Individual decision-making II
Marta Serra-Garcia, University of Munich
Outline
1. Reference – dependent preferences:
• Rabin and Köszegi, 2006, QJE
2. Reference- dependent preferences in the field
• Labor supply (Camerer et al, 1997, QJE) 3. Testing: what is the reference point?
• Expectations (Abeler et al, 2011, AER) 4. Measuring individual risk preferences
• von Gaudecker et al (2011, AER)
0. Refresher
• In Prospect Theory:
– Outcomes are evaluated as gains or losses – With respect to?
– A reference point...
– But what is the reference point?
• A usual assumption: reference point = status quo – Consistent with the Endowment Effect:
• Experimental subjects who own something feel a loss when selling it
– But, what about professional sellers when they trade in the market place?
1. Reference-dependent preferences
• Köszegi and Rabin (2006)
• Endogeneize the reference point
– Rational expectation, held in the ‚recent‘ past
• Intuition:
– In experiments where the Endowment Effect was observed – Subjects were given a mug or a pen, and did not expect to
trade it, rather to keep it
– In contrast, when professional sellers go to the market they do expect to sell – not selling might then be a loss!
1. Reference-dependent preferences
• Utility of consumption c, when reference is r )) ( )
( ( )
| ( )
|
(c r m c r m c m r
u = + µ −
Consumption utility
Gain-loss utility
• Gain-loss utility:
– μ(.) is continuous and strictly increasing – μ(.) features loss aversion
– μ(.) features diminishing sensitivity
1. Reference-dependent preferences
• Example:
– Suppose Sally faces a lottery
• (100, 0.5; -50, 0.5)
– And her expectation is the expected payoff of the lottery ..
– Thus her reference point – Thus her reference point
– If outcome is 100, her u=100+ μ(100-25) – If outcome is 0, her u=-50+ μ(-50-25)
– Suppose μ is linear and has coefficient 1 if gain, 2 if losses
1. Reference-dependent preferences
• Equilibria:
– Personal Equilibrium (PE):
• If Sally expects to choose F from a set D, a PE requires Sally to be willing to choose F from D, given that F is her reference point.
– Preferred Personal Equilibrium (PPE):
• A selection F is a PPE if it is a PE and it maximizes Sally‘s utility for all PE selections F‘ from D.
1. Reference-dependent preferences
• What do reference-dependent preference imply for shopping behavior?
– Expectations of behavior and price
– Become an important determinant of an individual‘s willingness to pay
• An Example:
• An Example:
• Andy goes shopping – in search for a pair of shoes – Utility of pair, c1={1 if bought, 0 not bought}
– Price, p
– Gain-loss utility,
• ηx if x>0
• ηλx if x<0
– Initial endowment, (0,0)
1. Reference-dependent preferences
• What is Andy‘s utility if:
– He expects to buy a pair at price p and buys?
• Suppose the expected price pE≥p
• U(B|B)= 1 – p + η(1-1) - η(p-pE)= 1 – p – ηp + ηpE
– He expects to buy a pair at price P and does not buy it?
• U(NB|B)= 0 + ηλ(0-1) - η(0-pE)= ηpE – ηλ
• Given than he expects to buy, what is the maximum price is willing to pay? pMAX
Consumption utility Gain-loss utility a) from item b) from price
1. Reference-dependent preferences
• What is Andy‘s utility if:
– He does not expect to buy a pair, and buys it?
• U(B|NB) = 1 – p – ηλ(p – 0) + η(1-0)= 1 – p – ηλp + η – He does not expect to buy a pair, and does not buy it?
– He does not expect to buy a pair, and does not buy it?
• U(NB|NB) = 0
• Given that he does not expect to buy, what is the highest price that induces him to buy? pMIN
1. Reference-dependent preferences
• Suppose prices are:
– p> pMAX : unique Personal Equilibrium, not to buy – p< pMIN : unique Personal Equilibrium, to buy
– Prices between pMIN and pMAX – Prices between pMIN and pMAX
• Both buying and not doing so are pure-strategy equilibria
• Why?
– If expected to buy, not buying feels like a loss – If did not expect to buy, buying feels like a loss
1. Reference-dependent preferences
• Conclusion:
– Expectations affect individuals‘ willingness to pay
• If expected to buy, may be willing to pay more than 1
• If did not expect to buy, may not be willing to buy if price is 1-ε, where ε small
price is 1-ε, where ε small
– Thus, decision making with reference-dependent preferences may differ substantially from that with
‚standard‘ preferences
2. Reference-dependent preferences in the field
NYC Cab Driver‘s supply (Camerer et al., 1997)
2. Reference-dependent preferences in the field
• Standard labor supply theory:
– If wages increase temporarily, work hours increase – Or leisure is substituted with labor...
• Why do we then observe a negative elasticity of labor supply?
2. Reference-dependent preferences in the field
• Why do we then observe a negative elasticity of labor supply?
– Narrow bracketing:
• What time frame is used for the income target? Day, month, year?
– Loss aversion:
• Falling below the income target is ‚particularly‘ painful
• Can this be explained by Rabin and Köszegi (2006)?
