The Return to Hours Worked within and across Occupations: Implications for the Gender Wage Gap

Abstract

Prior research suggests that gender differences in hours worked play an important role in the gender pay gap. Yet common estimates of the wage returns to hours worked are close to zero, implying that hours differences explain little of the gender wage gap, even though men work more hours than women on average. However, while the wage returns to hours worked within occupations are small, the authors document that the wage returns to average hours worked across occupations are large. They develop a conceptual framework that reconciles these facts. Findings show that, under some assumptions, gender differences in hours worked can account for a substantial portion of the gender wage gap and that increases in the returns to hours worked over the past four decades slowed progress in reducing the gender pay gap.

Keywords

hourly wage gender pay gap labor market flexibility gender wage differential wage dispersion

Employed women work, on average, three to five hours fewer than employed men, even controlling for demographics and occupation (based on 2016 US Census Bureau, American Community Survey data). A recent literature has argued these gender differences in hours worked and preferences for job flexibility are crucial to understanding the gender earnings gap. However, for hours worked to have a significant bearing on the gender wage gap, it must be the case that the wage return to hours worked is meaningful. While prior research has documented significant heterogeneity in the income elasticity of hours worked across occupations, the average estimated income elasticity is close to unity. This finding implies that the wage–hours elasticity is close to zero. In this case, the gender differences in hours worked would be incapable of explaining, in an accounting sense, a substantial fraction of the gender wage gap.¹

Motivated by this surprising finding, we carefully re-examine the relationship between weekly hours worked and wages. Using individual data from the US Census Bureau’s American Community Survey (ACS), we contrast the estimated returns to hours worked when estimated at the individual and the occupation level. To reconcile these differences in returns to hours within and across occupations, we construct a simple model of worker compensation and job choice to illustrate how worker preferences and constraints over hours worked could generate large returns to hours worked across occupations and yet small returns to hours within occupations. We then apply these insights to the gender wage gap and illustrate how the returns to hours worked across occupations can account for a substantial portion of the gender wage gap. We further illustrate how increases in the returns to hours worked across occupations over time has slowed the closing of the gender wage gap.

Related Literature

Our article naturally builds on a recent literature emphasizing that gender differences in hours worked and preferences for job flexibility are crucial to understanding the gender pay gap, including Bertrand, Goldin, and Katz (2010), Gicheva (2013), Cha and Weeden (2014), Goldin (2014), Goldin and Katz (2016), and Cortes and Pan (2019).² Much of this literature has documented important heterogeneity in the returns to hours worked across occupations, such as Bertrand et al. (2010), Goldin (2014), and Goldin and Katz (2016), who showed much higher returns to working longer hours in law and business occupations than in occupations such as pharmacists, and correspondingly larger gender wage gaps.³ In contrast to this existing literature, we focus on the average level of the gender wage gap and returns to hours worked for all workers and not the variation in gaps and returns across occupations.⁴

Prior work, including research by Goldin (2014), Cortes and Pan (2019), and Bick, Blandin, and Rogerson (2019), found that, on average, weekly hours worked are not strongly associated with higher wages within occupations.⁵ Our article finds similar results at the individual level but documents a much larger relationship between hours and wages at the occupational level.

Our emphasis on hours variation across occupations and jobs is consistent with observations in the current literature on the gender wage gap. Cortes and Pan (2019) conjectured that relaxing hours constraints faced by women “enabled [them] to enter a different job . . . within the same occupation” and generated a significant closing of the gender pay gap. Further, Wasserman (2015) documented that when the total hours worked at medical residencies were capped at 80 hours per week, this had a significant impact on which medical specialties women chose to enter, all within the occupation of “doctor.” Based on our findings, we agree with the assessment of Cortes and Pan (2019: 382) that “shifts in women’s position in the males’ earnings distribution are unlikely to occur if women simply worked more hours and stayed in the same job.”

Our results are consistent with recent work that demonstrates relaxing institutional constraints that limit women’s ability to work longer hours leads to an increase in hours worked and wages (Cortes and Pan 2019; Duchini and Van Effenterre 2019). It is also consistent with Hirsch (2005) who found that the wage losses associated with part-time work largely disappear when one controls for industry, occupation, and task measures.

Our analysis also relates to the literature on labor supply. Typically, studies of labor supply assume that workers can choose their hours in response to wages. In many settings, however, workers have limited discretion over hours worked, which complicates interpretation of the relationship between wages and hours worked.⁶ Several studies address this, and thus relate most closely to ours. Altonji and Paxson (1988, 1992) focused on changes in hours and wages among job switchers, arguing that job switching is a primary channel for workers to adjust their hours of work and associated compensation. More recently, Chetty, Friedman, Olsen, and Pistaferri (2011) studied labor supply decisions in a framework in which firms set hours constraints on workers, and thus, changes in hours worked induced by wage changes for individuals typically come when switching jobs. Our analysis confirms that choices across jobs and occupations are crucial to individuals’ labor supply decisions.

Within versus across Occupation Estimates of the Wage–Hours Relationship

We begin our empirical analysis by estimating the relationship between hours worked and wages at both the individual and the occupation level using data on hours worked and income from the Current Population Survey (CPS), the US Census, and the ACS. We focus on the civilian non-institutionalized population of workers between ages 25 and 55, dropping observations with missing occupation data as well as individuals who are self-employed. Our primary measure of weekly hours worked is given by an individual’s reported usual weekly hours worked for the prior year. We compute hourly wages by dividing total reported wage and salary income for the prior year by the product of usual hours worked and weeks worked in the previous year. Where incomes are top coded, we set them to be 1.5 times above the top coded level, and we drop observations with reported wages below half the minimum wage. We also drop observations with imputed usual hours, weeks worked, income, or occupation.

Our analysis establishes two key facts: 1) The relationship between hours worked and wages at the individual level is consistently small; and 2) the relationship between hours worked and wages at the occupation level is substantively larger. Figure 1 shows the relationship between raw wages and hours at both the individual (left panel) and occupational level (right panel), using data from the 2016 ACS. To illustrate the relationship between individual hours worked and wages, we divide individuals across percentiles of the logarithm of number of reported usual weekly hours. For occupations, we compute the average log hours and average log wages for occupations at the three-digit level. We plot the average log wages and average log hours for each individual bin or occupation as open circles on the figure, with the size of the circles corresponding to the size of the bin or occupation, as determined by survey weights and the number of workers in each bin or occupation. The line is the best-fit line from a bivariate regression.

For individual-level hours and wages, the relationship is not particularly strong, implying that a 10% increase in usual hours worked is associated with 2.4% higher hourly wages. By contrast, the relationship between occupational averages for hours and wages is much stronger, implying that a 10% increase in hours worked is associated with a 23.5% higher hourly wage. Thus, increases in hours across occupations are associated with an order of magnitude larger increase in wages than increases in hours by individuals.⁷

Within Occupation

We now show that the weak relationship between hours and wage at the individual level is robust across various samples and specifications. Table 1 reports estimates from a standard Mincer wage regression using individual-level data. Specifically, we estimate variants of the following model:

\ln w_{io} = β_{0} + β_{1} \ln h_{io} + X_{i} β_{2} + δ_{o} + ε_{io}

(1)

where i indexes individuals and o indexes measured three-digit occupation. The variables w and h represent wages and hours, respectively, and X_i is a vector of individual covariates including binary indicators for race (Black, Hispanic, Asian, and other) and gender, indicators for educational attainment (less than high school, high school only, some college, bachelor’s degree, master’s degree or higher), and a quartic in age. The parameter $δ_{o}$ represents a set of occupation fixed effects. All regressions are weighted with the person weights provided by ACS, and robust standard errors are clustered by three-digit occupation.

