Monday, June 20, 2005

Health Insurance and the Dangers of Making Assertions without Empirical Evidence

This week is easy. Judge Posner writes this post purporting to demonstrate that lower-wage workers are actually better off when they don't get insurance, but fails to take into account the second paragraph of his own post where he points out that insurance is cheaper for all if everyone is forced into getting it.

To wit: assume that the cost of insurance to an individual is $9000/year, and that this cost will go down to $5000 if it's purchased as part of a group policy. Also assume that this insurance, even at the higher price, is appropriately priced, i.e. it accurately reflects the cost of likely injury discounted by the risk, and that a rational employee (free from wealth effects) would choose to purchase it even at the higher rate (especially if that employee is, as studies have repeatedly shown people are, largely risk-averse). Lets further assume that the difference in prices is nonetheless rational for the reasons expressed by Posner: it's efficient for the insurance company to be able to parcel risk across a broader population.

Now lets take Posner's figures and correct them with this in mind.

Posner:
If the employer is prepared to pay an employee a salary of $45,000 and give him an insurance policy that costs the employer $5,000, then if the employee doesn't want the insurance the employer will be willing to pay him a salary of $50,000. Suppose the employee has no significant assets--a realistic assumption if he is a low-income employee. Then if he becomes ill he'll be able to obtain medical care free of charge under Medicaid, though it will be of lower quality than paid-for care. Suppose the value of that lower-quality care is only $3,000. Nevertheless the employee is better off without the insurance; his net income will be $53,000 ($50,000 in salary plus $3,000 in insurance value) versus $50,000 ($45,000 in salary plus an insurance policy worth $5,000) with the insurance.

Crit Cowboy:

If the employer is prepared to pay an employee a salary of $45,000 and give him an insurance policy that costs the employer $5,000, then if the employee is forced to purchase his own insurance, the employer will be willing to pay him a salary of $50,000, but the employee will have to spend $9,000 of his own money on insurance, suffering a net personal loss of $4,000. Alternatively, he can forego medical insurance altogether. Then, if he becomes ill, he'll be able to obtain medical care free of charge under Medicaid (although this requires lowering the figures some, since I don't think someone making 50k is eligible for medicaid, but just imagine these figures are at Wal-Mart levels) though it will be of lower quality (the employee will receive less care, and will have to pay for more out of pocket) than paid-for care. Suppose the value of that lower-quality care is only $3,000. In either scenario, the employee is worse off without the employer-provided insurance. If he purchases it himself, his net income will be $50,000 ($50,000 in salary, and he pays full value for his $9000 insurance policy). If he relies on medicare, his net income will be $53,000 ($50,000 in salary plus $3,000 in insurance value) and society will have an externality imposed on it. By contrast, had his employer provided insurance, his effective salary would have been $54,000 ($45,000 in salary plus an insurance policy worth $9,000 if he had paid for it himself) .

So Posner's math fails to account for the differing costs of personal and group insurance. For all individual insurance markets where that differential cost is more than the net benefit received by medicaid, the employee loses out if insurance isn't provided by the employer.

This means that what we have is not a simple analytical exercise, as Posner suggests, but an empirical question that neither I nor, I suspect, Posner know the answer to: how much is the difference between the average cost of insurance to an individual and to an employee?

Now lets move to Becker. Becker says that there's over-use of medical care. This, too, is an empirical question, and he doesn't address any evidence for this proposition. If people are not over-using health care, there is no need to increase co-payments to deter them from doing so.

Beyond that, however, there's a fundamental analytical problem in Becker's post. Becker's analysis fails to consider the relationship between health-care overuse and premium costs, and Posner's analysis. If people over-use health care, their premiums will rise over time. If their premiums rise over time, their salaries will go down. So they're not externalizing the costs onto anyone. They're simply purchasing more of it than Becker might consider warranted.

Is this a problem? To an economist? Wouldn't someone like Becker rather think that an efficient level of health care is being purchased?

Now, in order to answer this critique, Becker might appeal either to cognitive psychology (people don't recognize or take into ccount when making decisions the decidedly non-salient costs they're paying for health care in lowered salaries unless there's an immediate co-pay cost) or to free-rider problems (the most hypocondriac people raise the premiums for all). Neither would be sufficient. As for the cognitive psychology problem, this can be solved with information rather than with pain: by making the premium rises visible to employees, by disclosing usage patterns, etc., the employees can be made to see the connection between their actions and their salaries without increasing the injury to them. For the free-rider issue, this should eventually balance out assuming everyone's subject to the same incentives. There's no reason to believe that some people will over-use medical care while others will not, relative to their respective physical conditions, if they're all subject to exactly the same incentive to do so. Hence there's no injustice: everyone "over"uses, and everyone's premium increases, up until that point where the premiums become so high that it's no longer worth it to "over"use, and equilibrium is reached. It's really microeconomics 101: this is how it's supposed to work. (Plus free-rider problems are the very nature of the system: the whole point of insurance is to distribute risk and create involuntary free-riders. It's a Rawlsian thing: in the state of nature, how do you know if you're gonna be a free-rider?)