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

Singell, Larry D., Jr.

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 aggregated up over the cross-sectional units and that impose a common production function for all industries. Thus, our analyses improve on prior work by both testing the common production structure hypothesis and by obtaining more reliable estimates of the returns to hours by industry. Our analyses focus on the upward bias in the returns to hours because the potential bias from aggregation on the returns to other inputs is not likely to be systematic. For example, in the food industry, farms that employ relatively few workers may be capital intensive and productive or may be simply operating at subsistence. If some states have a high concentration of capital-intensive farms while others contain primarily subsistence farms, then disaggregation by state could yield an increase or decrease in the return to farm workers depending on weights used for aggregation. Moreover, the change in the return to workers from disaggregation is unlikely to depend on the productivity of hours or the level of hours across states in the industry. The subsequent empirical results suggest, in fact, that there is no significant bias in either the returns to workers or the returns to capital.

3. Industry Estimates Disaggregated by State

The Data

We first use cross-sectional variation by state to obtain industry-specific estimates. In particular, the Census of Manufactures (U.S. Bureau of Census 1972, 1977) and the Annual Survey of Manufactures (U.S. Census Bureau 1972-1978) contain data for two-digit-SIC industries in the U.S., disaggregated by state, for the period between 1972 and 1978. These data are drawn from a survey of firms in each industry. Observations for some states are not included for each industry because low industry participation yields high standard errors for some observations. The Census excludes observations that have a sufficiently high standard error. Our sample interval ends in 1978 primarily because capital expenditures are not available for the years between 1978 and 1982 in the state data. While it is possible to extend the sample period by extrapolating capital expenditures over the years of missing data, the number of states would be reduced due to missing observations for the other variables in the empirical model. Thus, we use the period from 1972 to 1978 because it maximizes the k by t number of observations. This time interval is similar to that used in prior aggregate studies and thus offers the advantage that differences in the estimated returns cannot be attributed to possible changes in the production function over time. Nonetheless, the severe recession, price and wage controls, and the energy crisis that occurred in the 1970s suggest that this may be a unique time period for U.S. manufacturing. Thus, these estimates are compared to the alternative estimates provided in the next section obtained using subindustry data over a more extended time period. This permits us to examine whether our results can be attributed to the use of state-specific or time-specific variation.(1)

Data on value added, the capital stock, and the number of hours and production workers are drawn from the Annual Survey of Manufactures (U.S. Bureau of Census 1972-1978). Value added is measured in 1972 dollars using price indices from the Survey of Current Business (U.S. Bureau of Economic Analysis 1972-1978). The capital series is constructed from data on the stock, which are available by industry and state only for 1978, and on new capital expenditures that are provided for the years 1972 to 1978. The capital stock at time t ([K.sub.t]) is calculated as [K.sub.t] = [K.sub.t-1] + [E.sub.t-1] - [Lambda][K.sub.t-1], where E is both new and used/rental capital expenditures and A is an industry-specific depreciation rate. [K.sub.t] is calculated using backwards induction from 1978 deflating by the price index for capital goods reported by the Bureau of Labor Statistics (1978). Several measures of cyclical variation are included in the model. Time dummies are included to capture possible business-cycle fluctuations. The capital-utilization rate from the Industrial Production and Capacity Utilization and Industrial Material (U.S. Bureau of Labor Statistics 1978) is also used, which varies over time but not by state. The capital utilization rate is thus excluded from the model when time dummies are included. We also use the unemployment rate as a measure of cyclical fluctuations, which is provided by the Manpower Report of the President (U.S. President 1978). The unemployment rate, because it varies by state and time, does not require the exclusion of the capital utilization rate.(2)

The number of workers is measured by the total employment of both production and nonproduction workers. However, the number of hours is measured by the average number of hours for production workers only because data on hours are not available for nonproduction workers in the Annual Survey of Manufactures. This is potentially problematic given the general shift from production to nonproduction labor that has occurred in U.S. manufacturing. However, estimates from the food industry that shifted toward production workers during the sample period yield the same qualitative conclusions as those industries that have shifted away from production workers. Moreover, the qualitative conclusions for the returns to hours and workers do not change in subsequent sensitivity tests that control for the proportion of production workers in total employment.

