Table 3.1: Correlation of weekly hours and wages by 4-Digit Industry across sample years

Some of the association between hourly wages and weekly hours may come from the institutionalized 40-hour workweek and the legal requirement for overtime pay rates for weekly hours beyond 40. But legally mandated overtime need not have any affect even when overtime is observed. If a firm is willing to pay $430 for 42 hours of work, the contract can stipulate 42 hours at $430/42 per hour, or, to comply with the law, the contract can stipulate an hourly rate of $10 with time and a half for over time. This wouldn’t have any effect at all on the observed wage-effort offer curve. What the mandated overtime law really does is limit the flexibility of contracts over time and it affects firms that experience variability in the demand for labor. Our focus on the longer-run aspects of the contract that are evident in the cross-section comparison of different industries means that mandated overtime is not a substantial concern. The fact that some industries appear consistently to require their workers to work more than 40-hour workweeks despite mandated overtime pay premiums is support for this idea.
Table 3.2: Capital per Production Worker
Our model links weekly hours and weekly wages to capital intensity. Table 3.2 reports the average and standard deviation of real log capital per production worker and the average of the percent of employees who are production workers for the 448 manufacturing sectors included in the sample. The capital intensity for each production worker is measured as total industry capital stock divided by the number of production workers.12 The numbers in Table 3.2 indicate that the average level of capital per production worker has been increasing steadily through the sample period while the standard error of the log has been decreasing. This growth in capital intensity may be due partly to errors in measurement.. For example, it is possible that there has been a shift of capital from production to nonproduction workers and it is also possible that the depreciation rates do not adequately account for obsolescence in this period of supposed rapid technological advance.

Estimation of the Wage-Effort Offer Curve with 4-Digit data

To infer the wage-effort offer curve we estimate two separate regressions, one for weekly hours and one for weekly wages.
We exclude the cubic of capital intensity from the hours equation because it is generally statistically insignificant. Data to estimate these equations are three-year averages centered on the years 1960, 65, 70, 75, 80, 85, 90 and 93. Observations are weighted by the number of production workers employed in the sector-year in order to prevent the small sectors from dragging the coefficients around. payday loans online same day

The results of these regressions are presented in table 3.3. The basic patterns of the results are as predicted and fairly constant over the sample period. Capital intensity explains close to 40% of the variation in weekly hours across sectors but somewhat more of the variation in weekly wages, 50% in 1960 and nearly 70% in the eighties. From the pair of estimated equations (3.1) and (3.2) we solve for the wage-effort offer curve by eliminating the capital intensity variable. Segments of these curves corresponding to observed capital intensities are plotted in Figures 3.5, 3.6 and 3.7. The capital intensity data has a large right tail so the capital range was determined as the minimum capital intensity observed in the data up to 2.5 standard deviations above the mean, roughly encompassing all but two outlying sectors of the sample, petroleum refining and blast furnaces. The lower left portions of the curves represent the wage-effort contracts in the relatively labor-intensive sectors, while the upper right portions represent the contracts in capital-intensive sectors. The eight regressions are divided into three sub-periods in which the shift of the curve takes a distinct form, 1960 to 1970, 1970 to 1980, and 1980 to 1993.