Compositional data analysis and zeros in micro data

The application of compositional data analysis methods in economics has some attraction. The methodology relies upon the use of 'log-ratios' in the statistical analysis. Such an approach is not possible when the data to be analysed include observations where the observed budget share is zero. We, therefore, consider and extend the methods of compositional data analysis in the situation where the data to be analysed include observations where the observed budget share is zero. The modified compositional data methods are discussed both in statistical terms and through potential economic interpretations of the method. Further, the modified methodology is applied to the 1988-89 Australian Household Expenditure Survey yielding estimates for a system of Engel curves.