Optimal Health Insurance for Prevention and Treatment

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1 Optimal Health Insurance for Prevention and Treatment Randall P. Ellis Department of Economics Boston University Willard G. Manning Harris School of Public Policy Studies The University of Chicago We thank Shenyi Jiang, Albert Ma,Tom McGuire, Joe Newhouse, Frank Sloan and seminar participants at Boston University and Harvard for their comments.

2 Rich literature on optimal health insurance Zeckhauser JET (1970) is classic article describing tradeoff between risk spreading and moral hazard Conventional approach emphasizes: Demand responsiveness Variance in health care spending Degree of risk aversion Insurance loading factor Focus of paper is on demand side incentives, ignoring supply-side moral hazard and supply-side cost sharing

3 New questions answered in this paper How should optimal insurance coverage be modified in the presence of Preventive care services? Multiple health care goods with correlated errors? Cross price elasticities of demand? Uncompensated losses that are correlated with health spending? Multiple time periods when health care spending is serially correlated over time?

4 Summary of what paper shows 1. Preventive care should be covered generously because consumers will ignore premium savings in their private prevention decisions. 2. Health care goods that are positively correlated with other health spending should be more generously covered 3. Health care goods that are substitutes should be covered more generously than complements. 4. Cover services generously that are positively correlated with uncompensated losses 5. Services that are positively serially correlated over time should be covered more generously than those that are uncorrelated

5 Optimal insurance coverage for preventive care has received relatively little attention Low variance suggests insurance not needed (Kenkel, AEA presentation 2007) Demand elasticity low relative to curative care (uncertain)? Insurance reduces value of prevention Primary versus secondary prevention Boundary between prevention and treatment is sometimes blurry (e.g. drugs, preventive treatment) We define prevention activities as costly services to the consumer that reduce the probability of being sick.

6 Five types of losses modeled Ex ante moral hazard loss from too little prevention Ex post moral hazard loss from overinsurance Inefficiency due to insurance loading factors Arrow-Pratt cost of risk Uncompensated losses due to ill health

7 Organization of paper Literature review Basic model use consumer surplus measure no prevention, homoscedastic error Utility-based models Prevention + one health treatment good Key role of uncompensated health losses Multiple health treatment goods Multiple periods Discussion and empirical relevance

8 Huge literature potentially related to these questions Most of Audience in this room! Optimal deductibles and copayments Demand responsiveness of specific services Optimal insurance with multiple goods Dynamic models of health spending Prevention Statistical models of the distribution of health care costs over time

9 Literature is ambiguous on insurance coverage for preventive care Low variance suggests insurance not needed (Kenkel, AEA presentation 2007) Demand elasticity low relative to curative care (uncertain)? Insurance reduces value of prevention (ex ante moral hazard) Primary versus secondary prevention Boundary between prevention and treatment is sometimes blurry (e.g. drugs, preventive treatment) We define prevention activities as costly activities to the consumer that reduce the probability of being sick.

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11 Basic model One health care good X Linear demand curve when sick of X = µ X B P X + θ Θ = random shock affecting demand for X (also health status shock) Marginal cost = 1 P X = c X = cost share of health care treatment

12 Adding in insurance and cost of risk Use Arrow-Pratt approximation for welfare loss from financial risk Cost of risk = (R A )(variance of out-of-pocket spending)/2 Assume probability of sickness = 1 - (Z) Health spending only if sick Insurance loading factor δ implies extra cost of using insurance funding is = δ (1-(Z)) (1-c X ) (µ X B c X ) Uncompensated loss from insurance = L

13 Four terms in loss function to be minimized 2 Ex post moral hazard loss from overinsurance = (1 / 2) (1 - c ) B Inefficiency due to insurance loading factors = (1 c ) ( Bc ) A 2 2 Arrow-Pratt cost of Min risk = R cx X X X X Uncompensated losses due to ill health = L( ), with expectation L 2 WL (1/ 2)(1- c ) B (1 c )( Bc ) R c 2 L 1 2 A 2 2 X X X X X c * X B B X A B2B R 2

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15 Results are interesting and plausible and many parameters can be calculated empirically BUT Does not suggest how to incorporate multiple goods Does not expand to multiple periods well Does not incorporate risk aversion in a fully satisfying way Only approximates a utility maximization framework

