A GENERALISED method of moments approach to fitting income distributions with limited/aggregated data

Accurate measurement of global income levels and trends are crucial if governments and individuals wish to monitor efforts to alleviate widespread poverty and high income inequality. Estimating these global levels and trends firstly require adequate modelling of income distributions at a country level. A major problem encountered when empirically modelling these country specific income distributions is that the passively generated data is only available in limited, aggregated forms. Chotikapanich, Griffiths and Rao (CGR) [1] attempt to overcome these limitations by estimating country specific parameters of a beta-2 distribution with a particular implementation of a Generalised Method of Moments (GMM) framework. While the GMM estimator is a natural candidate for dealing with aggregated data, the CGR implementation was incomplete and as a result the estimator was not the most efficient and it was not feasible to compute the standard errors of the parameters. This research addresses these shortcomings by completing the approach and consequently deriving the most asymptotically efficient estimator as well as allowing for the derivation of the asymptotic covariance. This research also develops the GMM approach to estimate parameters of the Singh-Maddala distribution which is a commonly used income distribution model. The thesis also reports results from a simulation experiment designed to assess the robustness of the estimated parameter values to different levels of aggregation.