Insurance suffers chronically from the problem that only bad risks want to get insured, which makes the cost of insurance prohibitive and the insurance market often collapses while its presence would be a clear welfare improvement. A workaround is to force everyone to participate, thereby avoiding that good risks could weasle out. This is the principle behind health insurance mandates in most of the Western world, and it is part of the so-called Obamacare. But such mandates are difficult when there is a large informal economy, as it makes difficult tracking people, especially if access to government services, paying taxes, etc. are the way the mandate is enforced. Could in fact a mandate increase informality?
Reyes Aterido, Mary Hallward-Driemeier and Carmen Pagés look at Mexico and ask a somewhat different question, but it is still informative: Does the provision of health insurance to those without social security (mostly informals) increase informality? They find the formal sector decreased by 0.4 to 0.7% points because fewer people join it. It is not surprising that fewer people see the need to be cover by social security and thus declared their jobs, yet I find it interesting that the effect on formality is so low in a country where it is so easy to disappears from the books. Transpose that to, say, the US, where having a job is currently pretty much a requirement for health insurance coverage. Would then a health insurance mandate lower the incentive to have job? Most likely yes, but seeing how small the impact was in Mexico and considering that the lower elasticity of the formal/informal margin in the States, that effect is very likely to be very small.