Resumen de Small area estimation methods for socio-economic indicators in ISTAT household surveys
Stefani Falorsi
Large scale sample surveys carried out National Statistical Institutes are typically intended to comply with the estimation of several parameters (such as overall amount, means or ratios) of the whole population as well as parameters of some of population sub-sets, e.g. corresponding to sub-populations of a geographical partition of the entire country (usually an administrative partition) or sub-population that are characterized by some socio-demographic or economic cross-classi cation of the units.
An estimator of a parameter of interest in a given sub-population is said to be a direct estimator when it is based only on data of sample units which belongs to it. For most surveys, however, the sample size is not large enough to guarantee reliable estimators for all sub-populations under study. A portion of a population for which there is not a direct estimator with the needed sample precision is called a small area or small domain.
The study of statistical methods for small area estimation is acquiring more and more importance for National Statistical Institutes; in fact, in recent years, the need for statistical information has been growing as basis for political decision at various administrative and government level (e.g. Ministries, Regions; Municipalities, Chambers of Commerce, et cetera).
This new requirement for information on statistical basis has caused an increasing and more specialized demand for small area estimates.
In past, the main Statistical Institutes responded to this demand for more detailed statistical information by increasing the survey sample size.
Italian National Statistical Institute (Istat, in the following) carries out several sample surveys on households and enterprises aiming to obtain estimates on several di erent social, demographic and economic phenomena. Anyway, since overall sample size of Istat surveys is usually planned only to produce estimators of required precision for large geographic domains (e.g. regions) and for some speci c sub-set of the population, it is not always possible to attain suitable accuracy for the speci c local objectives. Hence, for example, until 1990, Istat, in order to satisfy the need of statistical information on the employment and unemployment structure and dynamics at sub-regional economic and social context level (such as for provinces) on the basis of the Labour Force Survey data, used to enlarge the sample size to reach adequate precision for the usual calibration estimator at the desired area level.
In recent times, on the contrary, the nancial and practical constraints in addiction to the need for improving quality of collected data counteract with the use of sample size growth, hence Istat, as most of the main National and International centre for statistical di usion, has focused on the study of methodologies based on indirect estimators, known as small area estimators.
The most relevant from a theoretical point of view and mainly applied small area estimators can be classi ed according to either the framework of data collection they refer to, such as an occasional or a repeated in time survey, or they can be also grouped according the approach underlying them, i.e. design based estimators or, alternatively, model based estimators.
Compared with the direct estimators, small area estimators allow an improvement of precision in the estimates, by means of exploiting observed values on the target variables for a larger area, a macro-area, containing the small area, and/or sample values which are collected on di erent time occasions besides the current one.
In this context, inference is commonly based on a model describing the relationship among data of several small areas within a macro-area, and/or the link among di erent time occasions; by means of extra auxiliary information, correlated with the target variable, coming from census or administrative archives.
These methods, even if they may be a ected by some bias as the model hypotheses are not valid, generally permit to reduce the variability of the estimator with respect to direct estimators. However, since the hypotheses underlying the model never completely agree with the real phenomena, small area estimators, which on these models are based, are always a ected by some bias whose size is dicult to assess.
Then, for actual use of small area estimators in Ocial Statistics is necessary to take into account some theoretical and applicative issues.
Among the theoretical issues that has to be considered, the robustness of the proposed methods plays a central role in Ocial Statistics, in particular, the de nition of proper diagnostic criteria for the assessment of the validity of the hypotheses at the basis of methods is essential; moreover, great focus should be addressed to the de nition of models that adhere with complex real situations. Speci cally, the appropriate characterization of the relationships on which the inference has to be based on is related to the issues of achieving accurate external information.
Finally, it is necessary to evaluate the empirical properties of the small area methods in the real context of statistical sampling surveys. This empirical assessment of statistical properties can be carried out on census data or pseudo-population properly generated.
Hence, Istat involvement in National and International projects on small area estimation has been directed to the study of the ecacy of small area techniques with respect to the peculiarities of the real information systems and to the improvement of methods to reect as much as possible real context.
Methodological developments and the results of experimental studies have suggested the application of small area methods to the most important Istat sample surveys so to produce statistical information at a ner level than the design planned level.
This work reports the results on the analyses of the behaviour of small area methods when they are applied to Istat household sample surveys, whose sampling design is a complex strati ed two stage sample design.
In particular, the statistical properties of the methods and their concrete applicability in a real framework is assessed through two di erent simulation studies mimicking, the rst one, the labour force survey for the estimation of the unemployment rate in the local labour market areas and, the second, the consumer expenditure survey for the estimation of the poverty rate at provincial level.
These territorial levels represent unplanned domains for their respective surveys, and consequently the direct estimators may be a ected by a high sample variability.
