Race Differences in Cohort Effects on Non-Marital Fertility in the United States: Reply to Martin

We appreciate the opportunity to clarify and provide additional tests of the key elements of our age-period-cohort analysis of non-marital birth rates in this March 2009 issue of Social Forces. Where Steve Martin, in his commentary, has suggested specific alternative specifications or interpretations of our findings, we have re-estimated and performed explicit tests of the alternatives. In the end we have demonstrated the robustness of our results and strengthened the case for our interpretations. The points Martin raises and our responses should help to clarify the nature of cohort effects and our interpretation of them. We thank Martin for his close attention to our paper.

As Martin notes, in the typical rectangular age-period table there are the same numbers of cells/observations for each age, the same number of cells/ observations for each period, but different numbers of cells/observations for some of the cohorts. This is well known – yet cohort analysts persist in using such tables when studying cohort effects. These analysts know that if one does not take into account the age and period effects in such a table, then differences between cohorts could be produced by age and period effects. If one does control for the main effects of age and period, however, this will not create apparent cohort effects.

Martin suggests, however, that there are patterns of age*period interactions that are not related to cohort effects that could produce the patterns we observe along cohort diagonals. Certainly such patterns are possible: It is incumbent on the critic to point out these patterns and, given that our discipline considers theory important, to produce compelling reasons why such patterns might exist. Martin does both. He suggests that there is an interaction between age and period. He notes that "the non-marital birth ratio rose steeply for women in their 20s and slowly for women in their 40s." That is, increases in NFRs over time are different for different age groups. Martin then suggests that "[a] plausible explanation for this age*period pattern is that delays in marriage increased the unmarried population most rapidly among women in their 20s, so the rise in the non-marital birth ratio has been most pronounced among women in their twenties." His Figure 4 displays the differences in these slopes, and it is on this figure that much of his argument rests.

Figure 1.

Trends in Non-marital Fertility by Age, Period and Cohort

We redrew Martin's Figure 4 as our Figure 1, but we added bolded lines for the three cohorts with complete age data. Note the distinct differences in the trajectories of these three cohorts over time, even in the context of the differences in the slopes of NFRs for the different age groups. The cohort born 1948-1952 (represented by the bolded triple line) shows a decline in NFRs from ages 20-24 and ages 25-29 and then rises steeply until the last observation for the cohort at ages 40-44 in 1982. In contrast, the cohort born from 1958 through 1962 has an NFR that drops between ages 20-24 and ages 25-29 and then rises at a very slow rate until the last observation for the cohort at ages 40-44 in 1997. The cohort born in the years 1953-1957 has yet a different and distinct trajectory. We might well interpret this graph as showing both the interactions of the relationship between age-groups and NFR over time and the effects of cohorts – even when these interactions are taken into account. We are wary, however, of trying to eyeball cohort effects from graphs without controls for age groups, periods and in this case age-groups by period interactions.

Testing Martin's Alternative Explanations

Table 1.

Cohort Effects With and Without the Controls Implied by Martin

We first test whether these differences in steepness of the slopes for NFRs for women in...