Fung et al. (2019) conclude the following based on a 2017 survey of California residents:
…19 percent reported that they would not have purchased insurance had there been no penalty. We estimated that premiums would increase by 4–7 percent if these enrollees were not in the risk pool. The percentages of enrollees who would forgo insurance were higher among those with lower income and education, Hispanics, and those who had been uninsured in the prior year, relative to the comparison groups…Eliminating the mandate penalty alone is unlikely to destabilize the California individual market but could erode coverage gains, especially among groups whose members have historically been less likely to be insured.
In short, the individual mandate could help stabilize the individual market insurance pool. However, other insurance markets do exist without mandates, and–in California at least–the individual mandate may be helpful but not essential.