” collected at a particular historical moment, preventing investigation of changes over time.
  3. Conflation of family with households. These data are often part of household surveys where family members that are not co-resident are not included in the data.

As an illustration of some of these limitations, let us consider the United States Census data on familial households. These data provide rosters of household members and their relationships to the head householder. From this information, one can derive family structures within all households in the United States. However, these data only include measures of kinship relations that fall within the household boundary. What this means, in practice, is that non-co-resident family members (e.g. spouses working outside of the country, adult children off at college, adult siblings, independently-living parents, etc.) are entirely unaccounted for. Additionally, Census data on familial households are period measures, and so there is no way to track changes occurring within family networks over time.

In the absence of better observational data, one ready solution to the challenge lies in microsimulation. In situations where information is poor or unavailable, simulation frameworks enable the generation of high resolution data from low-resolution inputs. In my case, I rely on SOCSIM, a well-validated demographic microsimulator developed and maintained at UC Berkeley, to generate individual-level genealogical histories from population-level mortality and fertility inputs. In brief, SOCSIM achieves this by generating fictive individuals who are then “trained” to be born, reproduce, and die in such a way that their aggregate-level behavior accords with observed demographic behavior in real-world populations.


Figure 6. Schematic diagram of the SOCSIM procedure

All results that I present in subsequent sections of this post are calculated from data derived from this microsimulation strategy.

Comparison of Contemporaneous Populations

Earlier, we discussed the difficulty of uniquely identifying the effects of demographic forces on family structure. In a nutshell, the challenge amounts to answering the following question: How can we tell what effects fertility and mortality have on a particular population without some kind of counterfactual situation? Obviously, we cannot go back in time and change the rates at which people reproduce and die. However, one plausible (albeit imperfect) solution may be to compare two contemporaneous populations that differ in their demography, but share a common historical and geo-political context. Comparing the family structures and trajectories of these populations may serve to make visible the consequences of life and death constraints on kinship by having one sub-population essentially serve as the demographic counterfactual to the other.

The Case of Black and White Americans

In the U.S. context, perhaps no two national populations have differed as dramatically and as consistently with regard to their fertility and mortality profiles than black and white Americans. To illustrate the point, I plot life expectancies and total fertility rates observed over the last century stratified by race.


Figure 7. Life expectancy at birth (e0) and total fertility rate (TFR) of black and white Americans

Race differences in mortality and fertility can affect the experience of family by differentially constraining kin availability and kin trajectories. In this context, we can think of “kin availability” as simply levels of kinship, and “kin trajectories” as simply the sequences of kinship. The former denotes the probability of transitioning into or out-of a given kin relation, while the latter denotes the specific order in which those transitions are made. Using the data generated by SOCSIM, I am able to characterize these two components – differences in kin availability and kin trajectory – for black and white Americans over the past century. As an example of this characterization, I present some results for the 1980-1990 birth cohort (those who were 25-35 years old in 2015).

Kin Availability


Figure 8. Kin relations over age by race in the United States, 1980-1990 birth cohort

What is pictured here is the average duration in years of age spent in different kinship relations. The black horizontal bars represent black Americans and the gray horizontal bars represent white Americans. The durations are conditional on ever having transitioned into each of these kinship relations, and the numbers to the right of the bars in parentheses are the lifetime probabilities of ever having made this transition. For example: 47% of all black individuals in this cohort transition into grandparent-hood. For those who make this transition, they do so, on average, at age 45; and remain in that relation for 25 years.

The main black-white differences we observe are:

  1. Earlier transitions into new kinship relations for black Americans: driven by higher fertility at earlier ages (that make different types of kin available earlier on in life)
  2. Shorter durations in kinship relations for black Americans: driven by higher mortality at all ages (that make exit due to kin death more likely earlier on in life)
  3. Lower lifetime probabilities of transitions for black Americans: driven by a complex interplay between differences in fertility and mortality

Kin Trajectory



Figure 9. Typical age at kin death by race in the United States, 1980-1990 birth cohort

This plot presents the average ages at which black and white Americans experience the deaths of different types of kin for the first time. For example: the average black individual experiences the death of a child for the first time at age 32, while the average white individual experiences that death seven years later at age 39. (NOTE: These averages apply to only those individuals who are unlucky enough to see a child pass during their lifetime.)

As readily evident, the main black-white difference here is the more frequent occurrence of kin death at earlier ages for black individuals relative to their white peers. To apply a little perspective, we might focus on only those kin deaths likely to occur in the pre-adult years of life (ages 0-21).


Figure 10. Kin death during pre-adult years by race in the United States, 1980-1990 birth cohort

What we notice when we do this is striking: the average black American is expected to experience the death of a grandparent, a parent, and a sibling – all before the age of majority (21 in the United States) – while the average white American is only expected to experience the death of a grandparent over that same span of ages.

It is worth noting that these types of comparisons are not possible to make by simply using raw fertility and mortality data, but are only made visible by our microsimulation model of kinship.

Concluding Thoughts

Though I have relied on an entirely biological understanding of kinship for this exhibition, it is important for us to be mindful of the fact that the experience of family is a function of both biological and affective relations: friends and community members can step into familial roles, and the mere existence of blood relations does not ensure that they will be present in our lives. That said, kinship defined by consanguinity (in most cultures) continues to demarcate the genealogical boundaries within which families must be negotiated and formed.

By leveraging the right analytic tools, a demography of the family can help us delineate these boundaries. In the example presented above, we saw that these genealogical boundaries are far more constrained for black Americans than for white Americans. Applied with care, demographic microsimulation strategies have the potential to help us gain these kinds of rare insights, not just in the United States, but throughout history and the world.

(This post is based on ongoing research by the author. For more details, see his working papers: here.)


[1] For an excellent presentation of this early history see “Family Demography: Methods and their Applications”, an edited volume by John Bongaarts, Thomas Burch, and Kenneth Wachter.

[2]Vertical lines indicate descent (parentage) and horizontal lines indicate alliance (marriage)

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