© Blackwell Publishing Ltd/University of Adelaide and Flinders University of South Australia 2004. Blackwell Publishing, Ltd. Oxford, UK AEPA Australian Economic Papers 0004-900X © Blackwell Publishing 2004 September 2004 43 3 ORIGINAL ARTICLE THE ATKINSON INEQUALITY MEASURE AUSTRALIAN ECONOMIC PAPERS SEPTEMBER THE ATKINSON INEQUALITY MEASURE AND ITS SAMPLING PROPERTIES: BAYESIAN AND CLASSICAL APPROACHES DUANGKAMON CHOTIKAPANICH Monash University JOHN CREEDY* University of Melbourne This paper examines several Bayesian methods of obtaining posterior probability density functions of the Atkinson inequality measure and its associated social welfare function, in the context of grouped income distribution data. The methods are compared with asymptotic standard errors. The role of the number of income classes is investigated using a simulated distribution. If only a small number of groups is available in published data, there is a clear gain from generating the posterior probability density function when using an explicit income distribution assumption. Even with a small number of groups, the Bayesian approach gives results that are close to the sample values obtained using the corresponding individual observations. I. Introduction Extensive use is made of the Atkinson (1970) measure in comparing the degree of inequality in different distributions. However, few empirical studies examine the sampling properties of estimates. This paper proposes a Bayesian method of estimating the Atkinson measure and its associated abbreviated social welfare function, along with their precision, by obtaining the pos- terior probability density function. The results obtained using Bayesian methods are compared with those generated using a classical approach. The large sample properties of the estimates of Atkinson inequality and social welfare measures are obtained using the results given by Thistle (1990). 1 The Bayesian approach suggested here is designed to overcome the inherent loss of informa- tion arising from income grouping, which is regularly used by statistical agencies. Those wish- ing to make cross-country comparisons, or to measure changes in inequality over a longer period of time, are typically forced to use published grouped data. The information provided with grouped data is often not ideal. For example group means are not always given and it is unusual to have a large number of groups. The present paper compares the results of using different types of information. For example, the use of alternative assumptions regarding the distribution of income as a whole and the distribution of mean income within each group are discussed. * Correspondence: John Creedy, Department of Economics, University of Melbourne. Email: jcreedy@unimelb.edu.au. This research was supported by a Melbourne University Faculty of Economics and Commerce Research Grant. We have benefited from discussions with Bill Griffiths and helpful suggestions by two referees of this journal. 1 For general discussions of the large sample properties of inequality measures, see Cowell (1999) and Giorgi (1999).