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Online supplement for McClintock, E. A. (2017). Changing jobs and changing chores: Gender occupations and housework performance. Sex Roles. Elizabeth Aura McClintock, University of Notre Dame. Email: [email protected]

ONLINE SUPPLEMENT A: ROBUSTNESS

In this online supplement, I present results of several robustness checks. The measures and the

result of the analyses are described below and presented in Tables A1 and A2.

Measures

I follow England and colleagues (England, Herbert, Kilbourne, Reid, & Megdal, 1994) in

developing indicators for authoritative and nurturing jobs. Although they devised these measures for

the 1980 Census codes, it is easily adapted to later census coding systems (see McClintock 2017).

Occupational titles with the word manager, supervisor, or administration are authoritative. Occupations

in which incumbents spend a major share of working hours directly serving clients are nurturing. These

measures were employed in earlier studies of occupational sex composition and housework

(McClintock, 2017; Schneider, 2012).

I also consider broad occupational groups, following US Census 1990 classifications:

professional, sales, service, farm/forestry/fish, craft, operatives/laborers. The 1990 Census has pre-

categorized occupations into these groups and it is easy to adapt the schema for subsequent Census

years. In addition to varying in average sex composition, these occupational groups also vary in other

relevant characteristics such as income, social status, opportunities for career advancement, and

educational requirements. Most importantly, they arguably vary in cultural meanings, such as “blue

collar” masculinity, which are difficult to assess directly. I use sales as the reference category because it

is approximately gender-balanced and employs a substantial proportion of female and male PSID

respondents.

Finally, I create measures of occupational autonomy, supervisory responsibility, opportunities

for advancement, and performance-based pay from General Social Survey (GSS, 2017) data. In addition

mailto:[email protected]

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to core GSS data, these measures draw on several topical modules, including those on work

organizations, work compensation and shared capitalism. Occupational autonomy is in index capturing

respondents’ control over their work, participation in workplace decision-making and evaluations, and

opportunity to provide input (Cronbach’s alphas of 0.83). Supervisory responsibility is an indicator that

the respondent supervises other employees. Opportunities for advancement captures respondents’

perception that their job offers the possibility of future promotion. Performance-based pay indicates

that the respondent is paid in part by commission, bonuses, or tips. I code these measures at the

individual-level and then aggregate responses to the occupational level so that they represent the mean

score among all GSS respondents in a given occupation. Career is a scale aggregating these four

measures and indicates the degree to which an occupation qualifies as a career, as opposed to being

merely a job.

Results

Model 1, Removing spouses’ characteristics: Although I include spouses’ housework and work

hours in the models presented in the main text, these measures are somewhat endogenous to

respondent’s housework hours. In Model 1 I demonstrate that results are robust to removing spouses’

housework, occupation, income, and work hours from the model. This little changes the association

between respondents’ occupation and respondents’ housework hours.

Model 2, Full-time workers: Another possible concern might be that results are driven by part-

time workers. However, in Model 2 I demonstrate that results remain consistent when the sample is

limited to full-time workers (both spouses work thirty-five or more hours).

Model 3, Prime working age: Yet another concern might be that occupational sex composition is

serving as a proxy for career or life stage. In Model 3 I demonstrate that results remain robust when the

sample is limited to respondents of prime working age, which I define as 30-50 years. I selected this age

range because such workers are likely to have completed their education and settled into lasting

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occupations but are not yet near retirement age.

Model 4 & Model 5, Occupational characteristics: It is possible that occupational sex

composition is serving as a proxy for some other occupational characteristic that itself influences

housework. However, in Model 4 I show that results remain robust when I include a scale capturing the

degree to which an occupation qualifies as a career or a mere job. Although women decrease their

housework when moving into a more career-typed occupation, including the career scale does not alter

the within-individual association of occupational sex composition and housework. Model 5 presents

results removing occupational sex composition and including measures of occupational autonomy,

supervisory responsibility, opportunities for advancement, and performance-based pay (the individual

components of the career scale).

