Differential equation models for statistical functions

Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation models of data, and smoothing over complicated multidimensional domains. This paper aims to stimulate interest in this approach to functional estimation problems, rather than provide carefully worked out methods.     

Bootstrap tests: how many bootstraps?

In practice, bootstrap tests must use a finite number of bootstrap samples. This means that the outcome of the test will depend on the sequence of random numbers used to generate the bootstrap samples, and it necessarily results in some loss of power. We examine the extent of this power loss and propose a simple pretest procedure for choosing the number of bootstrap samples so as to minimize experimental randomness. Simulation experiments suggest that this procedure will work very well in practice.     

Structure and process in occupational mobility

The distinction between structure and process in occupational mobility has been a dominant theme in contemporary research. While successive attempts to “solve” the structure/process dilemma have typically focused on new methodological procedures, we emphasize the conceptual issues underlying the distinction as a basis for further analysis. We introduce a simple two-stage model for the specification of mobility structure and process and use this model to evaluate current methodological “solutions” to the analysis of mobility.     

Residential preferences and population distribution

Public opinion research has revealed decided preferences for living in rural areas and small towns, and proponents of population deconcentration have interpreted this as support for their policies. This study, based on a national sample, yielded similar results, but when we introduced the additional possibility of a preference for proximity to a larger city, then the rural areas preferred were found, for most respondents, to be those within the commuting range of a metropolitan central city. Although persons wishing to live near large cities were found to be looking for the same qualities of living sought by those who prefer a more remote location, these findings are not, in general, consistent with the argument that public preferences support strategies of population dispersal into nonmetropolitan areas. Instead they indicate that most of those who wish to live in a different location favor the peripheral metropolitan ring areas that have, in fact, been growing rapidly by in-migration.     

Racial and regional inequalities in school resources relative to their educational outcomes

A definition of inequalities in school inputs weighted according to their importance for educational and outputs is applied to the data from the 1966 Educational Opportunities Survey. The extent and source of inequalities due to race and region are examined. The results are discussed in terms of findings from more restricted definitions of inequalities, and practical policy considerations.     

Assessing the devolution revolution: How accurate are state-level estimates from the current population survey

The devolution of many social policy responsibilities from the Federal government to states has prompted increased interest in state-level measures of need. One data source that could be used to provide more state-level information on a variety of topics is the Current Population Survey (CPS). During the past ten years the CPS has been used to produce state-level estimates on a variety of measures. However, there has been little systematic evaluation of these data. This paper provides measures of accuracy for several state-level estimates derived from the CPS. These include standard errors for single-year estimates, three-year averages, and five-year averages of the March CPS measures; standard errors for three-year averages of 12-month CPS files; and comparison of CPS-based estimates to data from the Decennial Census. The paper also examines the relative accuracy of CPS estimates based on states' size. The information in this study will help analysts better understand the tradeoffs between timeliness and accuracy to be considered when using state-level estimates derived from the CPS.     

The perils of father-reported fertility data for household labour supply models

Many panel data-sets contain father-reported fertility data. Yet, since men tend to underreport past fertility--especially daughters or children from previous marriages--using such data can lead to significantly biased results when estimating household labour supply models. For example, when analysing fertility data from the Panel Study of Income Dynamics, which has a significant retrospective component, fathers' labour supply appears more responsive to the births of sons than to daughters (Lundberg and Rose, Review of Economics and Statistics 84(2): 251-268, 2002). However, no evidence for this differential can be found in a much larger sample of Current Population Survey data from the same population. It is important for researchers to consider the provenance of data on fertility variables and to undertake robustness checks with data reported by women whenever possible.