Reply to “Racial Differences in Time at Work Not Working” by William A. Darity Jr. et al.

Darity, Hamilton, Myers, Price, and Xu (2021) (hereafter D-H-M-P-X) have written a provocative piece criticizing our recent study of racial/ethnic differences in the fraction of time at work that individuals spend in non-work activities, such as eating, cleaning up, socializing, relaxing and leisure, and safety procedures (Hamermesh, Genadek, and Burda 2021; hereafter H-G-B). Whereas H-G-B concluded that statistically significant, albeit small, differences occur between non-Hispanic whites and both African Americans and non-Black Hispanics, D-H-M-P-X find no significant differences between the first two groups in time spent not working at the workplace. They conclude that, while we argued that the difference in time use can account for a not unimportant fraction of the racial wage differential, the impact on adjusted wage differentials is trivial.

Why the differences between their work and ours? In terms of the impact on measured wage differentials, we do not differ at all! D-H-M-P-X conclude that their calculations of racial differences in the fraction of non-work time at work (η) “would translate into a Black–White wage/earnings ratio of approximately 99%, or practically parity.” In our Table 6 we showed that the adjusted racial wage differential (after accounting for long vectors of demographics, industries, occupations, and union status) drops from −0.104 to −0.096, that is, by approximately 1 percentage point, when one also accounts for differences in non-work time at work. In other words, despite all the possible differences in method and data, results in both studies show that racial differences in η explain about 10% of the adjusted racial wage differential, accounting for a 1 percentage point difference in adjusted wages. We are grateful that they have confirmed this central finding of our study.

The authors claim to replicate our results, but they do not. Hamermesh (2007) classified replications into a three-level hierarchy, with the top being pure replication—same data, same model, and same method (as in the well-known Herndon, Ash, and Pollin 2014 replication)—essentially checking for mistakes. This hierarchy descends to different data, model, and method. The D-H-M-P-X study is in this last tier, as their data (several extra years) and method differ from ours, and it is unclear whether their model is the same. In our published article, as is customary, we offered the data and code to anyone requesting them. We never received a request for these files from D-H-M-P-X. If they had requested these data, we would certainly have sent them. That would have enabled them and us to isolate the sources of the differences in results between the two studies.

The absence of an initial true replication might matter in terms of the control variables used in the models that they estimate, since neither the text nor the tables in D-H-M-P-X specify these variables. For example, as the footnote in our Table 2 reports, our specifications included quadratics in both time at work on the diary day and reported usual workhours in the previous week. While there is no racial difference in our data in the average time reported at the workplace, reported usual weekly hours are a highly significant 1.2 hours lower among African American workers. Also, 24.5% of African Americans report usually working 50+ hours per week, whereas 30.8% of non-Hispanic whites report this many hours of work. A larger mass occurs further into the right tail of daily work time among non-Hispanic whites.

Both pairs of variables have highly significant independent U-shaped effects on η that reach minima at the sample means. With their distributions differing by race, their inclusion affects the estimated impact of the race indicator on η, so that their exclusion lowers the estimated racial difference in η (although including these work-time variables only in linear form does not change the estimate from what appears in our Table 2). Similar comments apply to other controls—we are not told what D-H-M-P-X include in their models and thus cannot infer how much of the differences in results arises from differences in specification.

The first major point in D-H-M-P-X, which comprises much of their comment (including their Figure 1 and Tables 1, 2, and 5), is about racial differences in response rates in the American Time Use Survey (ATUS). These differences are well known and were demonstrated by Abraham, Maitland, and Bianchi (2006) based on the first two waves of the ATUS. While they are important, they should not affect the results for two reasons. First, the ATUS sampling weights account for them (BLS 2021). In other words, by including both the ATUS sampling weights (the variable wt06 “person weight” in the IPUMS-provided ATUS data) and additionally weighting for racial differences in non-response, D-H-M-P-X are double-weighting, which is clearly incorrect. Second, more important and substantive, the lower African American response rate can affect the estimates if, and only if, η is lower among non-responding African Americans than among non-Hispanic white non-respondents. We cannot know this; such differences may exist, or they may go in the opposite direction. We just do not know.

D-H-M-P-X’s second major point notes that a larger fraction of non-Hispanic whites list η = 0 in their time diaries than do African Americans. In our data, the fractions are 0.345 and 0.294 (0.372 and 0.296 in their data). Indeed, excluding such respondents in both races (final column of D-H-M-P-X Table 6) causes even the raw differences in η to vanish. Since η is the crucial dependent variable, what they have done is truncated on values of the dependent variable.

They chose this truncation arguing that they “make a reasonable assumption that ATUS respondents are reporting falsely and/or in error spending zero time at work not working” and that these are “misreported zero minute[s].” This assumption is not innocuous, because it biases the results against finding any racial difference in η. ¹ But why exclude only zero responses—why not also exclude those with non-work time at work above 60 minutes, which in our data are 0.140 of non-Hispanic whites, but 0.188 of African Americans? Such large amounts of non-work time are no more believable than reports of zero non-work time. Their exclusion would strengthen the D-H-M-P-X results even further.

The entire distribution of non-work time at work, η, among African Americans lies further to the right than that among non-Hispanic whites. Their choice of excluding some responses is completely arbitrary, as our reductio ad absurdum of excluding others with very high reported non-work time would be. Such truncations on the dependent variable are simply incorrect and invalidate their comparison.

Among the less important differences between the two studies is the definition of the minority group. The issue is how to classify people who respond that they are African American and also that their ethnicity is Hispanic. H-G-B included in this minority those Hispanics who listed their race as African American, a slightly broader group than D-H-M-P-X used. Since the estimated impact on η among non-Black Hispanic males in H-G-B (Table 2) was greater than among African Americans, if also being Hispanic is associated with a higher η, the D-H-M-P-X definition of the minority will generate a (slightly) smaller racial difference.

Another difference is their use of the Blinder-Oaxaca decomposition to analyze their estimates. Although venerated, this decomposition was rendered somewhat obsolete by Gelbach’s method (Gelbach 2016), which H-G-B employed. It would have been interesting to compare results using alternative decomposition techniques. Not having their data set nor knowing what controls they used, it is impossible to assess the magnitude of any differences arising from this source.

D-H-M-P-X repeatedly use the word “laziness” or “shirking” to describe η. They take it to refer exclusively to workers’ behavior and to imply that H-G-B are impugning the behavior of racial minorities. Nothing could be further from the truth. We assiduously abstained from using these terms in the article on which they are commenting, not only because they are inherently judgmental but more importantly because they do not describe the phenomenon we are measuring.

Non-work at work need not have negative connotations. The original model (Shapiro and Stiglitz 1984) and the macro literature generally that followed make clear that the outcome results from worker–firm interactions—from behavior stemming from workers’ preferences in the presence of employers’ choices about monitoring. Both of these responses are endogenous. Moreover, unobservable effort withheld at the workplace might represent a rational endogenous reaction of workers to wage discrimination by employers, one that exists for reasons derived in Black (1995) and elaborated by Lang and Lehmann (2012). Indeed, in Burda et al. (2020) we demonstrated that employers’ desires to hoard labor to avoid incurring additional search, hiring, and training costs may be a more important cause of extra non-work at work time than anything stemming from workers’ desires to reduce effort. D-H-M-P-X stress supply behavior but, as always, the outcome is determined by behavior on both sides of the market.

We recognize that H-G-B may be controversial. ² The tone of the D-H-M-P-X comment mixes polemic and useful, constructive comment. The former is regrettable; for the latter, we are thankful.