Behavioral Insurance: An Introduction

Transcription

1 Jimmy Martínez-Correa Behavioral Insurance: An Introduction 7 th International Microinsurance Conference Brazil,November 8 th Center for the Economic Analysis of Risk Department of Risk Management & Insurance

2 Purpose of this Talk > Provide an 101 course in insurance economics and behavioral insurance. > No definite answers provided in this talk. > Present thought-provoking ideas as an entrée for this conference. > Provide three messages for researchers interested in Microinsurance.

3 Outline > What is Behavioral Insurance? > A Primer on Insurance Economics Theory > Behavioral Insurance at Work and Some Lessons > A Non-trivial Distinction: Risk vs. Uncertainty > Conclusions

4 Outline > What is Behavioral Insurance? > A Primer on Insurance Economics Theory > Behavioral Insurance at Work and Some Lessons > A Non-trivial Distinction: Risk vs. Uncertainty > Conclusions

5 What is Behavioral Insurance? > An example of a Behavioral Decision Science > So, what is a BDS? o Theory o Evidence o Econometrics and Statistics. > Behavioral Insurance studies insurance decisions using this trilogy.

6 Dynamics of the Trilogy Theory Evidence Behavioral Science Econometrics Statisctics

7 Dynamics of the Trilogy Theory Evidence Behavioral Science Normative Descriptive Econometrics Statisctics

8 Dynamics of the Trilogy Theory Evidence Behavioral Science Econometrics Statisctics Casual lobservation Thought Experiments Lab Experiments Field Experiments Natural Experiments (Harrison & List, 2004)

9 Dynamics of the Trilogy Theory Evidence Behavioral Science Structural Econometrics Nonparametric Statistics Sampling techniques The Randomistas etc Econometrics Statisctics

10 Outline > What is Behavioral Insurance? > A Primer on Insurance Economics Theory > Behavioral Insurance at Work and Some Lessons > A Non-trivial Distinction: Risk vs. Uncertainty > Conclusions

11 A Primer on Insurance Economics Theory > The focus of this talk will be on individual decision making.

12 A Primer on Insurance Economics Theory > The focus of this talk will be on individual decision making. o However, there is a huge literature on insurance markets.

13 A Primer on Insurance Economics Theory > The focus of this talk will be on individual decision making. o However, there is a huge literature on insurance markets. > Assumptions for now: o Expected Utility Theory o Insured is risk averse; insurer may be risk averse or risk neutral.

14 A Primer on Insurance Economics Theory > The focus of this talk will be on individual decision making. o However, there is a huge literature on insurance markets. > Assumptions for now: o Expected Utility Theory o Insured is risk averse; insurer may be risk averse or risk neutral. > Classic theoretical results: o Optimal risk sharing rules o Optimal insurance contracts t o Risk aversion and demand for insurance o Risk management: Prevention and risk-transfer mechanisms.

15 Optimal Risk Sharing > Borch, Karl, Equilibrium in a Reinsurance Market, Econometrica, 30, 1962, > Application of Arrow s [1953] GE model. o Risk is the only commodity traded.

16 Optimal Risk Sharing > Borch, Karl, Equilibrium in a Reinsurance Market, Econometrica, 30, 1962, > Application of Arrow s [1953] GE model. o Risk is the only commodity traded. > Result 1: Only aggregate social risk matters. o Individuals pool resources and get rid of idiosyncratic risk.

17 Optimal Risk Sharing > Borch, Karl, Equilibrium in a Reinsurance Market, Econometrica, 30, 1962, > Application of Arrow s [1953] GE model. o Risk is the only commodity traded. > Result 1: Only aggregate social risk matters. o Individuals pool resources and get rid of idiosyncratic risk. > Result 2: The distribution of risk among individuals depends d on the risk aversion and bargaining i power of every individual. o Assumptions on risk aversion simplify the rule.

18 Optimal Insurance Contracts > Arrow, Kenneth, Uncertainty and the Welfare,, y Economics of Medical Care, AER, 53, 1963,

19 Optimal Insurance Contracts > Arrow, Kenneth, Uncertainty and the Welfare Economics of Medical Care, AER, 53, 1963, > Result 1: If insurance loading is positive, the most preferred insurance contract is one with full insurance above a deductible.

20 Optimal Insurance Contracts > Arrow, Kenneth, Uncertainty and the Welfare Economics of Medical Care, AER, 53, 1963, > Result 1: If insurance loading is positive, the most preferred insurance contract is one with full insurance above a deductible. > Result 2: If insured and insurer are risk averse, the optimal arrangement is a coinsurance contract. o Application of Borch theorem on optimal risk sharing rules.

