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Estimation Of Income Characteristics For Regions In Poland Using Spatio-Temporal Small Area Models

Author

Listed:
  • Jędrzejczak Alina

    (Institute of Statistics and Demography, Faculty of Economics and Sociology, University of Łódź, Łódź, Poland .)

  • Kubacki Jan

    (Centre of Mathematical Statistics, Statistical Office in Łódź, Łódź, Poland .)

Abstract

The paper presents the comparison of estimation results for spatial and spatiotemporal small area models. The study was carried out for income-related variables drawn from the Polish Household Budget Survey and explanatory variables from the Polish Local Data Bank for the years 2003-2013. The properties of EBLUPs (Empirical Best Linear Unbiased Predictors) based on spatiotemporal models, which utilize spatial correlation between neighbouring areas as well as historical data, were compared and contrasted with EBLUPs based on spatial models obtained separately for each year and with EBLUPs based on the Rao-Yu model. The computations were performed using sae, sae2 and spdep packages for R-project environment. In the case of sae package, the eblupFH, eblupSFH and the eblupSTFH functions were used for point estimation along with the mseFH, mseSFH and the pbmseSTFH functions for the MSE estimation, whereas the eblupRY function was applied for the purposes of sae2 package. The precision of direct estimators was guaranteed by the adoption of the Balanced Repeated Replication method. The results of the analysis demonstrate that a visible reduction of the estimation error was achieved for the implemented spatiotemporal small-area models, especially when significant spatial and time autocorrelations were observed. These results are even more valuable than those achieved by the means of the Rao-Yu model. In the computations, three author-defined functions were adopted, which not only enabled the author to perform the extract of random effects for spatial, spatiotemporal and Rao-Yu models, but also made it possible to obtain their decomposition with respect to spatial and temporal parts, thus creating a novel solution. The comparison was carried out using choropleth maps for spatial effects and distributions of temporal random effects for the considered years.

Suggested Citation

  • Jędrzejczak Alina & Kubacki Jan, 2019. "Estimation Of Income Characteristics For Regions In Poland Using Spatio-Temporal Small Area Models," Statistics in Transition New Series, Statistics Poland, vol. 20(4), pages 113-134, December.
    • Handle: RePEc:vrs:stintr:v:20:y:2019:i:4:p:113-134:n:10
    DOI: 10.21307/stattrans-2019-037
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    References listed on IDEAS

    as
    1. Marhuenda, Yolanda & Molina, Isabel & Morales, Domingo, 2013. "Small area estimation with spatio-temporal Fay–Herriot models," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 308-325.
    2. Bivand, Roger & Piras, Gianfranco, 2015. "Comparing Implementations of Estimation Methods for Spatial Econometrics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i18).
    3. Jan Kubacki & Alina Jędrzejczak, 2016. "Small Area Estimation Of Income Under Spatial Sar Model," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 365-390, September.
    4. Monica Pratesi & Nicola Salvati, 2008. "Small area estimation: the EBLUP estimator based on spatially correlated random area effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 113-141, February.
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