Health Insurance Module: why people buy health insurance?

Presentation is organized in the following manner: Traditional Demand theory concepts of risk and uncertainty Methods for measuring risk and analyzing

individual’s attitude towards risk Health insurance: supply and demand

Choice Under Uncertainty• Traditional demand theory assumed a riskless world• But People mostly make choices under uncertainty – Most economic decisions are made in the face of risk or uncertainty (e.g., choosing an occupation, financing large purchases)

• Extension of traditional economic theory • Consumer choices are made under conditions of certainty, risk or uncertainty

Uncertainty and Consumer BehaviorTo examine the ways that people can compare and choose among risky alternatives, we take the following steps:1.In order to compare the riskiness of alternative choices, we need to quantify risk.2.We will examine people’s preferences toward risk.3.We will see how people can sometimes reduce or eliminate risk. 4.In some situations, people must choose the amount of risk they wish to bear. Such investments involve trade-off between monetary gains and the riskiness of that gain.

Risk and uncertainty in demand choices• Certainty– One possible outcome to a decision

• Risk– More than one possible outcome and the prob. of each outcome is known or can be estimated

• Uncertainty– More than one possible outcome and prob. of each outcome occurring is not known (e.g., drilling for oil in an unproven field)

In the analysis of choices involving risk, we utilize the following concepts• Strategy• States of nature• Pay-off matrix

QUANTIFYING RISKProbabilityThe probability of an event is the chance that the event will occur. By listing all the possible outcomes of an event and the probability attached to each, we get a probability distribution. The concept of P.D is essential in evaluating and comparing different outcomes.expected value associated with an uncertain situation is a weighted average of all possible values with all possible outcomes. The probabilities of each outcome are used as weights.The expected value measures the central tendency—the value that we would expect on average.Expected value = Pr(success)($40/share) + Pr(failure)($20/share)= (1/4)($40/share) + (3/4)($20/share) = $25/share E(X) = Pr1X1 + Pr2X2 E(X) = Pr1X1 + Pr2X2 + . . . + PrnXn

DESCRIBING RISKVariability●variability is the extent to which possible outcomes of an uncertain situation differ.

●deviation Difference between expected payoff and actual payoff.

OUTCOME 1 OUTCOME 2Probability Income ($) Probability Income ($)

ExpectedIncome ($)

Job 1: CommissionJob 2: Fixed Salary

.5

.99

2000

1510

1000

510

.5

.01

1500

1500

TABLE 1 Income from Sales Jobs

TABLE 2 Deviations from Expected Income ($)

Outcome 1 Deviation Outcome 2 Deviation

Job 1

Job 2

2000

1510

500

10

1000

510

-500

-990

DESCRIBING RISKVariability

Outcome 1DeviationSquared

DeviationSquaredOutcome 2

DeviationSquared

Weighted AverageStandardDeviation

Job 1

Job 2

2000

1510250,000

100

1000

510

250,000

980,100

250,000

9900

500

99.5

Table 3 Calculating Variance ($)

●standard deviation Square root of the weighted average of the squares of the deviations of the payoffs associated with each outcome from their expected values.

PREFERENCES TOWARD RISK

● expected utility Sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur.

PREFERENCES TOWARD RISKIn (b), the consumer is risk loving and she prefers an uncertain income to a certain one, even if the expected value of the uncertain income is less than that of the certain income. She would prefer the same gamble (with expected utility of 10.5) to the certain income (with a utility of 8).In (c), the consumer is risk neutral, and indifferent between certain and uncertain events with the same expected income. Marginal utility of income is constant for a risk neutral person.

PREFERENCES TOWARD RISK●

risk averse An individual who is risk-averse prefers a certain given income to a risky income with the same expected value.

● risk neutral A person who is risk neutral is indifferent between a certain income and an uncertain income with the same expected value.● risk loving An individual who is risk loving prefers a risky income to a certain income, even if the expected value of the uncertain income is less than that of the certain income.

People differ in their willingness to bear risk. Some are risk averse, some risk loving and some risk neutral.

Demand for Health Insurance

What is insurance?• The incidence of illness seems to be random and so, health care expenses are uncertain. Since health care expenses are unpredictable, they can be financially catastrophic for the households. • Insurance reduces the variability of incomes (or losses) of those insured by pooling a large number of people and operating on the principle of the law of large numbers.

• Consumers actually purchase a pooling arrangement when they buy a policy from an insurance company. Pooling arrangements help mitigate some of the risk associated with potential losses.

• Suppose, two individuals, Joe and Lee face the same distribution of losses. Both of them face a 20% prob. of losing $20 and an 80% prob. of losing nothing. So, the expected value of this distribution of losses: 0.2*$20+0.8*$0=$4.

• Joe can expect to lose $4. We are more concerned about the variability of the expected loss.

• Variance=0.2($20-$4), S.D.=$8• Both the expected loss of $4 and its s.d. can be

thought of as measures of risk.• Lets now show how Joe and Lee might mutually

gain from entering into an pooling arrangement.

• Entering into a pooling arrangement essentially replaces each person’s individual loss distribution with the average loss distribution of the group.

16

Why People demand for health insurance?

