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 the richness of the 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 Heimberger). In an effort to circumvent the 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 the 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 the extent of own-factor disequilibrium. Estimates were developed for several decades by including dummy variables in the 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 Heimberger published an article with a similar intent. They also explored several macro policy issues based on a synthesized

A test of the underinvestment, myopia and commodity bias hypotheses for U.S. agricultural research

“…However, the convention of deriving the output elasticity of labor as a residual means that only seven of the estimates are independent." More recently, Shumway et al (1979) have provided additional support for the factor shares approach. Griliches (1964, p. 970) found that observed factor shares in V.S.…”

“…Lyu et al (1984) and Chambers and Lee have concluded that slight decreasing returns to scale may in fact be the case. Peterson (1967), Bredahl and Peterson ( 1976) and Shumway et al ( 1979) have employed the Cobb-Douglas functional form with success. These results are taken as the empirical rationale for the maintained hypothesis of constant returns to scale in the production functions for the crop and livestock sectors.…”

A test of the underinvestment, myopia and commodity bias hypotheses for U.S. agricultural research

“…agriculture between 1949 and 1959 were statistically indistinguishable from those deduced from his estimated production function. More recently, Shumway et al (1979) have provided additional support for the factor shares approach.…”

“…962-964) was unable to reject the hypothesis of an elasticity of substitution of 1.0. Peterson (1967), Bredahl and Peterson ( 1976) and Shumway et al ( 1979) have employed the Cobb-Douglas functional form with success. Third, while there seems to be some agreement on the economies of scale question, and on the matter of the choice of functional form, very little consensus has been achieved on the value of particular output elasticities.…”

The Elasticity of Aggregate Australian Agricultural Supply: Estimates and Policy Implications

“…Three methods for estimating input shares have been used in past studies and all three are used here: the non-normalised gross output method, the normalised gross output method (normalised over capital inputs and labour only) and the total expenditure method (normalised over all inputs). Discussions of these methods can be found in Tyner and Tweeten (1965), Rayner (19706), Young (1971), Rosine and Helmberger (1974), Shumway et al (1979) and Pandey (1981).…”