Summary statistics for hours are provided in Table 1 and suggest several distinct patterns. First, consistent with findings of Leslie and Wise (1980) for British manufactures, the ranking of long-hour industries is relatively constant over time. For example, the paper and petroleum industries consistently employ longer hours, while printing and apparel consistently use the least. This suggests that some industries have high hour products and that the technology for these industries does not change dramatically over time. Second, hours use appears to be in decline for the sample period. For example, hour usage is lower for 17 of 19 industries in 1978 than in 1972; this suggests that changes in relative prices or technology have made labor usage [TABULAR DATA FOR TABLE 1 OMITTED] relatively less favorable over this time period, which may be the result of the supply shocks of the mid-1970s. Finally, the descriptive statistics also suggest greater variation in hours usage across states than across time and industries. Thus, previous studies that have used aggregate data over states may hide some of the variation in the return to hours.

Industry-Specific Results

Equation 1 is estimated controlling for fixed, unobserved state-specific heterogeneity for 19 separate industries and jointly for all 19 industries including industry-specific dummy variables.(3) An F-test comparing the combined residual sum of squares of the industry-specific specifications to that of the joint model yields a statistic of 14.96, indicating the hypothesis of equal coefficients across industries is rejected at the 1% level. Thus, industry-specific parameter estimates are presented in Table 2.

Three empirical points are worth emphasizing. First, an empirical disadvantage of using disaggregate data is that smaller economic units such as states are more likely to have inputs and outputs that are simultaneously determined. Hausman tests indicate possible simultaneity bias in 2 of the 19 industry-specifics estimates, nonelectrical machinery and furniture/fixtures. The production equations for these industries are estimated using lagged values of the explanatory variables as instruments, which does not significantly alter the coefficient estimates. Second, the models presented exclude the capital utilization rate both because its coefficient is [TABULAR DATA FOR TABLE 2 OMITTED] insignificant and its inclusion requires the exclusion of the time dummies that are generally significant. Prior studies, however, find that excluding the capital utilization rate biases the returns to hours upward (Hart and McGregor 1988). Thus, the inclusion of a capital utilization rate that varies by state and industry, if available, would likely further reduce our return-to-hours estimates. Finally, while the presence of first-order autocorrelation is rejected at the 5% level in all specifications, the Durbin-Watson statistic is within the inconclusive range for most industries. We use the Cochorane-Orcutt procedure to correct for a first-order autoregressive error for those industries in the inconclusive range. Comparisons of the uncorrected and autoregressive models indicate that the point estimates and their standard errors are robust to assumptions regarding the error structure.

The coefficients reported in Table 2 generally have the predicted sign, with return-to-hours and return-to-workers estimates that are significant at standard levels. The 13 significant return-to-hours estimates have an average value of 0.63, and most of the individual estimates are significantly less than one. This differs from prior worker-hour studies that typically find returns to hours that are greater than one. The results also cast doubt on the empirical regularity in prior work that returns to hours are greater than returns to workers. The return-to-hours estimates are less than those for the returns to workers in 9 of the 13 industries for which the hours coefficient is significant. The average of the rerum-to-workers estimate is 0.73, which is comparable to prior aggregate industry estimates for U.S. data (Feldstein 1967; Craine 1973). Thus, the smaller returns to hours than workers appears to be largely due to the bias in returns to hours. The analysis also indicates considerable differences in worker productivity across industries, which explains the rejection of the common production structure.

