## Abstract

Research on sex differences in humans documents gender differences in sensory, motor, and spatial aptitudes. These aptitudes, as captured by Dictionary of Occupational Titles (DOT) codes, predict the occupational choices of men and women in the directions indicated by this research. We simulate that eliminating selection on these skills reduces the Duncan index of gender-based occupational segregation by 20 % to 23 % in 1970 and 2012, respectively. Eliminating selection on DOT variables capturing other accounts of this segregation has a smaller impact.

## Introduction

The male-female gap in labor market compensation has declined significantly over the past three decades in many developed countries. In the United States, for example, the female/male ratio of median annual earnings for full-time workers increased from 0.62 in 1979 to 0.83 in 2014 (U.S. Bureau of Labor Statistics 2015). In countries that measure the gender gap in hourly earnings, the female/male ratio is even higher: for example, 0.88 (in 2014) in Canada (Statistics Canada 2015) and 0.91 (in 2015) in the United Kingdom (Office for National Statistics 2015). In comparison, the pace of change in the gender segregation of employment in recent decades has been glacial. Gross (1968) reported that the Duncan index1 of segregation was steady at roughly 0.67 from 1900 to 1960. In the five decades since then, it has fallen by just 25 %, to slightly more than 0.50 in 2012 (e.g., Blau et al. 2013). At 0.50, the index tells us that the segregation of males and females remains substantial: more than one-half of men (or women) would need to change occupations for the occupational distributions of male and female employment to be the same.

Understanding why gender occupational segregation persists is important. It accounts for part of the remaining gap between male and female compensation: in the United States, the within-occupation wage gap fell by nearly 50 % from 1970 to 2012, while the between-occupation component of the wage gap rose slightly. Persistent segregation of the genders across occupations implies that sectoral change that accompanies economic growth is likely to have important effects on the relative compensation of men and women. Finally, if occupational segregation is of intrinsic policy interest, an effective response must be rooted in an understanding of its sources.

In this study, we extend the literature by examining the potential importance of sex differences in sensory, motor, and spatial aptitudes—for example, the sense of touch, fingering abilities, and depth perception—to this segregation. To our knowledge, the links between these sex differences and occupational segregation have not been systematically investigated. Extensive research has documented sex differences in these skills, many starting at very young ages, and they are clearly relevant to job skills in many occupations.

We map the evidence of sex differences in these aptitudes into occupational aptitudes, as captured by the Dictionary of Occupational Titles (DOT) (e.g., U.S. Department of Labor, Employment and Training Administration 1991), which we in turn relate to occupational selection by men and women. With few exceptions, females and males select into occupations on the DOT attributes in accordance with the predictions of the research. These relationships largely remain after we control for other explanations of gender occupational segregation, including measures of cognitive demands, physical strength, people/things orientation, occupational risk (death, competition, and prestige), and time flexibility.

The estimated relationships are quantitatively important. We simulate that eliminating the observed correlation between these skill demands and male/female selection would reduce occupational segregation by approximately 20 % in 1970 and 23 % in 2012, which is relatively more than the combined effect of variables representing more traditional explanations of gender segregation.

A qualification to these conclusions is the difficulty of identifying the effect of specific job characteristics on an outcome because they may be correlated with other important unobserved characteristics. Gender differences in these unobserved characteristics, or unobserved demand-side employer discrimination, could potentially be driving the differential male and female occupational selection. For example, to use a better-known gender difference, it may be that males are found disproportionately in jobs requiring physical strength not because they are stronger, on average, but because employers in these occupations are more discriminatory against females.

To some extent, these concerns are mitigated by the facts that we are jointly testing for the effect of multiple skills—it is unlikely we would observe the precise pattern of selection predicted by previous research if it were not related to these skills—and that we control for variables capturing many of the competing explanations. We attempt to push further on this issue for the female advantage in the sense of touch, which (as explained later) has been attributed in part to their smaller average finger/hand size. This argument suggests that males with smaller fingers should select into touch jobs as females do. We identify these jobs using the DOT measure feeling, and using height as a proxy for finger size, we cannot reject the hypothesis that this is true. This suggests that an unobserved demand- or supply-side variable confounding the results for this attribute must be correlated with height (hand size) rather than gender.

## Previous Literature on Occupational Segregation

A large literature documents the existence of, and trends in, gender-based occupational segregation (e.g., Blau Weiskoff 1972; Blau et al. 2013). Explanations generally fall into three classes. The first highlights the role of differences in human capital or skills. A recent emphasis is females’ hypothesized advantage in social skills (e.g., Bacolod and Blum 2010; Black and Spitz-Oener 2010; Borghans et al. 2014; Levanon and Grusky 2016).2 More comparable to our focus is Bielby and Baron’s (1986) investigation of the relationship between occupational segregation in California in the 1960s and 1970s and DOT skill measures.