Table 1, column (1), presents estimates from the bivariate regression of log wage on log hours (as shown in Figure 1). The inclusion of race, gender, age, and educational attainment in column (2) further reduces the coefficient on log hours.

Table 1.

OLS Regressions of Ln(Wage) on Ln(Hours), 2016 ACS Individual Level

	(1)	(2)	(3)	(4)	(5)
Log wage	All	All	All	Male	Female
Log hours	0.244*** (0.046)	0.051** (0.026)	–0.117*** (0.002)	–0.149*** (0.004)	–0.108*** (0.003)
Demographic controls	No	Yes	Yes	Yes	Yes
Occupation FE	No	No	Yes	Yes	Yes
N	633,927	633,927	633,927	320,729	313,198

Notes: Robust standard errors in parentheses. Columns (1)–(2) use robust standard errors. Columns (3)–(5) include occupation fixed effects (FE). Observations are weighted using perwt. Sample includes prime-age workers 25–55. Demographic controls include a quartic in age, indicators for race/ethnicity (Black, Hispanic, Asian, other), sex, and indicators for educational attainment (less than HS degree, HS degree, some college, bachelor’s degree, master’s degree or more). Hours are derived from usual hours worked per week. Hourly wage is calculated as total reported wage and salary income for the prior year divided by the product of usual hours worked and weeks worked in the previous year. We trim wages that are below half of the federal minimum wage and inflate wages to 2012 dollars using the Bureau of Economic Analysis (BEA) National Income and Product Accounts Personal Consumption Expenditures. ACS, American Community Survey; OLS, ordinary least squares.

***

p <0.01; **p <0.05; *p <0.1.

To this point, we have not controlled for occupation fixed effects and consequently these point estimates represent some weighted average of the returns to hours within and across occupations. Including occupation fixed effects in column (3), we isolate the return to hours within occupations, which causes the estimated return to flip signs. Within occupation, a 10% increase in hours is associated with 1.2% lower hourly wages.

Columns (4)–(5) show that this same basic pattern holds true for men and women. In Online Appendix D, we show that the same general relationship holds for those with and without a bachelor’s degree, when controlling for major industry group, and in samples limited to full-time workers, defined as those working at least 35 hours per week.

Table 2 shows that these relationships are robust to a variety of alternative specifications using individual-level data from the March CPS or Outgoing Rotation Groups (ORG) of the CPS, pooled across years 2012 to 2017. Table 2, columns (1)–(3), mirror the results from Table 1 that use ACS data. As in the ACS data, the bivariate relationship is positive and significant (elasticity of 0.195) but falls to zero with the inclusion of basic controls and becomes negative with the inclusion of occupation fixed effects. In columns (4) and (5), we use the individuals with repeated observations in the Outgoing Rotation Groups of the CPS, which allows us to control for person fixed effects. One distinction from the CPS Annual Social and Economic Supplement (ASEC) and ACS/Census samples is that wages for wage earners in the ORG sample are collected directly rather than computed, and wages of salary earners are computed by dividing weekly earnings by usual hours worked.

Table 2.

OLS Regressions of Ln(Wage) on Ln(Hours), CPS Individual Level

	All workers
	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Log wage	OLS	OLS	OLS	OLS	OLS	IV: Lagged	IV: Actual
Log hours	0.195*** (0.039)	0.003 (0.020)	–0.144*** (0.003)	–0.09*** (0.006)	–0.110*** (0.006)	0.146*** (0.039)	–0.001 (0.024)
Demographic controls	No	Yes	Yes	No	Yes	Yes	Yes
Occupation FE	No	No	Yes	No	Yes	Yes	Yes
Individual FE	No	No	No	Yes	Yes	No	No
CPS survey	March	March	March	ORG	ORG	March	March
N	317,544	317,544	317,544	383,562	383,562	65,815	309,502

Notes: All columns use standard errors clustered at the occupation level. Columns (3), (6), and (7) include occupation fixed effects (FE). Columns (4) and (5) use data from the Outgoing Rotation Groups (ORG) in all months; all other columns use the March Supplement to the Current Population Survey (CPS). Column (6) instruments usual hours worked with usual hours worked, reported in the previous March. Column (7) instruments usual hours worked with actual hours worked the week previous to the survey. Observations are weighted using asecwt. Sample includes prime-age workers 25–55. Demographic controls include a quartic in age, indicators for race/ethnicity (Black, Hispanic, Asian, other), sex, and indicators for educational attainment (less than HS degree, HS degree, some college, bachelor’s degree, master’s degree or more). Hours are derived from usual hours worked per week. Hourly wage is calculated as total reported wage and salary income for the prior year divided by the product of usual hours worked and weeks worked in the previous year. We trim wages that are below half of the federal minimum wage and inflate wages to 2012 dollars using the Bureau of Economic Analysis (BEA) National Income and Product Accounts Personal Consumption Expenditures. IV, instrumental variables; OLS, ordinary least squares.

Regardless of whether additional demographic and occupation controls are included, we observe a negative relationship between hours and wages, suggesting that the relationship is not being driven by unobserved time-invariant heterogeneity.

Given that wages are constructed as the ratio of income and hours worked, measurement error in the hours worked variable would introduce a negative bias in our estimate of the impact of hours worked.⁸ To address this measurement error and resulting division bias, the specification in column (6) instruments for a worker’s reported usual hours this year with the usual hours the individual reported in the prior March. Although the coefficient increases from –0.14 to 0.15, it remains small. Alternatively, column (7) instruments for a worker’s reported usual hours this year using the number of hours the worker reported actually working in the prior week. The coefficient is –0.001 and statistically insignificant.

Table 3 uses the CPS’s ORG to examine the wage–hours relationship separately for salaried versus hourly workers. Given that, in salaried jobs, the marginal effect of additional hours worked on the wage is negative and that hourly wage workers may earn higher wages for overtime work, we would expect a stronger relationship for hourly wage workers relative to salaried workers. The wage–hours relationship is indeed slightly larger for hourly wage workers, though remains small for both groups. With the inclusion of occupation fixed effects, the coefficient on log hours is 0.17 for wage earners. This rises slightly to 0.23 when we instrument log hours using lagged hours. By contrast, the analogous specification for salary workers produces a negative relationship between log hours and wages of –0.22. Instrumenting for log hours with lagged hours increases the coefficient to 0.01, which is statistically insignificant.

Table 3.

