Journal Article On Stochastic Models of Size Distributions Get access A. F. Shorrocks A. F. Shorrocks London School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 42, Issue 4, October 1975, Pages 631–641, https://doi.org/10.2307/2296800 Published: 01 October 1975

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[An additively decomposable inequality measure is one which can be expressed as aweighted sum of the inequality values calculated for population subgroups plus the contribution arising from differences between subgroup means. The paper derives the entire class of measures which are additively decomposable under relatively weak restrictions on the form of the index. The subclass of mean indepedent measures turns out to be a single parameter family which includes thesquare of the coefficient of variation and two entropy formulae proposed by Theil.]

[The paper explores some of the issues involved in constructing measures of mobility when the data are provided in the form of a transition matrix. An initial set of axioms is proposed which is inconsistent. They can, however, be reconciled if empirically unlikely transition matrices are eliminated from consideration. The paper then discusses the problem of comparing matrices not defined over the same interval. An index based on the convergence speed in a Markvov chain process is able to compensate for differing time periods.]

THE age profile of individual asset holdings is frequently supposed to follow a hump pattern, increasing during the working lifetime and declining in later years. The theoretical explanation of such a relationship is firmly established, since it is a characteristic feature of life-cycle saving models. However, the empirical evidence has never been critically examined. A number of studies based on sample survey information have been regarded as confirming this hump pattern, but on closer examination the evidence is far from conclusive. Moreover the survey results conflict fundamentally with alternative estimates of the age-wealth relationship derived from estate tax data. This paper begins in section II by examining this basic conflict. In the following section the relevance of cross-section studies is questioned, and a cohort is identified whose lifetime wealth characteristics can be studied. The sequence of observed wealth distributions for this cohort is obtained by selecting successive ten years age groups from the Estate duty statistics at intervals of a decade. Section IV is devoted to an analysis of the variation in the composition of any cohort as it ages. These composition changes arise from the fact that wealthier individuals have a lower mortality rate and therefore tend to become a larger proportion of the surviving cohort independently of accumulation behaviour. In these circumstances the characteristics of the representative individual will not necessarily correspond to the representative behaviour of the group. It is, however, possible to correct for this change in composition so that the empirical estimates can be compared with the predictions of economic theory.