The second class of explanations relates occupational segregation to gender differences in preferences for job attributes. For example, because women are more likely to experience job disruptions related to family responsibilities, they may prefer to select into jobs that minimize the penalty for family leaves. Previous research has examined the penalty for career disruptions (e.g., Light and Ureta 1995; O’Neill and O’Neill 2006) and the influence of this penalty on occupation selection (e.g., Goldin 2014; Kosteas 2010 or Polachek 1981). Another focus is gender differences in preferences for risk, competition, and prestige (e.g., Akerlof and Kranton 2000; Buser et al. 2014; Goldin 2015; Pan 2015).3

A third class of explanations of occupational segregation explores the role of discrimination. Several studies using matched pairs of applicants or randomized resumés have found discrimination against female applicants in male-dominated jobs and against male applicants in female-dominated jobs (e.g., Riach and Rich 2006; see also reviews in Riach and Rich 2002)

In this article, we first extend research examining the role of gender differences in skills to differences in sensory, motor, and spatial skills. Second, we simultaneously examine the contributions of other explanations of occupational segregation. Of course, the distinction among skills, preferences, and discrimination is somewhat artificial. If discrimination or social norms affect skill and preference formation, our results will also pick up the effect of these processes. We consider this less likely for some of the sensory, motor, and spatial skills that have stronger biological origins or are evident at very young ages.

## Gender Differences in the Skills and Abilities

We briefly summarize the findings of research for the specific gender differences that we investigate here. A fuller discussion of the underlying research is available in Baker and Cornelson (2016a). Explanations of these differences include biological, evolutionary, and environmental factors. To be clear, our analysis does not shed light on the source of the differences.

### Gender Differences in Sensory Functions

Gender differences in the traditional five sensory functions have long been reported (Velle 1987; for an overview, see also Halpern 2012:105–107).

#### Vision

Males have a higher incidence of color blindness because the most prevalent forms (red/green) are a result of gene deletion or damage on the X chromosome, and color blindness is a recessive trait. Recent research has suggested that within a sample of college students, females exhibit greater sensitivity to color than males in populations with normal vision (Abramov et al. 2012b; Handa and McGivern 2015; Murray et al. 2012). In a sample of 16- to 23-month-old infants, a higher proportion of females could distinguish colors (Mercer et al. 2014).

Research has also found that adult males exhibit better visual acuity—that is, sensitivity to fine detail and rapidly moving stimuli (Abramov et al. 2012a; Velle 1987). Research using a sample of young adults found better accuracy in near space for females and in far space for males (Stancy and Turner 2010).

#### Hearing

Females have been observed to have a higher degree of auditory sensitivity than males (detecting weak sounds in quiet), especially at higher frequencies, starting in childhood (Halpern 2012; McFadden 1998; Velle 1987). Conversely, males have been observed to have a higher tolerance of noise, again starting in childhood (Velle 1987). Roughly speaking, females have been found to experience a given noise level twice as strongly as males.

#### Taste and Smell

Females have been observed to have a better sense of smell and taste (Brand and Millot 2001). Sex differences have not been observed for all smells, but where detected, they always favor females. Halpern (2012:106) reported that the advantage “extends across the entire lifespan.” The evidence on sex differences in taste recognition and perception are more mixed, suggesting that females perceive some tastes better but others not as well (Halpern 2012:107).

#### Touch

Females have been observed to have a better sense of touch—a finding that holds for both blind and sighted subjects and therefore one that is distinct from findings of sex differences in visual acuity (Halpern 2012). In one dimension, this difference appears to be biological because the perception of textures is hypothesized to be related to the density of sense perceptors—Merkel cells—in the hand. Smaller fingers have a higher density of these cells, so females’ smaller stature and finger size, on average, provides them an advantage (Peters et al. 2009). Touch sensitivity has been found to be similar between men and women with similar finger size.

### Gender Differences in Perceptual Motor Tasks

#### Motor Abilities

Tests of abilities for aiming at moving or stationary targets appear to favor males by a relatively large margin (Hall and Kimura 1995; Watson and Kimura 1991; but also see Auyeung et al. 2012), whereas females demonstrate an advantage in fine motor dexterity (Nicholson and Kimura 1996). Tests of both these abilities find similar sex differences among young children (Sanders and Kadam 2001).

Common tests of these abilities have been criticized for conflating any sex differences in perceptions of near and far space (see earlier discussion of vision) with any sex differences in specific motor skills. Controlling for sex differences in space, Sanders et al. (2007) presented evidence that females perform better in finger tasks, while males perform better in arm tasks.

Recent research has taken up this distinction between a gross motor movement advantage for males and a fine motor movement advantage for females (for an overview, see Sanders 2013). For example, females have an advantage in movements of the wrist and fingers (Sanders and Perez 2007; Sanders and Walsh 2007).

Sex differences in some perceptual motor tasks, especially those involving digits and alphabets, appear to favor females (e.g., Roivainen 2011). These include perceptual speed, fine motor manipulations, and tactile skills. For example, females have an advantage in the Digit Symbol task (formerly part of the Wechsler Scales) but not the Inspection Time task (Burns and Nettelbeck 2005; Halpern 2012). A female advantage in the Processing Speed Index of the Wechsler scales has been reliably found in a sample of primary and secondary school–aged children (Longman et al. 2007).

