William E. Griffiths

Using Time-Series and Cross-Section Data to Estimate a Production Function with Positive and Negative Marginal Risks

Abstract Two production-function models with error components for time and firms and a heteroscedastic disturbance are proposed. Unlike previous models, these two permit the variance of output to increase or decrease as one of the inputs is increased. When the models and some suggested estimators are applied to the pastoral zone of eastern Australia, the results indicate that labor, water, and possibly fencing, are likely to reduce the variance of wool production; and that sheep, and buildings and land, are likely to increase the variance.

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.

Estimation of Actual Response Coefficients in the Hildreth-Houck Random Coefficient Model

Abstract When the response coefficients in the general linear model are regarded as random variables, the mean of the distribution of these coefficients can be estimated using methods suggested by Hildreth and Houck. This article derives the minimum variance, linear, unbiased estimator for the actual response coefficients which were realized over the sample period. One might suspect that the best estimator of the mean of the response coefficients is also best when estimating the actual response coefficients. This is shown to be false.

Probability distributions for economic surplus changes: the case of technical change in the Australian wool industry.

Mullen, Alston and Wohlgenant (1989) (MAW) examined the distribution of the benefits of technical change in the Australian wool industry. Their conclusions are revisited by examining the probability distributions of changes in the welfare measures, given uncertainty about their model parameters. Subjective probability distributions are specified for the parameters and correlations among some of the parameters are imposed. Hierarchical distributions are also used to model diverse views about the specification of the subjective distributions. A sensitivity elasticity is defined through the estimation of a response surface to measure the sensitivity of the estimated research benefits to individual parameters. MAW’s conclusions are found to be robust under the stochastic approach to sensitivity analysis demonstrated in this article.

Small Sample Properties of Probit Model Estimators

Abstract When maximum likelihood estimates of the coefficients in a nonlinear model such as the probit model are obtained there are a number of asymptotically equivalent covariance matrix estimators that can be used. These covariance matrix estimators are typically associated with different computer algorithms. For example, with the Newton–Raphson algorithm the inverse of the negative of the Hessian matrix from the log-likelihood function is used; with the method of scoring the inverse of the information matrix is used; and with a procedure proposed by Berndt, Hall, Hall, and Hausman (1974), the inverse of the outer product of the first derivatives of the log-likelihood function is used. Although these three estimators are asymptotically equivalent, their performance can vary in finite samples. The main objective of this article is to use a Monte Carlo experiment to investigate the finite sample properties of the three covariance matrix estimators, in the context of maximum likelihood estimation of the pr...

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.

A Monte Carlo evaluation of the power of some tests for heteroscedasticity

Abstract Szroeters asymptotically normal test outperforms the Goldfeld-Qu2ndt test, the Breusch-Pagan Lagrange multiplier test and BAMSET, when it is possible to order the observations according to increasing variance. With no prior information on variance ordering, BAMSET is best. Some observations concerning degree of heteroscedasticity and model specification are made.

On Calculation of the Extended Gini Coefficient

The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator obtained by approximating the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or less groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.

Global income distributions and inequality, 1993 and 2000: incorporating country-level inequality modeled with beta distributions

Using a method-of-moments estimator, flexible three-parameter beta distributions are fitted to aggregate country-level income data to overcome an untenable assumption of previous studies that persons within each income group receive the same income. Regional and global income distributions are derived as weighted mixtures of country-specific distributions. Analytical expressions for Gini and Theils measures of inequality at country, regional, and global levels are derived in terms of the parameters of the beta distributions. Application to data for 91 countries in 1993 and 2000 reveals a high degree of global inequality, with evidence of declining inequality, largely attributable to growth in China.

On the relative efficiency of estimators which include the initial observations in the estimation of seemingly unrelated regressions with first-order autoregressive disturbances

Abstract The generalized least squares estimator for a seemingly unrelated regressions model with first-order vector autoregressive disturbances is outlined, and its efficiency is compared with that of an approximate generalized least squares estimator which ignores the first observation. A scalar index for the loss of efficiency is developed and applied to a special case where the matrix of autoregressive parameters is diagonal and the regressors are smooth. Also, for a more general model, a Monte Carlo study is used to investigate the relative efficiencies of various estimators. The results suggest that Maeshiro (1980) has overstated the case for the exact generalized least squares estimator, because, in many circumstances, it is only marginally better than the approximate generalized least squares estimator.