16 Utility-based model Three kinds of goods X = health care goods indexed by Y = all other consumption goods Z = spending on preventive care P X, P Y, P Z = prices of three types of goods π = insurance premium I = Income I = π +P X X + P Y Y + P Z Z

17 Sequence of moves 1. The insurer chooses coinsurance rates c X and c Z for treatment and prevention. 2. The consumer chooses Z to maximize ex ante utility in Period 1 by borrowing its cost against Period 1 income. 3. Nature decides on the consumer s state of illness θ 4. The consumer chooses X and Y 5. If a dynamic model, then repeat steps 3 and 4 (prevention is done one time in Period 0).

18 Expected utility framework used E U = E θ U(Y, H(X, θ)) Three key assumptions about utility function 1. U YH < 0 Favorable health care shocks reduce the marginal utility of income 2. X/I = 0 Zero income effects, so Consumer Surplus = Compensating Variation for health goods 3. Linear demand curves for X X = X B P X +

19 Assumed Effect of Income Changes on Optimal Consumption Bundles Ideal ICC Assumed ICC Other Goods (Y) Medical Service (X i )

20 Demand for each health service X when sick: P X AB P X y Use Roy's identity to derive risk neutral utility function when sick I P V I P A B P 2 S X X (, ) 2 PY PY PY Introduce stochastic element to demand A where F( ) with E( ) 0 X

21 Health shocks theta also affect uncompensated losses of two types: monetary and health Prevention increases probability of being healthy Full model with prevention Z Health shocks theta affect out-of-pocket costs 1 2 Bc ( X L) K cx X, and 2 11 ( Z) 1cXX BcX1cZZ H S 1 2 EV ( Z) V ( J ) (1 ( Z)) E V J K ( cx L ) L ( ) where J I c Z Prevention costs can either be paid out of pocket or covered by insurance Benefits of health treatment are quadratic in prices, c X,+L 1 Insurance loading factor increases premium by proportion delta Prevention reduces treatment costs covered by premium

22 Socially optimal choice of preventive care Z SOC differs from private choice Z PRIV in that private choice ignores change in premium SOC Compare Z and Z PRIV MC SOC Z PRIV '( Z ) '( ) = Z Z Z, = H S H S EV I V EV EV I V EV P SOC PRIV Z Z if ''( ) 0 Private choice results in too little prevention when P Z = MC Therefore prevention services should be subsidized Z

23 Optimal cost sharing on preventive care c * Z where P Q Z = 1 MC Q +1 c Bc Z X X X H QV EV E V S I

24 Model with multiple goods and no prevention Demand curves for two health treatment goods X - B c G c X - B c G c

25 Optimal cost share One health treatment good, no insurance loading c * 1 1 B R A C 1 * increases with B 1 and decreases with R A, 2 1 Confirms conventional results B

26 Optimal cost share One health treatment good, Insurance loading factor >0 c B B * B 2 B R A C 1 * increases with and 1

27 Optimal cost share One health treatment good Uncompensated losses from health shocks 2 S S B1 c1 1 EV E V I c11 c1 L 2 c B R A 2 L 1 * B R A c 1 * decreases with uncompensated losses and can be zero or negative at optimum

28 Optimal cost share Two health treatment goods Correlated health shocks and nonzero cross price elasticities c ( G B )( R G ) ( G B )( R B ) A A 2 * A 2 A 2 A 2 ( R 1 B1)( R 2 B2 ) ( R 12 G12 ) As limiting case, c 1 * should be lower for services with positively correlated health shocks As limiting case, c 1 * should be higher for complements than substitutes

29 Two period model = health shock serial correlation =discount factor c * X A BR L 1 s A 2 BR 1 1 s Services should have lower coinsurance when they are more highly serially correlated over time The higher the savings rate adjustment for health care shocks, the less insurance is needed If consumers discount the future more highly than the rate of interest, then there should be more insurance

30 Summary of what paper shows 1. Preventive care should be covered generously because consumers will ignore premium savings in their private prevention decisions. 2. Health care goods that are positively correlated with other health spending should be more generously covered 3. Health care goods that are substitutes should be covered more generously than complements. 4. Cover services generously that are positively correlated with uncompensated losses 5. Services that are positively serially correlated over time should be covered more generously than those that are uncorrelated

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