Some of these differences are again attributed to females’ predominantly smaller stature, on average. For example, females’ smaller hand size might contribute to their advantage in fine motor tasks (Peters and Campagnaro 1996; Peters et al. 1990).

### Gender Differences in Visiospatial Abilities

Sex differences in visiospatial abilities have been widely documented and generally favor males. Halpern (2012) reported a male advantage in spatial perception; mental rotation; spatiotemporal ability; and to a lesser extent, spatial visualization. Females have an advantage in remembering the spatial location of objects in an array (Sanders 2013). Gender differences in some of these abilities emerge at very young ages (e.g., Moore and Johnson 2008; Quinn and Liben 2008).

Among high school seniors, Baker and Cornelson (2016b) reported a gender gap favoring males in a test of three-dimensional mental rotation of 0.388 of a standard deviation in 1960 and 0.253 of a standard deviation in 1980.

## Data and Empirical Framework

### Occupational Characteristics Data

We link the sex differences documented in the last section to occupational segregation using information on occupational skill requirements from the 1977 and 1991 DOT. The DOT rates several thousand occupations for aptitudes, temperaments, interests, and physical demands. In Table S1 in the online appendix, we describe the DOT measures that we believe are most closely linked to sex differences outlined in the previous section. For a fuller discussion of the “expected signs” for these measures, see Baker and Cornelson (2016a).4

To assess the importance of sensory, motor, and spatial skills relative to other explanations of occupational gender segregation, we also attempt to capture an occupation’s (1) overall physical demands, (2) math and verbal skill requirements, (3) people/things orientation, (4) degree of risk and competitiveness, (5) social stature, and (6) time flexibility. As outlined in the online appendix, we capture these alternative explanations with additional DOT variables, occupational mortality rates derived from the U.S. Bureau of Labor Statistic’s Census of Fatal Occupational Injuries,5 measures of occupational competition and time flexibility from the O*NET database,6 and occupational status using the occupational prestige score proposed by Nakao and Treas (1994).7

### Occupations

We link the DOT measures and the other occupational characteristics to occupations in decennial census data and the 2012 three-year American Community Survey (ACS), denoted as “2012.” Our main analysis focuses on the 1970 and 2012 data sets linked to the DOT files. We use the intervening 1980, 1990, and 2000 census data to replicate basic statistics from earlier work. We use the crosswalk developed by Blau et al. (2013) to convert occupations in the earlier census years and the ACS to the 2000 census occupational coding. We are able to match DOT ratings to 476 of the 505 census occupational codes. Because the DOT occupations are more detailed than census occupations, we average the ratings across all DOT occupations within a census code, with weights corresponding to that occupation’s share of employment. As a result, although the DOT measures are categorical, they are continuous in our data. Where possible, we use 1977 DOT measures for the 1970 and 1980 censuses and use the 1991 DOT measures thereafter. We use the 1991 measures for all years for physical demands8 and certain environmental conditions that are available only in 1991. We use a crosswalk provided by the U.S. Census Bureau to link the O*NET measures and the fatality information from the Census of Fatal Injuries to census 2000 occupational codes. We are able to link O*NET measures to 468 census occupations (all of which also have fatalities information), which provide the final sample of occupations for our analysis. These occupations account for 98.4 % of the U.S. workforce in 2012 and have a Duncan index that is nearly identical to that for the U.S. workforce as a whole. Other details of the data construction are provided in the online appendix.

### Empirical Framework

Our objective is to estimate Duncan indices of gender occupational segregation net of any gender occupational selection on occupational differences in the DOT sensory, motor, and spatial attributes. The Duncan index is defined as
$D=0.5⋅∑jmj−fj,$
where fj is the fraction of all employed women who work in occupation j, and mj is the fraction of all employed men who work in occupation j. The index, which ranges between 0 and 1, is commonly interpreted as the proportion of women or men who would need to change occupations for the occupational distribution of men and women to be equal.
We start by estimating the relationship between our occupational attribute measures and the relative probability that men and women select into an occupation. Specifically, we regress the log odds of male to female employment in an occupation,
$lj=lnmj1−mjfj1−fj,$
1
on our measures of occupational characteristics. The term fj/(1 − fj) represents the odds that a randomly selected, employed female works in occupation j. The ratio of these odds for men and women tells us about the relative likelihood that men and women select into occupation j.
Our main regression equation is
$lj=α+βSj+εj,$
2
where Sj are measures of the characteristics of occupation j.
We use the results of estimating Eq. (2) to simulate the effect of removing any differential selection on skills across occupations. We first predict the log odds for each occupation that would occur if a particular set of occupational characteristics did not differentially affect the occupation choices of men and women. Let Sk denote a subset of occupational characteristics, and let S–k denote all of the remaining occupational characteristics. The predicted log odds for occupation j, eliminating differential gender selection on the characteristic set k, are
$l^j=α^+β^−kS−k+ε^j.$
3

Next, we find the unique occupational shares, $f̂j$ and $m̂j$, that solve these log odds and also keep each occupation’s total share of employment at its actual level, yielding 936 equations in 936 unknowns.9 Finally, we construct Duncan indices from these predicted shares.

