“Estimating Equilibrium in Health Insurance Exchanges,” P. Tebaldi (2016)

After a great visit to San Francisco for AEA and a couple weeks reading hundreds of papers while hiding out in the middle of the Pacific, it’s time to take a look at some of the more interesting job market papers this year. Though my home department isn’t directly hiring, I’m going to avoid commenting on work by candidates being flown out to Toronto in general, though a number of those are fantastic as well. I also now have a fourth year of data on job market “stars” which I’ll present in the next week or so.

Let’s start with a great structural IO paper by Pietro Tebaldi from Stanford. The Affordable Care Act in the United States essentially set up a version of universal health care that relies on subsidizing low income buyers, limiting prices via price caps and age rating limits (the elderly can only be charged a certain multiple of what the young are charged), and providing a centralized comparison system (“Bronze” or “Silver” or whatever plans essentially cover the same medical care, with only the provider and hospital bundle differing). The fundamental fact about American health care is less that it is a non-universal, privately-provided system than that it is enormously expensive: the US government, and this is almost impossible to believe until you look at the numbers, spends roughly the same percentage of GDP on health care as Canada, even though coverage is universal up north. Further, there is quite a bit of market power both on the insurer side, with a handful of insurers in any given market, and on the hospital side. Generally, there are only a handful of hospitals in any region, with the legacy of HMOs making many insurers very reluctant to drop hospitals from their network since customers will complain about losing “their” doctor. Because of these facts, a first-order concern for designing a government health care expansion must be controlling costs.

Tebaldi points out theoretically that the current ACA design inadvertently leads to high insurer markups. In nearly all oligopoly models, markup over costs depends on the price elasticity of demand: if buyers have inelastic demand in general, markups are high. In health care, intuitively young buyers are more price sensitive and have lower expected costs than older buyers; many young folks just won’t go to the doctor if it is too pricey to do so, and young folks are less likely to have a long-time doctor they require in their insurance network. Age rating which limits the maximum price difference between young and old buyers means that anything that leads to lower prices for the young will also lead to lower prices for the old. Hence, the more young people you get in the insurance pool, the lower the markups are, and hence the lower the cost becomes for everyone. The usual explanation for why you need young buyers is that they subsidize the old, high-cost buyers; the rationale here is that young buyers help even other young buyers by making aggregate demand more elastic and hence dragging down oligopoly insurer prices.

How can you get more young buyers in the pool while retaining their elastic demand? Give young buyers a fixed amount subsidy voucher that is bigger than what you give older buyers. Because buyers have low expected costs, they will only buy insurance if it cheap, hence will enter the insurance market if you subsidize them a lot. Once they enter, however, they remain very price sensitive. With lots of young folks as potential buyers, insurers will lower their prices for young buyers in order to attract them, which due to age rating also lowers prices for older buyers. It turns out that the government could lower the subsidy given to older buyers, so that total government subsidies fall, and yet out of pocket spending for the old would still be lower due to the price drop induced by the highly elastic young buyers entering the market.

Now that’s simply a theoretical result. Tebaldi also estimates what would happen in practice, using California data. Different regions of California have different age distributions. you can immediately see that prices are higher for young folks in regions where there are a lot of potential old buyers, and lower in regions with a fewer potential old buyers, for exactly the elasticity difference plus age rating reason given above. These regional differences permit identification of the demand curve, using age-income composition to instrument for price. The marginal costs of insurance companies are tougher to identify, but the essential idea just uses optimal pricing conditions as in Berry, Levinsohn and Pakes. The exact identification conditions are not at all straightforward in selection markets like insurance, since insurer marginal costs depend on who exactly their buyers are in addition to characteristics of the bundle of services they offer. The essential trick is that since insurers are pricing to set marginal revenue equal to marginal cost, the demand curve already estimated tells us whether most marginal customers are old or young in a given region, and hence we can back out what costs may be on the basis of pricing decisions across regions.

After estimating marginal costs and demand curves for insurance, Tebaldi can run a bunch of counterfactuals motivated by the theory discussed above. Replacing price-linked subsidies, where buyers get a subsidy linked to the second-lowest priced plan in their area, with vouchers, where buyers get a fixed voucher regardless of the prices set, essentially makes insurers act as if buyers are more price-elastic: raising insurance prices under price-linked subsidies will also raise the amount of the subsidy, and hence the price increase is not passed 1-for-1 to buyers. Tebaldi estimates insurance prices would fall $200 on average if the current price-linked subsidies were replaced with vouchers of an equivalent size. Since young buyers have elastic demand, coverage of young buyers increases as a result. The $200 fall in prices, then, results first from insurers realizing that all buyers are more sensitive to price changes when they hold vouchers rather than pay a semi-fixed amount determined by a subsidy, and second from the composition of buyers therefore including more elastic young buyers, lowering the optimal insurer markup. The harm, of course, is that vouchers do not guarantee year-to-year that subsidized buyers pay no more than a capped amount, since in general the government does not know every insurer’s cost curve and every buyer’s preferences.

Better still is to make vouchers depend on age. If young buyers get big vouchers, even more of them will buy insurance. This will drag down the price set by insurers since aggregate elasticity increases, and hence old buyers may be better off as well even if they see a reduction in their government subsidy. Tebaldi estimates that a $400 increase in subsidies for those under 45, and a $200 decrease for those over 45, will lead to 50% more young folks buying insurance, a 20% decrease in insurer markup, a post-subsidy price for those over 45 that is unchanged since their lower subsidy is made up for by lower insurer prices, and a 15% decrease in government spending since decreased subsidies for the old more than make up for increased subsidies for the young. There is such a thing as a free lunch!

Now, in practice, governments do not make changes around the margins like this. Certain aspects of the subsidy program are, crazily, set by law and not by bureaucrats. Note how political appearance and equilibrium effect differ in Tebaldi’s estimates: we decrease subsidies for the old and yet everyone including the old is better off due to indirect effects. Politicians, it goes without saying, do not win elections on the basis of indirect effects. A shame!

January 2016 working paper. The paper is quite concisely written, which I appreciate in our era of 80-page behemoths. If you are still reluctant to believe in the importance of insurer market power, Tebaldi and coauthors also have a paper in last year’s AER P&P showing in a really clean way the huge price differences in locations that have limited insurer competition. On the macro side, Tebaldi and network-extraordinaire Matt Jackson about deep recessions making a simple point. In labor search models, the better the boom times, the lower productivity workers you will settle for hiring. Thus, when negative economic shocks follow long expansions, they will lead to more unemployment, simply because there will be more relatively low productivity workers at every firm. Believable history-dependence in macro models is always a challenge, but this theory makes perfect sense.


2 thoughts on ““Estimating Equilibrium in Health Insurance Exchanges,” P. Tebaldi (2016)

  1. “a couple weeks reading hundreds of papers while hiding out in the middle of the Pacific”

    Why? Are you on the hiring committee?

    • afinetheorem says:

      Post AEA is a bit late for that! No, I am just starting a big new project and needed to catch myself up on a somewhat obscure literature from the 70s and 80s. I just read the job market papers for my own entertainment!

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