Uncertainty and Insurance

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1 Uncertainty and Insurance A risk averse consumer is willing to pay for insurance. If consumption levels are 100, 200 and 400, with probabilities 1/6, 1/2, 1/3, respectively, then expected value of cons. = (100/6)+(200/2)+(400/3) = 250. Actuarially fair insurance: Insurer's expected net payout = 0. Offered actuarially fair insurance, risk averse consumer insures fully (completely removes uncertainty) replaces uncertain consumption in example by sure 250. Certainty equivalent of the risky consumption is the sure consumption that the consumer considers just as good. For risk averse consumer certainty equivalent < expected consumption since certainty equivalent is just as good as risky consumption, but getting the expected consumption for sure is better.

2 Uncertainty and Insurance Insurer offering actuarially fair insurance gets expected payout equal to sure premium received, so expected net revenue =0. Private insurers charge higher premium to cover costs + profit. With premium higher than actuarially fair, rational risk averse consumers buy less than full insurance, accept some risk (insurance with deductible). Private vs public insurance. Benefits of private: flexibility; match product to preferences; competition tends to lower costs. Benefits of public: fixed costs spread over bigger population. Potential inefficiencies from asymmetric information. Insurance buyers know more about their risks than insurers. Riskier people more likely to buy, so buyers are more risky than ave. Insurers raise premium, more low risk people drop out making customer pool riskier: Death spiral (CA health ins)

3 Adverse Selection and Moral Hazard Insurance buyers know more about their risks than insurers do. Adverse selection from hidden info about trader's characteristics Inefficiency from externality: riskier buyer imposes costs on insurers and other buyers. Lose mutually beneficial trades. Second kind of asymmetric info: Moral hazard Economists' definition: hidden action affecting insurer's costs. Example: with unemployment insurance, don't look hard for job. Insurers' definition: buyer's actions (hidden or not) affecting insurer's costs. Example: people with health insurance getting more treatment. With low transaction costs, only hidden action moral hazard causes inefficiency. (First welfare theorem: distinguish goods by the situation in which they are produced or consumed.)

4 Social Security (SS) Pension System SS is Old Age, Survivors and Disability Insurance, OASDI. Annuity: buyer pays initially, gets periodic payment until death. After death, SS pays spouse and children up to age 18. US SS since 1935; first benefit 1940; after 1939 pay-as-you-go PAYGO current workers' payroll tax pays for benefits to retirees. Since 1983, partially funded: part of tax goes to SS Trust. Payroll tax 12.4% of earnings up to $106,800 cap in 2011, half paid by worker, half by employer ($'s inflation adjusted) Can start benefit at age 62 if paid tax in 40 quarters. Benefit depends on retirement age and 35 yr average indexed monthly earnings (AIME). Retire at 65, get (90% of first $744 of AIME) + (32% of AIME btw $744 and $4483) + (15% of rest of AIME). Get highest expected value retiring at age 67.

5

6 Social Security (SS) Pension System Retirees who stopped working long ago earned low wages since they worked long ago. SS formula for AIME adjusts for that. Example: A worker earned $10000 in 1974 and retired in The average wage was $8000 in 1974 and $37000 in 2005 so the worker's adjusted 1974 wage is $10000 x (37000/8000) $ AIME is the average of the worker's adjusted wages over the 35 yrs of highest adjusted wages. AIME raises early wages by more than an adjustment for inflation since wages grew faster than inflation.

7 Social Security (SS) Pension System Distribution of net benefits: See Gruber table SS favors early generations, low earners, women (longer lives), single-earner couples. Ave 1994 retiree gets 2% annual return SS less progressive than benefit formula: rich live longer. Later cohorts' lower return repays legacy debt of early cohorts. Private alternatives: personal saving (no ins); employer pension (bankruptcy risk); annuity (cost > 2.3 actuarially fair rate). Employer pension pools employee risks (less adverse selection); contributions tax free. Most pensions defined contribution: benefits based on market returns on specified contributions. SS is defined benefit: benefit according to formula. SS Trust Fund projected to run out by 2040 (probably sooner). This yr Trust Fund will shrink. PAYGO after it runs out.