To evaluate whether these predicted indices are significantly different from the actual Duncan index in each year, we compare them with a distribution of Duncan indices constructed from 500 rounds of resampling from the actual data. Because the sample size is large, this procedure produces bounds that are quite narrow. As a result, all our estimated Duncan indices are significantly different from the actual Duncan index at the 1 % level, and we therefore omit the standard indications of significance from the relevant tables.

## Regression Results

### An Overview of Gender Occupational Segregation

In Table 1, we report estimates of the Duncan index of occupational gender segregation by census year and for 2012 based on ACS data. Although the estimates differ slightly in magnitude, they are consistent with the findings in Blau et al. (2013). The Duncan index falls more than 10 percentage points between 1970 and 1990, and less than 4 percentage points in the next 22 years. In 2012, slightly more than one-half of men or women would need to change occupations for the occupational distribution of males and females to be equal.

The five occupations that make the largest contributions to the Duncan index in each year are shown in the next five next rows of Table 1. They are very stable over time: for example, secretaries and administrative assistants make the largest contribution in every year. The proportion of the Duncan index contributed by these top five occupations (seventh row) declines gradually from approximately 21 % to approximately 17 % over the period.10

A recent focus of economic research on occupational segregation is on science, technology, engineering, and mathematics (STEM) occupations. Despite the many reasons to focus on these occupations, their contribution to overall gender employment segregation is not one of them. The proportion of the Duncan index represented by segregation in these occupations (eighth row, Table 1) ranges from approximately 4 % at the beginning of the sample to 5 % in 2012.11 Similarly, many discussions of occupational segregation focus on women’s disadvantage in high-earning management and leadership occupations (e.g., Kosteas 2010). However, the final row in the table shows that management occupations account for just 6 % of occupational segregation in all years.

In the final rows of Table 1, we report the total number of occupational categories with positive employment in each year and indicators of the importance of the occupations making the largest contributions to the Duncan index to overall gender segregation. For example, only 25–30 occupations in each year, or just 6 % of the total number, can account for 50 % of the Duncan index. The disproportionate contribution of these occupations arises partially because of their relatively large size: in 2012, they represented approximately 35 % of total employment. However, these occupations are also substantially more segregated than a typical occupation. The odds of the dominant gender’s employment in a typical occupation (compared with the nondominant) are approximately 3:1; in the smaller set of observations that contribute most to the Duncan index, these odds are 5:1. Similarly, the last row of Table 1 shows that in each year, roughly 170 of 505 occupations can account for 90 % of the Duncan index. These results amplify the message that gender occupational segregation is concentrated in a relatively small number of occupations.

### Gender Occupational Selection on Aptitudes

Table 2 presents the results of estimating Eq. (2). For 1970 and 2012, we present both simple regression estimates from specifications in which the indicated skill is the only regressor and multiple regression estimates from a regression in which all aptitudes and skills are regressors. These latter estimates account for the fact that occupational characteristics are not necessarily independent of one another. For example, men may be more (rather than less) likely to work in jobs that demand color vision because these jobs also demand aptitudes for which they are relatively advantaged or because these jobs have other characteristics that men tend to value more than women.

The first row of Table 2 shows the result for the DOT variable for physical strength, which is a familiar attribute of male advantage and can be used as a baseline for the estimates for the other attributes. All occupational attributes are normalized to have a mean of 0 and standard deviation of 1, so the estimates are interpreted as the change in the log odds associated with a 1 standard deviation increase in a skill. As expected, occupations with higher demands for physical strength have higher log odds, indicating that there are more men in these occupations. This effect is substantial: the simple regression estimates indicate that in the 1970 data, a 1 standard deviation increase in the physical strength measure is associated with a 0.728 increase in the log odds of male employment in 1970 and a 0.996 increase in 2012. In the 2012 data, the odds ratio is slightly more than 2.7 in an occupation 1 standard deviation above the mean in physical strength. In the multiple regression results, these associations are attenuated, the estimates just more than one-half the simple regression values.

The next panel shows the results for the sensory attributes. In the simple regression results, the estimates for color vision and color discrimination are not of the expected sign, but those for the remaining skills are. Larger estimates are observed for far acuity and the two measures of auditory sensitivity; the estimates for noise are larger than the estimates for physical strength. In the multiple regression estimates, the “wrong signs” of the color variables are mostly rectified. Statistically significant relationships approaching the magnitude of the results for strength are observed for the noise and feeling variables.

The next panel of Table 2 contains the results for motor skills. In the simple regression results, most of the estimates are of the expected sign, with the exception of motor coordination and handling in 2012. The manual dexterity attribute involves both arms and hands, and we do not have a prediction for the sign of the effect. The result here indicates a positive association with male employment. In the multiple regression results, the estimates for many of the individual skills are now statistically insignificant and, of note, are of the wrong sign for eye-hand-foot.

