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.

Prejudice against female children: Economics and cultural explanations, and India evidence

Shows how economic theories based on parental self-interest may explain parental discrimination against daughters relative to sons. However, such theories often need to be adjusted (or even discarded) to allow for altruism of parents towards their children, and to take account of cultural influences on parental desires to have children of particular gender, and care equally for their children of different gender. The latter point is illustrated by a study of two different communities. In one situated in the Santal tribal belt I West Bengal, discrimination against daughters is found to be marked and accords (given the structure of society) with predictions of economic theories based on the pursuit of parental self-interest. By contrast, it is found that although the Knondh-dominated community in Orissa experiences similar economic conditions and social structures to the West Bengal communities, parental discrimination against daughters is almost absent. The differences seem to arise from a difference between the cultural values shared by the Kondhs in Orissa and those shared by the West Bengal community consisting of Santals and Bengali Hindus. This suggests that the applicability of economic theories of the family depends significantly on the social contexts in which they are to be applied. In this respect, both social structures and cultural values are important.