Small area estimation of the number of firms' recruits by using multivariate models for count data

The number of people recruited by firms in Local Labour Market Areas provides an important indicator of the reorganisation of the local productive processes. In Italy, this parameter can be estimated using the information collected in the Excelsior survey, although it does not provide reliable estimates for the domains of interest. In this paper we propose a multivariate small area estimation approach for count data based on the Multivariate Poisson-Log Normal distribution. This approach will be used to estimate the number of firm recruits both replacing departing employees and filling new positions. In the small area estimation framework, it is customary to assume that sampling variances and covariances are known. However, both they and the direct point estimates suffer from instability. Due to the rare nature of the phenomenon we are analysing, counts in some domains are equal to zero, and this produces estimates of sampling error covariances equal to zero. To account for the extra variability due to the estimated sampling covariance matrix, and to deal with the problem of unreasonable estimated variances and covariances in some domains, we propose an \u201cintegrated\u201d approach where we jointly model the parameters of interest and the sampling error covariance matrices. We suggest a solution based again on the Poisson-Log Normal distribution to smooth variances and covariances. The results we obtain are encouraging: the proposed small area estimation model shows a better fit when compared to the Multivariate Normal-Normal (MNN) small area model, and it allows for a non-negligible increase in efficiency