### Why might increased insurance coverage decrease Emergency Department use?

9/10/2014 02:01:00 PM
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Adriana McIntyre points us to a recent study in Health Affairs showing that the expansion of health insurance coverage to adults under 26 years old, under the new ACA rule that children can stay on their parents' plans, has actually decreased emergency department (ED) use. Though notably studying a different population, this is the opposite of what the Oregon Health Insurance Experiment (OHIE) found, where expansion of medicaid coverage increased ED visits. For some reason, prior to the OHIE, the idea that expanding coverage would reduce ED use became conventional wisdom, but as Aaron Carroll explained back then, it makes more sense for expanded coverage to increase ED use--as he put it, "Improved access will lead to, well, increased access." Indeed, insurance coverage makes ED visits cheaper, so why would making something cheaper decrease demand for it? Proponents of the insurance-reduces-ED theory have been extremely vague on exactly what is supposed to drive that result, and I think this lack of an explicit theory has hindered empirical study of the topic.

According to the study McIntyre cites, some individuals who would have chosen ED visits when they have no insurance would instead opt for an alternative with insurance (it helps to think of this as a choice between ED and doctor's office, but for our purposes "doctor's office" is just a stand-in for anything other than ED, including no care at all). Let $B$ represent their budget set without insurance, and $B'$ is the budget set with insurance, and denote the choice of ED over doctor's office as $e$ while $d$ denotes the choice of doctor's office instead of ED.[1] The relation $C\left(\cdot \right)$ tells us which element of a given budget set the individual will choose (note that the choice can be a set of alternatives that the individual is indifferent between). Since the study showed that gaining coverage--moving from budget set $B$ to budget set $B'$--caused some individuals to switch from $e$ to $d$, this implies that we have $$e\in B~and~e\in C\left(B\right)$$ as well as$$d\in B'~and~d\in C\left(B'\right).$$

Now, the fact that the study observed a decrease in ED visits means we have $d\in C\left(B'\right)$ but $e\notin C\left(B'\right)$ for at least some individuals (if not, then the study estimate isn't causal). What accounts for this difference in choice between the two budget sets?

Suppose that both the ED and doctor's visit are affordable without insurance, so that $e,d\in B$, and that they are both still affordable with insurance $e,d\in B'.$ This would mean we have a contradiction--this says that the consumer simultaneously considers the doctor's office a better option than the ED, while also considering the ED a better option than the doctor's office! If you are familiar with the theory, I'm invoking the Weak Axiom of Revealed Preference (WARP) here. The only way to avoid a contradiction is if either $d\notin B$ or $e\notin B'$. Assuming WARP holds, whenever anyone says expanding coverage reduces emergency room usage, they are really making one (or both) of two possible empirical statements: that either 1| an uninsured person can afford ED visits but not the doctor's office, or that 2| an insured person can afford the doctor's office but not an ED visit. It would be helpful to know which.

Most studies--including my own dataset comparing ED and clinic visits--suggest that the ED is somewhat more expensive than the alternatives, so it would be a bit weird if $d\notin B.$ Weird, but not totally impossible if you consider, for example, that many doctor's offices will turn away patients that do not have insurance, regardless of whether they can pay in cash. If this is what's driving the result in this study, then we've uncovered a useful policy insight: we can reduce health costs by requiring doctor's offices to accept cash in lieu of insurance. Another possibility is search costs: maybe doctor's offices are actually more expensive than EDs once you include the costs of finding a doctor who will accept you--a process that takes time and effort on the part of patients. It may simply be that EDs are easy to locate, while doctor's are not. That too would be useful to know.

On the other hand, maybe $e\notin B'.$ Although it may sound weird at first that gaining insurance access can mean you can no longer afford to go to the emergency room, but this is actually realistic for some people. Even though insurers pay a portion of the ED bill, consumers are in turn paying the premiums that pay for that portion of the bill, so that having insurance does not expand one's budget set overall. What insurance does do, however, is substitute some elements inside the budget set for some elements outside of the budget set, which would be the case if, for example, insurers require a higher co-pay for ED visits than for the alternatives. On twitter, Seth Trueger offered this bit of evidence for this:

Thus, having a clear theoretical model helps elucidate empirical study of the impact of insurance on ED use. Yes, gaining insurance can reduce ED use, and ascertaining exactly why can reveal important policy implications.

[1] Note, $e,d$ are actually vectors in which just one of the elements represents the choice of healthcare, and the rest of the elements represent the choices of all other goods and services. We are really talking about choices between consumption bundles, which is why it is ultimately possible that getting insurance--whose premium is deducted out of the budget--can make bundles associated with ED use less affordable than without insurance.