Wages, productivity, and work intensity in the Great Depression.

• Author: Darby, Julia

1. Introduction

   One of the most interesting puzzles concerning the behavior of real wages over the business cycle is their failure to adjust downward in the face of exceptional increases in unemployment during the Great Depression. In fact, evidence from the United States supports the view that real wages were not merely unresponsive to unemployment changes at this time but apparently positively related (Bernanke and Powell 1986). One potential reason is that indicators of external market conditions, such as the rate of unemployment, only partially represent the key forces acting on the wage. Firms' intensive margins matter. Theories of rent sharing, efficiency wages, and implicit contracts recognize the importance of within-company implicit or explicit agreements that serve to shield workers, at least in part, against excessive fluctuations in per period earnings stemming from external market forces.

   Bernanke (1986) provides perhaps the best known attempt to tackle the puzzle of counter-cyclical U.S. wages in the 1930s. This work brings the intensive margin prominently into play by emphasizing the role of hours of work. Weekly hours fell in response to the severe cyclical downturn. (1) However, if hours had been allowed to fall by the fully required amount, any value to workers of increased leisure would have been far more than offset by their loss of consumption due to reduced weekly earnings. Firms were constrained by workers' reservation utilities from cutting earnings to the same extent as the hours reductions with the result that average hourly earnings could remain constant, or even rise, as labor demand fell. Bernanke tests this story with industry-level earnings equations in which nominal weekly earnings are expected to relate positively to weekly hours and to industry employment as well as positively to workers' reservation utilities as captured by a group of variables that include union power and the cost of living.

   In Bernanke's story, the firm cuts working time in response to a demand fall, but, to ensure that employees turn up for work, it may feel constrained not to cut earnings to the same extent. This does not rule out the possibility, assuming diminishing returns, that hourly productivity remained fairly stable. We also emphasize the importance of the intensive margin. However, we concentrate on the fact that hourly labor productivity in manufacturing fell considerably during the period 1929-1933. (2) This meant, effectively, that work intensity reduced as represented by an increased excess of total paid-for to actual effective hours worked. We are concerned to find out whether this change in work intensity directly impacted on the wage.

   Technological and organizational constraints, scheduling requirements of suppliers and customers, and working time custom and practice may have variously prevented full downward hours adjustment to the severe fall in product demand experienced during the early 1930s. The implied reductions in hourly work intensity may have resulted from, among other possibilities, reductions in the speed of production throughout or in the number of required job tasks per unit of time or even through increases in the length of daily rest periods. In effect, changes in work intensity offered a means, alongside changes in earnings and employment, of adjusting to the new trading climate. In our setup, management and workers seek to reach agreement on the desired mix of earnings levels, labor inputs (workers and hours), and the degree of work intensity. There is some precedent for adopting this modeling approach. In a firm-union bargaining context, Johnson (1990) argues strongly that work intensity is an issue on collective bargaining agendas.

   Essentially, we follow an important paper by Taylor (1970) in this journal by proxying work intensity within an empirical wage specification that also embraces the unemployment rate. The latter variable enters our model via its influence on compensation in workers' alternative employment. Following Darby, Hart, and Vecchi (2001), our arguments are formalized within a simple efficient bargaining framework in which earnings, employment, hours and work, and work intensity are choice variables. We undertake empirical tests on U.S. manufacturing using a data set originally constructed and analyzed by Bernanke and Parkinson (1991).

2. An Efficient Bargain

   Ignoring the capital stock, (3) the firm's production function is given by

   Q = F([theta], h, N), (1)

   with F' > 0, F"

   Also ignoring fixed costs of employment for simplicity, (4) profit is expressed as

   [pi] = pF([theta], h, N) - yN, (2)

   where p is the product price and y is average weekly earnings. Specifically, y = wh, where w is the average hourly wage rate.

   For the representative worker, positive utility derives from wage earnings, while disutility stems from greater work intensity over the workweek and from the loss of leisure. Assuming fixed disutilities of work intensity and hours, utility is expressed as

   u = u(y - [gamma][theta]h - [beta]h - [y.sup.*]), (3)

   where [y.sup.*] is weekly compensation in alternative employment and [beta] and [gamma] are constants. (5) Assuming that the worker is risk neutral, or u' > 0, u" = 0, and aggregating over the whole workforce, N, gives workers' utility as

   U = N(y - [gamma][theta]h - [beta]h - [y.sup.*]). (4)

   The generalized Nash bargain (Svejnar 1986) is the solution to the problem

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

   where [alpha] represents workers' relative bargaining power (or "strength"), with [alpha] [member of] {0, 1}. From the first-order conditions, we obtain

   p[F.sub.h] /N = [beta] + [gamma][theta], (6)

   or the average marginal product of hours is equal to the cost of employing an extra hour. This cost is equal to the marginal disutility of hours worked. Similarly, we obtain

   p[F.sub.[theta]] / N = [gamma]h, (7)

   that is, the average marginal product, and marginal disutilities of effort are equated.

   Optimal employment is achieved by equating marginal value product to a worker's opportunity cost of work, or

   p[F.sub.N] = [gamma][theta]h + [beta]h + [y.sup.*]. (8)

   Of key importance to present developments, the equilibrium wage (6) is given by

   y = [alpha] pQ / N + (1 - [alpha])p[F.sub.N] (9)

   If the workforce has no bargaining power, or [alpha] = 0, the firm is on its demand curve, with marginal product equal to the marginal cost of an additional worker. At the other extreme, [alpha] = 1, the firm receives zero profit.

   Combining Equations 8 and 9 produces

   y = [alpha] pQ / N + (1 - [alpha])([gamma][theta]h + [beta]h + [y.sup.*]), (10)

   and this can be written in hourly terms as

   w = [[phi].sub.0] + [[phi].sub.1] pQ / Nh + [[phi].sub.2][[theta] + [[phi].sub.3] [w.sup.*], (11)

   where [w.sup.*] is the outside hourly wage ([y.sup.*]/h), (7) and [phi]s are parameters. This is our core wage equation: The wage rate is dependent on hourly productivity, hourly work intensity, and the outside hourly wage.

   As will be seen in the following section and beyond, our approach to estimation allows us to distinguish between long- and short-run influences on the wage. With this in mind, and without detracting significantly from our basic story, we believe that there are advantages to extending our interpretation of the roles of productivity and work intensity somewhat beyond the confines of our simple model. Rather than seek to reach agreement over current productive performance, we assume that the parties link the wage to potential productivity. (8) We can think of potential productivity as the maximum expected hourly output when all factors are fully utilized. Corresponding wage increases would depend on long-term technical, organizational, and human capital improvements. The work intensity term then serves to account for periods when actual productivity falls short of potential productivity and the parties recognize shorter-term wage adjustments may need to accommodate this.

   An immediate gain from these interpretations is that we can take advantage of the simple intensity expression of Fair (1985). This is given by

   [theta] = [phi] / [phi] *, (12)

   where [phi] = Q/Nh...