1. 1 Self-insurance and self-protection: the general case with endogenous technology of loss reduction and moral hazard problem Olga Kuzmina (ok2149@columbia.edu) Dmitry Levando (ie2003@list.ru) International College of Economics and Finance Higher School of Economics (Moscow, Russia)

2. 2 Market insurance – decrease of size of the loss if bad outcome occurs using market redistribution of risk (several economic agents). e.g: if a car accident occurs, insurance company pays for damage Self-insurance – investment in reduction of size of the loss if bad outcome occurs (only one agent, no market). e.g: fasten the seatbelt to lower personal injuries, if a car accident occurs Self-protection – investment in reduction of probability of loss (only one agent, no market). e.g: use hands-free during driving to lower probability of a car accident Types of insurance

3. 3 Examples of SI and SP Evaluation of client’s credit risk by a bank Monitoring of projects with asymmetric information Abramovich investment in personal security Clinical research of new medical drugs Market research for a new product Student preparation for an exam Driving and car safety: driving courses, seatbelts to lower possible losses of accident

4. 4 Method and notations Expected utility approach + indifference curves analysis Notations: Endogenous variables: – self-protection – self-insurance – market insurance Exogenous variables: – probability of bad state – a priori loss – gross income in good state – price of market insurance Functions: – loss technology – probability-of-loss technology – utility function

5. 5 Interaction: Ehrlich-Becker case market insurance + self-insurance: market insurance + self-protection: Insurance decision: SI + market or SP + market. However, they mention that distinguishing between self- insurance and self-protection is “somewhat artificial”.

6. 6 Interaction: Chang-Ehrlich case self-insurance + self-protection: self-insurance + self-protection + market insurance: Complex insurance decision: SI and SP with or without market insurance. There is no jointness of productivities (probability function and loss function are not altered by self-insurance and self-protection respectively).

7. 7 Joint productivities: our case self-insurance + self-protection: self-insurance + self-protection + market insurance: Complex insurance decision: SI and SP with or without market insurance. There is jointness of productivities (probability function and loss function are altered by self- insurance and self-protection respectively).

8. 8 Joint productivities: additive effect Our case: loss reduction technology is endogenous. Investment in self-protection allows to improve it. Usual case: size of loss depends on self-insurance only. Loss technology is exogenous. L(L e,x,y) y L(L e, x 1,y) L(L e, x 2,y) x 2 >x 1 L(L e,y) y y* L(L e,y*)

9. 9 Additive effect: example McDonalds: A special cautiory inscription that coffee is hot reduces the probability of getting burned as consumers read the caution. Probability of bringing a suit against MD decreases. Thus expenses to design a new coffee cup with inscription can be regarded as self-protection. This action also lowers losses of MD if it is brought to trial (it will not compensate damages from getting burned or the compensation will be lower since it warned about hotness, etc). Thus, losses also decrease.

10. 10 Joint productivities: self-deception Our case: probability-of-loss technology is endogenous. Investment in self-insurance worsens it. Self-deception is analagous to moral hazard when insured in the market. Usual case: probability of loss depends on self-protection only. Probability-of-loss technology is exogenous. p(p e,x) x 1 x* p(p e,x*) p(p e,x,y) x p(p e,x,y 2 ) p(p e,x,y 1 ) y 2 >y 1 1

11. 11 Self-deception effect: example Allergy is usually a persistent disease and this is only the amount of manifestations that can be reduced by antihistaminic remedies. Thus, they may be treated as self-insurance. On the other hand, eating tasty oranges or some other allergic food is a cause of allergy (increases the probability that it occurs and the probability that manifestations occur). When not self-insured (have not taken a remedy), she will eat fewer oranges (probability of manifestations is high and she dislikes them). When self-insured (have taken the remedy), she will eat more oranges (there will be relatively fewer manifestations due to the remedy effect). Therefore, with self-insurance, probability of manifestations will be higher.

12. 12 The model without market insurance FOC: – our joint optimality condition – Chang-Ehrlich case

13. 13 Implication Intuitively, self-protection is a desired good, since it both decreases the size of the loss and the probability of loss. Self-insurance has positive effect as it decreases the size of the loss, but it may have a negative effect due to self- deception effect (anyway, self-insurance is still a “good”, not a “bad”). Therefore, we may anticipate that there will be relatively more spent of self-protection than on self-insurance than in case of no jointness of productivities between them. Difficulty: how to show this analytically?

14. 14 The model with market insurance FOC: Price of market insurance may be responsive to SP and SI or not. Extreme cases: actuarilly fair insurance, and completely exogenous insurance premium.

15. 15 Implication: substitutability Consider substitutability of self-insurance and market insurance under fair price of market insurance. Holding amount of self-protection constant, we get: We argue that for some high values of, market insurance and self-insurance may be complements, i.e. ( ), which is contrary to the usual result of substitution between them. Discuss: is self-insurance still a ‘good’ in this situation?

16. 16 Technical problems: cross effects The second order condition for maximum is a complex expression with sufficient conditions that are not easily explained using economic intuition. Many of comparative statics results involve calculation of determinants of 3 rd order: signs are not obvious. If hold one variable constant, then the meaning can be lost.

17. 17 THE END Thank you for your attention!