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Solution Manual For Health Economics, 2013th Edition

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    2 Demand for Health Care Comprehension Questions Indicate whether the statement is true or false, and justify your answer. Be sure to cite evidence from the chapter and state any additional assumptions you may need. 1. Unlike with most types of goods, deriving a demand curve for health care is quite simple because people rarely skimp on health care. FALSE. Just as with any good, deriving a demand curve for health care is dif- ficult because it requires information about how the same population would react to different prices. This requires either parallel universes or, more real- istically, a randomized experiment. 2. The RAND study was especially useful for measuring price elasticities be- cause it randomly assigned insurance plans to participants (as opposed to letting them choose). TRUE. Randomization ensured that the groups facing different prices were statistically equivalent. That meant that any difference in demand between groups was attributable to price, not some other characteristic. 3. The Oregon Medicaid Experiment is not truly “randomized” because lottery winners did not all end up with insurance, and some lottery losers did end up with insurance. FALSE. Although the Oregon Medicaid Experiment was not exactly a con- 1

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    2 | Health Economics Answer Key trolled experiment, it did use randomization to assign participants to differ- ent groups, and one group (the “lottery winners”) were much more likely to obtain health insurance. 4. The RAND HIE found that people assigned to the free health plan had the same rate of hospitalization as people assigned to the cost-sharing plans. FALSE. The people assigned to the free plan visited the hospital more fre- quently and were more likely to visit the ER. 5. In the RAND HIE, the arc elasticity of demand for inpatient care was larger (in absolute value) than the arc elasticity of demand for outpatient care. FALSE. That result would imply that people are more price sensitive when it comes to more urgent health care. Instead, the arc elasticity of demand for impatient care was smaller in absolute value. 6. Unlike the usual measure of elasticity, an arc elasticity can be calculated from just one price-quantity data point. FALSE. Any measure of elasticity requires data from at least two price levels in order to measure responsiveness to price. 7. Both the RAND and Oregon studies find that demand for health care is ap- proximately unit elastic, that is,  ≈ − 1. FALSE. The RAND HIE finds that demand for health care is very inelastic, with arc elasticities around 0.2. 8. In the RAND HIE, being assigned more generous insurance did not gener- ally improve participants’ health outcomes, except among certain subgroups. TRUE. The RAND HIE finds that generous insurance only provided small health improvements to healthy people. However, high-risk participants (like those who were smokers or had high blood pressure) did receive sub- stantial health benefits from more generous insurance. 9. To date, no major health insurance experiment has studied the impact of un insurance, just different levels of insurance. FALSE. The Oregon Medicaid Experiment studied the impact of uninsur- ance. 10. Results from the Oregon Medicaid Experiment suggest that having health in- surance has a positive impact on health status. 2

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    Chapter 2 | Demand for Health Care | 3 TRUE. Lottery winners in the Oregon Medicaid Experiment were not more likely to survive than lottery losers, but they had better self-reported physical health and mental health. 3

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    4 | Health Economics Answer Key Analytical Problems 11. Suppose you are collecting data from a country like Japan where the govern- ment sets the price of health care. Each prefecture in Japan has a different set of prices (for example, Tokyo has higher prices than rural Hokkaido). Data for 1999 are displayed in Table 2.12. Table 2.12: Outpatient utilization in Tokyo and Hokkaido, 1999. Region Outpatient visits Price/visit Tokyo 1.25/month 20 U Hokkaido 1.5/month 10 U (a) What is the arc price elasticity of demand for health care consumers in Japan (using only these data)? We are given data on the number of doctor visits and their correspond- ing prices in Tokyo and Hokkaido prefectures in 1999. Let Q t 1 represent the number of doctor visits and P t 1 the price of doctor visits in Tokyo in 1999. Similarly, let Q h 1 and P h 1 represent the corresponding quantities for Hokkaido. The formula for calculating arc elasticities is:  = ( Q t 1 − Q h 1 P t 1 − P h 1 ) ( P t 1 + P h 1 Q t 1 + Q h 1 ) (2.1) Plugging the numbers into this formula yields an estimate (say,  1 ) for the arc elasticity of demand for medical care in Japan:  1 = ( 1.25 − 1.5 20 − 10 ) ( 20 + 10 1.25 + 1.5 ) = − 0.273 (2.2) (b) Suppose that incomes are generally much higher in Tokyo than Hokkaido. Is your answer to the last question an overestimate or underestimate of price elasticity? Justify your answer. Demand in Tokyo is lower than in Hokkaido because of the higher price, but it is higher than it would be in Hokkaido at that higher price due to the income effect. Therefore, the arc elasticity from the previous prob- lem is an underestimate; demand in each region will be more responsive to price than our answer suggests. See the figure below for an illustra- tion; note that demand curves with constant arc elasticity will not be 4

