On Sunday I looked at Washington state’s failed attempt to implement universal insurance coverage, after its individual mandate was repealed.

I heard from a number of readers questioning whether Washington state serves as a good analogy for what would happen to the Affordable Care Act, should its mandate be overturned. Most of the objections had to do with the fact that the federal law has insurance subsidies, which could make insurance affordable, where the Washington law did not. Bob Doherty at the American College of Physicians tweets, “WA didn’t have the ACA’s [health insurance] subsidies so even without mandate, may not lead to a ‘death cycle.’”

Lucky for us, MIT health-care economist Jonathan Gruber has studied this exact issue, probing the roll of subsidies and mandates in encouraging enrollment. His work has found that, while subsidies do help a bit, the mandate appears to play a critical role in increasing coverage.

Gruber published research last year in the New England Journal of Medicine, looking at the Massachusetts law. The state’s health-reform law offered fully-subsidized health insurance, for those below 150 percent of the federal poverty line, starting in October 2006. With the individual mandate not kicking in until December 2007, that created a natural experiment to look at what happens when subsidies are in place — but a requirement to buy coverage isn’t.

As you can see in the chart below, not much happens. Insurance enrollment rates did increase after the subsidies rolled out. It’s only after the mandate kicks in, however, that they seriously spike:

It’s worth noting here that the big jump in enrollment is concentrated among the healthier enrollees, the exact people the mandate is supposed to encourage to purchase coverage. The fact that it was a surge when the mandate went into effect — rather than healthy people merely being slower to take advantage of subsidies — suggests to Gruber and his colleagues, “that enrollment by the healthy was not simply slower than enrollment by the unhealthy, but rather that the mandate has a causal role in improving risk selection.”