It is useful to think about the uninsured as tuna and those who already have insurance as dolphins. The goal of environmentally conscious fishermen is to catch as many tuna as possible in their nets, while minimizing the number of dolphins who are caught by those nets (which happens since tuna and dolphins swim together in the ocean). If the uninsured tunas were swimming in a separate ocean than the insured dolphins, the problem would be minimized. And if the uninsured tunas greatly outnumbered the insured dolphins, then there would also be a minimal dolphin catch. But, in reality, the 47 million uninsured tunas mostly swim in a part of the ocean where there are 190 million privately-insured dolphins, making it difficult if not impossible for policymakers to design insurance nets to capture the tuna without pulling in the much more numerous dolphins.
...Indeed, roughly one-quarter of the uninsured work in firms that offer insurance. But these are very costly tuna to collect, because those uninsured who are offered insurance represent only about 7% of the total pool that is offered. So targeting this 7% of uninsured within firms without providing government subsidies to the other 93% already insured is very difficult.
Where this is leading is to an argument that health insurance mandates will be cheaper than health insurance subsidies.
Think of health insurance as military service. Suppose that at the going wage for soldiers, your do not generate enough volunteers for the army. If you raise wages to get more volunteers, you will have to raise wages for your existing soldiers, which is expensive. From a strictly budgetary standpoint, a mandate (the draft) is cheaper than a volunteer army, because you do not have to pay soldiers as much.
Of course, economists would argue that just because a draft imposes less budget cost does not mean that it causes less social cost. Forcing people to join the army is a cost to them.
Using this analogy, one could say that forcing people to buy health insurance (catching the "tuna" in Jonathan's metaphor) is a cost to them. Jonathan's "bang for the buck" analysis sets this cost to zero. After all, health insurance is good for them and/or society needs them to buy health insurance. So who cares about their individual preferences?
So drafting people into the army of the insured seems like a cost-effective thing to do.
Meanwhile, the Boston Globe is reporting that the "bang for the buck" of the Massachusetts health plan is falling far short of expectations. Maybe Gruber's fancy model needs to be re-calibrated.