On the Service Flow from Labour
For some time economists have been perplexed by the conflict between theoretical labour demand functions which posit decreasing returns to labour and measured labour demand functions which display increasing returns. Kuh [11], Brechling [5], Brechling and O'Brien [6], Ball and St. Cyr [3], and Coen and Hickman [7] are among the economists who, in the recent past, have published articles in which the implied elasticity of output with respect to labour exceeded one. Naturally, the estimates troubled them. Most of them assumed labour explained the observed high elasticity. The labour hoarding hypothesis, developed by Oi [14] and Soligo [17], includes adjustment costs for changing the stock of labour. As a result, firms hold a buffer stock of labour which augments labour productivity in a procyclical fashion. There are a number of other explanations, however. Anderson [2] presented a model with cyclical demand, production of an intermediate product, and production hoarding that led to shortrun increasingreturns in observed labour inputwith respect to final output. Puttyclay models (i.e., positive factor substitution in the planning stage and zero factor substitution once capital is installed, see Allen [1], p. 282) can account for the observed high elasticity of output with respect to labour through a variable capital utilization rate.2 Ireland and Smyth [10] reformulated a putty-putty model (positive factor substitution at any stage) to include a variable capital utilization rate determined by a capital utilization charge. However, their assumption that the ratio of factor rental rates-the cost of utilizing capital to the cost of labour-can be approximated by a constant makes their results equivalent to a clay-clay model. In the labour demand function they derive, the coefficient commonly identified as the elasticity of output with respect to labour in a Cobb-Douglas function is actually a returns to scale coefficient. This paper suggests a simple generalization that helps bring empirical results into closer agreement with theoretical models for any type of production function. We separate manhours, the surrogate for labour in most empirical studies into two heterogeneous components, men and hours. Feldstein [9] hypothesized that increases in average hours may increase labour productivity more than proportionally. His cross-section estimates of a three-factor Cobb-Douglas function (average hours, men, capital) for British manufacturing industries tended to confirm the hypothesis.3 This paper uses Feldstein's hypothesis as a base. We derive and estimate a model that posits the service flow from labour is a non-proportional function of men and hours. The model displays the conventional characteristics of decreasing returns to men and capital, but it has increasing returns for hours. Overtime costs limit the long run demand for hours per man.