• An extremely simplified example
– Suppose a taxi driver has a daily income target of $100 – Her costs of effort = 5$ per hour
2. Reference-dependent preferences in the field
– Her costs of effort = 5$ per hour
– Income per hour worked = high ($20/hour) or low ($10/hour)
• Suppose taxi driver expects income to be high and work 5 hours
– But income turns out to be low
• U(working 0 hours)= 0 + λη(0-100)- η(0-25)
• U(working 5 hours)=50 - 25+ λη (50-100)
• U(working 10 hours)=100 -50 + η(100-100) - λη(50-25)
• Suppose λ=2 and η=1
– U(working 0 hours)= - 200 + 25 = -175 U(working 5 hours)= 25 – 100 = -75
2. Reference-dependent preferences in the field
– U(working 5 hours)= 25 – 100 = -75 – U(working 10 hours)= 50 – 50 = 0
• Conclusion:
– For certain preference parameters and if individuals bracket at the daily level
– The negative relationship between hourly wages and hours worked can be explained with reference-dependent preferences
3. What is the reference point?
• Is the reference point really based on expectations?
• Abeler et al. (2011, AER) provide evidence
• Real – effort experiment
• Real – effort experiment
3. What is the reference point?
• Design
– Stage 1: 4 minutes to complete as many tasks as possible
• Subjects become familiar with task
• Productivity measure
Stage 2: subjects are given as much time as they want (but – Stage 2: subjects are given as much time as they want (but
<60)
• Payment:
– 50% chance piece rate
– 50% fixed payment (3 EUR and 7 EUR) – Does the fixed payment affect behavior?
3. What is the reference point?
• Conclusion:
– Individuals often work until
• Earnings under piece rate = earnings under fixed payment
• Why?
– If earnings turn out to be determined by piece rate
3. What is the reference point?
– If earnings turn out to be determined by piece rate – And the expectation was set by the fixed payment – Earning less that fixed payment feels like a loss – Would such a behavior be predicted by:
• Standard models? No
• If reference point is the status quo? No
4. Measuring Individual Risk Preferences
• In the general population,
– Are risk preferences observed in experiments robust?
• Do other age groups exhibit similar levels of risk aversion?
• Do they also exhibit loss aversion?
• Do they also exhibit loss aversion?
• Several studies have taken this approach recently – For Germany, Dohmen et al (2011)
– In the Netherlands, von Gaudecker et al (2011) – For Denmark, Harrison et al (2007)
E(A)
18.75
E(B)
6.75
Suppose Steven chooses A, B,B,B
What can we say about his preferences?
19.5
20.25
21
22.5
38.25
54
E(A)
18.75
E(B)
6.75
Suppose Mary chooses A, A,B,B
What can we say about her preferences?
19.5
20.25
21
22.5
38.25
54
4. Measuring Individual Risk Preferences
• If Mary chooses A,A,B,B, is she risk averse or loss averse?
Risk aversion u(x)=xα Loss aversion
Option A Option B Prob A Prob B E(a) E(b) α 0.5 λ 2.5
21 18 54 -9 0.25 0.75 18.75 6.75 4.328 -0.413 18.75 -3.375 21 18 54 -9 0.5 0.5 19.5 22.5 4.413 2.174 19.5 15.75 21 18 54 -9 0.75 0.25 20.25 38.25 4.498 4.761 20.25 34.875
21 18 54 -9 1 0 21 54 4.583 7.348 21 54
4. Measuring Individual Risk Preferences
• In previous table
– Both risky prospects
– Some with gains and some with losses
• Not possible to distinguish loss aversion from risk aversion...
• Solution: several tables
– 1 for risky prospects in the gain domain
– If we assume same risk preferences in loss & gain domains – 1 for risky prospects with losses and gains
– If we do not, then also 1 for risky prospects in loss domain
4. Measuring Individual Risk Preferences
• A common ‚problem‘
– Multiple switching
– How to interpret answers if a subject switches multiple times?
• von Gaudecker et al (2011) allow for errors
• von Gaudecker et al (2011) allow for errors
• Others: do not allow multiple switching
– After the individual has switched once, move on to another choice table
4. Measuring Individual Risk Preferences
• Assumptions on utility function
• For example, von Gaudecker et al (2011) specify Extension of an exponential utility
function
• Allows for loss aversion and risk aversion
• But assumes risk preferences are the same for losses and gains
4. Measuring Individual Risk Preferences
• Results
– More risk and loss aversion in the general population than in the lab
4. Measuring Individual Risk Preferences
Group
characteristics:
-Female -45-54
-Wealth>200,000
Group
characteristics:
-Female -18-34
-Wealth<50,000
5. Conclusion
• Reference points
– Key to define what the reference point is!
– May yield different theoretical predictions
– In the field, and in the lab, it seems to be determined by expectations (e.g. about future labor income)
• Measuring risk preferences
– Multiple choices of lotteries reveal bounds on loss and risk aversion
– In a representative sample, individuals are on average risk averse and loss averse
– Parameters measured in experiments with students seem to underestimate these
