Economics - Research Publications
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ItemGibbs samplers for a set of seemingly unrelated regressions( 2004-08)Bayesian estimation of a collection of seemingly unrelated regressions, referred to asa ‘set of seemingly unrelated regressions’ is considered. The collection of seeminglyunrelated regressions is linked by common coefficients and/or a common errorcovariance matrix. Gibbs samplers useful for estimating posterior quantities aredescribed and applied to two examples – a set of linear expenditure functions and acost function and share equations from production theory.
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ItemEstimating and Combining National IncomeDistributions using Limited Data( 2005-02)A major problem encountered in studies of income inequality at regional and globallevels is the estimation of income distributions from data that are in a summary form.In this paper we estimate national and regional income distributions within a generalframework that relaxes the assumption of constant income within groups. A techniqueto estimate the parameters of a beta-2 distribution using grouped data is proposed.Regional income distribution is modelled using a mixture of country-specificdistributions and its properties are examined. The techniques are used to analysenational and regional inequality trends for eight East Asian countries and twobenchmark years, 1988 and 1993.
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ItemSurvival on the Titantic: Illustrating Waldand LM Tests for Proportions and Logits( 2006-06)Students are very interested in lecture examples and class exercisesinvolving data connected to the maiden voyage and the sinking of the liner Titanic.Information on the passengers and their fate can be used to explore relationshipsbetween various tests for differences in survival rates between different groups ofpassengers. Among the concepts examined are tests for differences of proportionsusing a normal distribution, a chi-square test for independence, a test for the equalityof two logits and a test for the significance of the coefficient of a binary variable inlogit model. The relationship between Wald and LM test statistics is also examined.Two related examples are given, one to be used for step by step instructional purposesand one to be given as an exercise to students.
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ItemBayesian Assessment of Lorenz andStochastic Dominance in Income Distributions( 2006-02)Hypothesis tests for dominance in income distributions has received considerableattention in recent literature. See, for example, Barrett and Donald (2003), Davidsonand Duclos (2000) and references therein. Such tests are useful for assessing progresstowards eliminating poverty and for evaluating the effectiveness of various policyinitiatives directed towards welfare improvement. To date the focus in the literaturehas been on sampling theory tests. Such tests can be set up in various ways, withdominance as the null or alternative hypothesis, and with dominance in eitherdirection (X dominates Y or Y dominates X). The result of a test is expressed asrejection of, or failure to reject, a null hypothesis. In this paper we develop and applyBayesian methods of inference to problems of Lorenz and stochastic dominance. Theresult from a comparison of two income distributions is reported in terms of theposterior probabilities for each of the three possible outcomes: (a) X dominates Y, (b)Y dominates X, and (c) neither X nor Y is dominant. Reporting results about uncertainoutcomes in terms of probabilities has the advantage of being more informative than asimple reject / do-not-reject outcome. Whether a probability is sufficiently high or lowfor a policy maker to take a particular action is then a decision for that policy maker.The methodology is applied to data for Canada from the Family Expenditure Surveyfor the years 1978 and 1986. We assess the likelihood of dominance from one timeperiod to the next. Two alternative assumptions are made about the incomedistributions –Dagum and Singh-Maddala – and in each case the posterior probabilityof dominance is given by the proportion of times a relevant parameter inequality issatisfied by the posterior observations generated by Markov chain Monte Carlo.
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ItemA Gibbs' Sampler for the Parameters of a Truncated Multivariate Normal Distribution( 2002-09)The inverse distribution function method for drawing randomly from normal andtruncated normal distributions is used to set up a Gibbs' sampler for the posterior densityfunction of the parameters of a truncated multivariate normal distribution. The sampler isapplied to shire level rainfall for five shires in Western Australia.
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ItemIncluding Prior Information in Probit Model Estimation( 2001-10)The effects of including different kinds of prior information in estimation of the probit model is examined within the framework of Bayesian inference. Of interest is the effect on posterior information for coefficients, probabilities and elasticities. In a model designed to explain choice between fixed and variable interest-rate mortgages, we show that using Bayesian inference to include inequality information on the signs of coefficients yields inferences about probabilities and elasticities that are substantially different from those obtained using maximum likelihood estimation. In a second model, concerned with state voting behavior, we find that putting prior information on probabilities, rather than coefficients, has a dramatic effect on the posterior density functions for the model coefficients, probabilities and elasticities.
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ItemBayesian inference in the seemingly unrelated regressions model( 2001-04)Zellner's idea of combining several equations into one model to improve estimation efficiency (Zellner 1962) ranks as one of the most successful and lasting innovations in the history of econometrics. The resulting seemingly unrelated regressions (SUR)model has generated a wealth of both theoretical and empirical contributions. With the recent explosion of literature on MCMC techniques, Bayesian inference in the SUR model has become a practical reality. However, it is the author's view that, prior to the writing of this chapter, the relevant results have not been collected and summarised in a form convenient for applied researchers to implement. It is my hope this chapter will facilitate and motivate many more applications of Bayesian inference in the SUR m