Small area estimation in presence of non random non response. An application to the Italian Farm Structure Survey

Sample surveys are often designed to provide estimates of totals, means and other parameters only for the whole population or at most for few broad subpopulations. But since many years, the demand of such estimates for small geographic areas or domains such as socio-demographic groups is growing. Unfortunately the sample size for such domains is very small and is often reduced because of the nonresponse which is frequently related to the study variables. This situation concerns most sample surveys carried out by the National Statistical Institute (ISTAT). One of these is the two-yearly Farm Structure Survey, which has been designed to warrant accuracy only at regional level whilst policy makers are demanding estimates at a finer geographic level. Furthermore this survey, based on a stratified proportional random sample, adopt a weighting method for unit nonresponse adjustment which assumes homogeneity response behaviour within the strata. This technique inflates the original weights of the respondent farms multiplying them by the inverse of the response rate in the strata. In this work we empirically analyse the effects of nonresponse and its adjustment methods on the EBLUP estimator based on a unit level small area model. It is known that this estimator does not depend on survey weights. Moreover an essential assumption under this model is that the sample values obey to the model assumed for the population. This assumption is satisfied under simple random sampling from each area or more generally for sampling designs that use auxiliary information in the selection of samples from each area if these information are explicitly enclosed in the model. These assumptions may be valid for the complete sample but they hardly hold for subsets such as those represented by respondents in each area which usually cannot be assimilated to simple random sub-samples. Taking these issue as a starting point, in this work we evaluate the impact of different adjusting techniques for nonresponse on small area estimation. In order to perform such evaluation we considered the estimation of average surface allocated to grapevines in each Province (small area) of the Tuscany coming from the 2000 Italian Agricultural Census and from the Italian Farm Structure Survey, driven in 2003.