Bayesian approach for nonresponses

Studies on business have many sources of different origins, nature and contents but most of the information available have a lake of infos: “elderly” (old data), “myopic” (deals only with the enterprise structure e.g. ASIA the ISTAT annual statistical enterprise archive). That is why sector surveys become an essential source of information to study a specific economic activity area. Several methodological problems arise in these research field also due to the complexity of the issues raised (and therefore of the questionnaire). In this domain the main problem is the nonresponse where it is possible to define two principle type of missing data: cases whose coverage information is guaranteed by other sources of information (e.g. company size) and on the contrary cases without (e.g. there is information on new skills but not on stocks – Excelsior by Chamber-Union and Ministry of Labour). By these assumptions derives that missing data is the main issue that researchers have to face to, in such kind of studies (cfr. Little (1986), Rubin (1976), Rubin (1996), Rubin and Schenker (1986), Sisto (2006), Schafer and Graham (2002)). In literature many procedures have been presented to solve the missing data problem. Proposals by classic statisticians can be catalogued in two main categories bootstrap and EM algorithms. Bayesian approaches are instead focused on the ways to obtain the posterior distribution used to estimate the missing data. In this paper we apply classic and Bayesian procedures in a study on Italian Information Technology sector. This study considers many information about Italian IT firms such as the structure, areas of activity and technological skills; the customers; the IT market (prospects / perception); the association / institutional participation an so on. The full list of Italian IT enterprises (and their attributes) was supplied by the Milan Chambers of Commerce. Starting from the population of interest and considered the specific source used, incomplete auxiliary variables were discarded, so the stratification in the sample design has been made by various types of companies in business and by region (Nuts2). It was carried out simulations related to the nonresponse based on the different approaches considered. The benchmarck was used to measures the effectiveness and efficiency, and also the applicability and simplicity of the methods.