ON QUANTILES OF SUMS

In this paper we investigate the relationship between the quantiles of a sum of independent continuous random variables and those of its components. Results concerning this relationship are given for the special cases of symmetric distributions, gamma distributions, and for the difference of identically distributed random variables.     

The strength of primordial ties: Suburban community adaptation to school system retrenchment

Communities and local schools are attached to one another for many other reasons than the purely instrumental objectives of educating children. These highly symbolic interpenetrations of community and school include considerations of diffuse communal identity, religion, and ethnicity. Taken together with different priorities about wider educational goals, these narrower community objectives for local schools put contradictory strains on community-school relations in the heated climate of increased community participation in contracting school systems. Competing claims about the central purposes of local schools become extraordinarily salient parts of the external environment of school districts experiencing contraction, and play a major role in the process of adapting school district organizations to conditions of decline. For many citizens the desire to preserve the local symbolic and non-instrumental roles of neighborhood schools, in particular, may at times outweigh the goal of maintaining quality educational service delivery as seen from the perspective of school managers. For other citizens, the protection of quality programs, serving their children as stepping-stones to the wider society, outweighs considerations of local neighborhood solidarity and identity in adapting to declining enrollments and fiscal strains in the schools.An earlier version of this article was delivered at the 1984 Midwest Sociological Society Annual Meeting in Chicago. I am grateful to Virginia Bartot, Sally B. Kilgore, Gerald D. Suttles, and an anonymous reviewer for comments and suggestions.     

Optimal demogrants and taxes in a federal welfare state

This paper provides a framework for the simultaneous calculation of optimal commodity and income taxes in a federal framework with demogrants. The optimal income tax rate is shown to depend on a range of demographic and economic variables. Alternative models of fiscal federalism are proposed, and their implications for optimal commodity taxes and demogrants considered. Illustrative empirical evidence on Indian data confirms sensitivity of tax magnitudes to federal specification, and to assumptions about resource transfer between the federal and provincial authorities.Much of the work in this paper was done during my visit to the Scuola Superiore, S. Anna in Pisa (Italy) in the summer of 1991. The paper was revised during my visit to the Economics Research Centre, University of Western Australia, during May/June 1992. I am grateful to the staff and students of both institutions for their hospitality. I also thank two anonymous referees for helpful remarks. The disclaimer applies.     

Measurement of social development: an international comparison

PQLI and HDI are the two most popular measures of development, besides per capita income. Over the years, PQLI appears to be not much in use for regional comparisons, especially after the introduction of HDI. While PQLI considers only the physical variables—adult literacy, life expectancy at birth and infant survival rate, HDI has life expectancy at birth, educational attainment and real GDP per capita (PPP$). PQLI and HDI are similar, the main difference between the two being the inclusion of income in HDI and exclusion of the same from PQLI. In a sense, HDI represents both physical and financial attributes of development and PQLI has only the physical aspects of life. The present author took the lines of PQLI to express development in terms of physical variables and considering development as a multidimensional phenomenon, Ray (1989) [Ray, A. K. (1989). On the measurement of certain aspects of social development, Social Indicators Research (Vol. 21, pp. 35–92). The Netherlands: Kluwer Academic Publishers.] included as many as 13 physical variables to represent social development across 40 countries; no financial variable was included in the construction of composite index, termed as the Social Development Index, SDI. Incidentally, like PQLI, SDI was introduced before HDI. Unlike PQLI and HDI, SDI considers (i) a large number of indicators representing various concern areas and (ii) a set of objective methods for combining the development indicators as a composite index. Ray (1989) has been restated and updated in this article with newer cross-country information. In the present study, SDI has been constructed for over 102 countries, including 21 OECD countries, using 10 development indicators, instead of 13 indicators in the past. Apart from presenting objective methods for combining indicators into SDI, the present study asserts that SDI works better than HDI as a measure of development for an international comparison. The views expressed in the article are those of the author and not of the institution he serves.