Unformatted text preview: 9/23/11 PADP 8670 POLICY ANALYSIS I Uncertainty and Alloca/ons over Time Angela Fer7g, Ph.D. Overview Last 1me, 4 mkt failures as ra1onales for policy (public goods, monopoly, externali1es, info asymmetry) This 1me, 2 more ra1onales: Uncertainty (risk preference, insurance, moral hazard, adverse selec1on, risk percep1on, prospect theory) Intertemporal alloca1on of goods (Intertemporal consump1on, discount rates, price indices) 1 9/23/11 Uncertainty and Risk Preference People generally do not like uncertainty or risk risk aversion We assume that the u1lity func1on with respect to wealth/money for most is upward sloping and concave: Happier if richer, but not twice as happy if twice as rich Diminishing marginal u1lity of wealth Implica1on of this concavity: having money with certainty makes you happier than having it with some uncertainty people don't like risk Proof: Diminishing marginal u1lity of wealth risk aversion Expected u7lity func7on: U = i u(c i )
i=1 i=N EU is weighted average of possible u1li1es. If just 2 possible states: U=u(c1)+(1)u(c2) where if probability of state 1. If just 2 possible states, it is derived from a pt on a line connec1ng 2 pts on the U(wealth) curve If U(wealth) curve is concave, then a line connec1ng 2 points will always be below the curve. EU of risk with always be below U without risk. 2 9/23/11 U1lity of wealth A U1lity U1lity difference caused by risk when expected wealth=$20,000 given this gamble. Risk premium: amt will to pay to remove risk O 10 20 50 Wealth (thousands of dollars) Which person is more risk averse? U1lity Person A Person B O 10 20 50 Wealth (thousands of dollars) 3 9/23/11 Which gamble is preferred? A U1lity B Assume EV(blue)=20, EV(red)=26 O 10 20 26 50 Wealth (thousands of dollars) Response to risk: Insurance Insurance is a type of risk pooling: Risk pooling occurs when a group of individuals, each facing a risk that is independent of the risks faced by the others, agree to share any losses or gain among themselves. Note that the risks must be independent An actuarially fair price is when everyone pays a premium equal to their expected value of loss (e.g. 0.02*1000 per year = $20) By having more people in the risk pool the likelihood of observing many bad outcomes in the same year is diminished. Bad outcome pr=.1. Probability of the worst outcome for the group. 2 people .1*.1=.01 3 people .1*.1*.1=.001 4 9/23/11 Problems with Insurance Moral hazard: the change in behavior that arises from having insurance Insurance reduces the economic incen1ves that each individual faces to prevent losses, and this causes behavior to be different. Consequence: Higher costs, higher risk Adverse Selec1on: when an individual's demand for insurance is correlated with the individual's risk of loss This implies that higher risks buy more insurance. Consequence: uninsurance among low risk, high premiums among high
risk Risk percep1on How good are you at assessing the probabili1es of certain outcomes? What is the probability of flood damage to your home? What is the probability than you will be arrested next year? What is the probability that you will get the flu next year? What is the probability that you will re1re at age 65? What is the probability that your child will go to an expensive private university? What is the probability that you will get pregnant if you have unprotected sex one 1me? 5 9/23/11 Risk percep1ons (con1nued) Your ability to form accurate risk probabili1es depend on: personal salience of events (know anyone experiencing event) rarity of event; if risky event occurs oken, may have a beler es1mate knowledge (youth tend to poor judges of risk) Consequence: Policies to address uncertainty may not have expected effects if people are not behaving according to the expected u1lity hypothesis. Prospect Theory Theory developed by Kahneman and Tversky, as alterna1ve to expected u1lity maximiza1on theory, to explain how people make decisions under risk. Economist ar1cle: People just their wellbeing rela1ve to others, not in absolute terms Framing effect: people's ac1ons depend on the way choices are presented People are risk averse towards gains and risk seeking toward losses Endowment effect: people place more value on things they already own than equal value things they do not own 6 9/23/11 Fig. 6.1 U1lity func1on under Prospect Theory U1lity Losses Gains Which theory is correct? Expected U1lity Maximiza1on? Prospect Theory? What do John List's experiments show? 7 9/23/11 In any case... Behavioral economics (econ+psych) is growing field used to beler understand how people make choices. Intertemporal Alloca1on of Goods People make choices about current vs. future consump1on all of the 1me. Consump1on smoothing: Debt when you are young is ra1onal! But need to save for re1rement too. 8 9/23/11 Lifecycle Earnings and Consump1on Earnings Annual Income and Consump1on Consump1on O 20 40 65 Age of Primary Worker Intertemporal Alloca1on of Goods How do people make choices about investments in the future? Consumer choice model where 2 goods are consump1on now and consump1on in the future. 