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Improving the Representativeness of a Simple Random Sample: An Optimization Model and Its Application to the Continuous Sample of Working Lives

Author

Listed:
  • Vicente Núñez-Antón

    (Department of Econometrics and Statistics (A.E. III), Faculty of Economics and Business, University of the Basque Country UPV/EHU, 48015 Bilbao, Spain
    Current address: Avenida Lehendakari Aguirre 83, 48015 Bilbao, Spain.
    These authors contributed equally to this work.)

  • Juan Manuel Pérez-Salamero González

    (Department of Financial Economics and Actuarial Science, Faculty of Economics, University of Valencia, 46022 Valencia, Spain
    These authors contributed equally to this work.)

  • Marta Regúlez-Castillo

    (Department of Econometrics and Statistics (A.E. III), Faculty of Economics and Business, University of the Basque Country UPV/EHU, 48015 Bilbao, Spain
    These authors contributed equally to this work.)

  • Carlos Vidal-Meliá

    (Department of Financial Economics and Actuarial Science, Faculty of Economics, University of Valencia, 46022 Valencia, Spain
    Instituto Complutense de Análisis Económico (ICAE), Complutense University of Madrid, 28223 Madrid, Spain
    Centre of Excellence in Population Ageing Research (CEPAR), UNSW, 2033 Sydney, Australia
    These authors contributed equally to this work.)

Abstract
This paper proposes an optimization model for selecting a larger subsample that improves the representativeness of a simple random sample previously obtained from a population larger than the population of interest. The problem formulation involves convex mixed-integer nonlinear programming (convex MINLP) and is, therefore, NP-hard. However, the solution is found by maximizing the size of the subsample taken from a stratified random sample with proportional allocation and restricting it to a p -value large enough to achieve a good fit to the population of interest using Pearson’s chi-square goodness-of-fit test. The paper also applies the model to the Continuous Sample of Working Lives (CSWL), which is a set of anonymized microdata containing information on individuals from Spanish Social Security records and the results prove that it is possible to obtain a larger subsample from the CSWL that (far) better represents the pensioner population for each of the waves analyzed.

Suggested Citation

  • Vicente Núñez-Antón & Juan Manuel Pérez-Salamero González & Marta Regúlez-Castillo & Carlos Vidal-Meliá, 2020. "Improving the Representativeness of a Simple Random Sample: An Optimization Model and Its Application to the Continuous Sample of Working Lives," Mathematics, MDPI, vol. 8(8), pages 1-27, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1225-:d:389925
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    Cited by:

    1. Anne M. Garvey & Juan Manuel Pérez-Salamero González & Manuel Ventura-Marco & Carlos Vidal-Meliá, 2021. "From “Table 29” to the actuarial balance sheet: is it really that big a leap?," Documentos de Trabajo del ICAE 2021-05, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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    More about this item

    Keywords

    chi-square test; continuous sample of working lives; optimization; p -value; subsampling;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • H55 - Public Economics - - National Government Expenditures and Related Policies - - - Social Security and Public Pensions
    • J26 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Retirement; Retirement Policies

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