• The conventional theory or standard gamble model, assumes that people purchase health insurance to avoid or transfer risk. In this case, insurance serves as a pooling arrangement to replace the high risk or variability of individual losses with the reduced risk or variability associated with aggregated losses.

Logic• The consumer pays insurer a premium to

cover medical expenses in coming year– For any one consumer, the premium will be higher

or lower than medical expenses• But the insurer can pool or spread risk among

many insurees so that The sum of premiums will exceed the sum of

medical expenses

Characterizing Risk Aversion• Recall the consumer maximizes utility, with prices and income given–Utility = U (health, other goods)– health = h (medical care)

• Insurance doesn’t guarantee health, but provides $ to purchase health care• We assumed diminishing marginal utility of “health” and “other goods”

• In addition, let’s assume diminishing marginal utility of incomeUtility

Income

• Assume that we can assign a numerical “utility value” to each income level• Also, assume that a healthy individual earns $40,000 per year, but only $20,000 when ill

$20,000

$40,000

70

90

Income Utility

Sick

Healthy

Utility

Income$20,000 $40,000

90

70

Utility when healthy

Utility when sick

A

B

• Individual doesn’t know whether she will be sick or healthy• But she has a subjective probability of each event– She has an expected value of her utility in the coming year

• Define: P0 = prob. of being healthy P1 = prob. of being sick P0 + P1 = 1

• An individual’s subjective probability of illness (P1) will depend on her health stock, age, lifestyle, etc.

• Then without insurance, the individual’s expected utility for next year is:

• E(U) = P0U($40,000) + P1U($20,000)

= P0•90 + P1•70

• For any given values of P0 and P1, E(U) will be a point on the chord between A and B

Utility

Income$20,000 $40,000

70

90A

B

• Assume the consumer sets P1=.20• Then if she does not purchase insurance: E(U) = .80•90 + .20•70 = 86

E(Y) = .80•40,000 + .20•20,000 = $36,000

• Without insurance, the consumer has an expected loss of $4,000

Utility

Income$20,000 $40,000

90

70

A

B

$36,000

C•

•

•86

• The consumer’s expected utility for next year without insurance = 86 “utils”

• Suppose that 86 “utils” also represents utility from a certain income of $35,000– Then the consumer could pay an insurer

$5,000 to insure against the probability of getting sick next year

– Paying $5,000 to insurer leaves consumer with 86 utils, which equals E(U) without insurance

Utility

Income$20,000 $40,000

90

70

A

B

$36,000

C•

•

•86

$35,000

•D

• At most, the consumer is willing to pay $5,000 in insurance premiums to cover $4,000 in expected medical benefits

$1,000 loading fee price of insurance

• Covers– profits– administrative expenses– taxes

Determinants of Health Insurance Demand1 Price of insurance– In the previous example, the consumer will forego health insurance if the premium is greater than $5,0002 Degree of Risk Aversion– Greater risk aversion increases the demand for health insurance

Utility

Income$40,000$20,000

A

B

If there is no risk aversion, utility = expected utility, and there is no demand for insurance

3 Income – Larger income losses due to illness will increase the demand for health insurance

4 Probability of ILLNESS– Consumers demand less insurance for events most likely to occur (e.g. dental visits)– Consumers demand less insurance for events least likely to occur– Consumers more likely to insure against random events

Estimates of Price & Income Elasticities for Demand for Health Ins.• Price elasticities b/w -.03 and -.54– At the individual level– Enrollment or premium expenditure– Elastic or Inelastic demand?

• Income elasticities b/w 0.01 and 0.13

Estimates of Price & Income Elasticities for Demand for Health Ins.• What about when employees are choosing between the menu of plans offered by their employer?– Range of choices is more limited– Price elasticites are found to range between -2 and -8.4, depending on age, job tenure, medical risk category

• Dowd and Feldman 1994, Strombom et al. 2002

Assumptions underlying the theoretical model of health insurance demand• Consumers bear the full cost of their own health insurance• Insurance companies can appropriately price policies• Individuals can afford health insurance/health care The above 3 assumptions do not always hold in the real world

The majority of Americans have employer-provided health insurance

• Employer-paid health insurance is exempt from federal, state, and Social Security taxes

Employee will prefer to purchase insurance through work, rather than on his own

Example: Insurance and take-home pay when income is $1,000 per week and

income tax rate is 28%

• Employee Purchased

• $1,000• 28% tax <280>• after tax 720• insurance <50>• net pay 670

• Employer Purchased

• $1,000• insurance <50>• subtotal 950• 28% tax <266>• net pay 684

Employer Health Insurance Coverage of U.S. Population (percent)

58

59

60

61

62

63

64

65

Total Employment Based

19951998200020022005

Consequences for costs

• “Too many” services were covered by insurance– Coverage of more small claims increased

administrative costs– Employers offering more than 1 plan often fully

subsidized the more expensive plans

Insurance Terminology• Coinsurance: A cost-sharing requirement under a health insurance policy that provides that the insured will assume a portion or a percentage of the costs of covered services. • Co-payment: A cost sharing arrangement in which the insured pays a flat amount for a specified for a specified service. It does not vary with the cost of service, unlike the coinsurance that is based on some percentage of cost.

• Deductibles: Amounts required to be paid by the insured under a health insurance contract, before benefits become payable. In a sense, the insurance does not apply until the consumer pays the deductible.