The other explanatory variables included in the model do not appear to explain industry output. For example, the coefficient on the capital stock is significant at the 10% level in only 4 of 19 regressions. The relatively poor performance of the capital measure may be due to its sampling error. Unfortunately, adopting a decision rule that yields more reliable capital expenditure estimates critically reduces the number of observations in the data. In any case, measurement error with regard to capital is likely to inappropriately assign output increases to workers and hours, which would tend to bias upward their estimates.(4)

The results for the cyclical measures are mixed. The coefficients on the unemployment rate are generally insignificant and, when significant, do not have a consistent sign. While many of the coefficients on the time dummies (not reported)are significant at traditional levels, their sign and magnitude do not indicate a consistent pattern across industries. If industries respond differently to cyclical factors, this would provide a rationale for why prior cross-industry studies have found these factors to be insignificant. The results may also suggest that, although cyclical factors are important to production in an industry, economy-wide measures of cyclical variation are too broad to capture the industry-specific effects on the inputs of production.

Aggregate Results

The results of the industry-specific models support the proposition that return-to-hours estimates are biased upward in cross-industry studies. To confirm that this result is due to aggregation bias, we replicate these cross-industry regressions using two comparable aggregate data sets and a production function that imposes a common production structure across industries. Our first aggregate analysis is conducted by aggregating our data across states.(5) To make reliable comparisons between the individual and aggregate estimates, we restrict the industries to those 13 for which returns to hours are significant. Thus, the sample includes 91 observations for the 13 industries over the seven time periods. The estimates using industry-specific fixed-effects are provided in column 1 of Table 3. Because the Durbin-Watson statistic is in the inconclusive range, the estimates reported in Table 3 use the Cochorane-Orcutt procedure to correct for first-order autocorrelation.(6) A common autocorrelation coefficient is used in each of the analyses because a F-test cannot reject the hypothesis of a common autocorrelation coefficient across industries or across states.

Table 3. Aggregate Fixed-Effect Estimates for Two-Digit State
Data(ab)

 All Industries Nineteen Industries
 Coefficient Coefficient
Variable (SE) (SE)

Hours 1.02(**) 1.06(*)
 (0.55) (0.47)

Workers 1.28(*) 0.75(*)
 (0.25) (0.15)

Capital 0.07 0.37(*)
 (0.08) (0.08)

Unemployment 0.05 -0.01
 (0.05) (0.05)

Durbin-Watson 1.85 1.85

Degrees of Freedom 66 66

[R.sup.2] 0.34 0.34

a Both models are estimated correcting for first-order
autocorrelation.

b *, Significant at the 5% level; **, significant at the 10% level.

The results support the hypothesis that aggregation bias is present in cross-industry regressions. Specifically, the estimate of the returns to hours of 1.02 is larger than all but one of the individual industry estimates. The aggregate specification, unlike its industry-specific counterparts, includes the capital utilization rate that is available across time for major industry groups. The inclusion of the capital utilization rate is expected to lower the returns to hours. In fact, the return-to-hours estimate increases to 1.4 when the capital utilization rate is omitted from the aggregate regression.

While useful for demonstrating aggregation bias within the data set, the aggregate data are not identical to those used in prior cross-industry studies because some states and industries are excluded. To insure the apparent aggregation bias in our cross-industry analysis does not result from the exclusion of these observations, we perform a second aggregate analysis that uses the standard methodology and aggregate data sources for our U.S. manufacturing industries from 1972 to 1978. These data are from the Annual Survey of Manufactures and the Census of Manufactures (U.S. Bureau of Census 1972, 1972-1978, 1977). The tobacco products industry is again excluded from the analysis because data are not reported for the capital stock for each year. The estimates using these aggregate data are provided in the second column of Table 3. For consistency, a first-order autoregressive process is used, but the estimates are not significantly impacted by this specification choice. The results from this analysis are qualitatively equivalent to those from the cross-industry analysis using the aggregated state data. In particular, the return-to-hours estimate of 1.06 is very similar to the estimate from the aggregated state data, and the estimate is even greater when capital utilization is excluded. The returns to capital are now significant as well, while the coefficient on the unemployment rate remains insignificant.

