Directiva Nº 003-2012-EF/51.01- Cierre Contable y Presentación para la

I use structural equation modeling (SEM) for my co-construction analysis, a statistical technique useful for testing and estimating causal relationships (Byrne, 2010).

It is also well-suited for theory testing. SEM allows for the construction of latent measures which were not themselves included in the survey but, rather, estimate several manifest (measured) variables which ―tap into‖ the concept represented by the latent variable. In this way, the researcher is not required to measure every variable that might be part of a latent concept; several measures that each capture some facet of that latent concept are put together to make a stronger measure. The more tightly the variables hang together as a latent factor, the more coherent the concept is presumed to be.

Structural equation models consist of two components: a measurement model and a structural (or construct) model. The validity of both are measured with standard fit statistics. I present four for each model: the χ² and degrees of freedom (df), the

comparative fit index (CFI) which compares the fit of the hypothesized model with that

of an independent model, and the root mean square error of approximation (RMSEA), which accounts for both fit and model parsimony. A good CFI is larger than .900 and an acceptable fit is larger than .800. An RMSEA below .06 indicates a great fit and an RMSEA below .08 is acceptable (Byrne 2010).³⁴ I also include the squared multiple correlation, or the R² of the dependent variable, in each model. I first present the

confirmatory factor analysis (CFA) for each of the latent variable constructs I use in this chapter, then the structural components of causal models that use those latent variables.

To ensure discriminant validity between the four latent measures I use in this chapter, I compared the χ² and degrees of freedom between two models: one where the manifest measures predict their separate latent measures as usual and the four separate latent measures are correlated with one another, and a second model where all the manifest measures predicted a single latent measure. The significance of the difference in the χ² and degrees of freedom between the two models gives an indication of discriminant validity. I found discriminant validity significant at the .000 level in year 2 and year 5, for men and for women.³⁵

A note on timing of measurement: some of the most substantively important measures that make up the essentialist beliefs and gender category beliefs measures are only available in year 5. For these constructs, I run the models with both the year 2 and year 5 operationalizations.

34 RMSEA is a more accurate fit statistic with medium-size samples than CFI because the CFI may be deflated with sample sizes less than 300 or 400 (SEMs can be reliably interpreted with samples of 100 or more) (Chen, Curran, Bollen, Kirby, & Paxton, 2008).

35 I also ensured that none of the manifest measures were more highly correlated with a measure outside of its latent group than it was correlated with the measures inside of its latent group.

Self-Conceptions: I am Feminine

I constructed the ―I am feminine‖ self-conception latent variable from five attribute spectrum scales: ―Usually I am very masculine‖ to ―very feminine,‖ ―Usually I am very unemotional‖ to ―very emotional,‖ ―Usually I am very unfriendly‖ to ―very friendly, ―Usually I am very asocial‖ to ―very social,‖ and ―Usually I am very

individualistic‖ to ―very cooperative.‖ See Panel A in figure 2.3 for the CFA for the year 2 latent construct of feminine self-conception, and Panel B for the year 5 CFA. Of these five measures, ―I am friendly‖ and ―I am social‖ are conceptually much more similar to one another than any other pair of variables in this latent measure. Empirically, the correlation between these two measures (.633 for men, .538 for men) is also much higher than between other pairs of variables. I expect that, due to this conceptual and empirical overlap, the measurement errors on these two variables are likely also correlated. Thus, I include a correlated error term between the friendly and social measures in the latent measure for feminine self-conceptions for both men and women, and in both years 2 and 5. (This correlated error term is significant in year 2 and 5 for men, and in year 5 for women.)

Interestingly, I find that the ―I am cooperative‖ measure becomes less salient in women‘s feminine self-conceptions between year 2 and year 5.³⁶ This may point to a decoupling of cooperativeness or independence from notions of femininity and

36 I established the significance of this change by comparing the χ² and degrees of freedom difference between a model where the year 2 and year 5 latent measures of feminine self-conceptions were correlated and the coefficient estimates on the ―I am cooperative‖ measure constrained to equal one another, and a second model where these coefficient estimates were allowed to vary freely. The significance of the χ² and degrees of freedom change between the two models was significant at the .001 level for women, but was not significant for men.

masculinity as men and women proceed through an education process that tends to emphasize individual work.

Gender Schema Beliefs: Traditional Gender Role Beliefs, Gender Category Beliefs, and Gender Essentialist Beliefs

The following measures make up the traditional gender role beliefs latent variable: ―A wife should willingly take her husband‘s name at marriage‖ (1=strongly disagree to 5=strongly agree), ―a woman should not let bearing children stand in the way of a career if she wants one,‖ (recoded so that 1=strongly agree to 5=strongly disagree),

―women can have a full and happy life without marrying‖ (recoded so that 1=strongly agree to 5=strongly disagree), and ―I consider myself feminist‖ (recoded so that 1=strongly agree to 5=strongly disagree). ³⁷ Year 2 construction and CFA for the

traditional gender role belief latent variable is shown in Figure 3.4 Panel A, and the Year 5 CFA is shown in Panel B.

The year 2 and 5 constructs of feminine gender category beliefs includes:

―Usually, others of my same sex are very unfriendly‖=1 to ―very friendly‖=7; ―very individualistic‖=1 to ―very cooperative‖=7, ―very unemotional‖=1 to ―very

emotional‖=7, ―very asocial‖=1 to ―very social‖=7 (see Panel A and B of Figure 2.5).

My time-lagged examination of the effect of gender essentialist beliefs on self-conception is restricted by the presence of only one of the four essentialism questions in year 2: ―There are some jobs and professions that are more suitable for men than for women‖ (1=strongly disagree to 5=strongly agree). I include this as a single-measure

37 ―I consider myself a feminist‖ is a gender role belief measure and not a self-conception measure because being a feminist signals adherence to a coherent set of beliefs about the social roles about men and women.

It is more of an indication of the kinds of beliefs men and women have about the gender structure than a simple self-conception.

representation of gender essentialist beliefs in year 2. Year 5 repeats this variable and adds three other measures that tap gender essentialist beliefs: ―I expect members of the opposite sex to act differently than me at work‖ (1=strongly disagree to 5=strongly agree), ―The trend of occupational sex segregation in the U.S. exists because men and women are naturally talented at different things‖ (1=strongly disagree to 5=strongly agree), and ―Men and women should have equal rights, but they are different by nature‖

(1=strongly disagree to 5=strongly agree). See Panels A and B of Figure 2.6 for the year 2 and 5 constructs and CFAs.

Controls: All SEMs include controls for whether the respondent attended Smith (yes=1), Olin (yes=1), MIT (yes=1) or UMass (yes=1, the comparison category), and whether they identify as African-American (yes=1), Asian-American (yes=1), Hispanic or Latino (yes=1) or white (yes=1, comparison category).

The next sections present the results of this co-construction analysis. I then discuss these results and how they can inform our understanding of gender inequality more generally. All reported significance is calculated using two-tailed tests and I use maximum likelihood techniques for dealing with missing data.