21 Optimal Insurance Contracts > Arrow, Kenneth, Uncertainty and the Welfare Economics of Medical Care, AER, 53, 1963, > Result 1: If insurance loading is positive, the most preferred insurance contract is one with full insurance above a deductible. > Result 2: If insured and insurer are risk averse, the optimal arrangement is a coinsurance contract. o Application of Borch theorem on optimal risk sharing rules. > Result 3: Informational problems (MH and AS) can also explain incomplete risk transfer.

22 Optimal Insurance Contracts and Insurance Demand > Mossin, Jan, Aspects of Rational Insurance Purchases, JPE, 79, 1968,

23 Optimal Insurance Contracts and Insurance Demand > Mossin, Jan, Aspects of Rational Insurance Purchases, JPE, 79, 1968, > Result 1: Full insurance is optimal if insurance is actuarially fair. o Or, partial insurance coverage is optimal if premium is above the actuarially fair value. o Smith [1968] derived a similar result.

24 Optimal Insurance Contracts and Insurance Demand > Mossin, Jan, Aspects of Rational Insurance Purchases, JPE, 79, 1968, > Result 1: Full insurance is optimal if insurance is actuarially fair. o Or, partial Insurance coverage is optimal if premium is above the actuarially fair value. o Smith [1968] derived a similar result. > Result 2: Insurance demand is decreasing in wealth if individual has decreasing absolute risk aversion (DARA).

25 Risk Management: The Role of Prevention > Ehrlich, J and Becker, G., Market Insurance, Self-,,,, Insurance and Self-Protection, JPE, 80, 1972,

26 Risk Management: The Role of Prevention > Ehrlich, J and Becker, G., Market Insurance, Self- Insurance and Self-Protection, JPE, 80, 1972, > Result 1: With no market insurance, individual engages in self-protection (e.g., theft alarms) and self-insurance (e.g., savings) activities. o Marginal benefits are weighted against marginal costs of Self- Protection and Self-Insurance activities.

27 Risk Management: The Role of Prevention > Ehrlich, J and Becker, G., Market Insurance, Self- Insurance and Self-Protection, JPE, 80, 1972, > Result 1: With no market insurance, individual engages in self-protection (e.g., theft alarms) and self-insurance (e.g., savings) activities. o Marginal benefits are weighted against marginal costs of Self- Protection and Self-Insurance activities.. > Result 2: Self-insurance and market insurance are substitutes.

28 Risk Management: The Role of Prevention > Ehrlich, J and Becker, G., Market Insurance, Self- Insurance and Self-Protection, JPE, 80, 1972, > Result 1: With no market insurance, individual engages in self-protection (e.g., theft alarms) and self-insurance (e.g., savings) activities. o Marginal benefits are weighted against marginal costs of Self- Protection and Self-Insurance activities. > Result 2: Self-insurance and market insurance are substitutes. > Result 3: Self-protection and market insurance may be complements or substitutes.

29 Risk Management: Risk-Transfer Tools > Mayers, D. and Smith, C. W., The Interdependence of Individual Portfolio Decisions and the Demand for Insurance, JPE, 91, 1983,

30 Risk Management: Risk-Transfer Tools > Mayers, D. and Smith, C. W., The Interdependence of Individual Portfolio Decisions and the Demand for Insurance, JPE, 91, 1983, > Insurance choices should not be analyzed in isolation.

31 Risk Management: Risk-Transfer Tools > Mayers, D. and Smith, C. W., The Interdependence of Individual Portfolio Decisions and the Demand for Insurance, JPE, 91, 1983, > Insurance choices should not be analyzed in isolation. > The Big Picture of insurance and portfolio choices. o Risky traded assets o Risky non-traded assets (e.g. Human capital) o Insurable and non insurable risks.

32 Risk Management: Risk-Transfer Tools > Mayers, D. and Smith, C. W., The Interdependence of Individual Portfolio Decisions and the Demand for Insurance, JPE, 91, 1983, > Insurance choices should not be analyzed in isolation. > The Big Picture of insurance and portfolio choices. o Risky traded assets o Risky non-traded assets (e.g. Human capital) o Insurable and non insurable risks. > Insurance is just one of the hedging tools. o Risky assets can hedge human capital risk less insurance. o Correlation of Human capital and insurable risk more insurance.

