MichaelAMorrise_2020_Chapter4TheDemandForH_HealthInsuranceThirdE.pdf

CHAPTER

65

4THE DEMAND FOR HEALTH INSURANCE

Life is a gamble. Suppose we were to flip a coin. If it comes up heads, you lead a healthy, normal life. If it comes up tails, you become seriously ill. Medical science can return you to a healthy state, but medical science is

not cheap. Treatment will cost you $20,000, plus some associated pain and suffering. Are you willing to buy a health insurance policy to attenuate the financial consequences of your potential bad luck?

The correct response is “maybe.” It depends on the price of the policy and the nature of the coverage. In this chapter, we present the theory of insurance and develop four hypotheses about the conditions under which we would be willing to buy coverage. We also use these hypotheses to begin to explain some of the data on health insurance coverage that we examined in chapter 3. At first blush, the theory of insurance appears inconsistent with real-world experience. This is largely because the simple theory abstracts from real-world complexities. In particular, it ignores adverse selection, employer-sponsored health insurance, and the special tax treatment of health insurance. We will anticipate future chapters by introducing these topics and the roles they play in the demand for health insurance.

The Theory of Insurance

Friedman and Savage (1948) and Ehrlich and Becker (1972) viewed the demand for insurance as reflecting the maximum we would pay, over and above the expected loss, to avoid the consequences of the loss. The expected loss is the amount we would expect to pay, on average, if the event occurred many times. Thus, if we would have to pay $20,000 every time we flip a coin and heads occurs and pay $0 whenever tails appears, then the expected loss for 100 flips of our coin is $10,000 on each flip. Sometimes, we will have to pay nothing; we win. Sometimes, we will have to pay $20,000; we lose. On average, we will pay $10,000 per flip.

Again, consider the question of insurance against the financial conse-quences of the coin flip. Are you willing to pay more than $10,000 to avoid the coin flip? If so, you are like most of us and are risk averse. You are willing to pay more than the expected loss to avoid the consequences of the loss. Stated somewhat differently, you are willing to pay some loading fee over and above the actuarially fair premium to avoid the consequences. Insurance exists

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because there are enough of us who feel that way. The extra amount we are willing to pay, often called a risk premium, means that the potential exists for someone to come in and get 100 or more of us to buy an insurance policy from her. Her claims costs will be $10,000 on each policy, on average. The risk premiums we are willing to pay will compensate her for running the program.

Our simple insurance model suggests that many of us would pay a risk premium (plus the expected loss) to avoid the consequences of the coin flip. What is the maximum amount you would be willing to pay? It depends on three factors: how “chicken” you are, how much you would lose if the bad outcome occurred, and how great the chances are that the bad outcome will actually occur. How chicken you are is merely a reflection of your unwilling-ness to bear risk. The more chicken—that is, the more risk averse—you are, the larger will be the risk premium and the more you are willing to pay to get coverage. This fact raises an important point. Everyone does not have the same demand for insurance. Some will prefer broader or deeper cover-age. Others will prefer to buy much less. Some may prefer to buy none at all.

We need to formalize this discussion a bit. When we say that someone is risk averse, what we mean is that the loss of $1 reduces their well-being by more than the gain of $1 increases it. This is just another way of saying that risk-averse individuals have diminishing marginal utility of wealth. Each dollar of wealth makes them better off, but each additional dollar is not as satisfying as the one before. This idea is no different than the discussion you undoubtedly had in an introductory economics class, except that in that class, the discussion revolved around the diminishing marginal utility of beer, or pizza, or ice cream cones consumed at a single sitting.

Exhibit 4.1 illustrates this idea. The curve depicts total utility of wealth. The individual whose utility of wealth is graphed here receives 4,727 units of utility from $20,000 and 8,000 units of utility from $40,000. Each additional dollar increases total utility, so the curve is upward sloping. How-ever, each additional dollar gives less additional utility than the previous dol-lar, so the curve increases at a decreasing rate.

Now consider the coin-flip problem. If it comes up heads, the person represented in Exhibit 4.1 with an initial wealth position of $40,000 will have to pay $20,000. If it comes up tails, he pays nothing. The endpoints of the straight line in exhibit 4.1 reflect these outcomes. He could end up with $40,000 or $20,000. The midpoint of the line reflects the expected loss of many coin flips. The expected loss is $10,000, so he would move from a wealth position of $40,000 to one of $30,000. How much does he value the $30,000 wealth position? If he had $30,000, it would give him 7,090 units of utility. However, he doesn’t have $30,000; he has $40,000 and a 50/50 chance of losing $20,000. How much utility does that provide? The answer is 6,364 units of utility. According to exhibit 4.1, the individual gets just as much utility from a 50/50 chance of losing $20,000 as he does from having a certain $26,150.

