AREC 815: Experimental and Behavioral Economics. Measuring Risk Preferences. Professor: Pamela Jakiela

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1 AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences Professor: Pamela Jakiela Department of Agricultural and Resource Economics University of Maryland, College Park Expected Utility

2 Risk Preferences: the Standard Model A simple lottery: L = {p 1,...,p K ; x 1,...,x K } s.t. k p k =1 A set of probabilities (that sum to 1) and associated payoffs Continuity: for all simple lotteries L 1, L 2, L 3,thesets {α [0, 1] : αl 1 +(1 α)l 2 L 3 } [0, 1] and are closed. {α [0, 1] : L 3 αl 1 +(1 α)l 2 } [0, 1] Continuity means that preferences don t change discontinuously (for example, at the ends of the probability space) AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 3 Risk Preferences: the Standard Model Independence: for all simple lotteries L 1, L 2, L 3 and all α (0, 1), L 1 L 2 αl 1 +(1 α)l 3 αl 2 +(1 α)l 3. When a rational preference relation over lotteries satisfies the continuity and independence axioms, it admits an expected utility representation AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 4

3 Risk Preferences: the Standard Model VNM EU-maximizing preferences: Individuals have well-defined preferences over outcomes Outcome utilities are weighted by probabilities Risk aversion concave utility function over outcomes The expected utility of lottery L is given by: EU(L) = k p k u(x) where u( ) is a well-defined Bernoulli utility function over outcomes AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 5 Risk Preferences: the Standard Model What is risk aversion? u(x) Utility 0 0 x Outcome AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 6

4 Risk Preferences: the Standard Model The following are equivalent: The agent is risk averse u ( ) isconcave The certainty equivalent for all lotteries below the expected value For all x,ε>0, the probability premium π (x,ε,u) such that [ ] [ ] 1 1 u(x) = 2 π (x,ε,u) u (x ε)+ 2 + π (x,ε,u) u (x + ε) is positive. AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 7 Risk Preferences: the Standard Model Arrow-Pratt coefficients of risk aversion: a = u (x) u (x) and r = xu (x) u (x) Can t always rank utility functions in terms of risk aversion Arrow-Pratt coefficients depend on payoff level, x u( ) isstrictly more risk averse than v( ) exists a strictly concave function f ( ) such that u( ) =f (v( )) Some utility functions can be ranked in terms of a single parameter CARA: u(x) = e αx CRRA: u(x) = x 1 ρ 1 ρ AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 8

5 Measuring Risk Preferences Portfolio Choice Designs Choices from continuous sets power to estimate precise parameters Jakiela-Ozier (2016): Choi et al (2007, 2014): simple portfolio choice design state-contingent securities Different strategies for presenting the same (type of) choice problem Early examples: Loomes (1991), Gneezy and Potters (1997) AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 10

6 Portfolio Choice Designs Portfolio choice problem: Choose x m to invest in risky (but profitable) asset Agents maximize: p success u (m + λx)+(1 p success ) u (m x) Functional form assumptions lead to analytical solutions State-contingent securities problem: Make allocation to state-contingent securities s.t. y + q z m Agents maximize: p y u (y)+p z u (z) Analogous to portfolio choice problem when p y + p z =1 AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 11 Binswanger s Methodology Binswanger (1980) is: the original lab-in-the-field experiment, seminal experimental strategy for measuring individual risk aversion Menu of lotteries increasing in expected value, risk Subjects were Indian villagers (ICRISAT villages) Sequence of real and hypothetical choices over many weeks Stakes increased over time AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 12

7 Binswanger s Methodology Menu of lotteries in Binswanger s experiment: AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 13 Risk Preferences: the Standard Model u(w+2z) u(w+z) u(w) u(w-z) u(w-2z) 0 0 w-2z w-z w w+z w+2z x AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 14

8 Binswanger s Methodology AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 15 Binswanger s Methodology AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 16

9 Holt-Laury Methodology Multiple price list decision task: AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 17 Holt-Laury Methodology AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 18

10 Holt-Laury Experimental Design AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 19 Low Stakes vs. High Stakes AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 20

11 Low Stakes vs. High Stakes AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 21 Utility Parameters AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 22

12 Utility Parameters Propose to estimate a utility function of the power-expo form: 1 ρ 1 e αx u(x) = α Approaches CARA as ρ 0, approaches CRRA as α 0 Pool data across subjects, estimate a single set of parameters Parameter Estimate α ρ AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 23 Survey Questions Measuring Risk Attitudes Dohmen et al (JEEA, 2011) embed a simple question about risk in a large, representative survey of the adult German population How willing are you to take risks, in general? AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 24

13 Survey Questions Measuring Risk Attitudes Does a survey question capture risk attitudes/preferences? As a test of construct validity, they conduct an incentivized MPL experiment with a smaller representative sample of German adults AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 25 Are Risk Preferences Stable across Domains? AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 26

14 Measuring Risk Preferences Experimental design questions: Assumptions: EU? CRRA/CARA functional form? Incentivized vs. hypothetical choices Experimental designs: Discrete choices Multiple price lists Other discrete choice designs Continuous choice sets Other (e.g. survey) approaches AREC 815: Experimental and Behavioral Economics Measuring Risk Preferences, Slide 27