Opt Out or Top Up? Voluntary Health Care Insurance and the Public vs. Private Substitution

We investigate whether in a mixed insurance system, people enrolled into voluntary health care insurance (VHI) substitute public consumption with private (opt out) or just enlarge their private consumption without reducing reliance upon public provisions (top up). We specify a joint model for public and private specialist visits counts, allowing for different degrees of endogenous supplementary insurance coverage. We find evidence of opting out: richer and wealthier individuals consume more private services and concomitantly reduce those services publicly provided through selection into for‐profit VHI. Accounting for VHI endogeneity in the joint model of the two counts is crucial to this conclusion.