Dynamic Interrelated Factor Demand Systems: The United Kingdom 1950-78

Abstract

In a recent paper Berndt et al. (1979) proposed a new method for the estimation of factor demand systems by combining the Eisner-Strotz (1963) Treadway (1969; 1974) internal cost of adjustment model with some recent developments in duality theory. They were able to derive a set of factor demand equations consistent with firms' intertemporal cost minimisation objectives. This is a great improvement on the existing literature where it is usually assumed that adjustment coefficients are fixed (see for example Brechling (1975)) and the authors are to be applauded for their ingenious contribution. ' However, their solution is in several respects inadequate. In their model output is exogenous so that the only decision to be made is that of purchasing inputs. Clearly this is not an appropriate characterisation of the behaviour of a representative firm. But the exogeneity assumption has further undesirable implications. Their approach led the authors to select a quadratic approximation to the cost function. An intertemporal minimisation problem is then solved and a dynamic version of the Shephard lemma is used to derive the demand functions for variable factors; the demands for quasi-fixed factors are obtained from the first order conditions. In addition to the needless complexity that this approach entails the demand functions for variable factors are linear. Since the set of technologies that generate linear demand functions does not include the Cobb-Douglas, C.E.S. or Trans-log functional form, this property of their model is extremely suspect. Finally, for reasons not explained, the equations for quasi-fixed factors are linearised about a stationary point. The purpose of the research reported in this paper is to estimate dynamic cost of adjustment models by direct methods which avoid the problems mentioned above. A non-linear differential equation model of aggregate output, employment, and capital accumulation for the United Kingdom, 1950-78 is estimated using continuous time techniques. The major finding