The gender income gap and the role of family formation revisited

This article reports the results of a replication of Bobbitt-Zeher’s 2007 article “The Gender Income Gap and the Role of Education”. Models that emulate the original specifications (by and large) reproduce the original results. However, models that adhere to Bobbitt-Zeher’s theory concerning the gendered effect of family formation call into question her finding that “values appear to matter only modestly, while family formation has virtually no effect on the income gap”.


Introduction
The gender pay gap remains both a salient social problem and a puzzle to social scientists as it persists despite the institutionalization of egalitarian gender norms in the labor market and the reversal of the male advantage in education. To resolve the puzzle, scholars have sought to identify the relative contribution of different factors to the gender gap. Whereas research on work-family compatibility, overwork, and the motherhood penalty (Waldfogel 1997;Gangl and Ziefle 2009;Cha and Weeden 2014;Goldin 2014) suggests that the strongly gendered effect of family formation accounts for a substantial part of the gap, a highly-cited 2007 Sociology of Education article that scrutinized the contribution of educational factors relative to family formation among the college-educated concluded that "family formation has virtually no effect on the income gap" (Bobbitt-Zeher 2007: 13). It also found that "values appear to matter only modestly" (Ibid.). According to that study, gender differences in fields of study instead explain the lion's share of the income gap. In this article, I assess the robustness of these results by way of replication. This is an endeavor worth undertaking given that the original findings have important policy implications, as they suggest that improvements in work-family compatibility would do nothing to reduce economic gender inequality.
I first conduct a pure replication. Fitting statistical models that emulate those of the original study closely reproduce the original findings. However, I argue that these estimates are biased because Bobitt-Zeher restricts her sample to year-round full-time workers and thus conditions on labor force participation which, according to her own theoretical argument, mediates the effect of family formation on income. I show that her estimates for the importance of values are negatively biased for the same reason. Equally important, I also show that the original study misspecified and misallocated the hypothesized gendered effect of family formation in both relevant decompositions. The results from a series of models that subsequently correct for endogeneous sample selection and misspecification suggest the original study indeed severely underestimated the importance of family formation, and also that of values.
According to my findings these two factors explain nearly a third of the gender income gap in the sample at hand, and thus about as much as the educational factors emphasized in the original article.
For the sake of brevity, I choose not to debate here Bobbitt-Zeher's decision to analyze incomes rather than wages or the issue of omitted variable bias in testing the theorized devaluation of college majors. These issues have been discussed elsewhere (Petersen 1989, Morgan and Arthur 2005, Gerber and Cheung 2008, Ochsenfeld 2014).
My intention is not to single out Bobbitt-Zeher's analysis for criticism. In fact, studies published in the top U.S. and German sociology journals have drawn similar conclusions based on very similar designs before and after (Marini and Fan 1997;Leuze and Strauß 2009).
The purpose of this replication is thus to critically reflect on this enduring research tradition rather than to fault an individual author.

Overview of the original study
Bobbitt-Zeher (2007)  averages over women's and men's coefficients to obtain hypothetical gender-neutral rates of return to the covariates. It then uses these hypothetical rates to estimate the degree to which gender differences in income are due to gender differences in endowment with the various covariates and to which degree the difference in outcome is instead due to gender differences in the rates of return to these endowments. Compared with the first decomposition, Bobbitt-Zeher's Oaxaca-Blinder decomposition attributes less explanatory power to education-related factors and more to work-related variables. This is because the Oaxaca-Blinder decomposition ignores the causal order of variable groups and hence ignores the fact that work-related variables mediate the effects of the education-related characteristics on income. As in the second decomposition, family formation seemingly plays no role whatsoever in the generation of women's economic disadvantage.
Based on the results from the first and second decomposition, the author concludes that besides differences in job characteristics, horizontal sex segregation in fields of study was crucial to understand income differences between college-educated women and collegeeducated men, whereas "values appear to matter only modestly, while family formation has virtually no effect on the income gap for this sample of young workers." (Bobbitt-Zeher 2007: 13).

Pure Replication
My first set of analyses (replication A) aims to mimic as closely as possible the original model specifications and sample restrictions in order to reproduce the original results and to provide a reference for assessing the impact of corrections on the original design later on. An exact replication in the strict sense was not feasible because I could not obtain the original code. When preparing the analysis sample I therefore emulated the original article whenever possible and resorted to qualified guesses when instructions therein were insufficiently detailed. 1 A replication package documents these decisions in detail and is publicly and permanently available at the Harvard Dataverse (Ochsenfeld 2016a). The resulting analysis sample is slightly smaller (N=1,924) than that of the original study (N=1,946). A comparison of descriptive statistics (see table A1 in the appendix and Bobbitt -Zeher, 2007: 11, 18f.) indicates that the independent variables are distributed very similarly but not identically.
Average annual incomes are slightly lower in my sample for both women ($32,573) and men ($39,243) compared to the original study ($32,953 and $39,891, respectively). The resulting unconditional gender income gap is thus slightly smaller in my sample ($6,670) than in the original study ($6,938).
The original analyses were conducted on the NELS:88 Restricted Use Data. Because researchers outside the U.S. cannot access these data, my replication is based on the NELS:88 Public Use Data which is identical to the Restricted Use Data except that it does not include students' SAT scores and a measure for the selectivity of the college attended. However, because these variables were shown to be entirely peripheral in the original analysis, it is nevertheless possible to very closely replicate the original results as I demonstrate below.
With regards to percentage of the income gap explained by the various variable groups in the sequential decomposition, my results almost exactly reproduce those of the original study, except for work variables where explanatory power is lower than in the original study (table   1). I can only speculate that this may be due to potential differences in how I recoded certain industries and occupations to arrive at the categories reported in Bobbitt-Zeher (2007: 18f.).
The estimates from the Oaxaca-Blinder decomposition are nearly identical to those reported in Bobbitt-Zeher (2007). Only for grades is this not the case, in all likelihood because this variable group encompasses 12 th grade standardized test scores, 12 th grade grades, and SAT scores in the original study whereas my analysis cannot include SAT scores.
If I were to draw conclusions about the importance of education-related factors relative to family formation and values based on the results of this replication exercise, these would echo Bobbitt-Zeher's. Family formation seems to explain none of the gender income gap; gender differences in the importance of 'having lots of money' are almost irrelevant, but educationrelated factors -most notably segregation in college majors -explain a sizeable share (nearly a third) of women's lower incomes. In the following, I will argue that this conclusion needs to be revoked with respect to family formation and values. This argument suggests that gender moderates the effect of family formation on income:

Replication with corrections for endogeneous sample restriction and misspecification
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: 5) Figure 1 illustrates these statements.
[ Figure 1] In her study, Bobbitt-Zeher chose to restrict her sample to persons working full time (≥35 hours 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: 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 [Tables 1 and 2 about here.] The estimate for the contribution of family formation, however, continues to suggest the complete irrelevance of this factor (table 1, replication B). 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).
Model 5: Income = β 0 + β 1 female + … + β k-1 parenthood + β k marriage + ε Model 5b: Income = β 0 + β 1 female + … + β k-1 parenthood + β k marriage + β k+1 female × parenthood + β k+2 female × marriage + ε 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 C). The work-related covariates in turn add much less explanatory power (13 instead of 23 percent) because part of their association with income stems from them mediating the motherhood penalty ( figure 1) and therefore already gets picked up by model 5b (but not model 5). 3 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 (Jones and Kelley 1984;Jann 2008): The membership, coefficients and interaction components are often summarized into a single 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 A and B (table 2) merely refers to the endowment effect for family formation -the potentially higher incidence of parenthood and marriage among women compared with men.