The Factor Share Approach to Production Function “Estimation”: Actual or Estimated Equilibrium Shares?

Abstract

For years agricultural economists have been concerned with obtaining reliable estimates of production function parameters. Among other reasons, such estimates are needed to address policy issues involving resource misallocation, supply response, and factor demand in agriculture. The appeal of production function approaches to such problems, as contrasted with direct estimation of product supply and factor demand relationships, is with richness of model for addressing cross-price effects and matters of resource allocation. However, as is well known, problems of multicollinearity and technological change have thwarted most efforts to obtain reliable estimates of aggregate production elasticities by direct estimation (Doll; Rosine and Helmberger). In an effort to circumvent multicollinearity barrier posed by direct estimation, Tyner and Tweeten (1965) indirectly estimated aggregate production elasticities for U.S. agriculture using a factor share approach. Noting that in equilibrium, factor shares equal factor elasticities for an industry comprised of profitmaximizing firms, Tyner and Tweeten synthesized a Cobb-Douglas production function by estimating equilibrium factor shares based on historical data and Nerlove partial adjustment model. Equilibrium factor shares were estimated individually for each of nine input categories assuming that actual adjustment between any two years was a constant proportion of extent of own-factor disequilibrium. Estimates were developed for several decades by including dummy variables in model. In a subsequent article Tyner and Tweeten (1966) developed estimates of resource misallocation, product supply elasticity, and factor demand elasticities based on their indirectly estimated CobbDouglas production functions. In 1974 Rosine and Helmberger published an article with a similar intent. They also explored several macro policy issues based on a synthesized Cobb-Douglas production function for U.S. agriculture. They used a simpler model than Tyner and Tweeten, by assuming that production elasticities were given by actual factor shares. In effect, Rosine and Helmberger assumed instantaneous adjustment to equilibrium thereby avoiding numerous estimation difficulties. (See writings of D. Gale Johnson in 1948 and Ruttan and Stout in 1960 for examples of earlier expressions of interest in factor shares.) To develop normative estimates of production elasticities following a factor share approach, it seems clear, a priori, that Tyner-Tweeten approach should be preferable conceptually to that of Rosine and Helmberger. In words of Tyner and Tweeten, the use of [actual] factor shares as production elasticities trades intercorrelation problem for dubious assumption that economic equilibrium prevails (1965, p. 1462). The purpose of this paper is to evaluate practical effects of assumption of continual economic equilibrium (instantaneous adjustment) on production elasticity estimation.