Model 6, Occupational groups: As alternative measures of gendered work, I substitute

occupational groups for occupational sex composition. Men who move from sales (gender-mixed) into

professional occupations (mostly male) decrease their housework; otherwise, there is little within-

individual association. Differences are more evident between individuals and suggest that men in

female-typed occupation groups (like service) may do more housework than men in gender-mixed jobs

(the reference, sales), whereas men in male-typed occupational groups (farm/forestry/fish) do less

housework. However, these classifications are problematic for women because very few women work in

the most strongly-male occupational groups and also because they generally work in female-gendered

occupations within these male-typed occupational groups. For example, for those few women classified

as working in “craft” occupations, their average proportion female is 69%, whereas for men it is only 7%.

In other words, such women usually work in predominately female occupations despite these jobs

falling into an occupational group that is predominately male. Thus, occupational sex composition is a

much cleaner measure of gender-typed employment.

Model 7, Authority and Nurturance: As yet another measure of gendered work, in Model 5 I use

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classifications of occupations as nurturing (female-typed behavior) or authoritative (male-typed). Men

who enter authoritative jobs reduce their housework, reflecting the within-individual reduction in

housework for men who enter professional occupations. Similarly, women who enter authoritative jobs

reduce their housework whereas women who enter nurturing jobs increase their housework. These

within-individual changes provide some support for acclimation—the experience, context, or social

associations of gendered paid work may have implications for housework. Considering between-

individual variation, men and women who work in authoritative occupations do less housework; women

also do less housework when their husbands work in nurturing occupations. Thus, results are largely

robust to this alternative measure of occupational gender-typing.

Model 8, Multiple Imputation: In the main text I present models estimate dropping cases with

missing data. In Model 8, I show that results are robust to using multiple imputation. Using multiple

imputation increases the sample size by about 10% but does not change findings.

References

England, P., Herbert, M., Kilbourne, B., Reid, L. L., & Megdal, L. M. (1994). The gendered valuation of

occupations and skills: Earnings in 1980 census occupations. Social Forces, 73(1), 65–100. doi:

10.2307/2579918

General Social Survey (GSS). (2017, May 31). The General Social Survey. Chicago, IL: NORC at the

Univerisity of Chicago. Retrieved from http://gss.norc.org/

McClintock, E. A. (2017). Occupational sex composition and gendered housework performance:

Compensation or Ccnventionality? Journal of Marriage & Family, 79(2), 475–510. doi:

10.1111/jomf.12381

Schneider, D. (2012). Gender deviance and household work: The role of occupation. American Journal of

Sociology, 117(4), 1029–1072. doi: 10.1086/662649

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Table A1. Coefficients from mixed-effects models predicting changes in men’s weekly hours of housework. Married dual-earner couples. Panel Study of Income Dynamics 1981-2013.

Model # 1 2 3 4 5 6 7 8

Model description

No spouse

Full-time, both 35+

Age 30-50

Occ. career

Occ. traits

Occ. Groups

Auth. & nurture

Impute (MIM)

Within-individual effects

Occ. sex composition

His occupation (0-1) -.10 .26 .27 .03 .07

Her occupation (0-1) -.70* -.58* -.42* -.49*

Career-type occupation

He has career .15

She has career 1.05

Occ. groups (% female)

Him, professional (38%) -.43*

Him, sales (48%) REF

Him, service (42%) -.44

Him, farm/forestry (16%) .05

Him, craft (07%) -.20

Him, operative/labor (21%) -.24

Him, miscellaneous (14%) .61

Her, professional (66%) -.27*

Her, sales (67%) REF

Her, service (69%) -.44*

Her, farm/forestry (66%) -.77

Her, craft (69%) .28

Her, operative/labor (67%) -.06

7

Her, miscellaneous (64%) .46

Gendered work behavior

His occ. Authority -.28*

His occ. Nurturance .01

Her occ. Authority .02

Her occ. Nurturance -.19

Occupational characteristics

His occupational autonomy .15

His supervisory role -.19

His job opportunity -.35

His performance pay -.39

Her occupational autonomy 1.09

Her supervisory role .09

Her job opportunity .44

Her performance pay .78*

Income (2015 $10,000s)

