Simon D. Woodcock

Multiply-Imputing Confidential Characteristics and File Links in Longitudinal Linked Data

This paper describes ongoing research to protect confidentiality in longitudinal linked data through creation of multiply-imputed, partially synthetic data. We present two enhancements to the methods of [2]. The first is designed to preserve marginal distributions in the partially synthetic data. The second is designed to protect confidential links between sampling frames.

Glass Ceilings or Glass Doors? Wage Disparity within and between Firms

We investigate whether immigrant and minority workers’ poor access to high-wage jobs—that is, glass ceilings—is attributable to poor access to jobs in high-wage firms, a phenomenon we call glass doors. Our analysis uses linked employer–employee data to measure mean and quantile-wage differentials of immigrants and ethnic minorities, both within and across firms. We find that glass ceilings exist for some immigrant groups, and that they are driven in large measure by glass doors. For some immigrant groups, the sorting of these workers across firms accounts for as much as half of the economy-wide wage disparity they face. This article has the supplement materials online.

Distribution-preserving statistical disclosure limitation

One approach to limiting disclosure risk in public-use microdata is to release multiply-imputed, partially synthetic data sets. These are data on actual respondents, but with confidential data replaced by multiply-imputed synthetic values. A mis-specified imputation model can invalidate inferences because the distribution of synthetic data is completely determined by the model used to generate them. We present two practical methods of generating synthetic values when the imputer has only limited information about the true data generating process. One is applicable when the true likelihood is known up to a monotone transformation. The second requires only limited knowledge of the true likelihood, but nevertheless preserves the conditional distribution of the confidential data, up to sampling error, on arbitrary subdomains. Our method maximizes data utility and minimizes incremental disclosure risk up to posterior uncertainty in the imputation model and sampling error in the estimated transformation. We validate the approach with a simulation and application to a large linked employer-employee database.

Dynamically consistent noise infusion and partially synthetic data as confidentiality protection measures for related time-series

The Census Bureaus Quarterly Workforce Indicators (QWI) provide detailed quarterly statistics on employment measures such as worker and job flows, tabulated by worker characteristics in various combinations. The data are released for several levels of NAICS industries and geography, the lowest aggregation of the latter being counties. Disclosure avoidance methods are required to protect the information about individuals and businesses that contribute to the underlying data. The QWI disclosure avoidance mechanism we describe here relies heavily on the use of noise infusion through a permanent multiplicative noise distortion factor, used for magnitudes, counts, differences and ratios. There is minimal suppression and no complementary suppressions. To our knowledge, the release in 2003 of the QWI was the first large-scale use of noise infusion in any official statistical product. We show that the released statistics are analytically valid along several critical dimensions { measures are unbiased and time series properties are preserved. We provide an analysis of the degree to which confidentiality is protected. Furthermore, we show how the judicious use of synthetic data, injected into the tabulation process, can completely eliminate suppressions, maintain analytical validity, and increase the protection of the underlying confidential data.

Expanding School Choice Through Open Enrolment: Lessons from British Columbia

Is expanding the scope for parents to choose among competing schools an effective policy lever for improving the quality of education? What lessons can we take from British Columbia’s experience with greater school choice? In 2002, British Columbia implemented a new policy that makes it easier for parents to opt out of their neighbourhood school. Along with the province’s rich administrative and test score data, the introduction of this “open enrolment” policy provides a rare opportunity to estimate the extent to which increased public school choice affects student achievement, concentrates minority students in enclave schools and promotes cream-skimming. Our results support several conclusions about British Columbia’s experience with open enrolment. First, the fact that many more parents succeeded in enrolling their children in out-of-catchment schools demonstrates that the policy had a meaningful impact on the public school choice opportunities available to many families. Second, the evidence suggests that open enrolment contributed to the development of important academic skills, but the magnitude of this impact depended on the geographic concentration of public schools. In the Lower Mainland, 10 to 15 percent of neighbourhoods are dense enough to have generated fairly substantial improvements in academic achievement. The gains in these neighbourhoods were equivalent to reducing class size by between two and three students; compared to class-size reductions, open enrolment is likely to be a fairly cost effective strategy for improving student achievement as measured by test scores. In the remaining neighbourhoods, where school density is lower, the impact of open enrolment on test scores was quite small. Finally, open enrolment did little to either segregate or integrate Lower Mainland students according to their cultural and ethnic backgrounds. There is also little evidence that popular schools engaged in creamskimming high-achieving students. These generally positive results might encourage policymakers in other jurisdictions to give fresh thought to introducing greater school choice into their public education systems.

