CRAIG JONES AND RALPH HUSBY”

Constructing an Hourly Wage from Weeks and Hours Worked

IN COUNTLESS STUDIES involving hourly wage rates and labor force participation, data do not include direct measure of hourly wages. Rather, the hourly wage is constructed indirectly, using Bureau of the Census data on “earn- ings last year,” “weeks worked last year,” and “hours worked last week.” If, for example, the survey takes place in March 1970, then information on earnings in 1969, weeks worked in 1969, and hours worked during the week previous to the survey in 1970 is available. Conventionally, an hourly wage is constructed by divid- ing last year’s earnings by the product of weeks worked last year and hours worked last week. One obvious criticism of this construction is that the number of hours worked last week may not be typical of the number of hours worked per week during the previous year.

Furthermore, weeks worked and hours worked variables are not precise. Each worker is assigned to a weeks worked category-1-13, 14-26, 27-39, 40-47, 48-49, 50-52-as well as a hours worked category-1-14, 15-29, 30-34, 35-39, 40, 41-48, 49-59, and 60-plus. Conventionally, the hourly wage is constructed by using the mid-points of these weeks worked and hours worked categories, for example, 7 weeks for the 1-13 week category. This note offers evidence to suggest that the average number of weeks worked within a category is inaccurately represented by the mid-point. Thus, a serious bias is introduced into hourly wage estimates by using mid-points.

To investigate this hypothesis, data by occupational category are used.’ The 1970 Census includes data on workers in 411 separate Bureau of Labor Statistics occupational categories. Hourly wages were calculated for female workers2 em- ployed 50-52 weeks in 1969 for each c a t e g ~ r y . ~ These wages were computed by dividing, in each case, mean annual earnings for those in the 50-52 week category by 2,040 hours, reflecting a 51-week work year and a 40-hour week. In addition, the hourly wage for all female workers was calculated separately by race and sex in the conventional manner described, whereby earnings last year are divided by the product of weeks worked last year and hours worked last week, weeks and

*The authors are, respectively, Doctoral Candidate, Department of Economics, University of Illinois,

‘This technique has been used by Glen Cain, Married Women in the Labor Force (Chicago: University

*The bias discussed in this note was discovered while working with data on female workers. The bias

3Some of these categories were empty in our sample.

and Assistant Professor of Economics, University of Illinois.

of Chicago Press, 19661, pp. 92-93.

in the wage data, however, exists also for male workers.

115

11 6 / CRAIG JONES AND RALPH HUSBY

hours worked being approximated by mid-points of weeks worked and hours worked categories4

Results of Calculations The results of these calculations are presented in Tables 1 and 2.

W a is the wage calculated in the conventional manner, whereas w b is calculated from the occupational data. Only workers who were employed 50-52 weeks (full year workers) were included in these latter calculations: w b , for 50-52 week workers ($2.39 in Table 2) , is the mean wage of all full year workers over all occu- pational categories, weighted hy the occupational group distribution for full year workers; Wb for 1-13 week workers ($2.14 in Table 2) , is the mean wage of all full year workers weighted by the occupational distribution of 1-13 week workers; etc. The lower figures for the smaller weeks worked and hours worked categories reflect the fact that part time and part year workers are concentrated in the lower paying occupations. Wa, on the other hand, is higher for the smaller weeks and

TABLE 1

ALTERNATIVE ESTIMATES OF AWRAGE WACE FOR U.S. FEMALE. WORKERS FOR VARIOUS Houtis WORKED CATEGORIES- 1969

Hours worked categories Average _ _ ~ _ ~~~~

wage 1-14 15-28 30-34 35-39 40 41-48 49-59 6 0 + Part time ~ ~ ~ _ _ _ _

Wa 6 30 2 90 2.65 2.71 2.48 2.19 1.47 1.46 3.60 W b 198 2.22 2.35 2.47 2.41 2.52 2.31 2.29 2.20 Sourcrv Ware calculations based on 1970 Census 5 per cent sample tapes and data from U.S. Bureau of the Census,

1970, Subject Reports, Final Report PC(2 )-7A, “Occupational Characteristics” Censirs of the Popiilotion (Washington. D.C.: U.S. Government Printing Office, 19733. table 19, pp. 382-395.

TABLE 2

ALTERN4TIbE ESTIMATES O t AVERACE WACC FOR U.S. FEMALE. WOIIKhIiS FOR VARIOUS WEEKS WORKED CATEGORIES- 1969

Weeks worked caterories Average ~~ __._

wdre 1-13 14-26 27-39 40 47 48-49 50-52

Wa 5.31 3.06 3.36 2.89 2.74 2.55 W b 2.14 2.28 2.45 2.43 2.29 2.39 Source: See Table I .

hours worked categories. The figures for the 1-13 weeks worked and 1-14 hours worked categories are particularly striking and certainly appear unrealistic.

Further, Wa decreases with increasing hours worked categories until it is nearly the same as the wage calculated from occupation data, w b , at 40 hours per week. Likewise, W a decreases for increasing weeks worked categories, approaching W b at 50-52 weeks worked.

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‘For a more lengthy discussion of the problem of the appropriate wage construction, see Craig Jones, The Effect of Free Day Care on Womenb Labor Force Participation (unpublished Ph.D. dissertation, University of Illinois, 1975).

