Abstract
Official statistics are a fundamental source of publicly available information that periodically provides a great amount of data on all major areas of citizens’ lives, such as economics, social development, education, and the environment. However, these extraordinary sources of information are often neglected, especially by business and industrial statisticians. In particular, data collected from small businesses, like small and medium-sized enterprizes (SMEs), are rarely integrated with official statistics data.
In official statistics data integration, the quality of data is essential to guarantee reliable results. Considering the analysis of surveys on SMEs, one of the most common issues related to data quality is the high proportion of nonresponses that leads to self-selection bias.
This work illustrates a flexible methodology to deal with self-selection bias, based on the generalization of Heckman’s two-step method with the introduction of copulas. This approach allows us to assume different distributions for the marginals and to express various dependence structures. The methodology is illustrated through a real data application, where the parameters are estimated according to the Bayesian approach and official statistics data are incorporated into the model via informative priors.