Asymptotic Estimation Of The E-Gini Index

Under minimal assumptions on the distribution of income, we demonstrate that Chakravarty's empirical (1988, International Economic Review 29, 147–156) E-Gini index is consistent and asymptotically normal. We also derive an explicit formula for the asymptotic variance of the index and then construct a consistent and computationally straightforward estimator for it.Sincere thanks are due to the co-editor Oliver B. Linton and two anonymous referees whose constructive criticism, advice, and queries helped me in reshaping the paper considerably. As advised by a referee, I had the great pleasure of communicating with Garry F. Barrett and Stephen G. Donald and learning about their interesting and closely related results. The starting point of my work on the project was correspondence with Joseph L. Gastwirth in the spring of 2000 that resulted in our joint work on the S-Gini index. I am grateful to Joseph L. Gastwirth for his time, his advice, and his numerous suggestions that followed. The help, in addition to interest in the project, by Ying Zhang of the Statistical Laboratory at the University of Western Ontario is greatly appreciated; the analysis of the dependence of σF,α2 on parameters presented in Table 1 is due to her. This research was partially supported by an NSERC of Canada individual research grant at the University of Western Ontario.