Regressions of Log(Wage) on Log(hours), CPS Individual-Level Data, Wage vs. Salary Workers

	Wage earners					Salary workers
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	OLS	OLS	OLS	IV: Lagged	IV: Actual	OLS	OLS	OLS	IV: Lagged	IV: Actual
Log hours	0.304*** (0.035)	0.273*** (0.023)	0.167*** (0.002)	0.227*** (0.022)	0.177*** (0.014)	0.063 (0.040)	–0.110*** (0.026)	–0.220*** (0.004)	0.010 (0.046)	–0.189*** (0.025)
Demographic controls	No	Yes	Yes	Yes	Yes	No	Yes	Yes	Yes	Yes
Occupation FE	No	No	Yes	Yes	Yes	No	No	Yes	Yes	Yes
N	382,353	382,353	382,353	96,325	371,227	315,154	315,154	315,154	89,347	304,644

Notes: All columns use standard errors clustered at the occupation level. Columns (3)–(5) and (8)–(10) include occupation fixed effects (FE). Columns (4) and (8) instrument usual hours worked with usual hours worked, reported in the previous March. Columns (5) and (10) instrument usual hours worked with actual hours worked the week previous to the survey. Observations are weighted using earnwt. Sample includes prime-age workers 25–55. Demographic controls include a quartic in age, indicators for race/ethnicity (Black, Hispanic, Asian, other), sex, and indicators for educational attainment (less than HS degree, HS degree, some college, bachelor’s degree, master’s degree or more). Hours are derived from usual hours worked per week. Hourly wage is calculated as total reported wage and salary income for the prior year divided by the product of usual hours worked and weeks worked in the previous year. We trim wages that are below half of the federal minimum wage and inflate wages to 2012 dollars using the Bureau of Economic Analysis (BEA) National Income and Product Accounts Personal Consumption Expenditures. CPS, Current Population Survey; IV, instrumental variables; OLS, ordinary least squares.

Across Occupation

We now turn to estimates of the wage–hours relationship that rely on variation across occupations. Table 4 reports estimates from wage–hour regressions at the three-digit occupation level. Specifically, we estimate variants of the following model:

{\bar{w}}_{o} = β_{o} + β_{1} {\bar{h}}_{o} + β_{2} task s_{o} + ε_{o}

(2)

where ${\bar{w}}_{o} ({\bar{h}}_{o})$ indicates the average of log wages (hours) in occupation $o$ .

Table 4.

OLS Regressions of Ln(Wage) on Ln(Hours), 2016 ACS at the Occupational Level

	(1)	(2)	(3)	(4)	(5)	(6)
	Average log wage
Average log hours	2.352*** (0.243)	1.952*** (0.188)	1.156*** (0.204)	0.925*** (0.198)	1.804*** (0.189)	1.669*** (0.331)
Residualized against demographics	No	Yes	No	Yes	Yes	Yes
Residualized against person fixed effects	No	No	No	No	No	Yes
Task controls	No	No	Yes	Yes	No	No
Sample	ACS	ACS	ACS	ACS	CPS	CPS
N	474	474	467	467	531	522

Notes: Robust standard errors in parentheses. Columns (1)–(6) use robust standard errors. Columns (1) and (3) regress occupation average of log wage on occupation average of log hours. Occupations are weighted by the occupation total of individual weights. Columns (2), (4), (5), and (6) regress occupation average of residualized log wage on occupation average of residualized log hours. Residuals are constructed by regressing log wage (hours) on demographic controls and a full set of occupation fixed effects. We use the coefficients on the occupation fixed effects as measures of average residualized log wage and log hours. Demographic controls used in the residualization include Black, Hispanic, Asian, other race, less than HS degree, HS degree only, some college, bachelor’s degree, and a master’s degree or more, and a quartic in age. Person fixed effects are included using Outgoing Rotation Group (ORG) samples from the Current Population Survey (CPS), which include multiple observations per worker. Hours are usual hours worked per week. For details on the measurement of hours and wages, see notes to Table 1. Task data are constructed from the ONET 4.0 aggregated to the occ1990dd level. Five occ1990dd occupations are missing task data in the ONET 4.0, which yield missing task data for seven occs. Task controls include social skills, as defined in Deming (2017); abstract analytical, manual, and routine, as in Acemoglu and Autor (2011); and competitiveness as in Cortes and Pan (2018). See Appendix A for an explanation of how these composites were created. Task measures are standardized to be mean zero and standard deviation 1 across the occ1990dd distribution. ACS, American Community Survey; OLS, ordinary least squares.

***

p <0.01; **p <0.05; *p <0.1.

In contrast to the small estimated relationship between hours and wages at the individual level, the relationship between hours and wages at the occupational level is consistently large.⁹ As seen in Figure 1, the bivariate relationship between occupational wages and hours implies that a 10% increase in hours worked is associated with a 23.5% higher hourly wage. This relationship remains large when we residualize hours and wages to account for differences in the characteristics of workers in each occupation. To construct these residuals, we regress log wage (hours) on the same demographics used at the individual level (shown in column (3) of Table 1) as well as a full set of occupation fixed effects. We use the coefficients on the occupation fixed effects as measures of average residualized log wage and log hours. Table 4, column (2), shows the results of the bivariate regression of residualized log wage on residualized log hours. The relationship between hours and wages is still very large, with an elasticity of approximately 2. In Online Appendix D, we show that these large elasticities persist when we focus on a subset of occupations (high or low skill, male or female dominated, dropping the largest occupations), when we focus on particular subsamples of workers (men and women separately, full-time workers), and when we control for additional characteristics at the individual or occupational level (major industry group, fraction of women in each occupation, one-digit or two-digit occupations).

Although we control for observable measures of individual skill in column (2), it is possible that unobserved heterogeneity may account for the observed occupational-level relationship. For example, it may be that high-skill workers find working longer hours less unpleasant, and the large relationship between hours and wages across occupations simply represents worker sorting on the basis of this heterogeneity.¹⁰ To address this concern, we again use the ORG of the CPS to residualize both hours and wages on person fixed effects.

Column (5) of Table 4 shows that using CPS data yields substantively similar results to what we found in the ACS. Once we control for demographics and education, a 10% increase in occupational hours is associated with an 18% increase in occupational wages. Controlling for individual fixed effects, a 10% increase in occupational average hours is associated with a similarly sized 17% increase in occupational wages. These results suggest that differences in selection into occupation on the basis of individual time-invariant skills, preferences, or constraints do not drive the strong relationship between wages and hours at the occupation level.

Our estimates of the relationship between hours and wages across occupations may also reflect occupation characteristics. For example, it may be that certain occupational tasks are associated with longer hours and that these tasks are compensated with higher wages. Following the literature on occupational tasks, we control for five occupation-level task measures: social skills as defined in Deming (2017); abstract analytical, manual, and routine tasks as defined in Acemoglu and Autor (2011); and competitiveness as defined in Cortes and Pan (2018).¹¹ When we control for these tasks in columns (3) and (4) of Table 4, the return to average hours decreases substantially. This finding suggests that a substantial portion of the returns to hours worked across occupations stems from higher hours being associated with certain highly compensated job tasks.¹² Even when controlling for these tasks, however, the relationship between hours and wages remains quite large. In column (4), for example, the estimates suggest that a 10% increase in average hours worked is associated with 9.3% higher hourly wages. In the following section, we discuss how in some cases, the bivariate relationship between occupational wages and hours may be most relevant for understanding the returns to preferences regarding hours worked.