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Chapter 4: The Demand for Health Insurance 67

This individual is willing to pay up to $13,850 to avoid the coin flip: $10,000 reflects the expected loss, and $3,850 is the risk premium. Two points are important here. First, the risk premium is the measure of our willingness to pay for insurance. It is the amount over and above the expected loss that we are will-ing to pay to avoid the consequences of the loss. This risk premium is the reason insurance can exist. Insurers must pay to settle claims; claims are the expected losses. If insurers are to cover administrative and marketing costs and make at least a normal profit, they must collect something over and above the expected loss. The presence of a (big enough) risk premium allows this to occur.

Second, the risk premium reflects the most that we are willing to pay. If the insurance market is competitive, we may end up paying much less than what we are willing to pay for coverage, just as we often pay much less than what we are willing to pay for a cold beer.

Not everyone has the same degree of risk aversion. Most of us are at least somewhat uncomfortable dealing with risk, others are very uncomfort-able, and some love it. Thus, in principle, each of us has his own unique total utility curve like that shown in exhibit 4.1. The box How Risk Averse Are You? gives you an opportunity to determine your personal degree of risk aversion. Answer enough of the questions to allow you to plot four or five points on your own total utility curve and see how much you would be willing to pay to avoid this gamble. But be warned: Although the questions themselves are not hard, coming up with honest answers is!

EXHIBIT 4.1The Risk Premium

Utility of Wealth Total utility

Wealth

8,000

6,000

4,000

2,000

0

7,090

$10,000 $20,000 $30,000 $40,000 $50,000

$26,150

Risk premium,

$3,850

Expected loss,

$10,000

4,727

6,364

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How Risk Averse Are You?

To determine how risk averse you are, consider the following exercise. First, choose two dollar amounts—say, $40,000 and $20,000—as we did in exhibit 4.1. Next, assign arbitrary utility values to each. The only requirement is that the utility of $40,000 be greater than that of $20,000. In exhibit 4.1, we chose the utility of $40,000 to be 8,000 [U($40,000) = 8,000] and the utility of $20,000 to be 4,727 [U($20,000) = 4,727]. You choose whatever you like, and plot the two points on a graph like exhibit 4.1.

Now you are faced with a series of coin flips. Here is the first: If the coin comes up heads, you win $40,000. If it comes up tails, you win $20,000. What is the minimum amount you would accept to sell your right to this single flip of the coin? Your answer is $X. We now need to know the utility value associated with your answer. To do this, we compute the expected utility (EU):

EU = .5[U($40,000)] + .5[U($20,000)] = U($X)

That’s simply the probability of getting heads (.5) times the utility if heads occurs U($40,000) plus the probability of tails (.5) times the utility if tails occurs U($20,000). Substituting what we already know (from the example in the chapter discussion):

EU = .5[8,000] + .5[4,727] = U($X),

EU = 4,000 + 2,364 = U($X), and

EU = 6,364 = U($X).

If you said that the minimum you would accept was $26,150 (as we did in exhibit 4.1), then X = $26,150, and the U($26,150) is 6,364. Plot the point that emerged from your answer on your graph.

Now consider a second gamble. If heads occurs on your single coin flip, you get the value you chose for $X ($26,150 was our choice in exhibit 4.1), and if tails occurs, you get $40,000. What is the minimum amount you would accept to sell your right to this coin flip? Choose your answer and redo the math:

EU = .5[U($X)] + .5[U($40,000)] = U($Y),

EU = .5[U($26,150)] + .5[U($40,000)] =

U($Y) (in the case in exhibit 4.1),

EU = .5[6,364] + .5[8,000] = U($Y), so

EU = 7,182 = U($Y).

(continued)

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Chapter 4: The Demand for Health Insurance 69

Hypothesis I: The Degree of Risk Aversion

Your mother is likely to have a different tolerance for risk than you do. You know how she worries! Suppose your utility curve was shown in exhibit 4.1. Because your mother is less willing to take chances than you are, she is more risk averse. Her total utility will lie above yours over the relevant range shown in exhibit 4.2. When we again play out the 50/50 chance of losing $20,000, we see that her risk premium is $5,380. She is willing to pay $5,380 to avoid the consequences of the coin toss. This reflects the first hypothesis that emerges from the theory: As the degree of risk aversion increases, the size of the risk premium increases, and the probability that we will buy insur-ance increases. Because your mother is more risk averse than you are, she is more likely to buy insurance than you are, other things being equal. The other equal things are the conditions of the coin toss: the fair coin, the same possible outcomes, and the same initial wealth positions. This rather obvious hypothesis begins to give us some insight into the mix of people who do and do not have health insurance.