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    Chapter 2 | Demand for Health Care | 5 Response to exercise 11(b). The solid lines are the underlying demand curves in Tokyo and Hokkaido; the dotted line is the demand curve implied by the two datapoints. Q P Hokkaido Tokyo linear – this is just an illustration of the basic principle. The dotted line is steeper than the solid lines, which means the elasticity implied by the datapoints is an underestimate of the price elasticity in each region. (c) Using your estimated elasticity, what would the demand for health care be if the price in Tokyo were raised to 30 U per visit? What would the demand in Hokkaido be if the price were lowered to 5 U per visit? There are several acceptable ways to answer how the demand would change in each prefecture if the price were to change. The simplest way is to take each prefecture’s 1999 levels as the base price, calculate what the percentage change in price would be off this base, and then apply the elasticity estimate to derive the estimated percentage change in quantity demanded at the new price. If the price in Tokyo were raised to 30 U , this would represent a 50% in- crease over the base price of 20 U . Assuming a constant elasticity of de- mand of − 0.273 over this range of prices (a risky assumption, but there’s not much else to do here!) leads to a predicted 50% ∗ − 0.273 = 13.7% decline in demand. Since Tokyo’s base demand in 1999 was 1.25 visits per month, a 13.7% decline would mean 1.08 visits per month. If the price in Hokkaido were lowered to 5 U , this would represent a 50% decrease off the base price of 10 U . Using the same methodol- ogy leads to a predicted 13.7% (= − 50% ∗ − 0.273 ) increase in demand. Since Hokkaido’s base demand in 1999 was 1.5 visits per month, a 13.7% increase would mean 1.71 visits per month. 5

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    6 | Health Economics Answer Key Table 2.13: Outpatient utilization in Tokyo and Hokkaido, 2000. Region Outpatient visits Price/visit Tokyo 1.0/month 30 U Hokkaido 1.2/month 15 U You continue your observations of the Japanese health care system into the year 2000. For inscrutable reasons having to do with internal Japanese pol- itics, the government changed the price in both Tokyo and Hokkaido that year, and you observe the demand recorded in Table 2.13. (d) Calculate the price elasticity of demand for health care in Japan using only data from the year 2000. Let Q t 2 represent the number of doctor visits and P t 2 the price of doctor visits in Tokyo in 2000 and let Q h 2 and P h 2 represent the corresponding quantities for Hokkaido. Plugging the new data into the old formula yields a second estimate (say  2 ) for the arc elasticity of demand:  2 = ( Q t 2 − Q h 2 P t 2 − P h 2 ) ( P t 2 + P h 2 Q t 2 + Q h 2 ) = ( 1.0 − 1.2 30 − 15 ) ( 30 + 15 1.0 + 1.2 ) = − 0.273 (2.3) (e) Use data from both years to calculate the elasticity of demand for health care for Tokyo and Hokkaido separately. Using the data from both years, we can derive two different elasticity estimates – one for Tokyo (  t ) and one for Hokkaido (  h ). For Tokyo, we have:  t = ( Q t 2 − Q t 1 P t 2 − P t 1 ) ( P t 2 + P t 1 Q t 2 + Q t 1 ) = ( 1.0 − 1.25 30 − 20 ) ( 30 + 20 1.0 + 1.25 ) = − 0.556 (2.4) For Hokkaido, the elasticity estimate is:  h = ( Q h 2 − Q h 1 P h 2 − P h 1 ) ( P h 2 + P h 1 Q h 2 + Q h 1 ) = ( 1.2 − 1.5 15 − 10 ) ( 15 + 10 1.2 + 1.5 ) = − 0.556 (2.5) (f) Using your estimated elasticities, what would the demand for health care in each prefecture be if the price were raised to 60 U per visit next 6