While we acknowledge that the estimates we discuss above still may be subject to omitted variable bias, it is worth noting that the magnitudes of our estimates are consistent with recent quasi-experimental evidence aimed at a causal understanding of the role of hours worked in determining wage differences between men and women. For example, Duchini and Van Effenterre (2019) showed that changes in school schedules in France that reduced time commitments to child care for mothers raised average hours worked by 1% and average wages by 1.5%, implying an elasticity of 1.5, which lies in the middle of our cross-occupation estimates of the returns to hours worked.

Conceptual Framework

To understand possible reasons for the difference in the returns to hours at the individual and occupation level, and to understand what these differences mean for the gender wage gap, we make two theoretical points. The first is that when employers contract with workers over an expected workload instead of (or in addition to) the number of realized hours an individual works, the empirical relationship between average wages and average hours at the occupation level may be very different from the corresponding relationship at the individual level. We hypothesize that the occupation-level relationship may proxy for the types of trade-offs workers face when selecting across jobs within an occupation as well as when selecting jobs across occupations.

The second point is that when workers choose jobs on the basis of expected hours worked (possibly because of constraints that preclude selecting jobs with high hours), if those preferences are separable from preferences over the tasks of the job, the consequence for their wages is dictated by the bivariate relationship between hours and wages. For example, it may be the case that jobs requiring high levels of analytical reasoning pay high wages but typically require a high hours commitment as well. In this case, a worker who is constrained to select a job with low hours will miss out on both the direct effect of high hours on wages as well as the indirect effect of high hours operating through access to jobs requiring analytical reasoning. We note that this interpretation requires a causal ordering—workers select a job considering an hours constraint, which may affect the tasks performed. These tasks performed may have an effect on wages, which we refer to as an indirect effect. We outline this in more detail in our model in Appendix A found near the end of this article.

Expected versus Realized Hours

Consider a simple conceptual framework of employee compensation. The key feature of our framework is distinguishing between the expected hours of a job and the realized hours an individual may work at any point in time in a particular job. We assume that a job, j, is an employment contract offered by a firm and is associated with a compensation level, $c (h_{j}^{e}, h_{j})$ , which is a function of ex ante expected hours worked prior to starting the job, $h_{j}^{e}$ , and the actually realized hours worked, $h_{j}$ . These contracts are determined in hedonic equilibrium by firms offering contracts consistent with profit maximization and workers choosing jobs consistent with utility maximization. Note that we allow the return to expected hours to differ from realized hours.

A few illustrative examples of common compensation schedules that have this form may be helpful. Consider first the case of salaried workers. In this case, workers agree to a level of compensation based on an ex ante expected workload, but the salary does not adjust in the short run to the actual realized hours worked. This compensation is determined in a simple hedonic equilibrium between workers and firms. Realized hours worked may vary from expected hours due to variation in skill across workers, idiosyncratic expectations of a demanding or lenient supervisor, or other reasons.¹³ In the context of our framework, this implies that the compensation function has the following form: $c (h_{j}^{e}, h_{j}) = c (h_{j}^{e})$ . This leads to a potentially large return to expected hours across jobs if $c' (h_{j}^{e})$ is large, even as the individual’s personal compensation to realized hours worked is zero. The implication for the implicit hourly wage, $\frac{c (h_{j}^{e})}{h_{j}}$ , is that the effect of a marginal hour worked within a job is to reduce the wage.

While many jobs are salaried, other jobs pay wages at an hourly rate. In such jobs, it seems natural to model the compensation function in the following way: $c (h_{j}) = w h_{j}$ , where $w$ is the hourly wage. In such jobs, earnings scale linearly with hours worked, and the wage return to the marginal extra hours worked is zero. Even in these cases, however, the firm may place restrictions on the range of hours offered to the worker. As a consequence, it may not be possible to obtain a high wage hourly job without committing to a high expected hours of work, $h_{j}^{e}$ . In this case, the menu of compensation across jobs may take the following form: $c (h_{j}^{e}, h_{j}) = w (h_{j}^{e}) h_{j}$ . For an individual working an extra hour within a given job, the wage is fixed at $w (h_{j}^{e})$ ; however, moving across jobs, the wage may increase in expected hours if in equilibrium $w' (h_{j}^{e}) > 0$ . Hence, in hourly jobs the wage return of an increase in expected hours across jobs may be quite high, even as the wage is constant within a job.

A natural exception to this is when workers are paid a higher hourly rate when they are required to work overtime. This arrangement would suggest a higher relationship between realized hours worked and wages, which is consistent with what we observe when splitting our results into hourly wage workers and salaried workers in Table 3. However, if the possibility of overtime is available only in jobs with already high expected hours, this still implies that expected hours play a potentially substantial role in a worker’s compensation.

Both of these examples suggest that the wage return to expected hours of work across jobs may be substantially larger than the wage return of realized hours worked. Our descriptive analysis of the relationship between hours and wages is consistent with this conjecture. We believe that occupation average hours represents a good proxy for expected hours of a job since it is averaged across many workers, and thus interpret the returns to hours across occupations as representing a useful approximation of the return to expected hours, $h_{j}^{e}$ . By contrast, estimates of the return of an individual’s actual hours worked, controlling for occupation fixed effects, proxy for the return to realized hours.

Hours Choices and Compensation

Our second theoretical point is aimed at understanding why the returns to hours across occupations is so large and how we should think about the role of other job characteristics in this relationship. Our key insight is that hours considerations can have a direct effect on wage through the effect of hours on wages (holding job tasks fixed) as well as an indirect effect operating through the correlation of job task mix and expected hours. This circumstance generates ambiguity regarding whether one should control for task mix when estimating the return to hours worked.

To illustrate this intuition, we develop a simple model, which is included in Appendix A. In this model, individuals select jobs for a variety of reasons, including tasks, hours, and compensation. Moreover, wages are determined by the hours worked and tasks. Our framework explains how these forces interact to affect job choice.

In our model, an individual, facing a binding constraint over hours worked or preferring to work fewer hours, will experience low utility from all high hours occupations. This individual would tend to avoid such occupations, even if they are associated with lucrative or enjoyable tasks. As a consequence, constraints or preferences that lead to low hours reduce wages because of the direct relationship between hours and wages as well as the indirect effect operating through the correlation between hours worked and job tasks.

To illustrate this intuition empirically, we separate occupations by how much they use abstract tasks, a job feature associated with high wages and high hours. Figure 2 shows the occupation average hours for the occupations in the top and bottom quartile of occupation-level abstract task measures (using the 2016 ACS). Regarding Figure 2, first note that occupations with high abstract task content have high hours. Second, very few occupations with high abstract task content work fewer than 40 hours per week on average. These findings suggest that if a worker wants to work in a high abstract task occupation, they will generally need to work more hours than a worker in a low abstract task occupation. Hence, if a binding hours constraint induces a worker to work in an occupation with lower abstract task intensity than desired absent the constraint, controlling for abstract tasks will understate the total (direct and indirect) effect of hours on wages. Essentially, workers may need to commit to longer hours to access high abstract task jobs.

For some workers, the driver of occupation choice may be preferences or constraints over tasks or other job characteristics. Indeed, evidence suggests that discrimination, attachment to the labor force, and aversion to competition may be key factors in the gender-based sorting across jobs and occupations (see, for example, Blau and Kahn 2017). This sorting fundamentally changes the appropriate way to price any resulting hours differences between workers.