33 Outline > What is Behavioral Insurance? > A Primer on Insurance Economics Theory > Behavioral Insurance at Work and Some Lessons > A Non-trivial Distinction: Risk vs. Uncertainty > Conclusions

34 Behavioral Insurance at Work (1) > First reference in insurance economics: o Bernoulli, Daniel, (1738). Exposition of a New Theory on the Measurement of Risk, Econometrica, Vol. 22, 1954,

35 Behavioral Insurance at Work (1) > First reference in insurance economics: o Bernoulli, Daniel, (1738). Exposition of a New Theory on the Measurement of Risk, Econometrica, Vol. 22, 1954, > Bernoulli s Principle: o Moral Expectation =Expected Utility (vnm [1953])

36 Behavioral Insurance at Work (1) > First reference in insurance economics: o Bernoulli, Daniel, (1738). Exposition of a New Theory on the Measurement of Risk, Econometrica, Vol. 22, 1954, > Bernoulli s Principle: o Moral Expectation =Expected Utility (vnm [1953]) > Descriptively motivated t theory development o The St. Petersburg paradox. > Normative implications o Thresholds of wealth to buy or sell insurance for commodities shipped overseas.

37 Behavioral Insurance at Work (2) > We see people p buying insurance and gambling. g o In Colombia, some low-income households invest 2.1% of their income in insurance and 2.1% on lotteries (Remolina-Estrada, 2007). o Some households with higher income do the same spend less in lotteries (1.1%) and more in insurance (3%).

38 Behavioral Insurance at Work (2) > We see people p buying insurance and gambling. g o In Colombia, some low-income households invest 2.1% of their income in insurance and 2.1% on lotteries (Remolina-Estrada, 2007). o Some households with higher income that do the same spend less in lotteries (1.1%) and more in insurance (3%). > Normatively, one would rather see people investing gambling money in something else. o Especially low-income households.

39 Behavioral Insurance at Work (2) > First behavioral insurance discussion in the literature: o Friedman, Milton and Savage, Leonard J., The Utility Analysis of Choices Involving Risk, JPE, 56(4),1948, > Friedman and Savage explanation within EUT: o Puzzle: Decreasing marginal utility No gambling o Explanation: Utility function has a concave and a convex part.

40 Behavioral Insurance at Work > First behavioral insurance discussion in the literature: o Friedman, Milton and Savage, Leonard J., The Utility Analysis of Choices Involving Risk, JPE, 56(4),1948, > Friedman and Savage explanation within EUT: o Puzzle: Decreasing marginal Utility No gambling o Explanation: Utility function has a concave and a convex part. > A simpler explanation: People like to gamble o Utility of Gambling (vnm [1953]) > But let s focus on Friedman and Savage

41 Classic Utility Function: Diminishing Marginal Utility U(.) Income

42 Friedman-Savage Utility Function U(.) Region where insurance is bought EUT does not require U(.) to be concave. Region where gambling happens Income

43 Friedman-Savage Utility Function U(y) pu(y 1 )+ (1-p)U(y 2 ) EU without insurance y 1 y 0 y 2 Income (y) Risky income

44 Friedman-Savage Utility Function U(y) Utility with full insurance U(ŷ 0 ) pu(y 1 )+ (1-p)U(y 2 ) EU without insurance y ŷ 1 0 y 0 y 2 Income (y) Insurance premium

45 Friedman-Savage Utility Function U(y) Buy Lottery because: qu(y 1 )+ (1-q)U(y 2 ) > U(y 0 ) U(y 0 ) EU of buying the Lottery Ticket y 1 y 0 y 2 Income (y) Price of Lottery ticket

46 Insurance-Gambling Puzzle: Other Explanations at > More EUT explanations o Markowitz [1952]. People have a preference for positively skewed distributions: Preference for long shots (long right tail). o Chetty and Szeidl [2007]: Consumption Commitments. > Non-EUT explanations o Machina [1982]: There is action in the probabilities; the fanningout hypothesis can explain the preference for positively skewed distributions. o Quiggin [1982]: One part due to utility and the other part due to probability pessimism.

47 Behavioral Insurance at Work (3): What happens to insurance when wealth increases? > Mossin s prediction (Result 2): If individual s preferences p ( ) p exhibit DARA, insurance demand decreases.

48 Behavioral Insurance at Work (3): What happens to insurance when wealth increases? > Mossin s prediction (Result 2): If individual s preferences exhibit DARA, insurance demand decreases. Insurance Demand Insurance is an inferior good. Wealth

49 What happens to insurance when wealth increases? > Practitioner s view: Insurance demand increases with wealth. Enz [2000]; data points for 1998 only.

