Small Area Estimation with Correctly Specified Linking Models

  • P. A. V. B. Swamy
  • J. S. Mehta
  • G. S. Tavlas
  • S. G. Hall
Chapter

Abstract

It is possible to improve the precision of a sample estimator for a small area based on sparse area-specific data by combining it with a model of its estimand, provided that this model is correctly specified. A proof of this result and the method of correctly specifying the models of the estimands of sample estimators are given in this paper. Widely used two-step estimation is shown to yield inconsistent estimators. The accuracies of different sample estimates of a population value can be improved by simultaneously estimating the population value and sums of the sampling and non-sampling errors of these sample estimates.

Keywords

Misspecified linking model Specification error Unconditional inadmissibility Coefficient driver Conditional independence 

Notes

Acknowledgement

We thank Jean Roth of the NBER and Roslyn Gorin of Temple University for helping J. S. Mehta retrieve the data used in this paper from NBER Public Use Data Files and thank David Hill of Temple University for teaching J. S. Mehta how to use MATLAB.

Data Sources: NBER Public Use Data Files are the sources of our monthly data on direct state CPS estimates of employment, \( {\mathit{BP}_{\mathit{it} }} \), \( {\mathit{HP}_{\mathit{it} }} \), \( {\mathit{TP}_{\mathit{it} }} \), and “a” and “b” parameters of the CPS Generalized Variance Functions. The BLS website is the source of our monthly data on state CES and two-step estimates of employment.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • P. A. V. B. Swamy
    • 1
  • J. S. Mehta
    • 2
  • G. S. Tavlas
    • 3
  • S. G. Hall
    • 4
  1. 1.Federal Reserve Board (Retired)KingstowneUSA
  2. 2.Department of MathematicsTemple UniversityPhiladelphiaUSA
  3. 3.Economic Research DepartmentBank of GreeceAthensGreece
  4. 4.Leicester University and Bank of GreeceLeicesterUK

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