Suppose that, across workers, there are no differences in preferences or constraints over hours. However, differences in preferences or constraints over tasks lead to differences in hours worked because expected hours are correlated with tasks. In this case, our model would suggest that the resulting differences in hours should not be priced at all because differences in job tasks (and not hours) are the fundamental driver of wage differences between the two types of individuals.

To this point, we have laid out two extreme cases—one in which hours drive all wage differences and another in which hours have no role in generating wage differences. Of course, intermediate cases may occur. Suppose we use an alternative utility function for workers so that they select jobs lexicographically on the basis of tasks and then choose hours. In this case, it is appropriate to price hours holding constant job characteristics because differences in constraints to or preference for hours worked will lead to differences only across jobs with similar characteristics. Hence, a shift to a higher hours job will not be associated with any additional wage premium due to correlated changes in job tasks, although a shift to higher hours will still be compensated within job task categories.

As we move to considering the gender wage gap, whether one should or should not condition on job characteristics when pricing the gender hours gap depends on the precise model used. If the primary driver of the difference in job and occupational decisions between men and women is the difference in time constraints or preferences over long hours and workers exhibit a willingness to compromise on job tasks, then our theoretical framework suggests that the unconditional relationship between hours and wages across occupations may be appropriate. If, however, hours considerations are not the primary driver of occupational differences but rather one of several factors, it may be appropriate to price the gender hours gap controlling for occupational task mix. If preferences or constraints over hours do not drive differences in occupational choice at all, then the gender hours gap should not be used to explain the gender wage gap.

Our framework should help researchers interested in understanding the impact of an intervention that relaxes women’s constraints over hours such as subsidized child care. We would predict a substantial wage increase operating through the direct effect of expected hours. If workers are flexible with regard to other job characteristics, wages would also increase due to an indirect effect operating through correlated tasks. Because we are uncertain regarding worker flexibility across tasks, we present analyses of the gender wage gap using occupational returns to hours in which we both control and do not control for occupation characteristics besides hours.

Application to the Gender Wage Gap

It is well documented that, on average, female workers work fewer hours than working men. In 1980, the raw gender difference was 6.6 hours. Even after controlling for standard demographics and occupation fixed effects, the gender difference was still 4.9 hours. While work hours for men and women have converged over time, the gap has not closed. In the 2016 ACS, for example, employed women work an average of 39.0 hours compared with 43.5 for men, a difference of 4.5 hours. After accounting for race, age, education, and three-digit occupation fixed effects, we find that women work 3.2 fewer hours than men.¹⁴

Recent research emphasizes the importance of these differences in hours worked for the gender wage gap. Our analysis of the gender wage gap works within the following regression framework, similar to earlier regressions focusing on the returns to hours:

\ln w_{i} = π + α femal e_{i} + β \ln h_{i} + X Γ + ε_{i}

(3)

Note that the gender gap in hours is priced at rate $β$ and $α$ represents the residual wage gap. Given the positive hours gap between men and women, as $β$ rises, the residual wage gap will decline. Indeed, if $β$ becomes large enough, it is possible that the residual wage gap could be negative, even with a substantial unconditional gender wage gap. As we have demonstrated above, individual-level estimates of $β$ show hours worked has a very small positive or even negative correlation with wages (see Table 1). Thus, a simple regression adjustment for hours worked will do little to close the residual gender wage gap.

In Table 5, column (1), we present a baseline residual wage gap in which we do not account for hours or occupational choice at all. Regressing log wages on a female indicator variable as well as race, age, and education level, we obtain a residual wage gap of 0.25 log points. We now consider alternative specifications in which we make various assumptions regarding how hours should be taken into account.

Table 5.

Estimates of the Gender Wage Gap, 2016 ACS

Log wage	(1)	(2)	(3)	(4)	(5)	(6)
Female	–0.252*** (0.023)	–0.245*** (0.022)	–0.157*** (0.007)	–0.167*** (0.007)	–0.018 (0.023)	–0.086*** (0.020)
Log hours		0.051**(0.026)		–0.117***(0.020)	1.748***(0.158)	0.940***(0.192)
Demographic controls	Yes	Yes	Yes	Yes	Yes	Yes
Occupation FE	No	No	Yes	Yes	N/A	N/A
Occupation IV	No	No	No	No	Yes	Yes
Task controls	No	No	No	No	No	Yes
N	633,927	633,927	633,927	633,927	633,927	628,344

Notes: Columns (3)–(4) include occupation fixed effects (FE). Columns (5)–(6) are instrumental variables (IV) regression with individual log hours instrumented with occupation average log hours, thus occupation fixed effects cannot be included. Occupation average log hours are calculated using a leave-out mean by excluding the individual’s hours. Standard errors are clustered at the occupation level. Observations are weighted using perwt. Sample includes prime-age workers 25–55. Demographic controls include a quartic in age, indicators for race/ethnicity (Black, Hispanic, Asian, other), sex, and indicators for educational attainment (less than HS degree, HS degree, some college, bachelor’s degree, master’s degree or more). Hours are derived from usual hours worked per week. Hourly wage is calculated as total reported wage and salary income for the prior year divided by the product of usual hours worked and weeks worked in the previous year. We trim wages that are below half of the federal minimum wage and inflate wages to 2012 dollars using the Bureau of Economic Analysis (BEA) National Income and Product Accounts Personal Consumption Expenditures. ACS, American Community Survey.

In column (2), we add a simple control for the log of realized hours worked. In this specification we do not control for occupation fixed effects as occupational choice may be driven by differences in hours. This model implicitly assumes no difference between the returns to realized and expected hours. The coefficient on log hours worked is quite small at 0.05 and reflects the return to some combination of realized and expected hours (along with other occupation-specific factors that might be correlated with expected hours and wage). As a consequence, it does little to shrink the residual wage gap. This result clearly illustrates the difficulty in explaining the gender wage gap by a simple regression adjustment for hours worked.

In column (3), we add occupation fixed effects but eliminate the control for hours worked. This specification implicitly controls for differences between men and women in the expected hours associated with their occupational choices at the level of the three-digit occupation codes we observe. The inclusion of occupation fixed effects substantially reduces the residual gender wage gap to 0.16.¹⁵ This substantial reduction is attributable to the fact that the fixed effects control for not only the expected occupational hours but also any other occupational differences, such as job tasks, that drive compensation.

In column (4), we again include occupation fixed effects but also control for realized hours worked. This regression prices the wage–hour relationship at the individual level. In this model, the coefficient on log hours should be interpreted as the return to realized hours worked driven by idiosyncratic factors, for example, supervisor leniency or unobserved speed at completing tasks. We estimate a residual wage gap of 0.17, slightly larger than what we find in the prior specification (column (3)) in which we do not control for hours. This finding reflects that realized hours have a negative price in the regression. As a consequence, the fact that women work fewer hours within occupations means that they should have higher wages than men.