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    Chapter 2 | Demand for Health Care | 7 year (for both prefectures)? If the price of doctor visits were raised to 60 U in 2001 in Tokyo, this would represent a 100% increase over the price of 30 U in 2000. Apply- ing the  t estimate of demand elasticity in Tokyo yields a predicted de- crease in demand of 55.6% (= 100% ∗ − 0.556 ) from year 2000 demand levels. This yields a predicted 1.0 ∗ 0.444 = 0.444 visits per month in 2001 in Tokyo. If the price of doctor visits were raised to 60 U in 2001 in Hokkaido, this would represent a 300% increase over the price of 15 U in 2000. Apply- ing the  h estimate of demand elasticity in Hokkaido yields a predicted decrease in demand of 166.7% ( ≈ 300% ∗ − 0.556 ) from year 2000 de- mand levels. We would predict no outpatient visits at all in Hokkaido in 2001! This is of course very unlikely; this result illustrates the limita- tions of assuming a constant elasticity. (g) Combine the Tokyo and Hokkaido estimates from exercise 11(e) to get a single estimate of the price elasticity of health care demand for all of Japan. Assume that Tokyo is five times as populous as all of Hokkaido. To combine these elasticity estimates into a single national estimate (say  3 ), we can take a simple population weighted average of the two elas- ticity estimates,  t and  h , from the two prefectures. Let P t be the popula- tion of Tokyo, and let P h be the population of Hokkaido. The population average estimate is:  3 =  t P t +  h P h P t + P h (2.6) We are given that P t = 5 P h , so this expression can be simplified:  3 = 5  t P h +  h P h 5 P h + P h = 5  t +  h 6 (2.7) Applying this formula yields an elasticity estimate of  3 = − 0.556. Since the estimated elasticities were the same in each region, it would have been easy to jump straight to this answer without doing any math. 12. Preventative care refers to care taken to prevent future diseases rather than to treat current ones. Compared to emergency room care, preventative care is rarely urgent, and benefits can be difficult to measure – if you had the flu vaccine this year but did not catch the flu, it is impossible to tell if it was the shot or assiduous hand washing that preserved you. 7

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    8 | Health Economics Answer Key (a) Given this description of preventative care, would you expect preventa- tive care to be more or less price sensitive compared to inpatient care? Why? Because preventative care often seems like optional medical care to many people (unlike urgent medical care) intuition suggests that the demand for preventative care will likely be more price sensitive than the demand for other types of care. (b) Table 2.14 shows evidence on preventative care from the RAND HIE. Summarize the data in the table and note any interesting patterns. Was your prediction correct? For men of all ages, the rates of going to the doctor for preventative care are low – between 60% and 70% do not see their doctor for preventative care at all. There does not appear to be a statistically significant effect of higher copayments on the demand for preventative care. However, for older men, the point estimates suggest (approximately) a 12 percentage point decline in the demand for preventative care when copayments are imposed. Women have a higher level of demand for preventative care than men. Imposing copayments has a modest, statistically significant, effect on the demand for preventative care (except in the case of young womens’ demand for pap smears). Table 2.14: Percentage with preventative care in the last 3 years from the RAND HIE study Males 17-44 Males 45-64 Females 17-44 Females 45-64 any care any care any care Pap test any care Pap test Free 27.2% 39.1% 83.7% 72.2% 76.9% 65.0% Copay 23.1% 27.4% 76.9% ∗∗ 65.8% 65.3% ∗∗ 52.8% ∗∗ ∗∗ indicates statistically significant difference from the free at the p = 1% level. Source: Newhouse (1993). 13. In this exercise, assume that the term “admission” in Table 2.15 refers to in- patient care, while “any use” refers to inpatient and outpatient care. Table 2.15 contains a lot of information. Without looking at any specific values, summarize what type of data the table contains. Give an example of a broad question about income levels and demand for health care that the table might have the potential to answer. The table contains medical utilization and expenditure data for patients in 8

