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

Griffiths, W. E., Hill, R. C. and O'Donnell, C. J. (2006). A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model. In M. Holt and J-P. Chavas (Ed.), Essays in Honor of Stanley R. Johnson (pp. 1-13) Online: Berkley Electronic Press.

Author Griffiths, W. E.Hill, R. C.O'Donnell, C. J. A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model Essays in Honor of Stanley R. Johnson Online Berkley Electronic Press 2006 Other not found M. HoltJ-P. Chavas 1 13 13 21 2006 eng 340302 History of Economic Thought729999 Economic issues not elsewhere classified780101 Mathematical sciencesBX 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. BX no ISBN available, electronic publication only OCLC # 212379500

 Document type: Book Chapter Excellence in Research Australia (ERA) - Collection School of Economics Publications

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