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.

Comparative labor market performance of visaed and non-visaed migrants: Pacific islanders in Sydney

Using survey data for Tongan and Samoan migrants in Sydney the effects of visa restrictions on labor market performance of migrants are assessed. Univariate analysis suggests a positive association between unemployment and the unrestricted entry of Samoan step-migrants from New Zealand. A probit model of the determinants of unemployment is estimated with controls for human capital and demographic variables. While human capital endowments are important, visa restrictions do not have a significant effect on either group's employability. Implications for policy are discussed highlighting the complementarities between host country immigration policies and foreign aid programs.

Testing market efficiency: Evidence from the NFL sports betting market

This article examines the efficiency of the National Football League (NFL) betting market. The standard ordinary least squares (OLS) regression methodology is replaced by a probit model. This circumvents potential econometric problems, and allows us to implement more sophisticated betting strategies where bets are placed only when there is a relatively high probability of success. In-sample tests indicate that probit-based betting strategies generate statistically significant profits. Whereas the profitability of a number of these betting strategies is confirmed by out-of-sample testing, there is some inconsistency among the remaining out-of-sample predictions. Our results also suggest that widely documented inefficiencies in this market tend to dissipate over time.

Evaluation of liquid Bacillus thuringiensis var. israelensis products for control of Australian Aedes arbovirus vectors

Laboratory bioassay studies were conducted in southeast Queensland, Australia,: on the efficacy of Teknar (R), VectoBac (R) 12AS, and Cybate (R) (active ingredient: 1,200 international toxic units Bacillus thuringiensis var, israelensis [Bti]) against 3rd instars of the arbovirus vectors Aedes aegypti. Ae. notoscriptus, Ae. vigilax, and Ae. camptorhynchus. Probit analyses were then used to determine LD,, (median lethal dose), LD95, and lethal dose ratios (LDR). Aedes aegypti and Ae. notoscriptus, both container-habitat species, tolerated the highest Bti concentrations compared with saltmarsh Ae. vigilax and Ae. camptorhynchus. For example, the LDR for Ae. vigilax versus Ae. notoscriptus exposed to Cybate was 0.14 (95% confidence limit [CL] 0.03-0.61). Similarly, the Cybate LDR for Ae. camptorhynchus versus Ae. notoscriptus was 0.22 (95% CL 0.07-0.70). Teknar produced similar results with an LDR of 0.21 (95% CL 0.04-1.10) for Aedes vigilax versus Aedes notoscriptus. Differences in product efficacy were found when tested against the 2 container-breeding species. Cybate was less effective than Teknar with LDRs of 1.55 (95% CL 0.65-3.67) and 1.87 (95% CL 0.68-5.15) for Aedes aegypti and Ae. notoscriptus, respectively. The significant differences in susceptibility between mosquito species and varying efficacy between products highlight the importance of evaluating concentration-response data prior to contracting with distributors of mosquito control products. This information is crucial to resistance management strategies.