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Small-Area Incomes: Their Spatial Variability and the Relative Efficacy of Proxy, Geodemographic, Imputed and Model-Based Estimates

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Abstract

This paper uses data from a UK Census Rehearsal to explore the problem of small-area income estimation. First, the nature of the problem is revisited through an examination of the way in which incomes vary spatially. Residential rather than labour market sorting is found to be the dominant driver; and the rich are found to exhibit greater spatial segregation than the poor. Even so, location is shown to capture only a small fraction of the overall variation in incomes. Second, the performance of competing small-area estimation strategies is assessed, uniquely comparing proxy, geodemographic, imputation and model-based estimates; and validating all of these against directly observed values. An area-level model, ecological regression, performs best. Unit-record imputation approaches capture similar levels of spatial variation in mean income, but have higher variances and greater systematic biases. The same can be said of a simple univariate proxy (% professionals), which even so proves surprisingly effective.

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Notes

  1. The fewer responses per spatial unit, and the fewer the income bands used to classify their incomes, the fewer available degrees of freedom there are, and the greater the ‘structural’ component of between-area income variation will be. This structural component can be estimated by randomly assigning responses (adult and household incomes) across spatial units, subject to matching the marginal constraints captured in the Census Rehearsal of the number of respondents per income band and the number of respondents per spatial unit, and then measuring the resulting between-area variation. The ‘structural’ variation is taken to be the 100-run average of such measures.

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Acknowledgments

The research reported here arose from the ESRC-funded project ‘Income imputation for small areas’, award no. H507255166. Grateful thanks are due to the Census Custodians of England, Wales and Scotland for granting permission to access the Census Rehearsal dataset. A debt of gratitude is owed to a number of staff at the Office for National Statistics, in particular Keith Whitfield and Philip Clarke. Thanks are also due to David Voas for undertaking some of the preparatory work for this project. The Family Resources Survey, 1998, used to derive mean values for income bands, was sponsored and collected by the Department for Social Security, and supplied for research use by the UK Data Archive. Thanks also to two anonymous reviewers for their perceptive comments. All analyses and conclusions remain the sole responsibility of the author.

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  1. Department of Geography, Roxby Building, University of Liverpool, Liverpool, L69 7ZT, UK

    Paul Williamson

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Williamson, P. Small-Area Incomes: Their Spatial Variability and the Relative Efficacy of Proxy, Geodemographic, Imputed and Model-Based Estimates. Appl. Spatial Analysis 9, 463–489 (2016). https://doi.org/10.1007/s12061-015-9163-1

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