Research Note / 117

The difference between the two wage variables is particularly striking for part time workers. It seems highly unlikely that part time workers would have higher wage rates than full time, full year workers. But the data that would provide a comparison between hourly wages for part time, part year and full time, full year workers are not available. However, using survey data, Dean Morse found that 89 per cent of those women who worked part time at any time during the year were found in the trade and service industries.5 These are industries which require relatively low skill levels, and consequently they are relatively low wage industries. In 1970, the mean wage for 50-52 week female workers was $4,196 in trade and $2,978 in services, compared with an overall mean wage for women of $4,944.6 Morse goes on to say that there was a “clear association of part time employment with much less than full year employment in the great majority of indu~tr ies .”~ In the sample used in our study, the correlation between hours worked last week and weeks worked last year was ,334 for white women and .309 for black women.

In addition, persuasive evidence is provided by a special wage survey made in 1970, which found that low wage workers generally worked fewer hours per week.8 Of those workers paid less than $2 per hour, the arbitrarily selected low wage level, 48 per cent worked fewer than 35 hours per week, compared with 18 per cent of those whose hourly wage rate was above $2. The study points out a relation- ship among low wages, employment in particular industries such as services and trade, and a less than 35-hour work week. In retail trade, 44 per cent worked less than 35 hours and earned an average of $1.88 per hour, compared with those who worked more than 35 hours and earned an average of $2.48 per hour. In services, 35 per cent worked less than a 35-hour week for an average wage of $2.14, com- pared with $2.65 for those working more than 35 hours per week.

All the available evidence suggests that part time, part year workers earn lower hourly wages than full time, full year workers, yet Tables 1 and 2 show Wa to be higher for part time, part year workers. These figures must, therefore, be mislead- ing. One reason why part time wage rates might be higher is that part time workers are generally not recipients of fringe benefits to the extent of those received by full time workers. The wage rates of full time workers are therefore biased downward relative to those of part time workers to the extent that fringe benefits are not included in reported earnings. And, if this omission of fringe benefits were respon- sible for the higher wage rates in the lower hours worked categories, it would also help to explain the higher wage rates in the lower weeks worked categories to the extent that weeks worked and hours worked are correlated .g

However, this factor alone cannot possibly explain the extraordinarily high esti-

5Dean Morse, The Peripheral Worker (New York: Columbia University Press, 1969). ‘U.S. Bureau of the Census, Census of Population: 1970, Subject Reports, Final Report PC(2)-7B,

“Industrial Characteristics” (Washington, D.C.: U.S. Government Printing Office, 1973), pp. 115-116. ’Morse, op. cit., pp. 135-136. %even Sternlieb and Alvin Bauman, “Employment Characteristics of Low Wage Workers,” Monthly

Labor Review, XCV (July, 1972), 9-12. gEven if this factor did account for considerable bias, w b would be a more desirable estimate of

hourly wages. Since for all weeks and hours categories, it is constructed from the wages of full year workers, w b contains a similar downward bias for all categories, that is, the downward bias due to the omission of fringe benefits for full year workers. The bias in Wa, on the other hand, would vary since workers in the lower weeks and hours worked categories often don’t receive fringe benefits. Wb would therefore be the preferable wage construction for studies of labor supply.

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mates for Wa for the 1-13 weeks worked and 1-14 hours worked categories, both of which are well over twice as high as the wage estimated for full time, full year workers. Another possible explanation is that workers are concentrated toward the upper ends of some of the weeks worked and hours worked categories. This concentration above the mid-point seems particularly plausible for the 1-14 hours and 1-13 weeks worked categories. Workers, if they elect to accept employment, are likely to supply some minimum amount of labor. For example, at least 10-12 hours per week may be necessary to cover the fixed costs (e.g., transportation, uniforms, etc.) of employment. Furthermore, because of the correlation between part time and part year work, this would also account for some of the increasing differential between Wa and Wb as the weeks worked categories decrease.

This reasoning may also be applied to the 1-13 weeks worked category. If workers work some minimum number of weeks to cover minimum employment fixed costs, and if the mean number of weeks worked is subsequently greater than the mid- point of 7 weeks, then the computed wage, Wa, for workers in that category (1-13 weeks) would be biased upward. The effect would be particularly apparent in the 1-13 weeks and 1-14 hours worked categories, where the interaction would cause the greatest upward bias in Wa. References to Tables 1 and 2 indicates this is the case, the differential between Wa and Wb being the greatest for these categories.

The bias in the estimation of Wa could also possibly be because of errors in measurement, that is, misreporting of data on weeks worked and hours worked. The problem of reporting such information accurately, particularly if it relates to the previous year, is well known. To the extent that underreporting of weeks worked and hours worked places some persons in the inappropriate weeks or hours worked category, the hourly wage will be biased upward.

Conclusion In future studies of wages, researchers should exercise great caution

in using mid-points of weeks worked and hours worked categories to estimate hourly wages from data on annual earnings. The analysis and evidence presented here suggest that this approach will lead to a biased estimate of the hourly wage. Whether this bias is because of reporting errors or the inappropriate use of mid- points, a preferable alternative may be to assign wage rates based on reported occupational category, the method used in estimating Wb in this paper.