A Representation Index: Measuring the Representation of Minorities in the Income Distribution

Abstract The existence of glass ceilings and sticky floors suggests that disadvantaged workers will be under-represented in some parts of the income distribution, and over-represented in others. We present a representation index that measures the prevalence of population subgroups in different regions of the income (or any other) distribution. Our representation index is easily generalized to condition on characteristics (such as age, education, etc). Further, it generalizes naturally to an index of the severity (or cost) of under-representation to group members, which is based on dollar-weighted representation. Both representation and severity indices are easily calculated via existing regression techniques. We illustrate the approach using Canadian Census data on the earnings of ethnic minorities.

THE ECONOMICS OF EXOGAMOUS MARRIAGE IN SMALL-SCALE SOCIETIES

Marriage is a core institution in almost every human society, including small‐scale societies based on foraging or subsistence agriculture. A crucial dimension of the marriage systems in such societies involves endogamy and exogamy, that is, the choice of a marriage partner from within ones own community or from an outside community. We develop a model in which the exogamy rate is higher when good local matches are scarce due to small community sizes, and when productivity differs across communities due to environmental shocks. These theoretical predictions are supported by econometric analysis of data from the standard cross‐cultural sample.

Representation and Severity in the Distribution of Income

The existence of glass ceilings and sticky floors suggests that disadvantaged workers will be under-represented in some parts of the income distribution, and over-represented in others. We present a new index to measure the representation of population subgroups in different regions of the income distribution. Our representation index is easily generalized to condition on characteristics (such as age, education, etc). Further, it generalizes naturally to an index of the severity (or cost) of under-representation to group members, which is based on dollar-weighted representation. Both representation and severity indices are easily calculated via existing regression techniques. We illustrate the approach using Canadian Census data.

Valuing productivity loss due to absenteeism: firm-level evidence from a Canadian linked employer-employee survey

In health economic evaluation studies, to value productivity loss due to absenteeism, existing methods use wages as a proxy value for marginal productivity. This study is the first to test the equality between wage and marginal productivity losses due to absenteeism separately for team workers and non-team workers. Our estimates are based on linked employer-employee data from Canada. Results indicate that team workers are more productive and earn higher wages than non-team workers. However, the productivity gap between these two groups is considerably larger than the wage gap. In small firms, employee absenteeism results in lower productivity and wages, and the marginal productivity loss due to team worker absenteeism is significantly higher than the wage loss. No similar wage-productivity gap exists for large firms. Our findings suggest that productivity loss or gain is most likely to be underestimated when valued according to wages for team workers. The findings help to value the burden of illness-related absenteeism. This is important for economic evaluations that seek to measure the productivity gain or loss of a health care technology or intervention, which in turn can impact policy makers’ funding decisions.

Open Enrolment and Student Achievement

We investigate the effects of public school open enrolment, which allows students to enroll in any public school with available space, on fourth grade test scores. We find a small, positive effect on the average student; this benefit appears to stem from increased competition among schools, rather than directly through expanded choice opportunities. Among students whose catchment school is locally top-ranked according to test scores, greater choice is of no direct benefit; however, students whose catchment school is locally lowest-ranked earn higher scores when they have access to better local schools. Students in both groups benefit from increased school competition.