To explicate why I consider both the restriction Bobbitt-Zeher imposes on her sample and her model specifications to be at odds with her theoretical argument, I briefly summarize her argument regarding the potential effect of family formation on the gender income gap. She states that
The effects of family formation, particularly marriage and parenthood and their impact on participation in paid labor, are implicated in gender income disparities. For example, net of other factors, such as education, women with children make 10 percent to 15 percent less than do women without children, and there is a 7 percent wage penalty for each child that a young woman has. […] The same patterns do not hold for men; fathers experience no comparable wage penalty for their parental status. (Bobbitt-Zeher 2007, p. 4)
This argument suggests that gender moderates the effect of family formation on income: Whereas the effect is thought to be negative for women, it is thought to be non-existing for men. Furthermore, the author argues that labor force participation is a key mechanism that brings about the negative effect of motherhood on income:
The impact of family formation on gender differences in earnings appears to operate through women’s decreased labor force participation. Both length of job experience and part-time employment contribute to lower earnings. (Bobbitt-Zeher 2007, p. 5)
Fig. 1 illustrates these statements.
In her study, Bobbitt-Zeher chose to restrict her sample to persons working full time (≥35 h per week throughout the year). She provides no justification for this decision other than to “avoid part-time and inconsistent workers from biasing the analysis” (Bobbitt-Zeher 2007, p. 7). However, the reverse is likely to be true because she thereby conditions on hours worked which, according to her own theoretical argument, mediate part of the motherhood penalty (Fig. 1). In consequence, her estimates for the effect of family formation suffer from overcontrol bias (Elwert and Winship 2014).Footnote 2
Fig. 2 suggests that Bobbitt-Zeher’s decision to delete persons who work less than full-time year-round indeed disproportionately removes mothers from the sample and thus underreports the frequency of motherhood. Worse, this only retains mothers that experienced no or merely a weak effect of motherhood on hours worked: The difference in hours worked between mothers and fathers is significantly larger in the sample that includes part-time (≥10 h per week) and non-year-round workers than in the restricted sample (see Fig. 2).
The effect of values, too, is likely affected by overcontrol bias: Persons who did not find ‘making lots of money’ important during high school are prone to work fewer hours and earn lower annual incomes later in life for that reason. Hours worked thus mediate the effect of values (i. e. importance of ‘making lots of money’) on income. In this case Bobbitt-Zeher’s decision to restrict the sample to persons working full-time year-round puts downward bias on her estimate for the explanatory power of this factor. Finding ‘making lots of money’ unimportant in 12th grade is indeed weakly associated with not working full-time year-round 7 years later.Footnote 3
To assess how much Bobbitt-Zeher’s decision to restrict her sample to full-time year-round workers has biased the estimated explanatory power of family formation and values in her study, Table 1 (replication 1B) reports the results from a sequential decomposition that also includes persons who work less than year-round full-time and thus allows hours worked to bring about the effects of family formation and values. The explanatory power attributed to values in the sequential decomposition doubles from 8 to 16% – nearly half of what all education-related variables taken together contribute (34%).
The estimate for the contribution of family formation, however, continues to suggest the complete irrelevance of this factor (Table 1, replication 1B). This is, however, because Bobbitt-Zeher’s models do not reflect her theoretical argument. Her statement that gender moderates the effect of family formation on income (see above) suggests a model that includes gender and the family formation variables (parenthood and marriage) as well as terms that interact them with gender (model 5b). However, Bobbitt-Zeher’s models do not include the interaction terms (model 5).
$$\text{Model }5\colon \text{ Income}\, =\beta _{0}+\beta _{1}\text{female}+\ldots +\beta _{k-1}\text{parenthood}+\beta _{k}\text{marriage}+\varepsilon$$
$$\text{Model }5\mathrm{b}\colon \text{ Income}=\beta _{0}+\beta _{1}\text{female}+\ldots +\beta _{k-1}\text{parenthood}+\beta _{k}\text{marriage}+\beta _{k+1}\text{female}\times \text{parenthood}+\beta _{k+2}\text{female}\times \text{marriage}+\varepsilon$$
Once I use model 5b instead of model 5 in the sequential decomposition on the sample that includes part-time workers, family formation adds 15 percentage points to the explanation of the gender income gap rather than nothing at all (Table 1, replication 1C). The work-related covariates in turn add much less explanatory power (13 instead of 23%) because part of their association with income stems from them mediating the motherhood penalty (Fig. 1) and therefore already gets picked up by model 5b (but not model 5).Footnote 4
The same issue plays out somewhat differently in the Oaxaca-Blinder decomposition (Blinder 1973; Oaxaca 1973) that allows for a decomposition of the gender gap into membership, coefficients, and endowments components plus an interaction between coefficients and endowments (Fig. 3; Jones and Kelley 1984; Jann 2008).
The membership, coefficients and interaction components are often summarized into a single ‘unexplained’ or ‘discriminatory’ component. In the resulting two-fold decomposition the endowments component is conventionally referred to as the ‘explained’ or ‘non-discriminatory’ and the other components taken together as the ‘unexplained’ or ‘discriminatory’ component (Fig. 3). However, the interpretation of the sum of the membership, interaction and coefficients components as ‘unexplained’ is warranted if and only if indeed no theory of interest explains any part of these components (or as ‘discriminatory’ if indeed all components can entirely and unambiguously be interpreted in the light of discrimination theory). This condition usually holds in the most common application of the decomposition where human capital theory is tested against discrimination theory and wages are regressed solely on productivity-related characteristics (e. g. Braakmann 2013).
It does not hold in the study at hand, however, because Bobbitt-Zeher’s statements concerning the gendered effect of family formation provide a strong theoretical ground for attributing the coefficients effects for the variables parenthood and marriage to family formation. Given Bobbitt-Zeher’s above summarized argument (and given that she does not control for job experience), we do expect a direct effect of family formation on income that is more negative for women than for men. The coefficients effect regarding the parenthood and marriage variables should thus be treated as predicted by the family formation argument. In the original study, however, they were not. Instead, they remained unreported. The negligible percentage of total gap explained for family formation in the original study and in replications 2A and 2B (Table 2) merely refers to the endowment effect for family formation – the potentially higher incidence of parenthood and marriage among women compared with men. Table 2 reports both the endowments and coefficients effect for the family formation variables. For the unrestricted sample (Table 2, replication 2B), the coefficients effect of family formation explains 5% of the income gap.
This estimate, however, still does not reflect the full explanatory power of the family formation argument. To the degree that the gender difference in hours worked is an outcome of family formation, the endowment component for hours worked should be attributed to family formation.
Because virtually all other work variables (occupation, industry, sector, job training, job autonomy) can be expected to mediate the effects of education, values, and family formation, too, their inclusion in the Oaxaca-Blinder decomposition renders the decomposition results uninformative for its designed purpose, an assessment of the explanatory power of education-related variables relative to family formation. Table 2 (replication 2C) therefore shows results from a decomposition that excludes the work-related variables. These more meaningful results are in line with those from the previous sequential decomposition (Table 1, replication C) as they suggest that education, family formation, and values all independently explain sizeable shares of the income gap (Table 2, replication 2C).
Based on my preferred decomposition (Table 1, replication 1C), I conclude that values and family formation each explain approximately 15% of the gender income gap. Given that only few respondents (12%) have entered parenthood yet, I consider this to be a sizeable contribution of family formation.Footnote 5