Boundedly complete families which are not complete

Summary Completeness of a family of probability distributions implies its bounded completeness but not conversely. An example of a family which is boundedly complete but not complete was presented by Lehmann and Scheffe [5]. This appears to be the only such example quoted in the statistical literature. The purpose of this note is to provide further examples of this type. It is shown that any given family of power series distributions can be used to construct a class containing infinitely many boundedly complete, but not complete, families. Furthermore, it is shown that the family of continuous distributions , is boundedly complete, but not complete, whereU denotes the uniform distribution on [a, b] and {P _ϑ,ϑ ∈ IR}, is a translation family generated by a distributionP ₀ with mean value zero, which is continuous with respect to the Lebesgue measure.     

The excess burden of the tax and social premium system for Dutch married women

Summary The excess burden of a tax is the diminution of utility above that which would have occurred had the tax been collected as a lump sum. Computing the excess burden for the 1983 and 1985 Dutch tax and social premium system enables a partial welfare evaluation of the recent changes in the system, the so-called Tweeverdienersmaatregelen. Based on the equivalent and compensating variation, the excess burden as a percentage of the taxes and social premiums for the 1983 and 1985 system are valued at 27010 and 84010, and 37010 and 58010 respectively. This result indicates that, welfare-theoretically, the old system seems preferable to the new one.The author wishes to thank Hans Doodeman, Paul Renaud and Jacques Siegers for their critical remarks on an earlier version of this article.     

Population,agriculture, and the environment in Africa

An overview is provided of the World Bank study about the interaction between rapid population growth, poor agricultural performance, and environmental degradation. The links between these 3 phenomena are identified as traditional methods of crop and livestock production, land tenure systems, women's responsibilities, and methods of forest use. When land was abundant and capital limited, pastoralism, shifting cultivation, and setting aside fallow land was possible. Mobility and allowances for natural regeneration of vegetation could not continue with rapid population growth. Permanent settlements developed but cultivation methods remained the same; the result was deterioration of soil fertility, low yields, and erosion of soil as occurred in Rwanda, Burkina Faso, and parts of Nigeria. Technological innovation has been slow and poor roads have interfered with a market oriented economy. Inappropriate pricing, exchange rates, and fiscal policies also prevent productivity gains. A heavy demand is placed on women's time. Demand for children is high and is stimulated by environmental degradation, food insecurity, land tenure systems, and cultural traditions. Child labor is needed. The demand for contraception is 30-50% in North Africa, 36-55% in Asia, and 40-60% in South America. Land ownership problems have arisen under community ownership and between herders and settlers. Solutions have ranged from land nationalization and arbitrary designation of individual ownership. Open access situations have developed and lent themselves to exploitation. Fuelwood needs have exacerbated the destruction of forests. Commercial logging accounted for 10-20% of the forest loss. New approaches are needed to link cross-sectionally population, the environment, an agriculture. Emphasis should be on resource conservation, family planning, and environmentally benign intensive farming. Agricultural production needs to grow at 4%/year, fertility lowered by 50% over 30 years, and deforestation slowed. Women's time constraints should b alleviated and productivity improved. Open access and state ownership should be stopped.     

Projecting the future size and health status of the U.S. elderly population

"A projection model based on a multivariate continuous state, stochastic process is presented. The model allows multiple time-varying covariates to be used so parameters can be estimated from time series information on health changes and mortality, and their interaction. Health changes are simulated by altering parameters controlling the age trajectory and diffusion of risk factor means, variances, and covariances....By increasing the information used in projections it may be possible to better (a) anticipate the state of health at extreme ages, (b) forecast changes in health at specific ages over time, (c) stimulate the effects of specific interventions, and (d) determine the sensitivity of outcomes to a range of interventions."     

Couple's literacy level and acceptance of family planning methods: Lorenz curve analysis

The authors study the acceptance of family planning methods according to the level of couple's literacy in 14 states in India during 1986-87, using the Lorenz curve. The Gini Concentration Ratio and Index of Dissimilarity were calculated by level of couple's literacy for vasectomy, tubectomy, IUD, and all method combined. Firstly, analysis found literates to have accepted vasectomy and IUD more than tubectomy. Secondly, among the 3 methods, a high Gini Concentration Ratio was found for vasectomy when the wife was literate. Moreover, when the wife was literate, the Gini Concentration Ratio of IUD acceptance was higher than the acceptance of IUD by the wife whose husband was literate. Thirdly, the same trend was observed when the husband was illiterate. It is therefore clear that the level of a woman's literacy is a key factor in securing the acceptance of male or female methods of family planning. Planners should therefore concentrate on literacy programs for females independently of their age. Increasing the level of female literacy may ultimately help improve the understanding of family planning methods, while these women may also motivate their husbands to undergo vasectomy which will ultimately foster the success of the family planning program.     