His income (logged) -.14 .36* -.06 -.20 -.28 -.21 -.18 -.26

Her income (logged) -.19 .14 .20* .27* .22* .20* .20*

Relative income

Relative income (0-1) -2.19* -3.12* -1.81 -1.47 -1.25 -1.36* -1.67 -.71

Slope change at equality 1.29 -1.42 -.36 .21 .44 .16 .51 -.41

Between-individual effects


His occupation (0-1) -.32 .01 -.09 .36 .28

Her occupation (0-1) -1.03* -.52 -.28 -.35

8


He has career 1.48

She has career .79


Him, professional (38%) -.16


Him, service (42%) 1.93*

Him, farm/forestry (16%) -2.07*

Him, craft (07%) .04

Him, operative/labor (21%) .33


Her, professional (66%) -.04


Her, service (69%) -.50*

Her, farm/forestry (66%) .82


Her, operative/labor (67%) -.79*

Her, miscellaneous (64%) 4.07


His occ. Authority -.56*

His occ. Nurturance -.00

Her occ. Authority .41

Her occ. Nurturance .41*


His occupational autonomy 6.11*

9

His supervisory role .57

His job opportunity 1.04

His performance pay -1.70*

Her occupational autonomy -1.45

Her supervisory role .12

Her job opportunity .08

Her performance pay .64

Income (2015 $10,000s)

His income (logged) -.32* -.19 -.71* -.74* -.87* -.79* -.69* -.58*

Her income (logged) .47 1.20* .95* 1.16* .92* .99* .91*

Relative income

Relative income (0-1) -3.01* -1.57 -1.66 -2.78* -1.55 -3.08* -2.80* -2.46

Slope change at equality 1.23 -.31 4.41* 5.11* 4.44* 5.51* 4.89* 4.49*

N (person-years) 48,721 24,022 29,892 44,902 36,913 44,921 46,142 50,848

* p < .05, NA=Not applicable, REF=Reference. Models include all controls in Table 4 (work hours, spouse’s housework (except Model 1), personal/family traits, survey year, respondent, race).

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Table A2. Coefficients from fixed-effects models predicting changes in women’s weekly hours of housework. Married dual-earner couples. Panel Study of Income Dynamics 1981-2013.

Model # 1 2 3 4 5 6 7 8

Model description

No spouse

Full-time, both 35+

Age 30-50

Occ. career

Occ. traits

Occ. groups

Auth. & nurture

Impute (MIM)

Within-individual effects


His occupation (0-1) -.47 -.51 -.46 -.44

Her occupation (0-1) .87* .88* .79* .99* .92*


He has career .96

She has career -1.92*


Him, professional (38%) .16


Him, service (42%) .35

Him, farm/forestry (16%) .85

Him, craft (07%) .32

Him, operative/labor (21%) .08

Him, miscellaneous (14%) 1.60*



Her, service (69%) 1.46*

Her, farm/forestry (66%) .14


Her, operative/labor (67%) .63

11

Her, miscellaneous (64%) -3.82


His occ. Authority .08

His occ. Nurturance -.21

Her occ. Authority -.50*

Her occ. Nurturance .66*


His occupational autonomy -.70

His supervisory role .14

His job opportunity .28

His performance pay .27

Her occupational autonomy .14

Her supervisory role -.16

Her job opportunity -.77

Her performance pay -.86*

Income (2015 $10,000s)

His income (logged) -.70* .21 .20 .35 .26 .17 .08

Her income (logged) -.96* -.33 -.96* -1.11* -1.24* -1.11* -1.06* -.88*

Relative income

Relative income (0-1) -.29 2.93 .64 -.43 -.98 -.75 .01 .23

Slope change at equality 2.50* 3.95* 1.04 1.93 1.85 2.07 1.75 2.19

Between-individual effects


His occupation (0-1) -2.87* -2.93* -2.87* -2.91*

Her occupation (0-1) .50 1.51* .90 .53 .65

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He has career -1.55

She has career -1.05


Him, professional (38%) .35


Him, service (42%) .50

Him, farm/forestry (16%) 2.59*

Him, craft (07%) 1.80*

Him, operative/labor (21%) 1.44*




Her, service (69%) 1.10*

Her, farm/forestry (66%) 3.77*

Her, craft (69%) -.99

Her, operative/labor (67%) 1.56*

Her, miscellaneous (64%) -1.02


His occ. Authority -.13

His occ. Nurturance -1.32*

Her occ. Authority -1.32*

Her occ. Nurturance .20


His occupational autonomy .22

13

His supervisory role -.02

His job opportunity -.82

His performance pay .13

Her occupational autonomy 3.22

Her supervisory role -.38

Her job opportunity -2.24*

Her performance pay .08

Income (2015 $10,000s)

