On Exact Multicollinearity and the Estimation of the Cobb‐Douglas Production Function

Abstract

The assumptions of the economic model underlying the traditional Cobb-Douglas production function analysis imply that exact multicollinearity should exist among the inputs. Restricted estimation procedures may lead to parameter estimates with additional economic content. Conventional methods of input aggregation and model specification may result in biased or misinterpreted estimates.

Comparative Efficiency of Rice Farms in Central Luzon, the Philippines

“…Calculations show those for labour-area (0.77) and labour-fertiliser (0.60) to be quite high but this is not unexpected since, given a Cobb-Douglas production function, equal prices and assumed cost-minimising behaviour, all farms should use inputs in proportional (i.e., collinear) amounts at different points on the long-run expansion paths. As Doll (1974) observes, 'users of the Cobb-Douglas model who are dismayed to find multicollinearity among the independent variables should be pleased because the presence of multicollinearity serves as a verification of their economic model'.…”

“…The International Rice Research Institute has conducted a considerable number of cross-sectional studies into economic aspects of rice production over the past 20 years, but only limited information is available for tracing the impact of new rice technology over time on a similar group of farms. The 'loop' surveys in Central Luzon carried out in 1966, 1970, 1974 a notable exception and analysis of these surveys has been extensively carried out by Cordova et al The pooled data have, however, as yet not been subjected to more rigorous forms of analysis such as production function or profit function studies. One aim of the current study is to remedy the production function deficiency, to estimate marginal products of the various inputs.…”

“…This is possible using matched farm data for the period 1970-79 for 32 farms in the survey+. As Doll (1974) observes, 'it seems reasonable to consider management in a cross-section in much the same manner as technology in a time-series study. The two have much in common; neither are inputs in the conventional economic sense, both have a substantial impact on output, both may vary among firms and both are elusive to quantitative measures'.…”

Production Efficiency of Cauliflower (Brassica Oleracea Var. Botrytis) at Cirateun, West Java, Indonesia

“…i= 1 One of the weaknesses of this function when estimated by Ordinary Least Squares (OLS) is the existence of multi-collinearity (Doll, 1974). In this condition, the test is not very helpful in discriminating between a true and a false hypothesis.…”

An Index of Management Efficiency for Egyptian Agriculture: A Case Study of Large Farms

“…Hence it cannot be treated as a factor in the production function. Griliches (1957) andDoll (1974) suggest that the management coefficient in the Cobb-Douglas function should be omitted from the sum of factor coefficients which denote the returns to scale, since all farmers might be able to double their output with double inputs ~…”