The spatial skills are in the next panel of Table 2. In the simple regression results, the estimated relationships are mostly larger than for physical strength, but they are attenuated conditional on the other aptitudes. Nevertheless, the multiple regression estimates are of the expected sign and are comparable with the estimates for noise, feeling, and some of the strength estimates.

The estimates for the variables capturing alternative accounts of gender based occupational segregation are shown in the final panel of Table 2. Among the cognitive (GED) variables, math is a significant predictor of relative male employment in the multiple regression results. Relatively more females are in occupations requiring a temperament for dealing with people, although this relationship is statistically insignificant and small conditional on the other attributes. Relatively more males are in occupations requiring an interest in working with things, a result that is statistically significant in both specifications. The estimates for the remaining variables are of the expected signs but are statistically significant only in the multiple regression specification for competition, freedom to make decisions, and (to a lesser extent) mortality risk. The associations, however, are generally smaller than for attributes such as physical strength, noise, spatial skills, and math.

In unreported results (available upon request), we examine which variables appear to matter most for the differences in the estimates between the simple and multiple regression specifications and, in particular, instances of “wrong signs” in the simple regression results: for example, for math, prestige, work structure, color discrimination and vision, handling, and motor coordination. In all cases, these anomalies appear to be mainly accounted for by men’s tendency to select into more physical jobs as well as women’s tendency to select into more social/cognitive jobs. Including any of the variables physical strength, interest—things, temperament—people, or GED—language alone typically results in a change in the coefficients in the expected direction in both years. No other control variable has a significant effect on the simple regression coefficients for these variables.

In the online appendix (Table S2), we report how the results change in a series of robustness checks, including adding the ratio of male to female wages and average weekly hours12 at the occupational level as additional occupational attributes, omitting nominally duplicate skill measures (e.g., color vision and color discrimination), and investigating alternative DOT measures of people skills. Each of these modifications has little impact on the inference. We also estimate models that use either the 1970 or the 1991 DOT definitions for both the 1970 and 2012 data, finding minor changes in inference for one or two attributes.13

The message of this analysis is that estimated relationships between the male to female log odds ratio and the DOT measures of sensory, motor, and spatial aptitudes are largely the sign predicted by the cited research on sex differences, although multicollinearity is a challenge to isolating the relationships for individual skills.14 The estimates for the attributes/skills of noise, feeling, spatial, and depth perception stand out as making an empirically unique contribution to the log odds employment ratio. The analogs of these DOT skills in the research literature—hearing, touch, and spatial perception—are among the least controversial and widely acknowledged sex differences and have been documented at young ages.

## Omitted Variables: The Case of Feeling

As noted in the Introduction, omitted variables potentially confound our inference. Of concern would be gender-specific demand-side factors (such as employer discrimination) or unobserved supply-side factors correlated with our DOT measures. The growing literature on the hypothesized social skills of females (and things orientation of males) face similar challenges, which ultimately cannot be resolved absent some random variation in the aptitude of interest. Furthermore, even with random design, it is uncertain whether the resulting variation has external validity for the empirical difference in a given aptitude across the sexes.

Because some dimensions of the gender difference in the sense of touch are thought to be a function of finger size (which in turn is correlated with gender) rather than a function of gender per se, this aptitude provides an opportunity to make some progress on this issue. If the sense of touch is a function of finger size and not gender, then finger size should predict the occupational choices of males as it does those of females. This test helps us evaluate a hypothesis that a measure of touch is a proxy for some gender-specific demand-side factor.15

Our measure of touch is the DOT variable feeling. As documented in Table 2, this aptitude is a significant correlate of relative female employment. We are not aware of a representative data set that provides measures of finger or hand size. However, the National Health Interview Survey (NHIS) provides measures of respondents’ heights and of their occupational choices. A number of studies have documented that finger size and hand size and height are positively correlated (e.g., Garrett 1971; Guerra et al. 2014; Suseelamma 2014).

We next show that individuals select into jobs with feeling demands on the basis of height and that this selection is similar for men and women. Using the 1990–1994 NHIS surveys,16 we run a logit regression of the probability that individual i is observed in occupation j on the height of individual i, the skill demands of job j, the interaction between height and all skill demands, and a set of individual-level controls (age, race, and education.) An observation in this regression is an individual-by-job interaction, with the dependent variable equal to 1 for the job that the individual actually occupies and equal to 0 for all other occupations. In principle, this requires approximately 472 × 250,000 observations (472 occupations times the number of individuals in the NHIS). For computational ease, we add a random sample of five occupations in which the individual does not work to the occupation in which the individual does work, for a total of six observations per person. McFadden (1978) outlined the conditions under which this sampling of the “option set,” rather than using the full set of alternative options, results in consistent estimates.17 The coefficient on the interaction between height and feeling in this regression tells us whether taller individuals are more or less likely to select into jobs with a higher feeling rating. We estimate this regression separately for men and women.