His income (logged) -2.06* -1.08* -.89* -.83* -.36 -.91* -.98*

Her income (logged) -2.41* -1.05* -1.97* -1.95* -2.20* -1.79* -1.98* -1.88*

Relative income

Relative income (0-1) 4.15* 10.33* 6.81* 6.79* 5.57* 4.52* 6.53* 7.01*

Slope change at equality -2.02 -3.17 -1.48 -2.72 -1.44 -.78 -1.94 -2.78

N (person-years) 47,845 24,022 29,662 44,902 36,913 44,921 46,142 50,848

*p < .05, NA=Not applicable, REF=Reference. Models include all controls in Table 4 (work hours, spouse’s housework (except Model 1), personal/family traits, survey year, respondent, race).

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ONLINE SUPPLEMENT B: OCCUPATIONAL SEX COMPOSITION

In this online supplement, I present further details on my calculations of occupational sex

composition and the extent to which occupational sex composition is an accurate measure of gendered

employment.

Calculating Occupational Sex Composition

Percent occupation female is calculated from U.S. Decennial Census data and American

Community Survey (ACS) data. The PSID provides 1970 Census 3-digit codes from 1981-2001 and 2000

Census 3-digit codes from 2003-2013. If I were to use US Census 1970 data to calculate occupational sex

composition for 1981-2001 and US Census 2000 data to calculate occupational sex composition for

2003-2013, this would create two sources of inaccuracy. First, occupational sex composition changes

gradually over time, as occupations feminize (or, rarely, masculinize). Using US Census 1970 data for

PSID years 1981-2001 and US Census 2000 data for PSID years 2003-2013 would ignore this gradual

change and would create a disjoint between PSID years 2001 and 2003. That is, 2001 values for

occupational sex composition would reflect the realities of 1970, in sharp contrast with 2003 values

which would leap forward 30 years (from 1970 to 2000). Second, occupational codes themselves change

overtime to capture development/decline of new/old occupations. For workers whose occupations are

reclassified, this would create a further disjoint between 2001 (using 1970 codes) and 2003 (using 2000

codes).

To address these two concerns, I standardize occupational codes over time and linearly

interpolate gradual changes in occupational sex composition. To do this, I employ the crosswalk

developed by Integrated Public Use Microdata Series (Ruggles et al., 2010) which links 1970, 1980, and


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2000 codes to standardized 1990 codes. Thus, all years of PSID data use the same occupational codes

(standardized 1990 codes) even though the PSID initially provides occupational codes using two

different coding systems (1970 and 2000). In addition, I use 1980, 1990, 2000 US Census data and 2001-

2013 ACS data to linearly interpolate occupational sex composition, distributing changes equally across

each decade. That is, I assume that any change in a given occupation’s sex composition from 1980 to

1990 is distributed linearly across those ten years, change from 1990 to 2000 is distributed linearly

across those ten years, and so on. This provides a more accurate and temporally-continuous measure of

occupational sex composition over time. It consistently captures the two processes whereby individuals’

occupational sex compositions change: (1) gradually over time, as occupations feminize (or masculinize),

and (2) discretely, when individuals change jobs.

Table B1 illustrates the results of this process. It presents annual values for occupational sex

composition for every year of PSID data used in this analysis (1981-2013), separately by gender. It also

provides the sample size of married men and women for each of these years. As is to be expected,

regardless of the year, women work in mostly-female (65-71% female) occupations and men work in

mostly-male occupations (26-32% female). There is a slow trend toward occupational desegregation

over time, with men’s occupations becoming slightly more-female and women’s occupations becoming

slightly less-female.

Occupational Sex Composition as a Measure of Gendered Employment

Occupational sex composition, calculated as described above, is based on national trends and

may not capture individual experiences of gendered employment—that is, a given occupation’s

composition may vary at the local or establishment level, altering individual experiences of employment

in that occupation. However, as I will explain below, national trends may actually have greater

theoretical and practical salience than individual experiences. In addition, national trends and individual

experiences are in fact highly correlated—national-level measures of occupational sex composition are a

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good proxy for individual experiences, especially in strongly-gendered occupations. Finally, any

measurement error whereby individual experiences differ from national level trends is more likely to

create random “noise” in the data, increasing standard errors, than to systematically bias coefficient

estimates.

