A two-part beta regression with mismeasured dependent variable for modeling quasi-formal employment in Europe

Quasi-formal employment refers to a situation in which a formal employer and a formal employee agree to declare only part of the wage and the rest being paid in cash to avoid tax liabilities. This phenomenon is detrimental to government budgets and to worker protection. It is therefore crucial to understand its extent and its drivers. The Eurobarometer survey no. 498 provides the information to achieve these objectives. However, several issues in the data need to be addressed with credible solutions in order to rely upon the inferences drawn. These issues are primarily concerned with the reliability of the data, which is compromised due to the phenomenon of social desirability bias. This can be defined as the tendency of respondents to provide false information when answering sensitive questions relating to socially stigmatized behaviors, such as tax evasion. In this work, we present a unified framework for modeling such survey data that overcomes the problems raised by social desirability bias and accommodates the structure of the variables of interest. In particular, we propose a two-part beta regression model where the part one models the participation in quasi-formal employment, whereas the part two models the share of annual gross income earned under the table. We allow the dependent variables of both parts of the model to be mismeasured to handle social desirability bias and generalize the part two using a beta regression framework that is suitable for the limited dependent variable representing the incidence of wage paid in cash. The performance of the estimators is evaluated through a Monte Carlo simulation study and compared with those achieved through a standard procedure that ignores the issues arising from social desirability bias. An application to the Eurobarometer survey no. 498 on quasi-formal employment is provided.