• Two-Sided Markets, Part II: Health Insurance

    This post is cross-posted on The Finance Buff.

    This is the second of a two-post series on two-sided markets. The first post introduced basic concepts that I will apply to the discussion of health insurance markets below. I am aware of only a handful of studies that make explicit use of two-sided market theory in analysis of health insurance markets. There are many other studies that make ad hoc reference to elements of its two-sided nature.

    Two very similar papers by Bardey and Rochet (this and that), consider health insurance plans as platforms serving two groups: policyholders and health care providers. For this to be a genuine two-sided market framework we must be able to identify either (1) inter-group network externalities or (2) a sensitivity of transaction volume to how total price is split between the groups. These were the two essentially equivalent ways of defining a two-sided market discussed in my prior post.

    That the first definition (inter-group network externalities) applies is not hard to see. In general, health insurance policyholders prefer greater access to more providers. Thus, the greater the number of providers contracting with the insurance plan the more valuable that plan will be to policyholders. That’s a positive inter-group network externality. Likewise, providers prefer greater patient volume. Thus, all other things equal, more policyholders make contracting providers better off, another positive inter-group network externality.

    It is not immediately clear how to see that the second definition of a two-sided market (transaction volume sensitive to price allocation) also applies. What are the prices? What are the transactions? Policyholders pay a price: the premium. Do providers pay a price to contract with the insurer? They do. The price is the per-service discount they’re willing to provide the insurer for the expected patient volume.

    In the Bardey-Rochet model, a transaction is a unit of provider service. A sick individual consumes one unit of service and a well individual consumes none. The transaction price is the sum of premium and provider discount. Transaction volume is sensitive to the tradeoff between premium and discount. At the extreme of a zero premium, the discount would need to be so high that no providers would participate and transactions would go to zero. (This is similar in spirit to the pricing tradeoff faced by Dude in my prior post.) Very briefly (because it is not the focus of this post), Bardey and Rochet go on to use a two-sided market set-up to show that adverse selection can lead to higher, not lower, insurer profits due to the negotiating leverage the additional health care utilization provides with respect to provider discounts. Such a conclusion cannot be drawn with a one-sided view of the market as it is an inter-group phenomenon.

    The other paper I am aware of that explicitly uses two-sided market concepts in discussing the health insurance market is by Howell. Here a completely different type of two-sidedness is introduced. Insurance policyholders consist of two groups. One group consists of those who are healthy and not receiving any health care services, and the other includes those who are sick and are receiving health services (there are no preventative services in this model).

    The only way this set-up can be viewed as a two-sided market is if one can identify the transaction between the sick and healthy and if one can show that the transaction volume is sensitive to relative prices or that there are inter-group network externalities. So, where’s the transaction between the healthy and the sick policyholders? Howell’s argument is that one can interpret the health insurer’s role as balancing the interests of the healthy and the sick. In effect, the collective risk sharing arrangement establishes implicit contracts between the groups whereby the healthy provide financial resources and the sick spend them. A healthy individual is willing to enter such an implicit contract because there is a non-zero probability he will fall ill.

    But this doesn’t exactly pin down the transaction in a way that permits enumeration. My own interpretation is that the transaction is the health insurance policy itself, interpreted as a contract between the current (presumed) healthy state and the potential future unhealthy state.

    From this perspective it is not hard to see transaction sensitivity to allocation of total price between groups. If the sick pay relatively more (e.g. higher copayments relative to premium) then relatively more healthy will participate leading to a higher number of transactions (sold policies). If the healthy pay more (e.g. higher premiums relative to copayments) then relatively fewer healthy will participate, lowering the transaction volume. Alternatively, the inter-group network externalities are also easy to see. A larger group of healthy participants leads to a lower premium for all policyholders (favorable selection) while a greater number of sick raises it (adverse selection).

    Howell goes on to (rhetorically, not mathematically) embed this two-sided market model in the one involving policyholders and providers discussed previously. Another two-sided market can be found in the relation between sponsors who provide insurance subsidies (e.g. employers or the public) and policyholders. Howell calls this monstrously complex tangle of competing interests a “four-sided” market.

    It is beyond the scope of this post to lay out all the price sensitivities and inter-group network externalities for the four-sided model. It is worth noting, however, that such a model is something like what actually exists. That is, health insurers mediate an enormous number of competing interests many of which are opaque to one-sided analysis.

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    • I loved the first article’s example. Very easy to follow and is a great intro into health care.

      How do you explain my employer’s choice to only have one health care provider for its employees? The plan gives employees a certain amount of “credit” for out-of-pocket expenses. If you provide personal health information, they will increase that “credit” if you are in good health.

      Ignoring the blatant profit at the expense of privacy issue, is this adjustable cost a two-sided market model or something else entirely?

    • @LadyGeek – Thanks for the positive feedback!

      In general throwing employers into the mix makes it more complex. It is at least a three-sided market with the insurer mediating the interests of employers, individuals, and providers.

      But that’s not what you’re asking about. Your questions don’t fit into a multi-sided model framework because you’re talking about a single employer. Inter-group network externalities only apply when the number of members of one group affects the utility of another group. Your employer will only be one employer.

      To explain your employer’s behavior I don’t think you need that much complexity. The employer is minimizing costs. By directing all employees to one plan it can presumably negotiate a lower price.

      The employer is attempting to minimize health risks (hence costs) by rewarding good health with extra credit. So, if you stay in shape and don’t get high cholesterol and don’t smoke and can prove it to your employer you are cheaper for them to insure. They split the savings with you by giving you some extra health credits.

      I wouldn’t call this profit at the expense of privacy. The employer is trying to partner with you to reduce its costs and it is willing to share some credit with you. You could argue that you should get a bigger cut of the discount the employer gets. That’s a distributional issue. As a class all employees are benefiting fully from lower employer costs through higher wages and benefits. Are some getting bigger wage and benefit increases than others? That’s really the only point to argue (in general, not knowing your specific circumstances in greater detail).

    • OK, now I understand. The two-sided model does not apply in this case. It’s a simple cost reduction by the employer. “Partnering” with employees as a way to reduce costs is not the phrase we use at work.

      We see a cost increase with reduction in benefits. A lot of us are waiting for the final plan details so we can compare them to our spouse’s plan and decide from there. Understood that cost reductions are everywhere. At least there’s a maximum out-of-pocket expense – a good reason to maximize use of the Health Care Spending Account.

      What’s interesting is that it seems obvious that there are many “sides” to a market. Why wasn’t this done before? How many “sides” can you model before it reduces to either a flat or Gaussian distribution? Some food for thought.

      • @LadyGeek – The individual notions that underlie two-sided market theory are not new. They’ve been recognized for decades. What is new is putting them all together in one coherent, formal theory. That’s how theory frequently gets done. It is the formalization of ideas already known and the shedding of seemingly related ideas that don’t quite fit.

        All markets have “sides” in a loose form of the term. What is different in a two-sided market relative to a one-sided one is the presence of inter-group network externalities or volume sensitivity to relative prices (as I described in the post). You won’t see this in just any old market. While there are two “sides” in any exchange that does not make the market for that exchange a two-sided one in the formal sense. Apart from the effect on supply and demand that can be modeled in conventional one-sided market theory, in general there is no externally on buyers when there are more sellers and vice versa.

    • Now I get it. Thanks!