In Table 3, we report the estimates of the interactions between height and our various aptitudes for males and females separately. As hypothesized, both males and females select into feeling occupations on height and in a very similar way: taller individuals are less likely to work in jobs with high feeling scores. We cannot reject the hypothesis that the male and female estimates are the same (column 3). In addition, height is generally negatively correlated with fine motor skills, including finger dexterity, handling, and manual dexterity.

Many of the other statistically significant estimates in Table 3 are consistent with research on the correlates of height. For example, hearing is positively correlated with height (Barrenäs et al. 2005; Welch and Dawes 2007), as are spatial skills (Zhou et al. 2016). One could connect the positive relationship between height and occupational prestige, competition, and freedom to make decisions to research linking height to noncognitive skills (e.g., Lundborg et al. 2014; Persico et al. 2004; Schick and Steckel 2015). Perhaps surprisingly, given research linking height to cognitive skills (Case and Paxson 2008), height has little relationship with the GED variables, except with language for males. However, there is a positive and very similar association for males and females of height with clerical cognition.18

We next demonstrate that the relative propensity of females to select into jobs demanding feeling is attenuated after we limit males’ height advantage. We construct a predicted log odds of employment in each occupation. For females, this is based on their actual occupational choices in our NHIS sample. For males, however, it is based on a prediction of the male occupational distribution that would occur if males selected on the basis of height and job skill demands as per the logit regression estimates reported in Table 3 but had the same height distribution as females. Specifically, we adjust the number of men in each occupation by the following amount:
$Δm=∑HPrmjob=jh=Hx=X⋅Prm(x=Xh=H)⋅Prmh=H−∑HPrmjob=jh=Hx=X⋅Prm(x=Xh=H)⋅Prfh=H,$
4
where h represents an individual’s height, x represents the vector of individual covariates, and the summation sign is over all observed values of height. The first term represents the predicted number of men in each occupation based on the logit model’s results; the second term represents the number of men that would be predicted to be in each occupation if men selected on the basis of height the way they currently do but had the female height distribution. The difference between the two represents the change that would occur if we shifted men to the same height distribution as women. We use the predicted number of men (the actual number plus Δm from Eq. (4)) and the actual number of women to calculate predicted log odds, and then substitute them as the dependent variable in Eq. (2).

The first column of Table 4 shows estimates of the multiple regression version of Eq. (2) using the 1990 census,19 which is the census that temporally matches our NHIS data. The estimates are largely consistent with the multiple regression estimates for 2012 in Table 2. The second column of Table 4 shows the results of estimating a similar regression using the 1990–1994 NHIS data. These results are largely consistent with those in the first column, demonstrating that our inference is not affected by using the NHIS. In the third column, we present estimates for a restricted set of occupations using the NHIS because our predicted log odds procedure results in negative predicted values of men in some occupations, and we drop these occupations from our analysis. We find no major changes in the estimates from focusing on this smaller set of occupations.

Finally, the last column of Table 4 shows the estimates using the predicted log odds. For DOT feeling variable, the result is a substantively diminished correlation with relative female employment. This suggests that the estimates for feeling in columns 1–3 are substantially picking up an effect of being shorter rather than an effect of some other attribute of being female.

The estimates for most of the other attributes with statistically significant relationships with the log odds change in expected ways given the results in Table 3. For example, the spatial measures are less related to relative male employment after males’ height advantage is diminished. Similar changes are observed for occupational prestige, competition, and freedom to make decisions.

We interpret the results in Tables 3 and 4 as casting doubt that some gender-specific demand-side factor, such as employer discrimination, lies behind the relationship between feeling and the log odds of employment. They also suggest that any unobserved supply-side variable that accounts for a significant part of the association of feeling with the log odds of employment must be correlated with a worker’s height rather than their gender.

## Association of Gender Occupational Selection on Aptitudes With Gender Occupational Segregation

In Tables 5 and 6, we provide estimates of adjusted Duncan indices following Eq. (3). These estimates remove the impact of any sex difference in occupational selection on the indicated attribute, all else equal. Table 5 shows the Duncan indices constructed in this way from simple regressions, and Table 6 shows the effect of eliminating different groups of occupational attributes based on the multiple regressions. Because of the possibility of omitted variables bias in the underlying regressions, we view the results as telling us more about the relative importance of various attributes than about their absolute importance.

From an economic standpoint, the changes induced by individually removing the influence of many of the skills are quite small. For 1970, over the sensory and motor attributes, the predicted Duncan indices range from 0.610 to 0.651, representing changes of no more than 5.5 % from the actual Duncan index in that year. In 2012, some of these attributes have a larger effect: eliminating selection on hearing, noise, eye-hand-foot coordination, or clerical perception would reduce the Duncan index by 7 % to 12 %.

The spatial attributes have more traction. The predicted Duncan index removing the gender difference in selection on depth perception (which has the more significant effect) is 10.4 % and 16.1 % lower than the actual Duncan index in 1970 and 2012, respectively.