Theoretical Salience of National Trends and Individual Experience

I consider three theoretical perspectives: gender-deviance neutralization (GDN), self-selection

into occupations, and occupational acclimation. For both GDN and self-selection into occupations, it is

the popular perception of occupations as male or female-typed that is most salient, regardless of an

individual’s actual workplace sex composition. That is, both of these theories address the gendered

stereotypes labeling occupations as “normal” or “suitable” for a given gender, and as requiring gender-

typed behavior. Occupational sex composition is a very good proxy for this aspect of occupational

gender-typing. The degree of sex-segregation in an occupation is directly related the expectation that

gender-stereotypical traits are required for success in that occupation (Cejka & Eagly, 1999). Also, as

discussed in more detail below, there is very little regional variation in the sex composition of

occupations that are skewed male or female (gender-mixed occupations exhibit greater regional

variation: Perales and Vidal, 2015).

In contrast, occupational acclimation proposes that gendered work experiences might alter

housework performance over time. This might occur through contact with co-workers, the experience of

performing male or female-typed tasks on the job, or an adjustment of gender attitudes resulting from

the social image of employment in a gender-(a)typical occupation. The first of these process,

interactions with co-workers, depends on the sex composition of the workplace—I consider the degree

to which occupational sex composition reflects workplace sex composition below. But the latter two

processes depend on the sex composition of the occupation, not that of the workplace. Thus, overall, it

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is actually the sex composition of the occupation that is theoretically relevant, not the sex composition

of the workplace. Moreover, it is largely the perception of an occupation as male or female-typed that is

relevant, and local or workplace variations in occupational sex composition may not impact these

widely-shared perceptions.

National Trends as a Proxy for Individual Experience

Perales and Vidal (2015) find significant local variation in the sex composition of specific

occupations and occupational groups across England and Wales. However, the degree of local variation

is small, rarely exceeding 1-3% changes in the percentage of women in a given occupational group

(Table 1, p.587). For example, the proportion of women “managers and senior officials” (the first-listed

occupational group in Table 1) ranges from 34% to 39% and the proportion of women in “professional

occupations” (the second-listed occupational group in Table 1) ranges from 42% to 45%. Looking at

more detailed categories—equivalent to the level of detail I use in my analysis—suggests that regional

variation is most substantial among gender-integrated occupations and is minimal among predominately

male or predominately female occupations (Perales and Vidal 2015; Table 2 and Table 3, p.589). The

authors suggest that occupations segregated enough to be gender-typed in popular perception may, as

a result of this gender-typing, be similarly-segregated across local contexts. This suggests that national

average occupational sex composition is an excellent proxy for popular perceptions of occupations as

male-typed, female-typed, or gender-mixed—which is largely what I am hoping to capture with this

measure—and that it is not likely to vary substantially across regions.

However, Perales and Vidal (2015) used data on England and Wales; to my knowledge, no

studies have estimated the degree of local variation in the sex composition of specific occupations

across the U.S. (but see discussion of my results on this below). Researchers have estimated average

levels of occupational sex segregation across U.S. metropolitan areas, but this does not isolate variation

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driven by the composition of occupations within the local economy, as opposed to variation driven by

the gender composition of specific occupations (Gauchat, Kelly, & Wallace, 2012; Huffman & Cohen,

2004). That is, a given metropolitan area might be highly (minimally) gender-segregated as a result of

having a large (small) concentration of strongly-gender-segregated occupations (such as manufacturing),

rather than because the gender composition of specific occupations varies from the national average.

Thus, this literature is not helpful in gauging local variation in the sex composition of specific

occupations.

Accordingly, I used IPUMS data to calculate occupational sex composition at the county level, for

all metropolitan counties (rural counties are not populous enough; see below), and compared this to

occupational sex composition at the national level. In calculating occupational sex composition at the

national level, each individual is weighted equally. In calculating occupational sex composition at the

county level, individuals are weighted equally within counties. The resulting dataset has a unique

observation for every occupation-county-year combination, the average proportion female for that

occupation-county-year, and a corresponding national average at the occupation-year level. The county-

specific measure makes it possible to assess variability in occupational sex composition across counties.

