Compositional Data Analysis and Zeros in Micro Data

The application of compositional data analysis methods in economics has some attraction. In particular, this methodology ensures that the stochastic component of budget share models will satisfy the restriction of shares to the unit simplex. The methodology relies upon the use of "log-ratios" in the statistical analysis. Such an approach is not possible when the data to be analyzed includes observations where the observed budget share is zero. We, therefore, extend the methods of compositional data analysis to the situation where the data to be analyzed includes 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 Australian Household Expenditure Survey yielding estimates for a system of Engel curves.