Estimation of Australian Wool and Lamb Production Technologies under Uncertainty: An Error‐Components Approach

Abstract

A model of producer behavior, which explicitly accounts for both output price and production uncertainty, is formulated and estimated. If the production technology is multiplicatively separable in its deterministic and stochastic components, then the expected utility maximization problem implies cost minimization for planned or expected output. Consequently, our empirical model of three lamb-and woolproducing sectors in Australia involves the estimation of a system of input cost share and cost equations whose disturbances have an error-components structure. The empirical results are evaluated in terms of input demand elasticities, and estimates of the stochastic components of production are presented.

Imposing regularity conditions on a system of cost and factor share equations

“…Our empirical application has been motivated by the large number of regularity violations reported in the study by O'Donnell and Woodland (1995). Thus, our empirical model is based on the translog model of O'Donnell and Woodland and estimated using (a part of) their data set.…”

“…The process was repeated for each of our 23 sets of average input prices, and the means and standard deviations of these 23 samples are presented in table 2. When rounded to three decimal places, the means of the sample distributions of 8 out of 23 maximum eigenvalues are non-zero, implying there is positive probability that concavity is violated for at least 35 per cent of the price vectors, somewhat lower than the proportion of concavity violations reported by O'Donnell and Woodland (1995).…”

“…The duality approach to applied production economics often involves the estimation of £exible functional form cost or pro¢t functions. Examples include Bigsby (1994), Mullen and Cox (1996) and O'Donnell and Woodland (1995) using the translog functional form, Fisher and Wall (1990) and Shumway and Alexander (1988) using the normalised quadratic functional form, and Lopez (1980) and Lopez and Tung (1982) using the generalised Leontief functional form. Unfortunately, these estimated functions frequently violate the monotonicity, concavity and convexity conditions implied by economic theory.…”

“…In this article we illustrate how MCMC methods can be used to estimate a system of cost and factor share equations for a sector of the Australian wool-growing industry. This empirical application of the MCMC methodology is motivated by the large number of curvature violations reported in the study by O'Donnell and Woodland (1995). Although we retain most of the features of the O'Donnell and Woodland model, and we use their data set, we estimate a system of cost and factor share equations which has a less complex stochastic structure, and we focus on only one Australian woolgrowing sector (merino wool-growing) instead of three.…”

Demanda de insumos agrícolas en México un enfoque dual

“…The translog flexible functional form was developed by Christensen et al (1973). In the case of a production function, the corresponding translog cost function (Shephard's dual theory) is expressed as (Chung, 1994;O'Donnell and Woodland, 1995):…”