4. Industry Estimates Disaggregated by Subindustry Group

The Data

The industry-specific estimates using the state data for the 1970s suggest that the returns to hours are overstated in prior studies that use aggregate data over a similar time period. On the other hand, the use of data from a narrow time period that was plagued by a general reduction in manufacturing hours may also yield unrealistic production parameters estimates. In addition, state differences in factors such as labor laws or average firm size could also affect the variation in hours and workers across states. Thus, it is useful to compare the state results with those that use alternative data to examine whether the results are sensitive to the source of the cross-sectional variation and/or the time period.

In this case, we use subindustry data that are again drawn from the Annual Survey of Manufactures (U.S. Bureau of Census 1958-1994). In particular, production data for 431 four-digit-SIC subindustries over the period from 1958 to 1994 are made available by Eric J. Bartelsman, Randy A. Becker, and Wayne B. Gray on the National Bureau of Economic Research (NBER) web page (www.nber.org). Again, the number of observations varies for each industry and depends on the number of subindustry classifications. Thus, for example, the food industry includes 47 four-digit subindustries, while the tobacco industry contains only 3 subindustries. The NBER data include the value added denominated in 1987 dollars in each four-digit subindustry, which is used as a measure of output. In addition, the explanatory variables for the real value of the capital stock in 1987 dollars, the total number of workers, and the average hours of production workers are included in the data. These data are supplemented by the national annual unemployment rate and the capital utilization rate for major industry groups. In addition, time dummies are included to measure year-specific effects. Thus, we have each of the variables necessary to replicate the previous production specification, where subindustry variation is used rather than state variation to provide the required degrees of freedom to estimate industry-specific production functions.

The summary statistics for the three industries with the highest and lowest hour usage are presented in Table 4. The means confirm the earlier finding from the state data that industries differ systematically in their hour usage. In particular, high-hour industries in 1958 continued to be the high-hour industries in 1994, while the low-hour industries remain so over the entire time interval. The data also indicate the pattern of declining hours observed in the 1970s has since reversed, with hours per worker reaching a maximum for many industries toward the end of the sample period. These data provide an interesting test of the results from the previous section, both because of the different method of disaggregation and because the data cover periods where different economic conditions are present.

Industry-Specific Results

Table 5 reports the results for each of the 20 major industry groups. The specification of the production function using the subindustry data is identical to that estimated using the state [TABULAR DATA FOR TABLE 4 OMITTED] data; thus, the capital utilization rate is excluded in favor of time dummies. Again, the inclusion or exclusion of the capital utilization rate does not affect the qualitative conclusions drawn from the model. In addition, the same estimation technique is employed to estimate the industry-specific production functions with the subindustry data. In particular, the industry-specific production functions are estimated including subindustry fixed-effects and correcting for first-order autocorrelation. In this case, the Durbin-Watson statistic indicates significant autocorrelation in each of the industry-specific specifications, which is likely the result of the longer time interval.

The results using the subindustry data are remarkably similar to those found using the state [TABULAR DATA FOR TABLE 5 OMITTED] data. Specifically, 19 of the 20 return-to-hours estimates are significant at the 10% level or higher with an average estimate of 0.56, as compared to the average estimate of 0.63 for the state data. In addition, 16 of the estimates are significantly less than one at the 5% level, and two estimates are not significantly different from one. Jointly, the results from these two data sets provide strong evidence that returns to hours do not exceed one and that they may be less than one for most industries.

It is also interesting to compare the returns to hours and workers. The point estimates of returns to hours are less than returns to workers for most industries using the state data, but their differences are not statistically different. Here, all 20 of the industry-specific, return-to-workers estimates are significant at the 5% level, with an average estimate of 0.84. For these data, returns to workers exceed returns to hours for 17 of the 19 industries where both are significant. In the two industries where returns to hours exceed returns to workers, the 5% confidence intervals of the two estimates overlap. However, for 12 of the industries where returns to workers exceed returns to hours, the 5% confidence intervals do not overlap. Thus, contrary to prior work, returns to hours generally do not exceed the returns to workers and are significantly smaller in most industries.