In the context of auto safety, the National Highway Traffic Safety Administration (2003) says, “The apparent disregard for one’s own personal safety appears to be a defining element of youth.” If this is true, it suggests that young people are less risk averse than older folks. As such, they are will-ing to pay smaller risk premiums and, therefore, are less likely to buy insur-ance. This tendency could begin to explain why more than 30 percent of those in the 21–24 age group did not have health insurance prior to the ACA (see chapter 3). This difference in tastes for uncertainty would also imply that even if young folks had the same size and probability of loss, they would be less likely to buy coverage in the ACA.

If your answer is $30,770 (as was ours in exhibit 4.1), then the utility of $30,770 is 7,182. Plot the utility associated with your answer for $Y. From here on, simply set up similar gambles of two known dollar amounts, identify your minimum acceptance price, and then compute the utility value and plot it. Once your individual curve has been plotted out, you can consider losses as we did in the chapter discussion and determine your risk premium for a relevant potential loss.

Note, however, that your answers may differ greatly from those in the example. You have different tastes for risk than others do. As a consequence, your graph may look different from the one in exhibit 4.1. In fact, if you are a risk lover, your curve will be convex from below rather than concave. If so, the model predicts that you will not be buying any insurance!

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Hypothesis II: The Size of the Potential Loss

The size of the possible loss is also relevant. If heads in the coin toss only implied a $200 loss, you might be willing to pay only $10, plus the $100 expected loss, to avoid the consequences. At $20,000, you might be willing to pay $3,850, plus the $10,000 expected loss; at $200,000, you might be willing to pay $10,000, plus the expected loss of $100,000, to avoid the consequences. As the size of the possible loss increases, the risk premium we are willing to pay increases. Exhibit 4.3 demonstrates this effect. It reproduces exhibit 4.1 but includes the circumstance where heads on the coin flip yields a $30,000 loss instead of just $20,000. A very risk-averse individual is willing to pay a risk premium of $4,614 to avoid this risk, rather than the $3,850 risk premium to avoid the smaller risk. Thus, as the size of the possible loss increases, the risk premium gets larger, and we are more likely to buy insurance.

This hypothesis predicts, for example, that other things being equal, people will be more likely to buy hospital insurance than dental insurance. It also suggests that coverage for big-ticket, or catastrophic, loss is more valuable to consumers than is coverage for first-dollar losses. Thus, if health insurance were to become more expensive, we would expect consumers to

Utility of Wealth

Your total utility

Wealth

8,000

6,000

4,000

2,000

0$10,000 $20,000 $30,000 $40,000 $50,000

Your mother’s risk premium,

$5,380

Expected loss, $10,000

Your mother’stotal utility

EXHIBIT 4.2Effect of Change in Risk Aversion

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Chapter 4: The Demand for Health Insurance 71

shift away from coverage for physician office visits or prescription drug cov-erage but retain coverage for hospital care. They may do this by switching to a policy that has a higher deductible or one with larger copays associated with ambulatory service use. Note that this hypothesis provides some of the rationale for catastrophic health insurance plans and health savings accounts (HSAs). A catastrophic plan only provides coverage after a relatively large deductible, perhaps $3,000 or $4,000, has been met. An HSA is a form of health insurance that ties a catastrophic health insurance plan to a tax-sheltered bank account on which you can draw to satisfy the deductible. We discuss these plans in chapter 17.

Hypothesis III: The Probability of Loss

The size of the risk premium also depends on the probability of the loss occurring. If instead of a 1 in 2 chance of a bad outcome, suppose the chance were only 1 in 10. Then we would be willing to pay only a very small risk premium, perhaps only $400 in addition to the $2,000 expected loss (0.1 × $20,000 + 0.9 × $0 = $2,000) to avoid the gamble. Surprisingly, the model also suggests that we would not pay much above the expected loss for a policy that insured against an event that was virtually certain to occur. This

Utility of Wealth

Wealth

8,000

6,000

4,000

2,000

0$10,000 $20,000 $30,000 $40,000 $50,000

Risk premium with possible $30,000 loss

Risk premium with possible $20,000 loss

Source: Data from Health Insurance Association of America (1990).