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    Chapter 2 | Demand for Health Care | 9 Table 2.15. Various measures of predicted annual use of medical services by income group. Source: Manning (1987). the RAND HIE, broken down by income tercile. The table can tell us whether people from different parts of the income distribution have different price elasticities of demand for health care in general, and for inpatient care in par- ticular. Essay Questions 14. Here is a selection from an abstract of a recent study entitled “The Effect of Health Insurance Coverage on the Use of Medical Services” by Michael Anderson, Carlos Dobkin, and Tal Gross: Substantial uncertainty exists regarding the causal effect of health insurance on the utilization of care. Most studies cannot determine whether the large differ- ences in healthcare utilization between the insured and the uninsured are due to insurance status or to other unobserved differences between the two groups. In this paper, we exploit a sharp change in insurance coverage rates that results from young adults “aging out” of their parents insurance plans to estimate the effect of insurance coverage on the utilization of emergency department (ED) and inpatient services. [ In the United States, children are eligible for insurance cov- erage through their parents’ insurance only up to their 23rd birthday, at which point 9

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    10 | Health Economics Answer Key they lose eligibility. ] Using the National Health Interview Survey (NHIS) and a census of emergency department records and hospital discharge records from seven states, we find that aging out results in an abrupt 5 to 8 percentage point reduction in the probability of having health insurance. We find that not having insurance leads to a 40 percent reduction in ED visits and a 61 percent reduction in inpatient hospital admissions. (a) This study does not use randomization to assign people to different in- surance plans. What two groups are being compared in this study? This study compared people who were just under age 23 and just over age 23. Because of the law regarding coverage through parents’ insur- ance, these groups have significantly different rates of insurance cover- age. (b) Identify at least one important methodological differences between the design of this study and the RAND HIE. Give a hypothetical reason that this difference would bias the results. One important difference is that the study does not use randomization, but instead compares two similar groups with different health insur- ance coverage rates (those under age 23 and those over age 23). This methodology could bias the results if people over age 23 have less need for inpatient care than people under 23. In that case, a “natural” de- cline in inpatient use among 23-year-olds would be wrongly attributed to increased uninsurance. (c) Are the findings of this study generally consistent with the findings from the Oregon Medicaid Experiment? No. The Oregon Medicaid Experiment found that having health insur- ance had little to no effect on emergency room visits or inpatient stays, but this study finds that having health insurance makes patients much more likely to visit the emergency room and much more likely to receive inpatient care. 10

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    3 Demand for Health: The Grossman Model Comprehension Questions Indicate whether the statement is true or false, and justify your answer. Be sure to cite evidence from the chapter and state any additional assumptions you may need. Review the basic assumptions of the Grossman model before answering these questions. 1. In real life, investments in health can generate long-lasting benefits, but the Grossman Model neglects this aspect of health. FALSE . One of the central features of the model is that health is (in part) an investment good. If someone invests in his health today, it will be higher both today and in the future. 2. In the framework of the Grossman model, one’s level of health is completely controlled by her actions. Thus, in any given period, an individual is uncon- strained in her choice of health status. FALSE . Individuals do have a lot of control over their health level, but there may be high levels of health that they cannot achieve given time and income constraints. If someone invests all her time and money in improving health, she may still not be as healthy as she would like. 3. In the Grossman model, the marginal efficiency of investment in health care declines as health improves. 1

