LENGTH-BIASING, CHARACTERIZATIONS OF LAWS AND THE MOMENT PROBLEM

A positive random variable X with a finite mean has an induced length-biased law represented by Y, and Y is stochastically larger than X. An independent uniform random contraction of Y, UY, has the same law as X if and only if the latter is exponential. This property is extended to non-uniform contractions and a more general notion of length-biasing. The distributional equality of X and W leads to a functional equation for the moment function of X, which has either Infinitely many solutions or none. When U is constant, X can have a log-normal law, but it can also have laws with the same moment sequence as this log-nod law. The case where U has a certain beta, or generalized beta, law give t3 characterizations of generalized gamma laws, or to products of independent copies of them. This occurs even when these laws are not determined by their moment sequences.     

Fast retraction of evidence in a probabilistic expert system

We present and justify a propagation algorithm to facilitate the simultaneous calculation, for every node in a probabilistic exper system of the distribution of the associated random quantity, conditional on all the evidence obtained about the remaining nodes.     

FINITE HORIZONS, INFINITE HORIZONS, and THE REAL INTEREST RATE

Using an overlapping-generations model in which households may have either finite or infinite horizons, I derive the implications of each horizon for the steady-state real interest rate. I then formulate an econometric model of the steady-state real interest rate and devise tests that can distinguish between finite and infinite horizons. These tests are applied to annual and quarterly U.S. data, which span the period 1875–1988. The results are inconsistent with finite horizons, and broadly consistent with infinite horizons.     

The Farm Crisis and Mental Health: A Longitudinal Study of the 1980s1

Abstract This paper examines rural/urban differences and trends in mental health during the farm crisis of the 1980s in a large panel sample from a midwestern state. A community research perspective, which attributes differences to life styles, culture, and community context, is contrasted with an economic stress perspective, which focuses on individual differences in economic circumstances as determinants of rural-urban differences in mental health. Survey samples from 1981, 1986, and 1989 are used to examine differences among seven categories of community type. Multiple regression analysis of the trend and panel data provide support for both the individual economic distress and community context models.     

A note on inverse estimation in non-linear models

The problem of estimating the value of an x variable for a given proportion of an observed value of the y variable is consdered for a non-linear model. Asymptotic confidence limits are obtained and an application of the method is illustrated witreal data.     

Children's gender- and age-based categorization in similarity and induction tasks

The present studies examined children's and adults' preferences for gender- or age-based categorization using similarity and inductive inference tasks. Four-year-olds, 6-year-olds, and adults looked at pictures of people and decided which of two was more like a target (similarity condition) or which shared a novel age- or gender-related property with the target (inference condition). Age or gender-based matches were possible. The results are consistent with previous findings that gender-based classification decreases with age. However, they also demonstrate that children use gender more for judging similarity than for making inferences about novel properties. Distinct patterns emerge from the two tasks: 6-year-olds and adults in both conditions categorize more by age than gender; 4-year-olds categorize by gender more than age in the similarity task, but by age more in the induction task. Only adults differentiated by property in the inference condition. These findings suggest that the salience of gender categories cannot entirely be attributed to their inductive potential. Gender has a salience beyond what would be predicted by its power for directing novel generalizations.     

Determinants and Consequences of Social Trust*

This article provides an overview of social trust, examining its various aspects and components. Trust is best understood in a sociological sense by focusing on its important relational characteristic. Following this lead, the article discusses briefly how social trust relates to social capital and examines factors that shape the development of social trust, along with outcomes related to variations in trust, classifying them by analytical level (i.e., individual, community, group, organizational, and societal). The article concludes by assessing the strengths and weaknesses of existing research and by identifying some important questions that have not yet been adequately addressed.