EXHIBIT 4.3Effect of Change in the Magnitude of Possible Loss

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outcome is demonstrated in exhibit 4.4. Here, we again reproduce exhibit 4.1, but now we shift the probability of loss. A 50/50 chance of a loss was characterized in the original exhibit as bisecting the straight line between the two possible outcomes. If the chance of a loss is only 1 in 10, however, then the expected loss appears one-tenth of the way from our initial wealth posi-tion, and the risk premium in exhibit 4.4 is only a few hundred dollars. As the probability of a loss increases, the expected loss line in the exhibit shifts further to the left. As it does so, the risk premium continues to increase in size, reaches some maximum, and then starts to decrease. This is the third hypothesis. As the probability of the loss increases, the size of the risk pre-mium initially increases but then declines, and the probability of buying insurance initially increases but then declines.

This hypothesis is the least intuitive, but it is clear with a little thought. We do not buy insurance for very small-probability losses because the expected loss is very small and the risk premium associated with a small expected loss is even smaller. But as the probability of loss increases, cover-age is more attractive. However, we also do not buy coverage for very likely events. If you knew that the cost of some medical procedure was $20,000 and that you had a 95 percent chance of needing this procedure, then the expected loss would be $19,000. How much more than $19,000 would you pay to avoid the consequences of paying $20,000? The answer is “not much.” Thus, the theory says we do not buy coverage for virtually certain events.

Utility of Wealth

Wealth

8,000

6,000

4,000

2,000

0$10,000 $20,000 $30,000 $40,000 $50,000

Risk premium, 9 in 10 chance

Risk premium, 1 in 2 chance

Risk premium, 1 in 10 chance

EXHIBIT 4.4Effect of

Change in the Probability

of Loss

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Chapter 4: The Demand for Health Insurance 73

But you say, “Suppose I know that my probability of loss is 95 per-cent, but the insurer doesn’t know this. Surely, I would buy coverage under this circumstance.” The answer, of course, is yes, you would. The problem you raise is called adverse selection. You know more about your likely use of health services than does the insurer, and you use this knowledge to your best advantage when buying insurance. This issue is fundamental for insurers, and we will spend chapters 5, 6, and 7 dealing with it. The insurer tries to reduce this problem by putting you in a risk class that reflects your expected claims experience. In our simple insurance model, you and the insurer have the same (complete) information. So, you might like to buy the coverage designed for others but no insurer would sell it to you. Under the terms of the ACA, however, an insurer may not charge you a higher premium based on your higher expected loss. This law gives those with knowledge of their higher utilization an incentive to enroll in the insurance plan.

Hypothesis IV: The Wealth Effect

Finally, the maximum amount we are willing to pay depends on our wealth position. People with greater wealth are able in some sense to self-insure against losses that the rest of us might buy insurance to protect against. Exhibit 4.5 shows the effect of higher wealth. It takes the individual in exhibit 4.1 with the same 50/50 chance of losing $20,000. However, here

Utility of Wealth

Wealth

8,000

6,000

4,000

2,000

0$10,000 $20,000 $30,000 $40,000 $50,000

Risk premium, $40,000 wealth

Risk premium, $50,000 wealth

EXHIBIT 4.5Effect of Change in Wealth

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he has an initial wealth position of $50,000 instead of $40,000. The risk pre-mium associated with the expected loss of $10,000 is $2,307, less than the risk premium of $3,850 in exhibit 4.1. As wealth increases, the risk premium declines, and we are less likely to buy insurance.

This could also be called the Best Buy hypothesis. Whenever you pur-chase an electronic device or electrical appliance from Best Buy, the clerks ask if you wish to buy the extended warranty. They are asking if you want to buy insurance. We could test the wealth hypothesis by simply knowing the zip codes in which customers reside and whether they purchased the extended warranty. From the zip codes, we could go to recent census data and deter-mine the average household income in the zip code; this serves as a proxy for wealth. Insurance theory predicts that those in the more-affluent zip codes will be less likely to buy the extended warranty

Your reaction to this hypothesis is likely to be simple disbelief, because all the empirical data suggest that more-affluent people are more likely, not less likely, to have health insurance. This discrepancy between the theory and our real-world observations has to do with the complexity of the real world. Recall from chapter 1 that one of the key reasons for the growth of health insurance in the twenty-first century is the tax-exempt status of employer-sponsored health insurance. Factors such as this are excluded in our simple model.