8 Social Security (SS) Effects Labor Supply: Many retire at earliest age for SS benefits; many more retire at full benefit age, maximizing expected benefits. Some workers delay retiring to get bigger benefit; probably more retire earlier than if there was no SS; so labor supply falls, maybe not much: without SS few fulltime workers past age 70. Personal Saving. Effect of SS depends on reasons for saving. 1. Saving for retirement: If SS pays same "rate of return" (benefits as return on tax payments) as private market, then consumer chooses same consumption as without SS, so personal saving is reduced by the amount of the payroll tax (100% crowd-out of saving). Personal saving averages around 8% of income. Payroll tax is 12.4% of taxed earnings (about 65% of total income), so the tax is around 7% of total income; Model estimate: SS cuts saving by 45% (from 15% to 8%).

9 Social Security (SS) Effects 2. Precautionary saving (saving for unexpected expenses): This motive remains with SS. Payroll tax reduces disposable income, so precautionary saving falls, but not by $1 for each $1 of payroll tax. Saving falls less than in case Altruism: Higher SS benefit and tax transfers wealth from younger to older generation. A saver who cares about heirs' welfare and wants to give them gifts or bequest, continues to save in order to undo the effect of the wealth transfer. Probably the first two motives are more common, so SS probably reduces personal saving and capital accumulation. Because of motives 2 and 3, the amount of saving reduction is probably less than 45%. Quasiexperimental studies in US and Italy suggest saving reduction in the range from 15% to 40%.

10 Social Security (SS) Sustainability In PAYGO after 2040, benefit/ave wage falls or tax rises, or both. N=# workers, R= # retirees, t= tax rate, B= benefit, W= ave wage tnw = BR, tn/r = B/W = ave replacement rate 40% now. N/R 3.3 now, expected to fall to 2.1 in More retirees per worker: longer lifetimes, baby boom retirees. If B/W constant, t rises to 19%; if t constant, B/W falls to 26%. Proposals: 1. Remove payroll tax income cap; raise Full Benefits Age (with highest expected SS benefit) to 69; raise payroll tax rate 2.5% points. 2. Use consumer price index instead of wage index to adjust lifetime wages in AIME formula (lowers long run B/W to 23%). 3. Allow more immigration by young adults; plus other reforms.

11 Social Security (SS) Reform Proposal 4. (Feldstein, Samwick) Privatization: Raise payroll tax to 17%, part goes in private retirement account (PRA) managed by worker, rest pays benefits of current retirees. Return from PRA finances younger workers' retirement. Need historical ave annual stock return, 7%. But stocks are risky. Workers with low returns get low retirement income. Proposal could reduce stock returns: stock prices rise as baby boom generations buy stock; stock prices lower than otherwise as baby boomers sell stock to finance retirement. Interest rates likely higher than otherwise to attract buyers of gov bonds previously held by SS Trust fund. Private annuities market adverse selection problem remains. Workers can buy annuities to insure against low income when very old, but premium is much higher than actuarially fair.

12 Social Security (SS): Efficiency Issues Advantages of gov pension: 1. Dynamic efficiency? Growing population funds same consumption with less saving. 2. Adverse selection limits private market for annuities. 3. Administrative + decision-making economies from big standardized program. (Admin cost 0.2% of assets) 4. Some people don't plan well. In experiments, pension choice depends on framing of alternatives. (Paternalism) Bernheim, et. al. American Economic Review 2001, Disadvantages of gov system: 1. Lower saving can reduce capital accumulation and growth. 2. Less flexibility, poorer matching to preferences. 3. Funded saving can earn higher (riskier) expected return; unlikely to be as high as predicted by Feldstein, Samwick.

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