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    2 | Health Economics Answer Key TRUE . Someone who is very unhealthy receives major dividends from even a small improvement in health, but someone who is already very healthy receives little benefit. 4. Aging shifts the marginal efficiency of investment in health curve inward. FALSE . As aging occurs, the depreciation rate of health increases. This re- sults in a movement along the marginal efficiency of investment curve up- ward, which implies worse optimal health. 5. An hour spent exercising always pays for itself by decreasing the time spent sick by more than an hour. FALSE . This is only true in the “free lunch zone.” Once a certain level of health is attained, an hour spent exercising generates less than an hour of additional productive time. 6. Assume the PPF is as pictured in Figure 3.3. People might choose point E as their optimum even if they value the home good Z . FALSE . The only way someone might choose point E is if his indifference curves are vertical. But a vertical indifference curve means he does not value the home good, Z at all. 7. In the Grossman model, optimal health status declines with age. TRUE . See Figure 3.13 for an explanation. 8. The fact that older people spend more on health care is evidence against the Grossman model, which predicts that spending will decline as δ increases. FALSE . The Grossman model predicts that health optimally declines with age; it does not predict that health expenditures decline with age. The effect of aging on health expenditures is ambiguous in the Grossman model. As you age, you need to spend more money and time on health to maintain a fixed level because of the increasing depreciation rate of health capital. 9. People who drop out of high school are able to produce more health than college graduates because they have more free time to invest in health pro- duction. FALSE . In the Grossman model, more education shifts out the marginal effi- ciency of investment curve. This means that better educated people have a 2

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    Chapter 3 | Demand for Health: The Grossman Model | 3 PPF that is shifted upwards relative to people with fewer years of education. Thus, better educated people spend less time sick and have more productive time overall. See Figure 3.14. 10. According to the Grossman model, people choose an optimal time to die (bar- ring any unforeseen accidents). TRUE . In the Grossman model, death occurs when it no longer makes sense to invest in health because the depreciation rate of health capital is so high. 3

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    4 | Health Economics Answer Key Analytical Problems 11. The Grossman model envisions consumers deciding between investments in health H and investments in home goods Z . Figure 3.15 depicts a typical consumer’s production possibility frontier for health and home goods. Figure 3.15: The PPF in the Grossman model. H Z A B C (a) Succinctly describe why the graph is shaped the way it is between points A and B. The main reason is that the health production function exhibits dimin- ishing returns in health investment. Between A and B, small invest- ments in health result in such large improvements in health (and hence large declines in the time spent ill). The extra time not spent ill more than replaces the time required in health investment to produce the ex- tra time. Hence, the consumer can have both more health and more home goods over this portion of the curve. (b) Succinctly describe why the graph is shaped the way it is between points B and C. BC is downward sloping for the same reason that AB is upward slop- ing: diminishing returns in health investment. The difference is that between B and C, the consumer has hit the flat part of the health in- vestment curve. Hence the time spent on health investment does not decrease time spent sick by enough to offset the time exercising (for in- stance). To increase health over this portion of the curve thus requires a level health investment that will take time away from other productive activities, which will lead to fewer home goods. (c) Would any consumer with typical preferences ever pick a point on the graph between A and B? Explain succinctly (using Figure 3.15) why or why not. 4

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    Chapter 3 | Demand for Health: The Grossman Model | 5 No. Indifference curves are downward sloping in the Health-Home Goods space, since both are desirable. People choose health and home goods subject to the PPF graph above. The optimum occurs where the indifference curve and the PPF are tangent. Since the indifference curves are downward sloping, this tangency can only occur on the downward sloping portion of the PPF – that is, between B and C. 12. Suppose a new miracle pill is discovered that increases both the marginal health effects of health investment (at any given level of health investment) and the maximum level of attainable health from H max to a higher H max . (a) Draw the old production possibility frontier before the discovery of the miracle pill. The old production possibility frontier looks just like Figure 3.15. (b) On this same graph, draw a new production possibility frontier that cor- responds to the description of the miracle pill. The graph below shows what the new health production technology might look like before and after the discovery of the new pill. Because the pill shifts out the health production technology, it expands the pro- duction possibility frontier. Response to exercises 12(a) and (b). H Z old H max new H max (c) How will the miracle pill affect H ∗ ? The PPF bulges out because the increased efficiency of health invest- ment brought about by the miracle pill enables the consumer to pro- duce any given level of health with less health investment (holding all else equal) since it increases the marginal productivity of health invest- ment. Thus, the consumer can use those extra resources either to im- prove health or for additional home production, or both. 5

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