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.

An Economic Analysis of the Legal Concept of Trustees' Power of Investment

Authorised trustee status is a legal concept which has economic implications; one of the major implications is that it assists in the direction of investment funds into particular securities and areas of the economy. The concept of authorised trustee status, while attempting to achieve specific outcomes for the beneficiaries of trusts cannot be relied upon to secure these results. Economic analysis of the role of the trustee maintains that this role is one of portfolio manager; a role which is complex but which is explicable in terms of definable procedures and practices. The role of trustee as portfolio manager is one which requires greater financial knowledge than can be assumed is possessed by all trustees. The trustee as portfolio manager is required to maintain a review of decisions make under powers to invest trust assets. A solution to the problem of authorised trustee status is proposed. The solution takes two parts: the first is the adoption of the prudent person approach but with the codification of duties of the trustee and the explicit listing of the factors that a trustee should consider in using the investment powers. The second part of the proposed solution is to link the investment powers of trustees to the best practice features of securities advisers who are now licensed by a regulatory body, the Australian Securities and Investment Commission.