Comment: Distinguishing Cohort Effects from Age*Period Effects on Non-Marital Fertility

In the article "Cohort Effects on Non-marital Fertility," in this issue of Social Forces, Jean Stockard employs a novel strategy for disentangling cohort, period and age effects on the non-marital fertility ratio. In a model with fixed-effect controls for age and for time period, the author documents evidence for three cohort-specific factors affecting the non-marital birth ratio of a given cohort ages 20-44. The first is the non-marital birth ratio at the time a cohort is born. The second is the cohort percent enrolled in school at ages 18-21. The third is the cohort sex ratio at ages 20-24. In models for non-hispanic whites, two of these cohort variables have statistically significant coefficients, and in models for non-Hispanic blacks, all three variables have statistically significant coefficients.

Social researchers have often debated the relative importance of period and cohort effects on demographic processes (Namboodiri 1981; Pullum 1980). Stockard's finding, if it holds, would clearly strengthen the overall case for cohort effects. Unfortunately, the technique Stockard uses to identify cohort effects is open to an alternative interpretation. The cohorts in this analysis are censored in a manner typical of time-series data, and as a result, age-period interactions can create the appearance of a cohort effect. If the age*period interpretation holds, the cohort variables described by the authors have only a coincidental relationship with trends in the non-marital birth ratio.

In this comment, I begin by describing the cohort effect on non-marital birth ratios as it is described by Stockard. Then I explain how the same observed pattern could arise from an age-period interaction. Finally, I offer two arguments that would favor the age-period interpretation over the cohort interpretation. I limit my analysis to the results for non-Hispanic whites; results for non-Hispanic blacks and their interpretation are generally analogous to the results and interpretation for non-Hispanic whites.

A Cohort Effect?

Stockard analyzes non-marital fertility across five-year age categories: 20-24, 25-29, 30-34,35-39 and 40-44, and across five-year intervals from 1972 to 2002. This age range and time period includes partial or complete information from 11 five-year birth cohorts beginning with the 1928-1932 birth cohort (Cohort 1) and ending with the 1978-1982 birth cohort (Cohort 11).

In regression analyses, Stockard estimates fixed effects for each five-year age category and each five-year period. Key explanatory variables are each cohort's childhood non-marital birth ratio (henceforth childhood NMBR), percent enrolled at age 18-21, and sex ratio at age 20-24. All cohort variables are in log form. The outcome variable is log of the adult non-marital fertility ratio.

Figure 1.

Distribution of Cohort-Based Explanatory Variables for the Non-Hispanic White Sample

Figure 1 shows the distribution of the explanatory variables across cohorts. Log(percent enrolled) and log(sex ratio) increased steadily across cohorts. Log(childhood NMBR) had a non-linear pattern; it was flat until Cohort 6 (birth year 1953-1957), then rose rapidly across subsequent cohorts. With a little imagination, one can anticipate the cohort-based interpretation that can follow from Figure 1. NFR for a given cohort should be positively correlated with childhood NMBR to the extent that children grow up to model the behavior of their parents, and negatively correlated with percent enrolled at age 18-21 to the extent that adult education is incompatible with non-marital childbearing.

In Figure 1, the nonlinearity in childhood NMBR is important. Cohorts born from the late 1940s through the late 1950s (cohorts 5, 6 and 7) were still exposed to low childhood non-marital fertility, but school enrollment was already rising for these cohorts. As a result, one might anticipate that these cohorts would have lower non-marital birth ratios as adults than would be expected based on age and period alone.

Figure 2.

Cumulative Effect of Cohort-Based Explanatory Variables on...