Normalized measures of concavity and Ross’s strongly more risk averse order

The Arrow-Pratt (A-P) definitions of absolute and relative risk aversion dominate the discussion of risk aversion and defining “more risk averse”. Ross (Econometrica 49:621–663, 1981) notes, however, that being A-P more risk averse is not sufficient for addressing many important comparative static questions. Consequently he introduces “a new and stronger measure for comparing two agents’ attitudes towards risk…”. Ross does not provide a corresponding measure of risk aversion. This paper uses a normalized measure of concavity to characterize the Ross definition of strongly more risk averse on bounded intervals. Other properties and uses of these normalized measures of concavity are also presented.     

Impossibility Results for Nondifferentiable Functionals

We examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the existence of unbiased and regular estimators, we show that if the target object is not differentiable in the parameters of the data distribution, there exist no estimator sequences that are locally asymptotically unbiased or α‐quantile unbiased. This places strong limits on estimators, bias correction methods, and inference procedures, and provides motivation for considering other criteria for evaluating estimators and inference procedures, such as local asymptotic minimaxity and one‐sided quantile unbiasedness.     

Contraceptive sterilization in Puerto Rico

For twenty years Puerto Rico has had the world’s highest prevalence of sterilization. From the 1982 Puerto Rico Fertility and Family Planning Assessment we examine whether the probability of obtaining sterilization is changing and what impact sterilization has on fertility, finding that the use of contraceptive sterilization has not declined and will probably continue to increase in Puerto Rico. Nonuse rather than temporary methods of contraception is the second most likely circumstance after sterilization. We also find that sterilization has reduced the total marital fertility rate by over 33 percent, thus having a significant effect on reducing the rate of natural increase; by all indications, it will have a greater effect in the future.     

New estimates of the vital rates of the United States black population during the nineteenth century

The difficulties of obtaining credible estimates of vital rates for the black population throughout the entire nineteenth century are overcome in this study. The methodology employed the notion of deviating networks of mortality rates for each general mortality level, which was taken from the United Nations studyThe Concept of a Stable Population. Period life tables and vital rates for intercensal periods were generated from the new estimates of the black population at each census date. The results of this study are highly compatible both with the life tables for the death-registration states in the twentieth century and the recent Coale and Rives reconstruction for the period from 1880 to 1970 and with several estimates of vital rates previously made for the mid-nineteenth century. This study places the mean life expectancy at birth for the black population during the nineteenth century at about 33.7 years for both sexes. The infant death rate (1000m (0)) is shown to have varied between 222 and 237 for females and between 266 and 278 for males. The intrinsic crude death rate centered on 30.4 per thousand during the century, while the birth rate declined from 53.2 early in the century to about 43.8 at the end.     

Migration distances: An international comparison

Comparing the level or amount of migration within different countries has been a longstanding problem because the local administrative areas commonly used as the basis for measuring migration vary greatly in size and significance within and between countries. Distance moved is a critical aspect of most concepts of migration, and measuring it would facilitate cross-national comparisons. Apparently only the United States, Great Britain, and Sweden have measured migration distances for the country as a whole, and this information is used as the basis for comparative analysis of spatial mobility.     

Timing of the transition to nonvirginity among unmarried adolescent women

This article focuses on differences between teenagers who became sexually active in early adolescence (15 or younger) and those who did so in late adolescence (16–19). It reviews research on adolescent sexual behavior and summarizes findings on factors associated with adolescent coitus. The few findings on the meaning of first coitus are also noted. A study which used a sample of already-pregnant adolescents is presented in detail. While few differences between those who first had coitus during early adolescence and those who had it later were significant, most were in the predicted direction, and none were contrary to the hypotheses. A major significant difference concerned the relationship between sex and love; those who found the two related tended to start their sexual careers later than those who did not. Policy implications of research findings are discussed, especially those relevant to sex education.This research was supported in part by Grant No. HD 11099 NICHD, and in part by Grant No. 78-499, Charles Stewart Mott Foundation.This article is a revision of a paper presented at the Annual Meetings of the Society for the Study of Social Problems, August 26, 1980, New York, N.Y.     

Impact of product proliferation on the reverse supply chain

Product variety is one of the most important advantages in highly competitive markets. However, excessive product proliferation's reducing the profit margin has caused increased focus on developing a management method for maximal profit. In a closed-loop supply chain, product proliferation affects the reverse supply chain as well as the forward supply chain. Although increasing the number of product types can better satisfy diverse customer needs, complexity in the product recycling, remanufacturing, and resale processes may erode a firm's overall profits. In this study, we develop a mathematical model for analyzing a capacitated reverse supply chain consisting of a single manufacturer and multiple retailers. We reveal closed-form solutions for the optimal batch size and maximal profit, and discuss managerial insights into how the number of products and other factors can affect both batch size and profit. Finally, we investigate the relationship between product proliferation and the choice of logistics strategy.