Christopher J. O'Donnell

A Metafrontier Production Function for Estimation of Technical Efficiencies and Technology Gaps for Firms Operating Under Different Technologies

This paper presents a metafrontier production function model for firms in different groups having different technologies. The metafrontier model enables the calculation of comparable technical efficiencies for firms operating under different technologies. The model also enables the technology gaps to be estimated for firms under different technologies relative to the potential technology available to the industry as a whole. The metafrontier model is applied in the analysis of panel data on garment firms in five different regions of Indonesia, assuming that the regional stochastic frontier production function models have technical inefficiency effects with the time-varying structure proposed by Battese and Coelli (1992).

Predicting the severity of motor vehicle accident injuries using models of ordered multiple choice

This paper presents statistical evidence showing how variations in the attributes of road users can lead to variations in the probabilities of sustaining different levels of injury in motor vehicle accidents. Data from New South Wales, Australia, is used to estimate two models of multiple choice which are reasonably commonplace in the econometrics literature: the ordered logit model and the ordered probit model. Our estimated parameters are significantly different from zero at small levels of significance and have signs which are consistent with our prior beliefs. As a benchmark for comparison, we consider the risks faced by a 33-year-old male driver of a 10-year-old motor vehicle who is involved in a head-on collision while travelling at 42 kilometres per hour. We estimate that this benchmark victim will remain uninjured with a probability of almost zero, will require treatment from a medical officer with a probability of approximately 0.7, will be admitted to hospital with a probability of approximately 0.3, and will be killed with a probability of almost zero. We find that increases in the age of the victim and vehicle speed lead to slight increases in the probabilities of serious injury and death. Other factors which have a similar or greater effect on the probabilities of different types of injury include seating position, blood alcohol level, vehicle type, vehicle make and type of collision.

Measuring and Decomposing Agricultural Productivity and Profitability Change

Profitability change can be decomposed into the product of a total factor productivity (TFP) index and an index measuring changes in relative prices. Many TFP indexes can be further decomposed into measures of technical change, technical efficiency change, scale efficiency change and mix efficiency change. The class of indexes that can be decomposed in this way includes the Fisher, Tornqvist and Hicks–Moorsteen TFP indexes but not the Malmquist TFP index of Caves, Christensen and Diewert (1982). This paper develops data envelopment analysis methodology for computing and decomposing the Hicks–Moorsteen index. The empirical feasibility of the methodology is demonstrated using country-level agricultural data covering the period 1970–2001. The paper explains why relatively small countries tend to be the most productive, and why favourable movements in relative prices tend to simultaneously increase net returns and decrease productivity. Australia appears to have experienced this relative price effect since at least 1970. Thus, if Australia is a price-taker in output and input markets, Australian agricultural policy-makers should not be overly concerned about the estimated 15 per cent decline in agricultural productivity that has taken place over the last three decades.

Estimating State-Contingent Production Frontiers

Chambers and Quiggin (2000) use state-contingent representations of risky production technologies to establish important theoretical results concerning producer behavior under uncertainty. Unfortunately, perceived problems in the estimation of state-contingent models have limited the usefulness of the approach in policy formulation. We show that fixed and random effects state-contingent production frontiers can be conveniently estimated in a finite mixtures framework. An empirical example is provided. Compared to conventional estimation approaches, we find that estimating production frontiers in a state-contingent framework produces significantly different estimates of elasticities, firm technical efficiencies, and other quantities of economic interest.

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

Systems of equations comprising cost functions and first‐order derivative equations are often used to estimate characteristics of production technologies. Unfortunately, many estimated systems violate the regularity conditions implied by economic theory. Sampling theory methods can be used to impose these conditions globally, but these methods destroy the flexibility properties of most functional forms. We demonstrate how Bayesian methods can be used to maintain flexibility by imposing regularity conditions locally. The Bayesian approach is used to estimate a system of cost and share equations for the merino wool‐growing sector. The effect of local imposition of monotonicity and concavity on the signs and magnitudes of elasticities is examined.

Input Demands and Inefficiency in U.S. Agriculture

Markov Chain Monte Carlo (MCMC) methods are used to estimate a seemingly unrelated regression (SUR) system of input demand functions for U.S. agriculture. Our demand functions have flexible forms and allow for nonrandom technical inefficiency. Concavity constraints are imposed at individual data points, and the distributions of measures of relative technical efficiency are constrained to the unit interval. Results are evaluated in terms of characteristics of the posterior distributions of parameters, measures of relative technical efficiency, and other nonlinear functions of the parameters. Copyright 1999, Oxford University Press.

Using Demographic Risk Factors to Explain Variations in the Incidence of Violence Against Women

This article offers statistical support for the contention that demographic risk factors influence the incidence of some womens experiencing violence more than others. Our results were generated using a binary probit model and 6,332 observations from the 1996 Australian Womens Safety Survey. For purposes of comparison, we identified a set of benchmark demographic characteristics as those occurring most frequently in the data set and estimated that if a woman were to have all of these characteristics, the probability she would have experienced violence in the past 12 months was 6.7%. We found that the risk varied with levels of postschool education, income, ethnic background, number and age of children, marital status, and age. Employment status, school-leaving age, and socioeconomic status had no statistically significant effect on the risk of experiencing violence once other factors were considered. This analysis may provide a basis for violence reduction and prevention programs.

Optimal Paths and Costs of Adjustment in Dynamic DEA Models: With Application to Chilean Department Stores

In this paper we propose a range of dynamic data envelopment analysis (DEA) models which allow information on costs of adjustment to be incorporated into the DEA framework. We first specify a basic dynamic DEA model predicated on a number of simplifying assumptions. We then outline a number of extensions to this model to accommodate asymmetric adjustment costs, non-static output quantities, non-static input prices, and non-static costs of adjustment, technological change, quasi-fixed inputs and investment budget constraints. The new dynamic DEA models provide valuable extra information relative to the standard static DEA models—they identify an optimal path of adjustment for the input quantities, and provide a measure of the potential cost savings that result from recognising the costs of adjusting input quantities towards the optimal point. The new models are illustrated using data relating to a chain of 35 retail department stores in Chile. The empirical results illustrate the wealth of information that can be derived from these models, and clearly show that static models overstate potential cost savings when adjustment costs are non-zero.

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

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 wool-producing 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.

Data Envelopment Analysis in Small and Medium Enterprises: A Study of the Australian Food, Beverages and Tobacco Manufacturing Industry

Abstract Competitive pressures have led to growing interest in benchmarking small and medium enterprises (SMEs). We use Data Envelopment Analysis (DEA) to measure the relative efficiency of SMEs in the Australian food, beverages and tobacco manufacturing industry. Estimates of relative technical efficiency suggest that firms in this industry can, on average, produce the same level of output using approximately 20% less inputs. Estimates of relative cost efficiency suggest that firms can, on average, realise cost savings in the order of 32% by reducing both the level and mix of inputs. Tobit regression analysis is used to explain variations in efficiency levels as functions of firm and management characteristics. Results suggest that family firms and firms with low union membership are less efficient than other firms. We show how DEA can be used to identify appropriate role models (or peers) that can be used by poor performers to improve their efficiency.