Small area estimation ‒ model-based approach in economic research
Authors:   Department of Statistics, Econometrics and Mathematics, University of Economics in Katowice, Katowice, Poland, Krzciuk Małgorzata 
Published: April 2024

The growing importance of regions and regional policy – regional programmes, participation in European Union programmes, development of regional self-governance – also entails an increase in the importance of national databases with a very detailed territorial division – sources increasingly used by public statistics, such as PESEL, POLTAX, POMOST, and ZUS. This is also related to the growing demand for information at an increasingly lower level of aggregation, as well as the demand for methods that do not require large financial outlays, but make it possible to obtain accurate estimations of subpopulation characteristics quickly, without the need for a full survey. Small area estimation methods may be the answer to this demand, allowing estimation and prediction under conditions where classical estimation methods prove to be inefficient or too costly. They allow estimation even for very small sample sizes, and even when the sample size of a subpopulation is zero. The choice of the topic considered in this monograph is therefore related to the increasing demand for local cross-sectional analyses. Moreover, it is also due to the multitude of fields in which the methods of small area estimation have already found application, such as market analyses, regional policy, labour market and poverty analysis, agricultural economics, and economic aspects of health policy. The subject of this research will be the use of one of the main approaches in survey sampling, besides randomised and model-assisted – the model-based approach, in small area estimation for economic data. Aforementioned approach allows inference from purposive and random samples. The problem considered was the prediction of subpopulation characteristics and the analysis of predictor properties when there are different correlation relationships between random variables. The analyses took into account longitudinal data from the Local Data Bank, the largest organised collection of information in Poland on the socio-economic situation, demographics, and state of the environment, enabling multidimensional regional and local statistical analyses. The main theoretical and exploratory objective of this book is to propose methods for predicting subpopulation characteristics and to analyse the properties of the predictors, taking into account the correlation between the random variables. The practical objectives include: – adapting the methods of small area estimation, a model-based approach, for economic data obtained in longitudinal surveys; – proposing and using the author’s overpopulation models belonging to the class of general linear mixed models; – proposing and using original model verification methods; – proposing and applying the author’s methods of prediction and assessment of prediction accuracy of subpopulation characteristics for the proposed class of models; – demonstrating the applicability of the proposed methods to real economic data – simulation studies conducted using the Monte Carlo method. The implementation of the above objectives will serve to answer the following research questions: – Which models, belonging to the class of general linear mixed models, make it possible to take into account the occurrence of correlational relationships between random variables for prediction based on economic data obtained in longitudinal surveys? – How can the presence of a correlation between random effects be verified for the proposed class of models? – What effect does the inclusion of the presence of a correlation between random effects have on the properties of the considered predictors of subpopulation characteristics? – How will the use of prior period information affect the accuracy of the considered predictors compared to methods using single-period information? The monograph consists of five chapters. Each of them begins with an introduction. The first chapter of book discusses the theoretical basis of small area estimation. It presents the main approaches in small area estimation, including basic definitions, and issues concerning their development. Also presented are their selected areas of application in research of an economic nature, with examples. However, the greatest emphasis was placed on the presentation of the model-based approach. The process of building superpopulation models and their classification were discussed more extensively. Special attention was paid to the class of linear mixed models. The chapter presents the author’s proposals for some special cases of models of this class with correlated vectors of random effects with their applications in small area estimation and generalisations of selected predictors to the case of longitudinal data. The chapter also discusses the author’s proposals for the possibility of using permutation tests and those based on the parametric bootstrap method in verifying the significance of the parameters of the proposed superpopulation models. The second chapter deals with the issue of repeated surveys over time. It discusses the essence of statistical longitudinal studies, including the main reasons for interest in and development of this type of research. It presents a classification of repeated surveys in time, together with conducting schemes and examples of economic research conducted both in Poland and worldwide. The essence of panel studies, and studies with partial and complete rotation are discussed in more detail. The chapter emphasises the advantages and disadvantages of repeated surveys over time. It also discusses the benefits and limitations of this type of research in the context of analyses based on it. Chapter three discusses the problem of prediction using BLUPs and EBLUPs, including those proposed by Henderson (1950) and Royall (1976). Particular attention was paid to these classes of predictors in terms of the classification of linear mixed models into type A and B models. The author’s proposal for the use of EBLUP under the assumption of a linear mixed model with correlated random effects in small area estimation is also presented. The chapter also addresses the issue of possible modifications as well as properties of the EBLUP class. Modifications of known methods for estimating the mean squared prediction error allowing for the estimation of the accuracy of EBLUP taking into account the correlation between random effects vectors are proposed. This part of the paper also included a review of selected economic applications of the above predictors. The fourth chapter is focused on the class of empirical best predictors and plug-in predictors. The author’s proposals for the use of predictors belonging to these classes in prediction based on models with correlated random effects vectors are presented. The problem of evaluating the mean squared errors of the proposed predictors is also addressed. The chapter also presents selected examples of applications of the discussed predictors in economic research. Chapter five provides a description of the actual data set considered in the following section. It also presents the assumptions and results of the simulation studies carried out. Each of the subchapters was focused on one of the analysis variants, each of which was carried out according to the model-based approach. The problem of predicting total values and medians in domains under the assumption of a linear mixed model taking into account the correlation between random effects was addressed. The properties of the three proposed predictors belonging to the BP, EBP and plug-in classes were simulation tested. A comparison was made with selected predictors, assuming no correlation between random effects and selected estimators. This chapter, like the others, concludes with a brief summary of the issues raised. In the monograph, the author used methods of mathematical statistics and multivariate statistical analysis, as well as computer simulation techniques. The simulation studies used self-written programs in the R language (R Core Team, 2022). Analyses were conducted using actual data from several periods.