A quantitative estimate of the elasticity a requires values for eKH and for the average value tjh the value of this elasticity in the case of the “steady-state” factor ratio around which one considers perturbations). Using (2.5), the latter parameter may be calibrated from the average labor share, given an estimate of the average markup, resulting in a = (1 — “ !)• (In this last expression, all symbols refer to the average or steady-state values of the variables.)
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With a markup \x near one, a labor share of .7 and an elasticity of substitution Ckh of .5, this formula gives a value of a equal to -.4. Table 2 reports the resulting correlations between ft and predicted declines in GDP for markups based on both the nonfinancial corporate and the private labor shares. Not surprisingly, markups are now much more countercyclical. However, the contemporaneous correlation of the markup with detrended output is still smaller in absolute value than the correlation with lagged output. Also, as in the case where we do not adjust the labor share, the correlations with leads of output are greater than the contemporaneous correlation. These are actually positive for output led more than 3 quarters.
In deriving (2.5) – (2.7), we assume constant returns to scale. An important reason why this may be inaccurate is the presence of overhead costs. Particularly relevant to the above calculations would be the existence of overhead labor. Suppose that each firm’s production function16 is of the form Y = F(K.z(H — #)), where F is homogeneous of degree one as before, and H > 0 represents “overhead labor” that must be hired regardless of the quantity of output that is produced. Note that an overhead labor requirement implies increasing returns (average cost exceeding marginal cost), although marginal cost remains independent of scale.
where 77# now refers to the elasticity of output with respect to the effective non-overhead labor input. Under this definition, 7jH is again constant in the case that F takes the Cobb-Douglas form, and countercyclical if the elasticity of substitution between capital and labor is less than one. The new factor in (2.8), 77377, is a monotonically decreasing function of H if H > O.18 Allowing for overhead labor thus provides a further reason to regard markups as more countercyclical than is indicated by the labor share alone. A similar conclusion is reached if one assumes fixed costs in production that do not take the form of overhead labor alone, e.g., if one assumes a production function of the form
It is easily seen that one must have p