Fuzzy multidimensional poverty measurement: an analysis of statistical behaviors

Summary

Using the 2006 round of the British Household Panel Study dataset, I explore the statistical behavior of three fuzzy measures of poverty through a simulation (Monte Carlo) method. The measures [totally fuzzy (TF), totally fuzzy and relative (TFR), and integrated fuzzy and relative (IFR)] acknowledge that (1) poverty is a multidimensional concept, and (2) the ‘poor’ and ‘non-poor’ are not two mutually exclusive sets and the distinction can be ‘fuzzy’. I find that the sampling distributions of the fuzzy measures are quite normally distributed, and they are robust to arbitrary choice in the estimation as well as reliable with relatively small sample size, though there is some differences between the methods. Also, I show that they are robust to measurement errors: allowing random measurement errors in all indicators, the measures still yield strongly reliable results. Finally, I investigate the identification performance of each measure and show that IFR measure has strong consistency, while both TF and TFR measures significantly underestimate the number of people whose fuzzy index values are very high.