Three Models of Firm Behavior; Theory and Estimation, with an Application to the Dutch Manufacturing Sector

Abstract

IN the last decade much research has been done in the field of estimating the parameters of production functions. Quite recently, stress has been laid on obtaining estimates that are logically consistent within the context of a completely specified theoretical model of firm behaviour. As a first attempt, Coen and Hickman (1970) have applied the dynamic adjustment model, suggested by Dhrymes (1967), to the estimation of the parameters of the CobbDouglas (CD) function. In this paper the dynamic adjustment model has been used to estimate the parameters of the Constant Elasticity of Substitution (CES) function. In addition to this theoretical model, two other models of firm behaviour are brought forward and empirically tested, the assumptions underlying these models being deterministic and expected profit maximization, respectively. With regard to the lastmentioned model, a generalization of Hodges' (1969) result is given to include monopsony situations on the factor markets as well as a monopoly situation in the output market. In the field of estimation, a method' is presented which obtains the asymptotic variancecovariance matrix of the various maximum likelihood estimates by means of a direct estimate of the Hessian matrix of the log-likelihood function. This and the application of a direct search method to compute the maximum of the likelihood function, makes it unnecessary to calculate the untractable first and second order derivatives of a non-linear likelihood function, such as the one at hand, and provides a rather easy method for solving similar small-order non-linear estimation problems. The order of discussion will be as follows. First the theoretical models will be derived in section II. Then section III will be devoted to the data and a few problems stemming from aggregation and the use of index numbers. Finally, in section IV the results of the estimation will be presented.