The correlation of occupational sex composition at the national and county levels is 0.82

(p<0.001). Calculated nationally, the average occupational sex composition from 1970-2010 is 0.391

with a standard deviation of 0.292; calculated at the county level, average occupational sex composition

is 0.386 with a standard deviation of 0.361. That is, in general, the sex composition of a given occupation

calculated nationally is very similar to the composition of that same occupation calculated at the county

level. More to the point, the variation in occupational sex composition is not dramatically larger at the

county level than at the national level, even though variation is necessarily increased at the county level

due to insufficient sample sizes.

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Of course, local variation is not the only reason why individual experience might differ from

national-level occupational sex composition. Occupational sex composition may vary at the

establishment level. Even if a given occupation has a similar sex composition across regions, specific

establishments may be outliers. Additionally, occupational sex composition is only a proxy for the

degree of other-sex and same-sex contact at work. Whereas some occupations tend to be concentrated

within certain industries, others span industries. For example, receptionists are predominately female

regardless of industry (author’s calculations from U.S. Census data; not shown) but they work in many

industries (schools, banks, construction firms, etc.) and the sex composition of industries is highly-

variant. Likewise, some workers may be surrounded by co-workers of their same occupation while other

workers may be the sole representative of that occupation in their place of employment. To continue

the same example, some receptionists work alone (especially in small establishments) and others work

in groups (common in large establishments).

In practice, prior studies indicate that Census-based measures of occupational sex composition

(like the one I use) closely approximate the job distribution of women and men (Tomaskovic-Devey,

1993) and occupational sex composition is highly correlated with workgroup sex composition

(workgroup sex composition represents the sex composition of co-workers reporting to the same

supervisor as the focal individual: Kmec, McDonald, & Trimble, 2010). Thus, although there are

doubtless exceptions, occupational sex composition is, in general, a decent approximation for the sex

composition of the co-workers with whom one most interacts. Below, I consider the likely influence of

exceptions to this general pattern on coefficient estimates and standard errors. However, it is important

to emphasize again that I am most interested in the perception of occupations as male or female-typed,

not the sex composition of co-workers, and that occupational sex composition is an excellent proxy for

such perceptions.

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Measurement Error: When Individual Experiences Differ from National Trends

Given that occupations that are gender-skewed exhibit minimal local variation in occupational

sex composition (Perales and Vidal, 2015), and that occupational sex composition is closely associated

with gendered perceptions of occupations (Cejka & Eagly, 1999), occupational sex composition is an

excellent proxy for perceptions of certain jobs as “women’s jobs” or “men’s jobs.” That is not to say that

using occupational sex composition to label jobs as male/mixed/female is a perfect measure, but it is

arguably a very good measure. Gender-mixed occupations exhibit more local variation in occupational

sex composition (Perales and Vidal, 2015) and it is plausible that popular stereotypes of workers in these

occupations are also less definite; however, I have little interest in subtle differences among gender-

mixed jobs. My interest in is strongly-gendered jobs and using occupational sex composition to identify

them is unlikely to introduce much inaccuracy or bias. In this sense, there is little reason to be concerned

that coefficient estimates and standard errors are imprecise or biased.

Occupational sex composition is also a reasonable measure of workplace sex composition (Kmec

et al., 2010; Tomaskovic-Devey, 1993). But it may not be as precise an estimate of workplace sex

composition as it is of occupational gender-typing. This might introduce imprecision in coefficient

estimates and standard errors, but there is no reason a priori to expect it to introduce bias. Importantly,

imprecision will not systematically bias coefficient estimates, but it may make standard errors larger,

increasing the chance of false-negative results (that is, of erroneously accepting the null hypothesis that

occupational sex composition is unrelated to housework). Imprecision is not likely to generate false-

positive results; thus, the strong and statistically-significant effects evident in my analysis are unlikely to

be artifacts of imprecise measurement.

References

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Cejka, M. A., & Eagly, A. H. (1999). Gender-stereotypic images of occupations correspond to the sex

segregation of employment. Personality and Social Psychology Bulletin, 25, 413–423.

Gauchat, G., Kelly, M., & Wallace, M. (2012). Occupational gender segregation, globalization, and gender

earnings inequality in U.S. metropolitan areas. Gender & Society, 26(5), 718–747. doi:

10.1177/0891243212453647

Huffman, M. L., & Cohen, P. N. (2004). Occupational segregation and the gender gap in workplace

authority: National versus local labor markets. Sociological Forum, 19(1), 121–147.

