Chapter 3 Demand for Health Care Services

1. Chapter 3Demand for Health Care Services

2. Outline • Introduction of health insurance • Theoretical model of health insurance • Empirical estimates of demand from the literature • Practice problems • The RAND Health Insurance Experiment • Example: Interpreting results from a regression on abortion demand

3. Why Health Insurance? • Medical expenditure is extreme volatile • 1% use 25% exp • 5% use 50% exp • 20% use 75% exp • Difficult to self-insured because some people are sicker than others • Health insurance is relatively new (at the end of 19th century) since treatment was not very effective before

12. Formalizing This Intuition: Expected Utility Model • Let p stand for the probability of an adverse event. Then expected utility is: • Where C0 and C1 stand for consumption in the good and bad states of the world, respectively.

13. Formalizing This Intuition: Expected Utility Model • This model can be used to examine the individual’s demand for insurance. • Imagine, for example, that there was a 1% chance that Sam will get into an accident that caused $30,000 in damages. • Sam can insure some, none, or all of these medical expenses. • The policy costs m¢ per $1 of coverage. If Sam buys a policy that pays him $b in an accident, his premium is $mb. • Full insurance in this case would cost m x $30,000. • In the state of the world where Sam does get hit, he will be $b-$mb richer than if he hadn’t bought insurance. • If he doesn’t get hit by the car, he will be $mb poorer than he otherwise would have been.

14. Formalizing This Intuition: Expected Utility Model • That is, the insurance policy translates Sam’s consumption from periods when it is high to periods when it is low. • Sam’s desire to buy the policy depends on the price that is charged. • An actuarially fair premium sets the price charged equal to the expected payout.

15. Formalizing This Intuition: Expected Utility Model • In this case, the expected payout is $30,000 x 1%, or $300 per policy. So a $300 premium is actuarially fair. • With actuarially fair pricing, individuals will want to fully insure themselves to equalize consumption in all states of the world.

16. Formalizing This Intuition: Expected Utility Model • Consider the case, for example, when the utility function is: • Also assume that C0=30,000. Then expected utility without insurance is:

17. Formalizing This Intuition: Expected Utility Model • If, instead, you bought actuarially fair insurance for $300, expected utility is: • Utility is higher, even though the odds are that the premium was paid for nothing. This is because you would rather have equal consumption regardless of the accident, rather than a very low level in the bad state of the world. This is illustrated in Table 1.

18. Table 1

19. Formalizing This Intuition: Expected Utility Model • The central result of expected utility theory is that with actuarially fair pricing, individuals will want to fully insure themselves to equalize consumption in all states of the world. • Clearly Sam’s utility is higher in row 2, with full insurance, than in row 1, with no insurance. • Yet, Sam also prefers full insurance to any other level of benefits. Row 3, which shows coverage for half of the costs of the accident, gives lower expected utility.

20. Formalizing This Intuition: Expected Utility Model • Thus, even if insurance is expensive, so long as the price (premium) is actuarially fair, individuals will want to fully insure themselves against adverse events. • The implication: the efficient market outcome is full insurance and thus full consumption smoothing.

21. The role of risk aversion • Risk aversion is the extent to which an individual is willing to bear risk. • Risk averse individuals have a rapidly diminishing marginal utility of consumption; they are very afraid of consumption falling. • Individuals with any degree of risk aversion will buy insurance when it is priced actuarially fairly. But when the insurance is not fair, some will choose to not buy insurance.

22. Insurance with Fixed Spending • One person: • U(x, h) • U’>0, U’’<0 • One illness • sick with probability p • fixed treatment cost: m • H(h, m)=H(1, m)=H(0,0) • Two states • Sick (s): U(y-m, H(1,m)) • Health (m): U(y, H(0,0))

23. Without insurance

24. With insurance • Fair insurance: π= pm

25. Comparing With and Without Insurance • Taking Taylor’s expansion, we have

27. The insurance plan specifies the amount of money transferred to the bad state

28. Problem with Fixed Spending • Complete information • All the sicknesses known • All the treatment known • No wasted resources in the policy • The insurance specifies the amount of money being transferred during the sickness (contingency plan) • The policy completely insures the health, but s it possible to insure someone’s health?

