# THE LENGTH OF THE WORK DAY: Explanations 5

Table 6 shows that demand for daily hours worked from workers in the 90th wage decile barely increased relative to demand for daily hours from workers in the 10th wage decile. Of course, the computed relative demand shift is only a partial measure of the total demand shift. Relative changes in productivity may have changed the ratio of daily hours of workers in the lowest to the highest wage decile even within a broad occupation or industry category. Fixed costs per worker (arising from health insurance, social security payroll taxes, or capital deepening) may have disproportionately increased for either higher or lower paid workers. The Fair Labor Standards Act of 1938 and subsequent extensions, none of which may affect the highly paid, raised the price of overtime.

I determine changes in the supply of daily hours worked of men and women in a given wage decile by explicitly estimating labor supply equations for each period and then using the estimated regressions to predict daily hours of work within each wage decile. The equations that I estimate are

for 1991 and 1973, where h is hours worked, w is the hourly wage, and ж is a vector of demographic characteristics, such as age and number of dependents. Endogeneity between the wage and hours presents potential problems. Because individuals may influence their own wage through investment in human capital the wage is likely to be correlated with the stochastic error term due to unobserved tastes and abilities that help determine the wage and that determine current labor supply. I therefore use industry dummies as instruments.

Table 7 presents estimates of wage elasticities for the 1890s, 1973, and 1991. Note that the supply curve of daily hours in the 1890s was very backwards bending, with an elasticity for all male workers of -0.304 (a much larger estimate than when ordinary least squares is used). I obtain negative labor supply elasticities within broad occupation and industry groups as well when I use ordinary least squares. Labor supply elasticities for women were even slightly more negative than those of men. That the labor supply curve in the 1890s was backwards bending is consistent with other estimates for the period (e.g. Whaples 1990; Rosenbloom 1992) and with contemporary observations. For example, the French statistician and economist Simiand examined the wages of French coal miners from 1847 and 1902 and noted that in years when tonnage rates were decreased daily output increased whereas in years when rates were greater, output per day either diminished or did not increase (cited in Douglas 1937: 295).