Prior work indicates a steady shift away from production workers toward nonproduction workers in U.S. manufacturing, which may reflect that many industries have experienced laborsaving technical change (Berman, Bound, and Griliches 1994). It follows that the returns to hours and workers could be biased due to the fact that the worker measure does not distinguish between production and nonproduction workers. This bias would be expected to be particularly large in the subindustry data that covers a long time interval. Thus, the standard model is re-estimated including a variable measuring the percent of production workers in total employment. A comparison of the return-to-hours and workers estimates from the standard specification (columns 1 and 2, Appendix) with those that control for the mix of production and nonproduction workers (columns 3 and 4, Appendix) continue to show returns to hours that are generally less than one and less than the returns to workers. The results using the state data, while not reported for brevity, are similarly robust. Thus, aggregation bias does not appear to depend on the mix of employment.

The return-to-capital estimates, unlike those from the state data, are generally significant. The greater significance of the capital variable in the subindustry versus the state data could be due to smaller sampling error from measuring each subindustry over all states and/or the greater degrees of freedom. Of the 14 significant return-to-capital estimates, 12 fall in the range 0.100.31. The unemployment rate is also significant in each industry, although its exclusion has little effect on returns to hours and workers. Overall, the results derived using the disaggregate subindustry data yield the same qualitative conclusions to those drawn from the disaggregate state data, although the subindustry results are generally more precise due to their greater degrees of freedom.

Aggregate Results

The effects of aggregation are re-examined using the subindustry data. In particular, Table 6 includes production-function estimates that use data aggregated over the subindustry groups and impose common production parameters across each of the industries for the period from 1958 to 1994. The specification of the production function in Table 6 is identical to both the industry-specific estimates using the subindustry data and the aggregate estimates using the state data.

The effects of aggregation in the subindustry data are directly comparable to those found for the state data. Specifically, the aggregate return-to-hours estimate of 1.12 is numerically greater than all but one of the industry-specific estimates and is significantly greater than most. The results confirm that aggregation yields significant upward bias in the returns to hours. Moreover, aggregation bias seems mostly limited to hours, as the returns to workers and capital are close to the individual industry averages. Thus, the results support the contention that high-hour industries are more efficient than low-hour industries, which does not appear to coincide with high-worker industries being more or less efficient.

Table 6. Aggregate Fixed-Effect Estimates Using Four-Digit SIC Data
for 1958-1994(ab)

Industry Coefficient (SE)

Return to Hours 1.12(*)
 (0.16)

Return to Workers 0.77(*)
 (0.05)

Return to Capital 0.22(*)
 (0.05)

Unemployment Rate 2.30(*)
 (0.08)

a Models are estimated including 36 time dummies. Each model
corrects for first-order autocorrelation based on the Durbin-Watson
statistic.

b *, Significant at the 5% level.

Our disaggregate analyses still involve some degree of aggregation that could bias the results. Specifically, in the subindustry data, each observation is given equal weight even though the subindustries employ a different number of workers and produce a different level of output. Thus, for example, the largest food subindustry (i.e., SIC 2011) employees an average of 120,000 production workers over the period, which is over twice the size of any other subindustry and 30 times as large as the smallest (i.e., SIC 2021). Thus, it may be inappropriate to give equal weight to each of the subindustries because they vary markedly in their share of total production for the industry. To examine the sensitivity of the results to this type of aggregation, the individual and aggregate production specifications are re-estimated using weighted least squares, where the number of production workers serves as the weight. The estimates for the returns to hours and workers are provided in columns 5 and 6 of the Appendix. The weighted least squares estimates yield an average return to hours of 0.77, with 14 of the 16 significant estimates less than one. The application of weighted least squares to account for size differences among states yields comparable results for the state data (not reported). Thus, the qualitative conclusions are unaffected by using generalized least squares.

