An Evaluation of Company Performance Using the Fay-Herriot Model

Grażyna Dehnel, Michał Pietrzak, Łukasz Wawrowski


Information about monthly characteristics of the small business sector is currently provided mainly by sample surveys conducted, among others, by the Central Statistical Office. Sample size enables parameters of interest to be estimated with acceptable precision only at the country or voivodeship level or by NACE section. The growing demand for reliable estimates at a low level of aggregation is the motivating force behind research into the application of indirect methods of estimation based on auxiliary sources of information. Hence, the article seeks to evaluate the possibility of applying the Fay-Herriot model to estimate one of the basic economic variables that characterise small business, i.e. revenue, based on information collected in administrative registers maintained by the Ministry of Finance.


small area estimation, indirect estimation, administrative registers, Fay-Herriot model, economic statistics

Full Text:



Benavent, R. and Morales, D. (2015) “Multivariate Fay-Herriot Models for Small Area Estimation”. Computational Statistics & Data Analysis 94: 372–90,,

Boonstra, H. J. and Buelens, B. (2011) “Model-based Estimation”. Statistics Netherlands, 0/2011x3706.pdf. Accessed: 2 May 2016.

Dehnel, G. (2015) “Robust Regression in Monthly Business Survey” in W. Okrasa (ed.) Statistics in Transition – New Series 16(1): 1–16, Warszawa,

Fay, R. and Herriot, R. (1979) “Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data”. Journal of American Statistical Association 74: 269–77.

Guadarrama, M., Molina, I. and Rao, J. N. K. (2016) “A Comparison of Small Area Estimation Methods for Poverty Mapping”. Statistics in Transition. New Series and Survey Methodology 17(1): 41–66,

Horvitz, D. G. and Thompson, D. J. (1952) “A Generalization of Sampling without Replacement from a Finite Universe”. Journal of the American Statistical Association 47: 663–85.

The Methodology of the 2011 National Population and Housing Census – Selected Aspects (2011). Warsaw: Central Statistical Office.

Pratesi, M. and Salvati, N. (2008) “Small Area Estimation: the EBLUP Estimator Based on Spatially Correlated Random Area Effects”. Statistical Methods and Applications 17: 113–41,

Rao, J. N. K. (2003) Small Area Estimation. Hoboken, NJ: Wiley.

Wawrowski, Ł. (2014) “Wykorzystanie metod statystyki małych obszarów do tworzenia map ubóstwa w Polsce”. Wiadomości Statystyczne 9: 46–56,