Among variables capturing the competing accounts, physical strength and competition have the largest effect on the Duncan index in 1970, each reducing the index by approximately 5 %. In 2012, physical strength, the temperament for dealing with people, and mortality risk have the largest effect, in the 4 % to 6 % range.

Table 6 shows the results eliminating the impact of selection on different groups of skills based on the multiple regressions in Table 2. The impact of eliminating skill selection in groups is much larger than in the simple regression results. In 1970, the effect of eliminating selection on sensory and motor skills is to reduce the Duncan index by 4.2 % and 5.1 %, respectively; the effect of eliminating selection on spatial skills is higher, at 10.9 %. In 2012, eliminating selection on sensory skills and motor skills would reduce the Duncan index by 7.1 % and 3.3 %, respectively. Again, spatial skills are quantitatively more important, with a predicted reduction of approximately 10.4 %. In total, eliminating selection on sensory, motor, and spatial skills would reduce the Duncan index by 20.8 % in 1970 and 22.6 % in 2012.

The effect of eliminating selection on the variables representing the alternative hypotheses is generally smaller for the 1970 data, ranging from 1.9 % to 3.4 %. In total, eliminating selection on these variables controls would reduce the Duncan index by 14.4 %. For the 2012 data, the impacts of the different groups range from 0 % to 6.3 %, with a combined effect of 18.3 %.

Eliminating selection on all occupational attribute measures reduces the Duncan index to 0.420 in 1970 (a 34.8 % reduction) and 0.299 in 2012 (a 41.1 % reduction.) Selection on observable occupation attributes therefore accounts for a large portion of occupational segregation, although the majority of the Duncan index remains unexplained.20

## Conclusions

We bring research on sex differences in a number of sensory, motor, and spatial aptitudes to the puzzle of persistent gender-based occupational segregation in the U.S. labor market. Our results suggest that males and females select into occupations in ways predicted by this research. For example, males have been found to have a higher tolerance of noise and to be disproportionately employed in noisy occupations. We simulate that conditional on our mapping of these sex differences into DOT occupational attributes and absent this selection, the Duncan index of occupational segregation would be, all else equal, 20 % to 23 % lower than its observed levels in both 1970 and 2012.

We also compare the quantitative importance of these variables to a set of variables intended to capture competing hypotheses of the sources of gender segregation. Although some of these alternative hypotheses do account for gender segregation, they are generally less important quantitatively than our measures of sensory, motor, and spatial skills. Gender differences in spatial skills in particular appear to have an important relative impact on gender segregation.

These comparisons are contingent on the ability of the DOT data to capture the different explanations of gender-based occupational segregation and any bias from important factors that are omitted from our regressions. We argue that the first message of the analysis is the relative importance of gender differences in sensory, motor, and especially spatial aptitudes for occupational segregation.

The findings also highlight a lesson from the literature on these sex differences for research on the task content of jobs. The choice of specific DOT or O*NET skills to represent specific tasks may not be innocuous, particularly if differences across genders are to be compared or contrasted.21

## Acknowledgments

We gratefully acknowledge the research support of the Social Sciences and Humanities Research Council (#410-2011-0724) and a Canada Research Chair at the University of Toronto. Fran Blau kindly provided the occupational crosswalk for the 2000 census occupational coding. We thank the referees for helpful comments as well as Dwayne Benjamin, Diane Halpern, and Gary Solon for their input on an early draft. We also thank seminar participants at UBC–Kelowna, UBC–Vancouver, and the WOLFE workshop at the University of York.

## Notes

1

The Duncan index, which we define shortly, ranges between 0 and 1 and is interpreted to indicate the proportion of women or men who would need to change occupations to produce a similar occupational distribution of men and women.

2

Levanon and Grusky (2016) examined a number of the occupational characteristics examined here aggregated into composite measures.

3

See also Croson and Gneezy (2009) and Eckel and Grossman (2008) on risk aversion; Gneezy et al. (2003), Niederle and Vesterlund (2007), and Cotton et al. (2013) on competition; and Deleire and Levy (2004), Leeth and Ruser (2006), Bonin et al. (2007), and Grazier and Sloane (2008) on earnings and mortality risk.

4

We do not use the DOT physical demand codes of kneeling, climbing, balancing, stooping, crouching, crawling, talking, and reaching. We also exclude the aptitude form perception (the ability to perceive pertinent detail in pictures and graphs), the physical demands accommodation (the adjustment of the eye to bring things into focus), and field of vision.

5

We convert information on the number of fatalities for each occupation in 2012 to a mortality rate using employment information. The earliest data on fatalities are from 1992. Because these data are provided for different occupational codes, however, we can match them to only 431 occupations (as opposed to the 468 used in our main analysis) in the 2000 census. The results are similar if we use the 1992 fatalities information for our 1970 analysis.

6

O*NET, produced by the U.S. Department of Labor, has supplanted the DOT in recent years and provides many similar measures of occupational requirements as well as some additional characteristics. For time flexibility, we use Goldin’s (2014) proposed measures. The structure variable is reverse-coded in the O*NET, with higher values indicating more freedom for the worker to determine tasks, priorities, and goals.