Kmec, J. A., McDonald, S., & Trimble, L. B. (2010). Making gender fit and “correcting” gender misfits: Sex

segregated employment and the nonsearch process. Gender & Society, 24(2), 213–236. doi:

10.1177/0891243209360531

Panel Study of Income Dynamics (PSID). (2016). A national study of socioeconomics and health over

lifetimes and across generations. Retrieved from https://psidonline.isr.umich.edu

Perales, F., & Vidal, S. (2015). Looking inwards : Towards a geographically sensitive approach to

occupational sex segregation. Regional Studies, 49(4), 582–598.

Ruggles, S., Alexander, J. T., Genadek, K., Goeken, R., Schroeder, M. B., & Sobek, M. (2010). Integrated

public use microdata series: Version 5.0 [Machine-readable database]. Minneapolis: University

of Minnesota.

Tomaskovic-Devey, D. (1993). Gender and racial inequality at work: The sources and consequences of job

segregation. Ithaca, NY: ILR Press.

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Table B1. Average occupational sex composition over time. Married dual-earner couples. Panel Study of Income Dynamics 1981-2013.

Average % Female Sample size

Survey year Men Women Men & Women1

1981 .26 .71 1,717

1982 NA2 NA2 NA2

1983 .26 .71 1,807

1984 .27 .70 1,871

1985 .26 .69 1,932

1986 .26 .70 2,037

1987 .27 .70 2,097

1988 .27 .69 2,101

1989 .27 .68 2,172

1990 .28 .69 2,672

1991 .28 .69 2,651

1992 .28 .68 2,783

1993 .29 .67 2,677

1994 .29 .67 1,688

1995 .29 .68 2,134

1996 .29 .68 1,794

1997 .28 .68 1,805

1999 .30 .65 1,195

2001 .29 .66 1,011

2003 .30 .67 2,276

2005 .31 .68 2,295

2007 .31 .67 2,066

10

2009 .31 .68 1,848

2011 .33 .69 1,187

2013 .32 .69 1,046

All years (average, total) .28 .68 46,142

1The sample size is the same for women and men because missing data are dropped if either spouse lacks valid occupational information.2Housework is not asked in 1982 so this year is excluded from my analytic sample.

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ONLINE SUPPLEMENT C: MIXED-EFFECTS MODELS

Mixed-effects regression models combine the advantages of fixed-effects and random effects

regression models (Allison, 2009, p.617). Fixed-effects regression models isolate within-individual

variation over time, thus controlling for stable individual traits, even those that are unmeasured. It is

possible to estimate a fixed-effects model by expressing all variables as deviations from their person-

specific means, and then estimating an ordinary least squares (OLS) regression model on the mean

deviation variables (Allison, 2009, 617); this approach to fixed effects provides a useful baseline for

understanding mixed-effects models. To estimate fixed-effects models in this way, one would first

calculate each individual’s average value on each variable across time, such as average income or

average proportion occupation female. Second, one would take the value at each time point (yearly,

daily, weekly, biennially, etc.) and subtract the individual (across time) mean, resulting in a mean

deviation variable at each time point. Third, one would estimate an OLS regression using these mean

deviation variables, correlating errors within individuals across time. Time-invariant variables would be

dropped from the model—by subtracting the individual mean of all variables, one is left with a value of

zero for all cases because the mean of a time-invariant variable equals its value at any given time point.

This isolates within-individual variation and controls for all time-variant traits, even those that are

unmeasured, without including them in the model. The equation for a fixed-effects regression model is:

yit - yi = (μt - μ) + β(xit – xi) + (εit - εi) [Equation 1]

In Equation 1, it is evident that the person-specific means (xi) are subtracted from the person-

time specific values (xit), leaving mean deviations (see Allison, 2009, 330-331 for a derivation of Equation

1). The advantage of this approach is that it is able to isolate within-individual variation across time,


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controlling for between-individual differences in time-invariant traits. This can eliminate substantial bias.

However, it can also be inefficient and it cannot include time-invariant variables or provide insight into

between-individual differences. Random effects models include time-invariant variables and exploit

both within- and between-individual variation, but they do not isolate these two sources of variation.