To summarize: This simple model is the basis of the demand for health insurance. In the absence of employers, tax subsidies, and the like, we expect to see four sorts of behavior:

• People who are more risk averse will buy more health insurance.• People will be more likely to buy insurance for events that have large

financial consequences.• People will be less likely to buy insurance for events that are very

unlikely or very likely to occur.• People will be less likely to buy insurance as their wealth position

increases.

“Health Insurance: The Access Hypothesis” provides an additional hypothesis.

Taxes and Employer-Sponsored Health Insurance

Analysis of the demand for health insurance is complicated by the fact that most people in the United States get their insurance through their workplace. The reason for this is twofold: Workers value health insurance, and it is less costly when purchased through an employer. Both points are important.

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Chapter 4: The Demand for Health Insurance 75

Workers do value health insurance. A Harvard Business Review study (Jones 2017) reported that when choosing between a high-paying job and a lower-paying one with better benefits in 2016, 88 percent of respondents said better medical benefits would get some or serious consideration. More flexible hours got the same consideration; all other options were less appeal-ing. Thus, because many people value health insurance, they are willing to trade some of their compensation for health benefits. (This willingness to trade wages for benefits is key to understanding employer-sponsored health insurance; we consider it in chapter 14.)

Health insurance also tends to be less expensive when purchased through an employer for three reasons. The first has to do with “favorable selection,” the flip side of adverse selection. Employed people tend to be healthier, on average, than those who are unemployed. Employment serves as a good signal of lower expected claims costs, and consequently, an employer group can usually purchase coverage at a lower price than can an individual.

Health Insurance: The Access Hypothesis

In addition to the four classic rationales for the purchase of health insurance presented here, Nyman (1999) argued for a fifth consideration: the access motive. The argument is straightforward. Some health conditions, should they occur, are so expensive that they exhaust your wealth. Because you could not pay for such treatment in the first place, under the traditional rationales, you would not buy insurance to avoid the consequences of the event occurring. Nyman argued that health insurance may be the only mechanism whereby you could obtain such treatment and that people do buy coverage to have such treatments available to them, should they need them.

The second reason for lower costs has to do with the nature of the existing tax laws. Health insurance is not taxed as federal or state income, nor is it subject to Social Security and Medicare payroll taxes. Thus, if an employee values a dollar of health insurance as equivalent to a dollar of take-home pay, an employer need only spend a dollar on health insurance rather than a dollar plus tax on money compensation. Third, there are economies of scale in the marketing and administration of employer group plans, relative to individually purchased insurance.

Tax advantages have provided a significant incentive for employer pro-vision of health insurance. As discussed in chapter 1, employer contributions to group health insurance are exempt from federal and state personal income taxes. They are also exempt from federal payroll taxes for Social Security and

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Medicare. This tax treatment can be viewed as a subsidy for the provision of health insurance (Feldstein and Allison 1974; Miller 2003). Workers in the 25 percent federal income tax bracket, paying 5 percent state income tax and 7.65 percent in Social Security and Medicare taxes, would find that an extra dollar of employer-sponsored health insurance effectively cost them less than 63 cents. If workers are in a higher tax bracket, the tax subsidy for employer-sponsored health insurance is even greater.

This tax incentive is likely to explain why we observe that more-affluent people have more health insurance. With a progressive tax system as in the United States, higher incomes imply higher tax rates. Higher tax rates reduce the effective price of employer-sponsored health insurance, and at these lower effective prices, people buy more coverage. Thus, the tax subsidy provides an incentive for broader and deeper coverage.

In the simple insurance market discussed earlier, someone may not purchase dental coverage because the size of the potential loss is relatively low. The tax subsidy reduces the effective price, encouraging workers to press their employers to include dental coverage in the benefit package. Similarly, the tax subsidy encourages the coverage of events with low expected losses, such as well-baby care and preventive services.

The purchase of health insurance through the employer is a complex issue. It involves not only the premium charged but also the tax rates of workers and the relative costs across firms. (We will examine the empirical literature on the effects of tax law changes in chapter 15.)

