In theis paper binomial choce models of order 1 and 2 are distinguished. They are all based on 'F(X t beta)', where 'F(.)' is some cumulative distribution function. In usual order 1 models, 'X t' consists of original explanatory variables 'W tj', while order 2 models also use squares and products of 'W tj', thus making 'X t beta' a second order polynomial in 'W tj'. We use the cumulativwe distribution function of the two-parameter family of skewed Student -'t' distributions as the functional form of 'F'. This allows us to test special cases, which are based on a symmetric 't' distribution or on a normal distribution (the probit model). In the (skewed) Student case (with unknown degrees of treedom), the likelihood function does not integrate to a constant and the ML estimator has unknown properties. Also, in order 2 models multicollinearity can be a severe problem. Hence we advocate the Bayesian approach with proper priors for the parameters and propose the Metropolis-Hastings MCMC algorithms to draw from the posterior. Our example uses the proposed Bayesian model and the data on consumer loans (from 39040 bank account) in order to assess risk of an individual loan. Empirical results show that our order 2 model cannot be reduced to its order 1 submodel. Also, the CDF of the Skewed -'t' distribution with very low degree of freedom and strong left skewness is most adequate from the statistical viewpoint, making the probit model unsatisfactory.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
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