At the other extreme, one can instead assume that the hours differences between men and women, both across and within occupations, is driven entirely by gender differences in preferences or constraints over hours worked, and they manifest in choosing jobs with different levels of expected hours worked. Under this assumption, researchers would wish to price the gender difference in hours at the expected wage–hours rate. One tractable way to implement this thought experiment is to instrument individuals’ realized hours with the occupation-level average hours, omitting the individual’s own contribution to this average.¹⁶ Note that we are not using the instrumental variables (IV) approach here to address omitted variable bias, as is often the case. The IV approach here is simply a convenient way to use the across occupation variation to identify the wage–hours relationship in the context of an individual-level wage regression.¹⁷

Column (5) of Table 5 shows these results. Consistent with our expectation, the coefficient on hours worked is 1.7, quite similar to the aggregate cross-occupation return to average hours worked that we presented earlier. In this specification, the residual gender wage gap virtually disappears. In this extreme case, these results would suggest that gender-correlated choices over hours worked could account for the largest share of the difference in wages between men and women.

Given that other considerations may also play an important role in the gender differences in job choice and the significant correlation between occupational hours and occupational-level task measures, we also consider how the gender wage gap is affected when we hold fixed the set of occupational tasks. Depending on preferences, if we do not control for occupation task measures, we may misrepresent the nature of occupational choices by women and overstate the role of hours worked. By using a measure of the returns to hours across occupations that holds fixed job tasks, we adopt a more conservative measure of the relationship between hours and wages.

In column (6) of Table 5, we show our results when we control for all occupational tasks. Again, we instrument hours worked with average occupational hours (omitting the reference individual). However, we control in the second stage for the set of occupational tasks discussed earlier. This method has the effect of lowering the return to hours worked to 0.94. Relative to the prior specification, controlling for task mix expands the residual gender wage gap to 0.09. The gap, however, remains substantially narrower than cases in which hours are priced at the realized hours rate implicit in the individual-level regressions.¹⁸ Thus, even with a conservative pricing of the occupational relationship between hours and wages, we still find an important role for hours differences in accounting for the gender wage gap.

Collectively, our results show that in spite of the low observed returns to hours worked within occupations, gaps in hours worked between men and women may yet represent an important component of the gender wage gap. Although it is not possible to provide a definitive pricing of the gender hours gap given available data, our findings are consistent with recent work showing men and women differ in their willingness to pay for flexible work arrangements (e.g., Mas and Pallais 2017; Wiswall and Zafar 2017). Further, our framework shows that modeling choices about hours worked meaningfully affect the conclusions about hours’ contribution to the gender wage gap.

Gender Wage Gap over Time

We now consider how changes in the returns to hours worked over time have affected the evolution of the gender wage gap. Since the 1980s, the difference between women’s log wages and men’s log wages has shrunk considerably (dashed blue line in Figure 3), and at the same time the gender gap in log hours has also been shrinking, albeit to a lesser extent. And yet, over this same time period, the returns to hours worked has increased substantially, magnifying the impact of the gap in hours on the gap in wages.

Figure 4 plots the estimated wage–hours elasticities from both within and across occupation models in 1980, 1990, 2000, and 2016. These estimates come from the coefficient on log hours in each year corresponding to the regressions with individual controls and occupation fixed effects (Table 1, column (3)) and the residualized occupation regressions (Table 4, column (2)). Looking at the individual level wage–hours estimates, we see the relationship has increased modestly between 1980 and 2016 but is always negative and small in absolute magnitude. Examining the relationship between occupation-level wages and hours, we see a much more dramatic change. In 1980, a 10% increase in occupation average hours was associated with a 9.1% increase in average wages. By 2016, the relationship had doubled so that a 10% increase in average hours was associated with a 19.5% increase in average wages.¹⁹ Even when controlling for occupational tasks in Figure 5 (using the same tasks as in Table 4), we see that the coefficient on log hours remains large and positive across all time periods and is still trending upward over time. With controls, the coefficient on hours is 0.44 in 1980 and rises to 0.92 by the year 2016.

Taken together, these findings suggest that wage convergence between men and women would have been larger if the wage premium for hours worked had remained the same. To quantify how the return to hours worked influenced evolution of the gender gap, we conduct a simple counterfactual exercise. We calculate what the evolution of the gender gap would have been if the returns to hours worked had remained at 1980 levels. This exercise examines the “unconditional” gender wage gap—that is, not conditioning on hours but controlling for other characteristics such as age and education. We provide more detail regarding this procedure in Online Appendix C.

Again, we are faced with the question of what price should be used to relate the hours gap to the wage gap period by period. In Table 6, we present these results for four different prices for log hours worked. In each of the cases, row (1) shows the evolution of the “total” wage gap, that is, the residual wage gap plus the wage gap that can be explained by the gender gap in hours. Row (2) considers the counterfactual evolution of the gap assuming that the residual gap evolved according to the observed time series but the prices on hours are held constant at 1980 levels. Row (3) shows the percentage difference between row (1) and row (2)—how different the gender wage gap would have been if returns to hours remained constant at 1980 levels.

Table 6.

Evolution of the Gender Wage Gap

		1980	1990	2000	2016
	Hours priced according to OLS regression of individual log wages on individual log hours
(1)	Residual gap plus hours gap	0.433	0.320	0.259	0.252
(2)	Residual gap plus CF hours gap	0.433	0.275	0.217	0.205
(3)	% Diff (1) & (2)		14.2%	16.4%	18.4%
	Hours priced according to OLS regression of individual log wages on individual log hours with occupation fixed effects
(1)	Residual gap plus hours gap	0.317	0.235	0.172	0.152
(2)	Residual gap plus CF hours gap	0.317	0.193	0.136	0.117
(3)	% Diff (1) & (2)		17.9%	20.7%	23.4%
	Hours priced according to IV regression of individual log wages on individual log hours using occupation hours as instrument
(1)	Residual gap plus hours gap	0.434	0.320	0.257	0.240
(2)	Residual gap plus CF hours gap	0.434	0.258	0.173	0.137
(3)	% Diff (1) & (2)		19.4%	32.8%	43.0%
	Hours priced according to IV regression of individual log wages on individual log hours using occupation hours as instrument, controlling for occupation tasks
(1)	Residual gap plus hours gap	0.426	0.311	0.234	0.205
(2)	Residual gap plus CF hours gap	0.426	0.264	0.193	0.152
(3)	% Diff (1) & (2)		15.2%	17.4%	26.2%

Notes: Observations are weighted using perwt. Sample includes prime-age workers 25–55. The residual wage gap plus hours gap is defined as $α^{t} + β^{t} {gap}_{h}^{t}$ , where the gap in hours ( ${gap}_{h}^{t})$ corresponds to the difference between male and female log hours in year t. The residual gap plus counterfactual (CF) gap is defined as $α^{t} + β^{1980} {gap}_{h}^{t}$ . In the first panel, $β^{1980}$ is the coefficient on log hours from a regression of log wage on a female dummy and a set of demographic controls. The second panel adds in occupation controls to derive the coefficient on log hours, $β^{1980}$ . In the third panel, $β^{1980}$ is the coefficient from log hours in an instrumental variables (IV) regression of log wage on female, demographic controls, and individual log hours instrumented with occupation average log hours. Occupation average log hours are calculated using a leave-out mean by excluding the individual’s hours. In the fourth panel, we add occupation tasks controls to derive the coefficient on log hours, $β^{1980}$ . In each panel, $α^{t}$ is the coefficient on female and $β^{t}$ is the coefficient on log hours from the corresponding regression in year t. For details on measurement of hours, wages, tasks, and control variables, see notes to Tables 1 and 4. OLS, ordinary least squares.