50 Is insurance an inferior or a normal good? > Simple explanation: Richer people buy more stuff, so the p p p p y, insurance demand is higher in value.

51 Is insurance an inferior or a normal good? > Simple explanation: Richer people p buy more stuff, so the insurance demand is higher in value. o Foncel and Treich [2009]: Even controlling for this, insurance is still a normal good and financial decisions of subjects are consistent with DARA.

52 Is insurance an inferior or a normal good? > Simple explanation: Richer people p buy more stuff, so the insurance demand is higher in value. o Foncel and Treich [2009]: Even controlling for this, insurance is still a normal good and financial decisions of subjects are consistent with DARA. > Cummins and Mahul [2004]: Upper limits in coverage can induce a risk averse individual with DARA to increase insurance demand when wealth increases.

53 Is insurance an inferior or a normal good? > Simple explanation: Richer people p buy more stuff, so the insurance demand is higher in value. o Foncel and Treich [2009]: Even controlling for this, insurance is still a normal good and financial decisions of subjects are consistent with DARA. > Cummins and Mahul [2004]: Upper limits in coverage can induce a risk averse individual with DARA to increase insurance demand when wealth increases. > Chen and Mahani [2009]: Consumption commitments can induce insurance demand to be a normal good in certain ranges of wealth.

54 What happens to insurance when wealth increases for the Poor? > Liquidity constraints can explain an increase in the insurance demand in the poor. o Crocker, Harrison and Phillips [2011]-ongoing project presented in conference plenary. o George Zanjani, also in the plenary.

55 What happens to insurance when wealth increases for the Poor? > Liquidity constraints can explain an increase in the insurance demand in the poor. o Crocker, Harrison and Phillips [2011]-ongoing project presented in conference plenary. o George Zanjani, also in the plenary. > Why? Need three ingredients to explain it. o Precautionary saving (PS) o Effect of liquidity constraint on PS (Carrol and Kimball [2005]) o Saving and insurance are substitutes (Moffet [1977])

56 What happens to insurance when wealth increases for the Poor? > Liquidity constraints can explain an increase in the insurance demand in the poor. o Crocker, Harrison and Phillips [2011]-ongoing project presented in conference plenary. o George Zanjani s also in the plenary. > Why? Need three ingredients to explain it. o Precautionary saving (PS) o Effect of liquidity constraint on PS (Carrol and Kimball [2005]) o Saving and insurance are substitutes (Moffet [1977]) > Less liquidity constraints reduce the need for PS, liberating resources for insurance purchases. o Need to understand the set of hedging tools available to the Poor to identify the role of insurance.

57 Outline > What is Behavioral Insurance > A Primer on Insurance Economics Theory > Behavioral Insurance at Work and Some Lessons > A Non-trivial Distinction: Risk vs. Uncertainty > Conclusions

58 The Poor are More Vulnerable to Risk

59 The Poor are More Vulnerable to Risk > Not only in Colombia. > The Poor are more vulnerable to risks everywhere. > But, what do we mean by risks? > Let s do the following thought experiment.

60 A Thought Experiment 50/50 chance

61 A Thought Experiment 50/50 chance 50/50 chance???

62 A Thought Experiment Do you prefer to bet $100 on Heads? Or, do you prefer to $100 on Rain? 50/50 chance 50/50 chance???

63 A Thought Experiment Risk Uncertainty 50/50 subjective chance??? 50/50 objective chance

64 A Non-Trivial Distinction: Risk vs. Uncertainty > Probabilities may feel different depending on the source. o Objective probabilities vs. subjective probabilities.

65 A Non-Trivial Distinction: Risk vs. Uncertainty > Probabilities may feel different depending on the source. o Objective probabilities vs. subjective probabilities. > Why is this relevant to Microinsurance?

66 A Non-Trivial Distinction: Risk vs. Uncertainty > Probabilities may feel different depending on the source. o Objective probabilities vs. subjective probabilities. > Why is this relevant to Microinsurance? > A researcher wants to analyze microinsurance demand. o Elicit risk attitudes with the objective probabilities. o Make recommendations about decisions that involve subjective probabilities (e.g., weather insurance). > There is a chance that the policy recommendations are misleading.

67 A Non-Trivial Distinction: Risk vs. Uncertainty > This distinction has a long tradition in decision theory: o Knight [1921], Keynes [1921], Savage [1954], Fellner [1961] and Ellsberg [1961, 2001]. > In the literature today, uncertainty is called ambiguity. > There are now many models that takes into account this distinction: o Segal [1988] version of Quiggin s [1982] RDU o Gilboa and Schmeidler [1989]: Maxmin EU o Schmeidler [1989]: Choquet Capacities o Klibanoff, Marinacci and Mukerji [2005] > Classic insurance theory results may not hold.