The tax incentives also complicate the business decision to change the coverage of health benefit plans. Suppose, for example, that a benefits manager discovers the cost-saving implications of implementing greater cost sharing in the form of larger out-of-pocket payments for health services. The firm implements this change in a new health insurance plan. As expected, claims costs decline. However, workers correctly view this change in benefits as a diminution of their compensation. To keep the best workers from leaving for other firms, the employer decides to raise wages. Indeed, if full-coverage insurance caused workers to consume units of healthcare that were only of minimal extra value to them, the cost savings from reduced claims should be enough to make the workers whole and have something left to enhance firm profits. That is, the employer has to add something to the compensation bas-ket to make up for the reduced health insurance coverage, thus “making the worker whole.” As a result, benefits changes have to not only save money, but save enough money to make workers whole—after tax considerations. This hurdle is a high one to cross.

The tax treatment of employer-sponsored health insurance also plays a role in the ACA. The law requires that in 2018 (later changed to 2022), any employer-sponsored plan that provides individual coverage greater than

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Chapter 4: The Demand for Health Insurance 77

$10,200 or family coverage of greater than $27,500 will face an excise tax of 40 percent of the amount in excess of these thresholds. Based on our frame-work in this chapter, we should expect that this tax will result in reductions in the generosity of health benefits in plans subject to the tax. We should expect that the plans will reduce benefits that are least valuable to workers, subject to the limits imposed by essential benefits provisions of the ACA.

Summary

• Insurance exists because enough people are willing to pay something over and above the expected loss to avoid the consequences of the loss. This willingness to pay is called the risk premium.

• The greater the risk premium, the more likely we are to buy insurance.• The greater the extent of risk aversion—that is, the greater the level of

discomfort with uncertain outcomes—the larger the risk premium we are willing to pay.

• The greater the size of the potential loss, the larger the risk premium.• The risk premium increases with the probability of a loss, reaches some

maximum, and then declines with higher probabilities of loss.• The risk premium declines with greater wealth.• The tax treatment of employer-sponsored health insurance serves to

reduce the price of health insurance and may outweigh the effects described by the pure theory of insurance.

Discussion Questions

1. Suppose that health insurance premiums have increased substantially in the past year. You are a member of your firm’s fringe benefits committee and have been charged with reducing the cost of health insurance. Based on the analysis in this chapter, what sort of changes to the benefits package would you recommend? Why?

2. Suppose that Congress was successful in reducing the marginal income tax rates on money wages. What effect would you expect this to have on the nature of health insurance benefits offered by employers? Why?

3. One of your high school buddies has just graduated with her master’s in business administration and accepted a great job in a small consulting firm. However, the firm does not offer health insurance. Over dinner one night, she asks you whether she should buy some health insurance, and if so, what kind. What do you say? Why?

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4. How would your answer to question 3 have changed prior to 2019, when the ACA coverage mandate penalty was eliminated?

5. Prior to the ACA, some insurers offered “mini–medical plans.” These plans cover routine services, provide little hospital coverage, often cap payouts at $10,000 or less, and can cost as little as $40 per month. Ignoring ACA issues, is an insurance plan of this sort consistent with the hypotheses developed in this chapter? Why? What might people be buying with a mini–medical plan if they are not buying insurance?

For the Interested Reader

Friedman, M., and L. C. Savage. 1948. “The Utility Analysis of Choices Involving Risk.” Journal of Political Economy 56 (4): 251–80.

Nyman, J. A. 1999. “The Value of Health Insurance: The Access Motive.” Journal of Health Economics 18 (2): 141–52.

References

Ehrlich, I., and G. Becker. 1972. “Market Insurance, Self-Insurance and Self- Protection.” Journal of Political Economy 80 (4): 623–48.

Feldstein, M. S., and E. Allison. 1974. “Tax Subsidies of Private Health Insurance: Distribution, Revenue Loss, and Effects.” In The Economics of Federal Subsidy Programs, 977–94, Washington, DC: US Government Printing Office.

Friedman, M., and L. C. Savage. 1948. “The Utility Analysis of Choices Involving Risk.” Journal of Political Economy 56 (4): 251–80.

Jones, K. 2017. “The Most Desirable Employee Benefits.” Harvard Business Review. Published February 15. https://hbr.org/2017/02/the-most-desirable- employee-benefits.

Miller, T. 2003. “How the Tax Exclusion Shaped Today’s Private Health Insurance Mar-ket.” Report of the Joint Economic Committee, US Congress, December 17.

National Highway Traffic Safety Administration. 2003. Traffic Safety Facts, 2003: A Compilation of Motor Vehicle Crash Data from the Fatality Analysis Reporting System and the General Estimates System. US Department of Transportation. Washington, DC: National Center for Statistics and Analysis.

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