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. We allow fixed costs to vary across industries, resulting in overlapping productivity distributions between formal and informal firms in the aggregate, but strict duality within industries. In doing so, we are able to generate and test predictions with regard to heterogeneity in informality across industries for the case of Indian manufacturing establishments. Consistent with the model, we find that the overlap between formal and informal establishments in the aggregate is larger than the overlaps within industries. Informality tends to decrease with average industry productivity and establishment size. Finally, more productive industries have greater overlaps in productivity between formal and informal establishments.