Barzel(1973) added another curved portion to the budget constraint based on the assumption that labor productivity falls as the number of working hours increased within a fixed period of time, leading to the reversed ’S’ shaped budget constraint cited in such empirical work as Moffit(1984). BarzePs and Oi’s budget curves are displayed in Figure 2.6.

There has been a substantia] amount of empirical work in this field, although again most of this work has been more concerned with labor supply than labor demand.. Sherwin Rosen(1973) was one of the first to investigate the interindustry relationship between wages and hours. His reasoning of the apparent wage-hour tradeoff was neatly summarized in his introduction fully.

“Hours of work are an important non-pecuniary aspect of employment, even though ‘industry’ per se is not. On the other hand, wage and hour differences can persist because firms find certain attributes of their employees more productive and desirable than others and are willing to incur extra costs to obtain them.”
He divides his analysis into supply and demand sides. On the demand side he, like Oi, correlated hours with the fixed costs of employing labor, including hiring costs, specific training and unemployment insurance premiums above the minimum levels. The demand for hours per employee is a decreasing function of the wage rate and an increasing function of these fixed costs. While he has no direct measure of these fixed costs across the industries in his sample he derives what he believes to be suitable industry proxies from a number of demographic variables including age, education and race. No mention of capital intensity is included in his work. He also considers short run adjustments by including a variable to measure the sectoral growth rate and also other external effects including unions. In general he has more success measuring the demand side of the equation than the supply side.

On the labor supply side are papers by Moffit(1984), Lundberg(1985) and Biddle and Zarkin(1989). These are primarily concerned with identifying the factors that influence the hours worked by individual workers, and the relationship between hours and wages as measured from the worker’s perspective. They all point out that traditional OLS wage regressions which include hours worked as a right hand side variable will not adequately measure the wage-hour relationship because of the endogeneity of hours. Biddle and Zarkin specifically control for this endogeneity and find the bias to be significant.