7

The occupational prestige score is based on data from the 1989 General Social Survey, in which respondents were asked to rank occupations on scale of social standing from 1 to 9. The initial scores were based on the 1990 census occupational coding. We obtain the measures for the 2000 census occupational coding using data from IPUMS (Ruggles et al. 2015).

8

The exception is for physical strength, which is available in both years.

9

This procedure produces occupation shares mj and fj that do not sum to 1. We rescale so that the shares do sum to 1 by allowing the total number of men and women in the labor market to change. In practice, the changes in the total size of the labor force are fairly small: approximately 3 % for men and 1 % for women.

10

In Table 1, we report results for all 505 census occupation categories. In the analysis of skills, we use the 468 occupations that can be matched to DOT codes. This makes very little difference: the Duncan index for our 468 occupations is 0.644 in 1970 (the same as for the full set of occupations) and 0.508 in 2012 (vs. 0.506 for all occupations).

11

Our definition of STEM jobs is from Beede et al. (2011).

12

Weekly hours are provided in intervals in the 1970 census data. We use the midpoint of each interval to impute weekly hours.

13

We calculate the log odds ratio separately for the age groups 18–24, 25–34, and 35–64 and estimate the pooled regression testing for interaction effects between dummy variables for the younger age groups and the DOT aptitude measures. The estimates of these interactions are uniformly statistically insignificant. We also pool the 1970 and 2012 data and estimate a pseudo-panel model, with occupation fixed effects for the limited number of aptitudes coded separately in the 1977 and 1991 data. Slightly more than one-half of the estimates from this specification are of the expected sign, but less than one-half are statistically significant because the standard errors are generally much larger (one statistically significant estimate is of the wrong sign). The temporal variation of the DOT codes in this analysis could be due to sub-occupational compositional changes, and only 9 of the 28 aptitudes/skills in Table 2 are available for this analysis.

14

We estimate the models reported in Table 2 using the shrinkage estimator least absolute shrinkage and selection operator (LASSO). For 1970, the estimates from this method are 0 for color vision, manual dexterity, and motor coordination. For 2012, the estimates are 0 for color vision, near acuity, hearing, manual dexterity, motor coordination, and eye-hand-foot coordination. For both years, the estimates for noise, feeling, handling, and the spatial measures are mostly modestly smaller than in Table 2. These results are available from the authors on request.

15

As another test, we investigated whether simply adding a control for height diminishes the correlation of the log odds of employment and the DOT feeling variable. We calculated the average male height by occupation using the 1990–1994 NHIS and entered this as an additional control in regressions specification reported in Table 2. The results, reported elsewhere (Baker and Cornelson 2016a), indicated that adding this measure of height diminishes somewhat the correlation between the log odds ratio and the feeling variable, but also does not have a substantive effect on the correlation between the log odds and our measures of cognitive and noncognitive skills.

16

The NHIS does not provide detailed occupational coding after 1994.

17

The uniform conditioning property implies that every alternative randomly sampled from the choice set has some positive probability of being observed. McFadden (1978:544) gave several examples of selection procedures that satisfy this property; our selection procedure corresponds to his example C-1.

18

Importantly, the correlation of height with an attribute does not necessarily imply that the average height difference between males and females rationalizes the sex selection that we see in the data. On one hand, a dimension of the sense of touch is hypothesized to be mechanically related to finger size, and males and females of similar finger size have been found to have similar senses of touch. On the other, although taller men and women select into jobs that require better hearing, and research indicates that stature is positively related to hearing for each sex, females (as we noted earlier) have more acute hearing in some dimensions despite their smaller stature.

19

For these regressions, we switch to the 1990 census occupational codes, which is the coding available in the NHIS. Because 472 occupations have nonmissing log odds in the NHIS data, we limit analysis to these occupations.

20

We also examine the implications of selection on these skills for the gender wage gap. Holding wages and overall employment in an occupation fixed, we examine the effect on male and female average wages of eliminating differential gender selection on observable occupational attributes. In many cases, skill-based occupational segregation favors women in terms of compensation. Eliminating selection on physical strength or people/things orientation substantially increases the gender wage gap in both years, and eliminating selection on sensory or motor skills increases the wage gap in 2012 (yet decreases it in 1970). In contrast, eliminating selection on cognitive skills (particularly math), spatial skills, and measures of occupational risk leads to a lower gender wage gap in both years, but particularly in 2012. These results underline that the significance of the segregation of males and females in employment for the gender gap in pay is dependent on the relative prices of these skills at a particular time and place. These results are available from the authors on request.

21

For example, the DOT aptitudes Finger Dexterity (a fine motor skill) and Eye-Hand-Foot Coordination (a gross motor skill) are used to represent routine and nonroutine manual skills, respectively, in the Autor et al. (2003) taxonomy of tasks. Tables 24 show that these skills have strong relationships with the log odds of male employment, particularly when used in isolation.

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).
Intrinsic spatial knowledge about terrestrial ecology favors the tall for judging distance
.