5. Concluding Remarks

Some policy analysts in the U.S. and Europe have suggested that employment can be increased by restricting the standard workweek and inducing firms to substitute workers for hours. A crucial criticism of this policy is that firms will be forced to substitute highly productive hours for less productive new hires, thus offsetting any possible positive employment response. Prior empirical studies have been supportive of this criticism, generally finding returns to hours to be greater than one. We argue that prior estimates are biased upward due to previously unmeasured differences in production technology between industries. In particular, our analysis uses similar techniques and data to those in prior studies but relaxes the common production structure across industries imposed in earlier work. Our industry-specific production function results indicate that the returns to hours are less than one for most U.S. industries, while the imposition of a common production structure on the data yields returns to hours that are greater than one. Furthermore, our results suggest that returns to workers are greater than returns to hours for most U.S. industries, which casts some doubt on the proposition that a marginal substitution from hours to workers will result in a decrease in labor productivity.

The importance of return to hours estimates is noted in studies that simulate the employment response of a shorter workweek. For example, a simulation by Brunstad and Holm (1990) using Norwegian data indicates that a 2.5-hour reduction in the workweek generates 53,000 jobs when the return to hours is 0.6 and only 4000 jobs when the return to hours is 1.4. Our results, nonetheless, indicate significant variation in the returns to hours across industries, suggesting that the effectiveness of a workweek reduction may vary greatly across industries. Moreover, unions are also likely to push for wage adjustments to reduce the loss in income from a workweek reduction and/or market forces could also hypothetically cause a shift in wages; such wage adjustments may partially or fully offset any positive employment effects (Hart 1987; Trejo 1993). Thus, while our return-to-hour estimates provide a more optimistic assessment of the likely employment effects from a workweek reduction, the effects could vary across industry and be limited by worker demands for higher wages. The results also have little to say about returns to labor inputs outside of manufacturing and thus are only relevant for a fraction of the U.S. labor force. It is within U.S. manufacturing, however, that hours reduction is most likely to become an issue. While employment in U.S. manufacturing has been stagnant during recent decades, average worker hours has actually increased, a trend not apparent in the manufacturing sectors of other high-income countries (Fitzgerald 1996).

The empirical results are also useful in analyzing the effects of another work-sharing policy, raising the overtime premium. Legislation in 1994 that proposed reducing the workweek also mandated an increase in the overtime premium from 1.5 to 2. While there is generally more agreement that this would cause an increase in employment rather than a workweek reduction (Hart 1987), the size of the increase depends on the return to hours. Again, high returns to hours limit the substitution to more workers and also adversely affect the competitiveness of U.S. manufacturing firms. In comparison to previous studies, our return-to-hours estimates suggest a larger employment increase and a smaller increase in production costs.

In summary, recent labor negotiations indicate that workers are concerned with hours of work as well as wages, suggesting the worksharing policies may increasingly become an issue in labor negotiations. Theoretical worker-hour models suggest reliable estimates of the returns to hours are important in understanding the opportunity costs of possible tradeoffs between hours and workers. Our results provide preliminary evidence that prior estimates of the returns to hours are biased upward by aggregating across industries and that hours reductions are not likely to significantly increase labor costs or decrease productivity. Nonetheless, our analysis does not explicitly account for the use of part-time work or overtime hours but relies on mean hours of work that may cover up significant variation in the worker-hour mix by industry. Thus, further work must be done to examine the extent to which the mix of workers and hours varies with their returns.

The authors would like to thank the two anonymous referees, whose comments greatly improved the paper. Any remaining mistakes are our own.

1 The tobacco industry is excluded because of missing data for capital expenditures.

2 The unemployment rate, while also available by industry over time, is measured by state over time because the firm's labor supply depends largely on the state labor market and because the relatively larger state versus time dimension allows for greater variation in the unemployment measure.

3 Our fixed-effects specifications follow prior analyses, which are supported by Hausman tests that cannot reject the hypothesis that fixed-effects are appropriate. However, the industry-specific regressions are re-estimated using random effects to test the sensitivity of the results to assumptions regarding unobserved heterogeneity. The random-effects estimates yield 11 significant return-to-hour estimates, of which 10 are significantly less than one.

4 Random-effects specifications yield much more precise and plausible parameter estimates for the capital stock. In particular, 16 of the 19 coefficient estimates are significantly positive in these specifications, with magnitudes ranging from 0.7 to 0.04. This may suggest that random effects are better able to account for the measurement error in capital.