The bias eliminated in fixed-effects models (by controlling for all time-invariant variables) may taint

random effects models. This is evident in the equation for random effects models:

yit = μt + βxit + γzi + αi + εit [Equation 2]

Unlike the fixed-effects model, the random effects model includes zi, a vector of time-invariant

variables. The random effects equation also includes the error term α i, which captures time-invariant

variation across individuals (this source of error is eliminated in a fixed-effects model). The random

effects model does not control for unmeasured time-invariant traits, only for those that are measured

and included in the model, and it is only unbiased if α i is uncorrelated with the included covariates

(Allison, 2009, 570-598). Finally, because random effects models do not isolate within- and between-

individual variation, the coefficients (β) on time-variant variables (xit) are weighted averages of the

“within” and “between” coefficients (Allison, 2009, 643).

The mixed model combines the advantages of fixed and random effects models by including

mean deviation variables (as in fixed effects) but also including the individual means as independent

variables (Allison, 2009, 617-643; Neuhaus and Kalbfleisch, 1998; Neuhaus and McCulloch, 2006). Here

is an equation for a mixed-effects model:

yit = μt + β(xit – xi) + γxi + γzi + αi + εit [Equation 3]

This equation includes mean deviation variables (xit – xi), as a fixed-effects model would. But it also

includes the individual means of time-variant variables (xi) and individual values of time-invariant

variables (zi) as predictors. This equation further differs from a fixed-effects equation in that the

dependent variable, yit, is not transformed into a deviation variable, and in that there are two sources of

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error (Allison, 209, 617; Neuhaus and McCulloch, 2006). The error term α i captures time-invariant

variation across individuals (again, this is eliminated in a fixed-effects model) and the error term ε it

captures variation across individuals and across time. The strength of the mixed-effects model is that

allows researchers to estimate both within-individual differences and between-individual effects.

Moreover, in an otherwise-equivalent model, the coefficient (β) and standard error estimates for the

mean deviation variables (xit – xi) are identical to those from a conventional fixed-effects model (Allison,

2009, 617). Thus, these estimates are unbiased by individual variation in unmeasured fixed (time-

invariant) traits (represented by αi in Equations 2 and 3). However, the coefficient (γ) and standard error

estimates for the mean variables (xi) and included time-invariant covariates (zi) may be biased, if they

are correlated with αi.

In the case of occupational sex composition and housework, using mixed-effects models allows

me to isolate within-individual changes in occupation and housework over time, and also to consider

differences between different women and men who select into different types of occupations. This

allows me to evaluate both of McClintock’s (2017) proposed processes—self-selection (captured by

between-individual variation) and acclimation (captured by within-individual variation). When the

coefficient and standard error estimates for the mean deviation variables differ from those for the

corresponding mean variables, this indicates that individual variation in unmeasured time-invariant

traits is correlated with the included time-variant covariates (Allison, 2009, 634-643). That is, α is

correlated with x. Specifically, if I observe significant within-individual effects of occupational sex

composition on housework, this suggests that the experience of working in a male/female occupation

alters individuals’ housework performance over time, supporting acclimation. If I do not observe

significant within-individual effects of occupational sex composition on housework, but I do observe

significant between-individual effects of occupational sex composition on housework, this suggests that

unmeasured individual differences (α) explain the association of occupational sex composition and

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housework performance over time, supporting self-selection.

References

Allison, P. D. (2009). Fixed effects regression models: 160 (Quantitative Applications in the Social

Sciences) (Kindle Locations 619-620). Thousand Oaks, CA: Sage.

McClintock, E. A. (2017). Occupational sex composition and gendered housework performance:

Compensation or Ccnventionality? Journal of Marriage & Family, 79(2), 475–510. doi:

10.1111/jomf.12381

Neuhaus, J. M., & Kalbfleisch, J. D. (1998). Between- and within-cluster covariate effects in the analysis

of clustered data. Biometrics, 54(2), 638–645. doi: 10.2307/3109770

Neuhaus, J. M., & McCulloch, C. E. (2006). Separating between- and within-cluster covariate effects by

using conditional and partitioning methods. Journal of the Royal Statistical Society. Series B

(Statistical Methodology), 68(5), 859–872. doi: 10.1111/j.1467-9868.2006.00570.x

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