Strict duality and overlapping productivity distributions between formal and informal firms

This paper develops a multi-industry general equilibrium model where entrepreneurs within each industry can decide to operate formally or informally. The model generates a rich set of predictions including productivity cut-offs for formal and informal firms to operate within different industries. In doing so, it matches empirical research that finds an overlap in the aggregate productivity distributions of formal and informal firms, while being consistent with theoretical predictions of strict duality within industries. Our explanation for this outcome is that it is natural result of fixed costs varying across industries. We offer evidence that the overlap between formal and informal firms in the aggregate is larger than the overlaps within industries for the case of Indian manufacturing establishments. Our model is also consistent with other features of the data in that it can explain high levels of competition between formal and informal firms that decrease with formal firm size.