The return to hours and workers in U.S. manufacturing: evidence on aggregation bias.

• Author: DeBeaumont, Ronald

1. Introduction

   In the 1980s, the statutory workweek was shortened in some British and all French manufacturing industries to discourage the use of overtime and to hypothetically increase employment of standard-time workers (Marchand, Rault, and Tarpin 1983; White and Ghobadian 1984). While interest in this policy was initially limited to European countries, the increasing reliance by U.S. firms on either overtime or part-time work over the last decade has generated a similar interest in the U.S. (Trejo 1991; Stratton 1996). In fact, 1994 legislation backed by organized labor was introduced in the House of Representatives to reduce the standard workweek from 40 to 30 hours in an effort to spread the existing work over more employees (Fitzgerald 1996). In 1997, the United Auto Workers' strike against General Motors emphasized excessive use of overtime work, while the Teamsters' strike against the United Parcel Service focused primarily on the use of part-time rather than full-time workers. Thus, the appropriate mix of hours and workers appears to be a major point of contention between organized labor and employers (Kahn and Lang 1995).

   The effectiveness of policies that seek to exploit the worker-hour tradeoff depend on the returns to hours and workers in the production process. Theoretical worker-hour models predict a reduction in hours can cause worker productivity and employment to decline if the returns to hours are sufficiently high (Hammermesh 1996, chapter 7). Simulations of worker-hour models using both U.S. and European data predict that firms are more likely to convert overtime to new hires for a given reduction in the workweek when the returns to hours are small (van Ginneken 1984; Whitley and Wilson 1986; DeBeaumont 1993; Holm and Jaakko 1993). Accurate return-to-hours estimates are thus important in analyzing the productivity and employment effects of a workweek reduction.

   Prior worker-hour studies estimate the rerum to hours and workers using longitudinal manufacturing data for U.S. and European industries and impose a Cobb-Douglas production function across industries that requires fewer degrees of freedom than more general functional forms. A survey of empirical analyses by Hart and McGregor (1988) indicates that the return to hours is greater than the return to workers and may exceed one.

   Leslie and Wise (1980), however, reject the hypothesis of a common production structure across industries using an F-test. They contend that the imposition of a common production function confounds productivity of hours with different technology or labor use patterns across industries and biases the returns to hours upward. Leslie (1991) finds, in fact, that heavy overtime users often assign an additional shift that may be more productive than an extra hour at the end of a shift for occasional overtime users. This suggests that work hours are greater in industries for which hours are relatively productive and that the production function should be estimated separately by industry. Leslie and Wise (1980) provide the only industry-specific return-to-hours estimates in the literature. However, their estimates are insignificant because of limited degrees of freedom from the small time dimension of their data.

   In this paper, the aggregation-bias hypothesis is tested in two parallel analyses that use U.S. manufacturing data disaggregated by industry. In particular, industry-specific data by state from 1972-1978 and by four-digit-SIC code from 1958-1994 are used to estimate worker-hour production functions for each two-digit-SIC industry. The results are remarkably robust across the two data sets and indicate that the returns to hours are significantly less than one for most industries. Moreover, the findings also suggest that returns to hours are generally less than returns to workers. The two sets of industry-specific estimates are compared to estimates that impose a common production function across industries and use data that aggregate across states or subindustry. In both cases, the aggregate return-to-hours estimates are greater than one and greater than most individual industry-specific estimates. Jointly, these analyses provide strong evidence of aggregation bias in prior worker-hour studies and suggest that the returns are likely to be less than one for most U.S. industries.

2. Empirical Model

   Following the worker-hour literature, we estimate the returns to hours and workers using a Cobb-Douglas production function that distinguishes between the number of workers and hours in the production process (Leslie and Wise 1980; Hart and McGregor 1988; Hammermesh 1996). A Cobb-Douglas production function is adopted here and in the literature because it uses fewer degrees of freedom than more general functional forms. In fact, tests of the restriction imposed by the Cobb-Douglas using a translog are statistically unreliable due to the relatively small number of observations in our data. Nonetheless, by using a Cobb-Douglas specification, we insure that any differences in our results from prior work are not due to functional-form differences in the estimating equation.

   As a point of departure, we propose a production function for an industry that varies in a cross-sectional dimension by state or by subindustry (k) and over a time period (t)

   ln [Y.sub.kt] = [a.sub.0] + [a.sub.1]ln [N.sub.kt] + [a.sub.2]ln [H.sub.kt] + [a.sub.3][K.sub.kt] + [a.sub.4]ln [U.sub.kt] + [a.sub.5][Z.sub.kt] + [[Epsilon].sub.kt], (1)

   where Y is the value added, N and H are the average number of workers and average weekly hours per worker, respectively, K is a measure of the capital stock, U is a measure of capital utilization, and Z is a vector of variables that includes measures of cyclical and time variation. This specification differs from prior empirical models only in that the cross-sectional variation by state or subindustry permits a relaxation of the common production structure across industries imposed in prior work. A number of factors may cause the production function to differ by state or subindustry. For example, state-specific variation in the productivity of resource-based industries (e.g., precious metals or mining) is likely to arise from natural resource endowments, and institutional factors such as right-to-work laws may affect labor productivity in the state. Likewise, the production function for natural gas is likely to differ from those of other petroleum subindustries. Nonetheless, the use of two sources of cross-sectional variation to estimate Equation 1 is important because it provides some evidence of whether the results are sensitive to possible unobserved and unmeasured sources of variation in the cross-sectional dimension.

   The variables controlling for U and Z are included in Equation 1 because prior work suggests that their omission may bias the results for N, H, and K. Specifically, Feldstein (1967) argues that the productivity of hours is positively correlated with the level and utilization of capital: He uses two-digit British manufacturing data over several years and finds that omitting U can cause an upward bias in the return to hours. This finding is supported by Hart and McGregor (1988). In addition, Z includes measures that account for cyclical factors because, for example, industries often pay more for hours in downturns than would appear to be cost minimizing (Fay and Medoff 1985). This type of labor hoarding would make hours appear more productive in an empirical analysis, as actual labor hours would increase more in an upturn than measured hours.

   Our contention is that the inappropriate aggregation across production structures in prior work causes an upward bias in the return-to-hours estimates. This aggregation bias is similar to the upward bias found for the return to education when there are insufficient controls for ability (Blackburn and Neumark 1993). A heuristic demonstration of aggregation bias can be seen in Figure 1, which includes two production functions for competitive firms in different industries that differ in their return to hours. Suppose these firms are price takers in the input market such that they face the same real wage. Profit-maximizing firms set the real wage equal to the marginal product of an hour, which is reflected by the tangency between the production function and the parallel wage lines A and B. It follows that firm 2, which has both a larger intercept and a higher marginal return to hours, hires more hours ([H.sub.2]) than firm 1 ([H.sub.1]). However, by imposing a common production structure on the two firms, the return-to-hours estimates are based on the slope of the regression line that connects [H.sub.1] and [H.sub.2], which is greater than the true return to hours in either firm 1 or firm 2. This bias in the return to hours would be present even with fixed-effect controls for intercept differences because of the differences in the slope of the production functions.

   Two parallel empirical analyses subsequently use cross-sectional variation by state or by subindustry to provide a sufficient number of observations to estimate worker-hour production functions separately for each industry, Each set of estimates is compared to an alternative model that uses data that have been...