# Insurance choice can be bad

This is a followup to the previous post about health insurance elaborating on the fact that it can be bad to let individuals make choices about their insurance policy. I stated without much detail that “assuming sufficient options and perfect competition, the result of this individual choice would be exactly the same as if the insurers were allowed to use knowledge of $K$.” The “sufficient options” assumption is important (and not necessarily realistic), so more explanation is warranted.

Imagine there’s a genetic test that predicts the occurrence of a particular disease with overwhelming probability. Let’s call this disease H (for Huntington’s disease or maybe HIV/AIDS). Further imagine that the disease is treatable, but the treatment is expensive (not true for Huntington’s yet, unfortunately). Say the price of treatment is $c$.

If insurers are allowed to administer the genetic test and adjust policy prices accordingly, prices will converge towards being $c$ greater for those with $H$. If you have $H$, you’ll pay the entire cost yourself. This situation is clearly bad, so we’ll ban insurers from knowing about the genetic test.

However, individuals still know about the genetic test, and are allowed to make decisions accordingly. Let’s say an insurer provides two insurance policies, identical except that one pays for the treatment for $H$ and one does not. Anyone who knows that they’re $H$-negative will buy the policy that doesn’t treat $H$, and anyone who has $H$ will buy the other. If the insurer is allowed to charge different amounts for the two policies, they will adjust the prices to match the different expectations of cost. This different is $c$.

Can we ban insurers from having one policy that covers $H$ and one that doesn’t? Possibly, but it’s hard. First, we have to choose all or none; if one insurer covers $H$ and a different one doesn’t, the non-$H$ people will flock to the second insurer, and the same thing happens. Second, the connection between $H$ and the treatment for $H$ may be far from obvious, and certainly can’t be expected to be known at the time we pass any particular law. For example, Down’s syndrome increases the likelihood of recurrent ear infections, so allowing policies to not cover recurrent ear infections would penalize anyone with Down’s syndrome. This might be harmless by itself, but a thousand similar options could add up quickly.

There are probably examples of insurance policy choices which wouldn’t be problematic, but figuring out which these are is an extreme subtle proposition. Moreover, this issue will become rapidly more important as our knowledge about genetic risk factors and relations between different diseases expands. I have no confidence that these nuances can be encoded in any kind of government regulation.

Does this mean we can only have one insurance policy for everyone if we want to be fair? Unfortunately to a first approximation, it seems like the answer is yes. I’d love to hear details if anyone knows of a type of policy choice which doesn’t suffer from this problem, though.