Statistical Decision Problems and Bayesian Nonparametric Methods

This paper considers parametric statistical decision problems conducted within a Bayesian nonparametric context. Our work was motivated by the realisation that typical parametric model selection procedures are essentially incoherent. We argue that one solution to this problem is to use a flexible enough model in the first place, a model that will not be checked no matter what data arrive. Ideally, one would use a nonparametric model to describe all the uncertainty about the density function generating the data. However, parametric models are the preferred choice for many statisticians, despite the incoherence involved in model checking, incoherence that is quite often ignored for pragmatic reasons. In this paper we show how coherent parametric inference can be carried out via decision theory and Bayesian nonparametrics. None of the ingredients discussed here are new, but our main point only becomes evident when one sees all priors—even parametric ones—as measures on sets of densities as opposed to measures on finite-dimensional parameter spaces.     

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."     

The aggregated excess demand function and other aggregation procedures

Summary Two theorems are given; the first extends the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set ofn2 commodities to all of the 2 ⁿ –(n+1) subsets of two or more commodities. The second theorem concerns spatial voting models for k2 candidates over a space of n2 issues. The theorem characterizes the sincere elecion rankings of thek candidates over all of the 2 ⁿ –1 subsets of one or more issues. Both theorems have the same kind of conclusion; anything can happen. By demonstrating the mathematical reasons for these conclusions and by recalling related, recent results from statistics, voting, and economics, it is argued that this anything can happen conclusion is the type one must anticipate for aggregation procedures; particularly for the processes commonly used in economic models where the procedure is responsive to changes in agents' preferences, changes in data, etc.I am pleased to acknowledge conversations with L. Hurwicz, A. Mas-Colell and C. Simon about this material. In particular, I want to thank J. Jordan for his several helpful suggestions. Also, I benefited from comments made at meetings and seminars where these results were presented; this includes a June, 1990, conference in Stockholm, Sweden. Some stylistic suggestions were made by Arvid and Padon Kalinen. This research was supported, in part, by NSF Grant IRI-8803505.     

Airline networks as joint goods: Implications for competition policy

This article derives a model of airline services as joint goods. Using this model, the article shows how the existence of higher fares in certain hub routes may imply the market has generated a solution to the problem of covering joint costs by having a larger proportion of those costs come from hub routes, rather than the existence of any general market failure. The model is then used to make recommendations for competition policy.