29. Estimating Demand for Medical Care • Quantity demanded = f( … ) • out-of-pocket price • real income • time costs • prices of substitutes and complements • tastes and preferences • profile • state of health • quality of care

30. Empirical Evidence • Demand for primary care services (prevention, early detection, & treatment of disease) has been found to be price inelastic • Estimates tend to be in the -.1 to -.7 range • A 10%  in the out-of-pocket price of hospital or physician services leads to a 1 to 7% decrease in quantity demanded • Ceteris paribus, total expenditures on hospital and physician services increase with a greater out-of-pocket price

31. Empirical Evidence (cont.) • Demand for other types of medical care is slightly more price elastic than demand for primary care • Consumers should be more price sensitive as the portion of the bill paid out of pocket increases

32. Out-of-Pocket Payments in the U.S. • Hypothesis: Consumers are more price sensitive if they pay a larger % of the health care bill • The fall in the % of out-of-pocket payments may explain the rapid rise in health care costs

33. Out-of-Pocket Payments in the U.S. • Total Expenditures and % Paid Out-of-Pocket, 2007 • Hypothesis: Consumers are more price sensitive if they pay a larger % of the health care bill • Higher hospital and physician expenditures may be due to the low % paid out-of-pocket

34. Out-of-Pocket Payments in the U.S. (cont.) • The previous 2 slides argue that:  insurance coverage   expenditures • But it may be the opposite:  expenditures   insurance coverage. • We cannot identify a causal effect using just this data

35. Empirical Evidence (cont.) • Studies which have examined price and quantity variation within service types have found that: • The price elasticity of demand for dental services for females is -.5 to -.7 • The own-price elasticity of demand for nursing home services is between -.73 and -2.4

36. Empirical Evidence (cont.) • At the individual level, the income elasticity of demand for medical services is below +1.0 • The travel time elasticity of demand is almost as large as the own-price elasticity of demand • Little consensus on whether hospital care and ambulatory physician services are substitutes or complements

37. International Estimates of Income Elasticity • Are health care expenditures destined to consume a larger portion of GDP as GDP grows? • Regression Analysis • Sample - developed countries Ln(Real per capita Ln(Real per = a + b + e health expenditures) capita income) • Estimates of b range between 1.13 and 1.31

38. Applying Demand Theory to Real Data • Demand analyses in health care must take insurance into account • Demand analyses are critical in shaping managerial and public policy decisions

39. The Rand Health Insurance Experiment (HIE) • Research issues: • How does cost sharing affect demand for personal health care services? • How does cost sharing affect demand for particular services, e.g., hospital care, dental services? • Does use of personal health care services improve health? • How does a change from fee-for-service payment to capitation affect demand for personal health care services? • Rationale for studying HIE 30+ years after HIE completed

40. The Rand Health Insurance Experiment • A large, social science experiment to study individuals’ medical care under insurance • A large sample of families were provided differing levels of health insurance coverage • Researchers then studied their subsequent health care use

41. The Sample • 5,809 individuals, under 65 • 6 sites • Dayton OH, Seattle WA, Fitchburg MA, • Charlston SC, Georgetown County SC, Franklin County MA • 1974 – 1977 • Cost : $80 million

42. Insurance Plans in the Experiment • Families randomly assigned to 1 of 14 insurance plans differing in cost sharing rates and in maximum dollar expenditures per year (MDE or stop loss) • Free fee-for-service (FFS).- i.e., no coinsurance • 25% copayment per physician visit • 50% copayment per physician visit • 95% copayment per physician visit

43. Insurance Plans in the Experiment • Individual deductible - $150 deductible for physician visits; all subsequent visits free • HMO - Not the same as free fee-for-service - Since HMO receives a fixed annual fee, it seeks to limit physician visits

44. Table 3.3. Sample Means for Annual Use of Medical Services per Capita

45. Table 3.3. Sample Means for Annual Use of Medical Services per Capita

46. Table 3.3. Sample Means for Annual Use of Medical Services per Capita

47. Table 3.3. Sample Means for Annual Use of Medical Services per Capita

48. Results (cont.) • No statistically significant difference in inpatient (hospital) expenses by insurance type • Does NOT necessarily imply inelastic demand for hospital services • Experiment included $1,000 cap on out-of-pocket medical expenses; 70% of hospital admissions costs $1,000 + • As coinsurance ↑‘s, probability of ANY use ↓‘s

49. Results (cont.) • As consumers’ copayments drop, demand for medical care becomes more price inelastic • The data confirms the theory