This exercise suggests that the changing returns to hours over time have had a significant countervailing effect on closing the gender wage gap. When we price the hours gap at the rate implied by the return to realized hours (Table 6, top panel), the gender wage gap would have been nearly 20% smaller in the year 2016 had the returns to hours worked not increased over the time period; adding occupation fixed effects (second panel), the gap would be roughly 23% smaller. In the bottom two panels, pricing the hours gap at the rate implied by the cross-occupation wage–hours schedule, the counterfactual wage gap would have been even lower had the hours premium remained at 1980 levels—43% lower using the unconditional relationship between hours and wages and 26% lower when controlling for tasks.

Conclusion

In this article, we examine the wage returns to hours worked, and the extent to which hours differences can explain the gender pay gap. We demonstrate that, while the hours worked by an individual have only a weak relationship with wages, the average hours within an occupation are much more strongly related to wages. This relationship holds, controlling for individual characteristics and occupation tasks. Indeed, a 10% increase in occupational hours worked is associated with a 10 to 20% increase in wages depending on the specification.

We then revisit the gender wage gap. Because hours have such a weak relationship with wages, they explain very little of the gender wage gap when priced using individual data. We demonstrate that the extent to which the gender wage gap is mediated by hours worked depends crucially on assumptions regarding the origins of hours worked differences between men and women. If we assume that the gender difference in hours worked should be priced according to the relationship we observe across occupations, then hours worked can account for a large portion of the unexplained gender wage gap. If we price hours according to the cross-occupation schedule and control for the occupational task mix, hours differences still account for approximately half of the gender wage gap. Critically, these approaches require different assumptions about the origins of differences in hours worked across gender.

We also examine the potential role of hours differences in the evolution of the gender wage gap over time. Consistent with Cha and Weeden (2014), the increase in returns to hours worked implies that the counterfactual wage gap would have been substantially narrower had the price of hours not increased over time. Significantly, if we price hours worked according to the occupation-level relationship, the counterfactual gender wage gaps would have been between 26 and 43% smaller. This finding suggests that the increase in the return to occupational hours worked made it increasingly difficult for women to achieve wage parity with men.

While this article illustrates the importance of thinking carefully about the returns to hours worked and how such differences should inform analysis of issues like the gender pay gap, we recognize that further research is needed. It is still not clear which factors drive the observed differences in hours worked across gender, or the relative importance of various factors. For example, even if hours differences explain a large portion of the gender wage gap, these hours differences could be driven by discriminatory barriers to particular occupations, unobserved differences in work experience, or other forces. It would also be useful for researchers to examine further why some occupations have higher hours on average, and why the returns to hours have increased over time. We leave these questions to future research.

Supplemental Material

sj-pdf-1-ilr-10.1177_00197939211045376 – Supplemental material for The Return to Hours Worked within and across Occupations: Implications for the Gender Wage Gap

Supplemental material, sj-pdf-1-ilr-10.1177_00197939211045376 for The Return to Hours Worked within and across Occupations: Implications for the Gender Wage Gap by Jeffrey T. Denning, Brian A. Jacob, Lars J. Lefgren and Christian vom Lehn in ILR Review

Footnotes

Appendix A

Consider a simple model of job choice. Suppose that a group of individuals, perhaps women with a particular skill level, has the following utility function defined over occupations:

(A.1)

U_{ij} = β_{0} + β_{1} \ln (w_{j}) + β_{2} \ln (h_{j}) + β_{3} T_{j} + ϵ_{ij}

where $i$ indexes the group of individuals, $j$ indexes a job, $w_{j}$ is the wage of the job, $h_{j}$ is the hours of the job, $T_{j}$ represents some other job characteristic (such as tasks of the occupation), and $ϵ_{ij}$ is a type 1 extreme value random utility component. Although we model preferences as a function of hours worked, these can reflect constraints as well as preferences. Consequently, it is most useful to think of this simple utility function as a reduced form representation reflecting both preferences and constraints. Given that we are modeling job choice, $h_{j}$ is the most naturally interpreted as the expected hours of the job, $h_{j}^{e}$ . Since we only have one measure of hours in this section, we suppress the superscript in this section.

Now suppose there are $J$ different jobs with different combinations of $w$ , $h$ , and $T$ , which in equilibrium exhibit the following relationship:

(A.2)

\ln (w_{j}) = π_{0} + π_{1} \ln (h_{j}) + π_{2} T_{j}

Given this framework, assuming that individuals choose their job to maximize utility, by virtue of the type I extreme value random utility component, the share of individuals within the group that choose job $j$ will be given by

(A.3)

γ_{j} = \frac{e^{β_{0} + β_{1} \ln (w_{j}) + β_{2} \ln (h_{j}) + β_{3} T_{j}}}{\sum_{j = 1}^{J} e^{β_{0} + β_{1} \ln (w_{j}) + β_{2} \ln (h_{j}) + β_{3} T_{j}}}

and the average wages and hours of the group will be given by:

(A.4)

E [\ln (w)] = \sum_{j = 1}^{J} γ_{j} \ln (w_{j})

(A.5)

E [\ln (h)] = \sum_{j = 1}^{J} γ_{j} \ln (h_{j})

With this simple framework, we can better conceptualize what it means for there to be a causal relationship between occupational hours and wages. One natural thought is to conceptualize the causal effect of hours as $π_{1}$ from Equation (A.2). This value is the price of hours holding tasks and other job characteristics fixed; however, for this parameter to reflect the tradeoffs that individuals make between hours and wages, it presupposes that every combination of tasks and hours is available. If instead a menu of jobs is available and a correlation occurs between occupational hours and tasks, then in order to find an occupation with fewer hours, an individual may also have to compromise on the set of tasks associated with the chosen job.

Alternatively, we can conceptualize the trade-off between hours and wages is to see how equilibrium hours and wages change as $β_{2}$ , the preference (or constraint) over hours from Equation (A.1), changes. We perform this analysis by differentiating Equations (A.4) and (A.5) with respect to $β_{2}$ :

(A.6)

\frac{\partial E [\ln (w)]}{\partial β_{2}} = \sum_{j = 1}^{J} ω_{j} [\ln (h_{j}) - \bar{\ln (h)}] [\ln (w_{j}) - \bar{\ln (w)}] = cov [\ln (h_{j}), \ln (w_{j})]

(A.7)

\frac{\partial E [\ln (h)]}{\partial β_{2}} = var [\ln (h_{j})]

where $\bar{\ln (h)}$ and $\bar{\ln (w)}$ are the share weighted averages of the log of hours and wages across occupations. Note the effect of a change in preferences or constraints over hours on wages depends solely on the covariance between hours and wages. Or, in other words, if we construct the implicit wage–hours relationship from changes in preferences or constraints over hours, we obtain:

(A.8)

\frac{\frac{\partial E [\ln (w)]}{\partial β_{2}}}{\frac{\partial E [\ln (h)]}{\partial β_{2}}} = \frac{cov [\ln (h_{j}), \ln (w_{j})]}{var [\ln (h_{j})]} = (π_{1} + π_{2} \frac{cov [\ln (h), T]}{var [\ln (h)]})

where the last part of the expression is obtained by substituting in Equation (A.2). Note, the expression in Equation (A.8) is simply the regression coefficient from an unconditional regression of wages on hours.

