Estimating the size of undeclared work from partially misclassified survey data via the Expectation–Maximization algorithm

Undeclared work (UW) is pervasive in economies. This explains the interest of public authorities in knowing its size and drivers. Unfortunately, this is a very complex task because several issues often arise in the collected data, due to the sensitivity of the topic. In sample surveys, one major problem is misclassification. Without appropriate adjustments, inference would provide biased estimates, the reason being the concealing of undeclared status. In order to overcome such problem, we developed a methodology based on a Expectation–Maximization algorithm that accounts for misclassification due to dishonest answering. Through the proposed approach, we are able to estimate the prevalence of UW and its determinants. The reliability of the methodology is validated through an extensive simulation study. An application to the Special Eurobarometer survey no. 402 on UW is provided.