5 The capital stock is determined by first aggregating the data by state and then employing the earlier procedure of backwards induction from the 1978 capital stock using new capital expenditures from 1972 to 1977.

6 Estimates that use the full aggregate data for all 19 industries yield estimates of returns to hours and workers that are of a similar magnitude to those presented; these estimates are insignificant, however, at traditional levels.

References

Berman, Eli, John Bound, and Zvi Griliches. 1994. Changes in the demand for skilled labor within U.S. manufacturing: Evidence from the annual survey of manufactures. Quarterly Journal of Economics, 109:367-97.

Blackburn, McKinley L., and David Neumark. 1993. Omitted-ability bias and the increase in the return to schooling. Journal of Labor Economics 11:521-44.

Brunstad, Rolf J., and Thomas Holm. 1990. Can shorter hours solve the problem of unemployment? Unpublished Paper, Institute of Economics, University of Bergen.

Craine, Roger. 1973. On the service flow from labour. Review of Economic Studies 40:39-46.

DeBeaumont, Ronald. 1993. Worker/hour labor demand models and policies to increase employment through worksharing. Ph.D. dissertation, University of Oregon, Eugene, OR.

Fay, Jon A., and James L. Medoff. 1985. Labor and output over the business cycle: Some direct evidence. American Economic Review 75:638-55.

Feldstein, Martin. 1967. Specification of the labour input in the aggregate production function. Review of Economic Studies 34:375-86.

Fitzgerald, Terry J. 1996. Reducing working hours. Federal Reserve Bank of Cleveland Economic Review 32:13-22.

Hamermesh, Daniel S. 1996. Labor demand. Princeton, NJ: Princeton University Press.

Hart, Robert A. 1987. Working time and employment. Boston: Allen and Unwin.

Hart, Robert A., and Peter G. McGregor. 1988. The returns to labour services in West German manufacturing industry. European Economic Review 32:947-63.

Holm, Pasi, and Kiander Jaakko. 1993. The effects of work sharing on employment and overtime in finnish manufacturing 1960-87: Comparison of three alternative models. Applied Economics 25:801-10.

Kahn, Sulamit B., and Kevin Lang. 1995. Causes of hours constraints: Evidence from Canada. Canadian Journal of Economics 28:914-28.

Leslie, Derek G. 1991. Modeling hours of work in a labour services function. Scottish Journal of Political Economy 38:19-31.

Leslie, Derek, and John Wise. 1980. The productivity of working hours in UK manufacturing and production industries. Economic Journal 90:74-84.

Marchand, O., D. Rault, and E. Turpin. 1983. Des 40 heures aux 39 heures: Processus et reactions des enterprises. Economie et Statistique 3-15.

Stratton, Leslie S. 1996. Are 'involuntary' part-time workers indeed involuntary? Industrial and Labor Relations Review 49:522-36.

Trejo, Stephen J. 1991. Overtime pay regulation on worker compensation. American Economic Review 81:719-40.

Trejo, Stephen J. 1993. Overtime pay, overtime hours, and labor unions. Journal of Labor Economics 11:253-78.

U.S. Bureau of Census. 1958-1994. Annual survey of manufactures.

U.S. Bureau of Census. 1972, 1977. Census of manufactures.

U.S. Bureau of Economic Analysis. 1972-1978. Survey of current business.

U.S. Bureau of Labor Statistics. 1978. Employment and earnings.

U.S. Bureau of Labor Statistics. 1978. Industrial production and capacity utilization and industrial material.

U.S. President. 1978. Manpower report of the President.

van Ginneken, Wouter. 1984. Employment and the reduction of the workweek: A comparison of seven European macro-economic models. International Labour Review 123:35-52.

White, Michael, and Abby Ghobadian. 1984. Shorter hours in practice. London: Policy Institute Studies.

Whitley, J. D., and R. A. Wilson. 1986. The impact on employment of a reduction in the length of the working week. Cambridge Journal of Economics 10:43-59.