Is Germany a model for managers?

Most American managers have a hard time making sense of Germany. The country has a fraction of the resources and less than one-third the population of the United States. Labor costs are substantially higher, paid vacations are at least three times as long, and strong unions are deeply involved at all levels of business, from the local plant to the corporate boardroom. Yet German companies manage to produce internationally competitive products in key manufacturing sectors, making Germany the greatest competitive threat to the United States after Japan. The seemingly paradoxical nature of the German economy typically evokes one of two diametrically opposed responses. The first is to celebrate the German economy as a "model" worth emulating--indeed, as the answer to declining U.S. competitiveness. The alternative, more skeptical response is to question Germany's staying power in a new, more competitive global economy. According to Kirsten Wever and Christopher Allen, the problem with both points of view is that they miss the forest for the trees. Observers are so preoccupied with praising--or blaming--individual components of the German economy that they fail to see the dynamic logic that ties these components together into a coherent system. In their review of recent research on the German business system, Wever and Allen argue that managers can learn an important lesson from Germany. In the global economy, competition isn't just between companies but between entire socioeconomic systems. Germany's ability to design a cohesive economic and social system that adapts continuously to changing requirements goes a long way toward explaining that country's competitive success.     

The relationship between wellness participation and health care benefit utilization

To examine the relationship between participation in a wellness program and the amount of absenteeism and medical claims, seven years of retrospective absenteeism and medical claims records were collected for 207 employees (pre- and postwellness intervention) and entered into a database. A proportional stratified random sample of workers by wellness participation was selected. While there was no significant change in the amount of sick leave taken over time, a log transformation revealed a significant increase in the dollar amount of medical claims over time, particularly for the middle-aged group of employees. This confirms that wellness intervention slowed the rate of increasing claims among middle-aged participants after just three years of wellness intervention.     

Markovian equilibrium in a class of stochastic games: existence theorems for discounted and undiscounted models

Summary We study a strategic version of the neoclassical growth model under possible production uncertainty. For a general specification of the problem, we establish (i) the existence of stationary Markov equilibria in pure strategies for the discounted game, and (ii) the convergence, under a boundedness condition, of discounted equilibrium strategies to a pure strategy stationary Markovian equilibrium of the undiscounted game as the discount factor tends to unity. The same techniques can be used to prove that such convergence also obtains in all finitestate, finite-action stochastic games satisfying a certain full communicability condition. These results are of special interest since there are well known examples in the literature in which the limit of discounted equilibria fails to be an equilibrium of the undiscounted game.We are grateful to Marcus Berliant, M. Ali Khan, Mukul Majumdar, and an anonymous referee for helpful suggestions, and to Bonnie Huck for technical assistance. The first author acknowledges research support from the Columbia University Council for the Social Sciences.     

Preliminary test estimators of the parameters of simple linear model with measurement error

In this paper, we discuss the properties of preliminary test estimators (PTE) of the parameters of simple linear model with measurement error (ME model) when the slope of the linear model is suspected to be zero. Expressions of the bias, MSE and efficiencies are obtained under conditional as well as unconditional situations with known reliability coefficient. Conditional model results are compared to the standard model without measurement error. We also provide the unconditional model analysis in finite samples. Asymptotic theory under local alternatives is developed when the variance of measurement error or the ratio of the variance of the model error relative to the variance of the measurement error is known. Asymptotic expressions of bias and MSE of the estimators along with their efficiencies are obtained. In every case, it is shown that the measurement error tend to increase the variability of the estimators compared to the estimators without measurement error. Graphs and tables are provided to see these results and to determine optimum level of significance for minimum guaranteed efficiency. Received October 2001 RID="*" ID="*"  A. K. Md. E. Saleh is a Distinguished Research Professor and H. M. Kim is a Ph.D. candidate in the School of Mathematics and Statistics, Carleton University, Ottawa. Acknowledgment. The authors gratefully acknowledge the constructive suggestion of the referees to improve the paper. The research is supported by NSERC grant A3088.