68 Outline > What is Behavioral Insurance > A Primer on Insurance Economics Theory > Behavioral Insurance at Work and Some Lessons > A Non-trivial Distinction: Risk vs. Uncertainty > Conclusions

69 Conclusions > Behavioral Insurance is an example of a behavioral decision science: o Theory-Evidence-Econometrics/Statistics. > The distinction between risk and uncertainty is potentially important for policy implications. > Behavioral Insurance can help to understand and develop Microinsurance products: o Insurance is one among many hedging tools. o Need to understand the (formal and informal) risk management tools available to the Poor before we make normative recommendations.

70 How the Poor Manage Shocks: An Example

71 THANK YOU

72 Additional References (1) > Arrow, Kenneth J., Le rôle des valeurs boursières pour la répartition la meilleure de risques, in Econométrie, CNRS, Paris, 1953, English version: The Role of Securities in the Optimal Allocation of Risk-Bearing, Review of Economic Studies, 31, 1964, > Arrow, Kenneth J., Liquidity Preference, Lecture VI in Lecture Notes for Economics 285, The Economics of Uncertainty, Stanford University, undated, > Carroll, Christopher D., and Kimball, Miles S., Liquidity Constraints and Precautionary Saving, Working Paper, > Chen, Hua and Mahani, Reza S., Optimal Demand for Insurance with Consumption Commitment, t Working Paper, > Chetty, Raj and Szeidl, Adam, Comsumption Commitments and Risk Preferences, the Quarterly Journal of Economics, 122(2), 2007, > Cummins, J. David and Mahul, Olivier, i The Demand for Insurance with an Upper Limit it on Coverage, The Journal of Risk and Insurance, 71 (2), 2004, > Ellsberg, Daniel, Risk, Ambiguity and the Savage Axioms, the Quarterly Journal of Economics, 75(4), November 1961,

73 Additional References (2) > Ellsberg, Daniel, Risk, Ambiguity and Decision (New York: Garlang Publishing Inc, 2001). > Enz, Rudolf, The S-Curve Relation Betweeb Per-Capita Income and Insurance Penetration, The Geneva Papers on Risk and Insurance, 25(3), July 2000, > Fellner, William, Distortion of Subjective Probabilities as Reaction to Uncertainty, American Economic Review, 48(5), 1961, > Foncel, Jérôme and Treich, Nicolas, Insurance as a Normal Good: Empirical Evidence for a Puzzle, Working Paper, > Gilboa, Itzhak and Schmeidler, David, Maximin Expected Utility with Non-Unique Prior, Journal of Mathematical Economics, 18, 1989, > Harrison, Glenn W. and List, A. John, Field Experiments, Journal of EconHomic Literature, 42(4), December 2004, > Keynes, John M., A Treatise in Probability (London: Macmillan and Co, 1921). > Klibano, Peter, Marinacci, Massimo and Mukerji, Sujoy. (2005). A Smooth Model of Decision > Making under Ambiguity, Econometrica, 73, 2005, >

74 Additional References (3) > Knight, Frank, Risk, Uncertainty and Profit (Boston, MA: Houghton Mifflin Co, 1921). > Machina, Mark, Expected Utility Analysis without the Independence Axiom, Econometrica, 50(2), March 1982, > Markowitz, Harry, The Utility of Wealth, Journal of Political Economy, 60(2), April 1952, > Moffet, Denis, Optimal Deductible and Consumption Theory, The Journal of Risk and Insurance, 44(4), December 1977, > Quiggin, John, A theory of Anticipated Utility, Journal of Economic Behavior and Organisation 3(4), 1982, > Savage, Leonard J., The Theory of Statistical Decision, Journal of the American Statistical Association, 46(253), March 1951, > Schmeidler, David,. Subjective Probability and Expected Utility without Additivity,.Econometrica, 57, 1989, > Segal, Uzi, Does the Preference Reversal Phenomenon Necessarily Contradict the Independence Axiom? American Economic Review, 78(1), March 1988, >

75 Additional References (4) > Smith, Vernon, Optimal Insurance Coverage, Journal of Political Economy 76(1), 1968, > von Neumann, John. and Morgensten, Oskar, Theory of Games and Economic Behavior (Princeton, NJ: Princeton University Press, 1953; Third Edition; Princeton University Paperback Printing, 1980). >