A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Bioeconomic analysis of aquaculture's impact on wild stocks and biodiversity

Anderson theorizes that development of the aquaculture of a species of fish (also captured in an open-access fishery) favours the conservation of its wild stocks, if competitive market conditions prevail. However, this theory is shown to be subject to significant limitations. While this is less so within his model, it is particularly so in an extended one outlined here. The extended model allows for the possibility that aquaculture development can impact negatively on wild stocks thereby shifting the supply curve of the capture fishery, or raise the demand for the fish species subject both to aquaculture and capture. Such development can threaten wild stocks and their biodiversity. While aquaculture development could in principle have no impact on the biodiversity of wild stocks or even raise aquatic biodiversity overall, its impact in the long-term probably will be one of reducing aquatic diversity both in the wild and overall.

Comparison of funding and demand for the conservation of the charismatic koala with those for the critically endangered wombat Lasiorhinus krefftii

This study contrasts the actual conservation spending and the Australian public’s demand for conservation funding for two Australian mammal species, the koala and the northern hairy-nosed wombat. It involves a survey of 204 members of the Australian public. Willingness to fund conservation action to protect the northern hairy-nosed wombat was found to be higher than that for the koala despite the koala’s immense popularity. The critically endangered status of the northern-hairy nosed wombat and the more secure conservation status of the koala is a factor likely to have influenced the comparative willingness-to-pay decisions. Actual annual conservation expenditure for both species is lower than the estimated aggregate willingness-to-pay for their conservation. Furthermore, conservation funding for the koala is much more than that for the northern hairy-nosed wombat even though the estimated public willingness-to-pay (demand) for funding koala conservation was less than for this wombat species. Reasons for this are suggested. They may also help to explain misalignment between demand for conservation funding of other species involving differences in charisma and endangerment.