9 9/23/11 Individual Consump1on Choice with Savings Opportuni1es (no borrowing) Future Consump1on C1 W o(1+r') Wo is the wealth endowment in 1me 0; Assume no earnings in 1me 1. W o(1+r) To get the extreme points on the budget constraint set savings in 1me 0 and 1 = 0 C1 O Co Wo Current Consump1on Co Savings Shape of the indifference curve indicates the marginal rate of subs1tu1on between the future and present Savings is just deferred consump1on The budget constraint is exactly the same as before but prices are interest rates Wo = 1Co + (1/1+r)C1 10 9/23/11 Individual Consump1on Choice with Borrowing and Savings Opportuni1es Previous model was too simplis1c since there were no borrowing opportuni1es. Now assume that the individual earns income and both periods. An individual's wealth equals the present value of the income streams. Income, consump1on Y1+Y o(1+r) Budget Constraint when savings and Future borrowing are possible Saver Y1 Endowment Borrower O Yo Y0+Y 1/(1+r) Current income, consump1on 11 9/23/11 Income, consump1on Y1+Y o(1+r) What happens when interest rates Future rises? Budget Constraint aker interest rate increase Saver: higher future cc subs1tu1on effect move toward future consump1on, income effect posi1ve (richer). Borrower: future cc unclear subs1tu1on effect move toward future consump1on, income effect ambiguous (borrow less but pay more for loan). Y1 Endowment O Yo Y0+Y 1/(1+r) Current income, consump1on Choosing a Discount Rate The social rate of marginal 1me preference (discount rate) should be equal to the market interest rate in equilibrium: If <r, save $1 now, get $1+r in the future, which is worth (1+r)/(1+)>$1 now so should save un1l =r If <r, borrow $1 now, pay $1+r in the future, which is worth (1+r)/(1+)<$1 now so should borrow un1l =r Should our choice of discount rate be influenced by the riskiness of the outcome, or by the poten1al catastrophic consequences of failing to act? 12 9/23/11 Choosing a Discount Rate Current prac1ce of the federal Office of Management and Budget is to use a 7 percent real discount rate (Circular A94, 1992). The implica1ons of using this discount rate are that the benefits of an investment diminish quickly Dividing by 1.07^10=1.97; 1.07^20=3.87; 1.07^30=7.61 Thus the benefit derived 30 years from now is worth $.13 for today's $1 Uncertain Future Prices and Index Construc1on Uncertainty about prices and earnings makes intertemporal resource decisions more difficult. In economics real measures are infla1on adjusted Nominal measures are not adjusted for infla1on. One way to cope with this is to adjust for infla1on and calculate all measures as real. Adjus1ng for infla1on is accomplished by using an index that relates prices (typically) in the past to those in the present. Indices alempt to convert prices so as to hold their purchasing power constant. Indexa1on is extremely important in policy analysis and policy design Social Security benefits are indexed. Tax bracket cut points are indexed Example of using index numbers hlp://data.bls.gov/cgibin/cpicalc.pl hlp://www.bls.gov/cpi/#tables 13 9/23/11 Two types of indexa1on Both are cost of representa1ve bundle of goods: Paasche's price index: ra1o of expenditure at period 1 to expenditure at period 0 using the new consump1on bundle at period 1. Laspeyre's price index: same, but old consump1on bundle from period 0 is used instead Paasche's Index underes1mates the cost of living. Start at A move to B as a result of the price increase. Hold quan1ty of Y fixed at B Quan1ty of Y A B Paasche's Index doesn't take into considera1on subs1tu1on effect and uses old prices as base. Px increase Quan1ty of X 14 9/23/11 Laspeyre's Index overes1mates the cost of living. Start at A move to B as a result of the price increase. Hold quan1ty of Y fixed at A. Quan1ty of Y A B Laspeyre's Index doesn't take into considera1on subs1tu1on effect and uses new prices as base. Px increase Quan1ty of X How does uncertainty and intertemporal alloca1on of goods affect policy analysis? You have to understand the problem before you can develop a solu1on: Is asymmetric informa1on or uncertainty/risk causing inefficient outcomes? If you regulate insurance, will moral hazard or adverse selec1on lead to unintended consequences? Are people making inefficient choices because of risk percep1ons, framing problems or endowment effects? Why doesn't everyone (e.g. borrowers) save more when interest rates rise? Why is it difficult to convince policy makers to investment in projects that do not show large financial benefits for 30 years? 15 9/23/11 For next 1me Read Ch. 7 Do Prac1ce Problems 16 ...
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