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Benchmarking techniques for reconciling Bayesian small area models at distinct geographic levels

Author

Listed:
  • Ryan Janicki

    (U.S. Census Bureau)

  • Andrew Vesper

    (Deloitte Consulting LLP)

Abstract

In sample surveys, there is often insufficient sample size to obtain reliable direct estimates for parameters of interest for certain domains. Precision can be increased by introducing small area models which ‘borrow strength’ by connecting different areas through use of explicit linking models, area-specific random effects, and auxiliary covariate information. One consequence of the use of small area models is that small area estimates at a lower (for example, county) geographic level typically will not aggregate to the estimate at the corresponding higher (for example, state) geographic level. Benchmarking is the statistical procedure for reconciling these differences. This paper provides new perspectives for the benchmarking problem, especially for complex Bayesian small area models which require Markov Chain Monte Carlo estimation. Two new approaches to Bayesian benchmarking are introduced: one procedure based on minimum discrimination information, and another procedure for fully Bayesian self-consistent conditional benchmarking. Notably the proposed procedures construct adjusted posterior distributions whose first and higher order moments are consistent with the benchmarking constraints. It is shown that certain existing benchmarked estimators are special cases of the proposed methodology under normality, giving a distributional justification for the use of benchmarked estimates. Additionally, a ‘flexible’ benchmarking constraint is introduced, where the higher geographic level estimate is not considered fixed, and is simultaneously adjusted, along with lower level estimates.

Suggested Citation

  • Ryan Janicki & Andrew Vesper, 2017. "Benchmarking techniques for reconciling Bayesian small area models at distinct geographic levels," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 557-581, November.
  • Handle: RePEc:spr:stmapp:v:26:y:2017:i:4:d:10.1007_s10260-017-0379-x
    DOI: 10.1007/s10260-017-0379-x
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    References listed on IDEAS

    as
    1. M. Ghosh & T. Kubokawa & Y. Kawakubo, 2015. "Benchmarked empirical Bayes methods in multiplicative area-level models with risk evaluation," Biometrika, Biometrika Trust, vol. 102(3), pages 647-659.
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    4. Pfeffermann, Danny & Barnard, Charles H, 1991. "Some New Estimators for Small-Area Means with Application to the Assessment of Farmland Values," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 73-84, January.
    5. Malay Ghosh & Rebecca Steorts, 2013. "Two-stage benchmarking as applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 670-687, November.
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    Cited by:

    1. Nandram, Balgobin & Cruze, Nathan B & Erciulescu, Andreea L & Chen, Lu, 2022. "Bayesian Small Area Models under Inequality Constraints with Benchmarking and Double Shrinkage," NASS Research Reports 327250, United States Department of Agriculture, National Agricultural Statistics Service.

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