These equations imply that as individuals either prefer fewer hours or are constrained to work fewer hours, the consequence for their wages is represented by both the direct effect of occupational hours on wages as well as the indirect effect operating through the correlation of hours with tasks. This consequence applies to other characteristics as well. For example, if an individual wishes to work at a job with high levels of social interaction, this will imply a change in wages due both to increased social interaction and the change in correlated tasks and hours.²⁰

The implications of this model are specific to the form of the utility function we have chosen. Alternative utility functions could generate different implications regarding the implicit relationship between hours and wages. For example, suppose that workers choose jobs lexicographically on the basis of tasks and then choose hours. In this case, differences in preferences or constraints over hours may generate variation in hours worked, but it will not generate differences in the task mix, which remains fixed.

Acknowledgements

We thank Joe Altonji, Claudia Goldin, Larry Katz, Jessica Pan, and Jesse Rothstein for useful comments. We also thank Sam Higbee and Shawn Martin for excellent research assistance. We are grateful for research support from the College of Family Home and Social Science of Brigham Young University. An Online Appendix is available at .

ORCID iD

Jeffrey T. Denning

For information regarding the data and/or computer programs used for this study, please address correspondence to jeffdenning@byu.edu.

1

It is still possible for hours worked to explain gender wage differences through other channels (e.g., by increasing the likelihood of promotion in the future).

2

More generally, offered an excellent overview of the evidence on the size and explanations for the gender wage gap in the cross section and over time.

3

Job characteristics beyond hours are important in thinking about the gender wage gap. For example, a job with relatively low hours but rigid requirements about scheduling may be disproportionately unappealing to women. We abstract from this in the current article as is common in this literature, for example, Goldin (2014), Cortes and Pan (2019), Cha and Weeden (2014). Men and women may also differ on actual experience, which is an important determinant of wages (Blau and Kahn 2013). Cubas, Juhn, and Silos (2017) demonstrated that employees who work at peak times of the day are paid a higher wage, which may affect occupational choice and the gender earnings gap.

4

What drives the returns to longer hours across occupations is an interesting and important research question in itself. Several explanations have been suggested in prior work. One explanation involves compensating differentials, that is, individuals receive additional remuneration for the disamenity of long hours. Most other explanations stem from some feature of the production function in various occupations. As suggested, another explanation is that workers in some jobs are less substitutable for each other. It may also be that worker effort in high-hours occupations are less easily observable to supervisors, so these jobs pay efficiency wages to ensure optimal effort. Or perhaps some long-hour jobs also require scarce skills that demand higher wages (e.g., leadership in the case of CEOs). Finally, there may be increasing returns to hours spent in production—essentially returns to experience but on a shorter time frame.

5

See, for example, figure 3 of and table 2 of Cortes and Pan (2019). However, some occupations have non-negative wage returns; see Goldin (2014) for discussion.

6

In some atypical settings it is quite plausible that workers can adjust hours, for example, stadium vendors (Oettinger 1999) or taxicab drivers ().

7

The results in Figure 1 show that the variation in average hours worked across occupations is notably lower than the overall variance in hours worked across workers. In terms of occupational variation, approximately 80% of the variation in average hours can be explained by the fraction of workers in that occupation who work part time. We discuss robustness of our findings to focusing just on full-time workers in . In terms of specific occupations, those with the highest average hours are senior management occupations (including CEOs), lawyers, doctors and EMTs, workers in oil/gas mining (drillers, engineers, miners), and high-skilled sales occupations (particularly financial sales). Erosa, Fuster, Kambourov, and Rogerson (forthcoming) also analyzed within-occupation variation in hours and its relationship to average hours in an occupation.

8

This bias is not specific to our use of wages on the left-hand side of our specifications. If we were to use income instead of wages, as in , there would be no division bias, but the coefficient would still be biased by measurement error leading to attenuation. In fact, the coefficient would mechanically be the coefficient we obtain from the wage regression plus one.

9

By averaging hours across many people, the occupation-level regressions will suffer less from certain types of measurement error. However, our estimates of the wage–hours relationship at the occupation level remains substantially higher than estimates from the IV specification in , which attempts to address measurement error in hours worked.

10

Another potential source of unobserved heterogeneity is actual work experience, which is not observable in the ACS or CPS. As pointed out in , measures of actual experience have significant explanatory power for the gender wage gap beyond measuring potential experience (based on age and education).

11

We include abstract analytical, manual, routine, and social tasks constructed from the ONET 4.0. For more detail on how the task measures are constructed, see . Seven occupations for which task measures are unavailable are dropped in these regressions.

12

High task intensity of any of these tasks is generally predictive of higher hours worked in an occupation; this may be attributable to high task intensity implying higher specialization and lower worker substitutability. However, in terms of predicting higher occupational wages, abstract tasks have the largest impact, followed by competitive and social tasks. Thus, the occupational wage–hours relationship is most sensitive to the inclusion of these three tasks.

13

Our notion of realized hours worked differs conceptually from the measure of “actual” hours worked used in to instrument measures of “usual” hours worked in the CPS. In the CPS, usual hours worked corresponds to typical weekly hours of that particular worker once employed; actual hours worked corresponds to the actual hours worked in the prior week. Our notion of expected hours worked corresponds to a worker’s expectation of the work hours prior to beginning the job and our notion of realized hours worked corresponds to the hours worked once a worker is employed. Hence, realized hours in our framework may correspond more closely to usual hours worked as measured in the ACS and CPS. The ACS and CPS do not contain a similarly close analog to our concept of expected hours, instead we proxy for this using average hours worked by occupation.

14

If we limit our analysis to full-time, full-year workers, women work 1.8 fewer hours than men in 2016.

15

Additionally, we have experimented with including interaction terms between hours worked and occupation fixed effects, which would allow for an occupation-specific wage–hours elasticity. This approach does not significantly change the point estimate on the residual gender wage gap.

16

We do not control for occupational fixed effects, since they are collinear with the occupational average hours. This method is similar to that used in .

17

Note here we are implicitly assuming that the expected hours wage rate is the same across measured occupations as well as across jobs within a measured occupation. In reality, it is possible that the return to expected hours may differ across jobs. But because three-digit occupation is the finest level of job we can observe, we are unable to assess how this return may differ across jobs within occupations. For the current exercise, we believe the assumption of a constant return to expected hours as a reasonable first-order approximation of the truth that will allow us to gain insight into the role of hours in explaining the gender gap. We acknowledge that some evidence supports that the returns to hours varies across occupations (Goldin 2014; ).

18

The number of observations is slightly lower in column (6) compared with columns (1) through (5) because a small number of occupations do not have ONET task information. If we replicate the specifications in columns (1)–(5) on the sample used in column (6), the results are qualitatively the same.

19

We have calculated analogous measures for the CPS, looking at 5-year moving averages of the coefficients to take into account the smaller sample size. We also examined both ordinary least squares (OLS) and IV estimates of the return to individual hours worked. For the IV specifications, we instrument usual hours worked in the reference year with usual hours worked in the prior year to account for measurement error. All these specifications generate a similar pattern.

20

This finding does not depend on the specific structure of the compensation function. is not necessary but is useful for explaining the intuition of the model.

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