5. Choice, Time, and Risk

Question 1

In this topic how do we review the relationship between orthodox sequential choice principles and expected utility theory?

Answer 1

Using a dynamic form of common ratio effect and a simplified version of framework from Cubitt, Starmer & Sugden 1998

Question 2

Frame independence

Answer 2

The agent makes the same decision in any two decision problems with the same decision tree regardless of how the decision is framed

Question 3

Separability

Answer 3

The agent makes the same decisions at the root node in tree ‘A’ as they would make at node n in a full tree where node n represents an identical sub tree to tree ‘A’

Question 4

Equivalence

Answer 4

Making the same choice between up and down in each tree

Question 5

Timing independence

Answer 5

In a sequential decision problem, the agents behaviour matches what she would choose if she had to pre-commit all choices to the start. This is analogous but not identical to dynamic consistency

Question 6

If an agent violated EUT by having CRE preferences in sequential choice problems what must they violate

Answer 6

Separability or timing independence or reduction principle of compound lotteries or frame independence principle

Question 7

What are the most famous ways to extend non-EU models

Answer 7

By dropping separability (e.g. Machina 1989) or frame independence (e.g. T & K 1979)

Question 8

What does CSS 1998 find is violated?

Answer 8

Timing independence

Question 9

What is the common theme between non-exponential discounting causing conflict between dynamic consistency and forward looking consequential rationality whilst non- EU preferences cause conflict between similar principles?

Answer 9

Behavioural preference models pose issues of intra-personal conflict in sequential decision problems

Question 10

Whet causes indifference curves to kink?

Answer 10

Loss aversion- how preferences are affected by reference- point bundle

Question 11

What do Kozegi & Rabin 2006 model?

Answer 11

How Time, uncertainty, reference points inter-relate in environment in which reference points are endogenous

Question 12

What do Kozegi & Rabin 2006 argue determines the reference point?

Answer 12

Status quo not always the reference point. Recently held expectations are the underlying reference- point. This coincides with status quo in some but not all cases. The reference point may be formed in the face of uncertainity

Question 13

What are the two components of utility?

Answer 13

Consumption utility- depends on level of consumption of goods
Gain-loss utility- depends on deviation of actual consumption- utility from reference level

Question 14

In the stripped down version of the Kozegi & Rabin 2006 model, what is overall utility a sum of

Answer 14

Consumption util of x: mx(x)
Consumption util of y: my(y)
Gain loss util from x: mu(mx(x)-mx(rx))
Gain loss util from y: mu(my(y)-my(ry))

Question 15

3 core ideas of Kozegi & Rabin 2006 model

Answer 15

-consumption maximises overall utility so it is unaffected by reference bundle
-reference bundle determined by rationally formed expectations about consumption
-there is price and/or income uncertainty

Question 16

What are the steps towards an equilibrium between consumption and reference point?

Answer 16

1. Agent learns probability distribution over set Beta of possible budget sets
2. Agent predicts own consumption bundle. Let predicted bundle be (x^e, y^e)
3. Agent sets reference level of consumption for each good rx= x^e, ry= y^e
4. Agent learns actual budget set B
5. Agent sets actual consumption bundle (x,y)

Question 17

What is optimal consumption levels given by?

Answer 17

X= x(B, rx, ry)
Y* = y*(B, rx, ry)

Question 18

What is a personal equilibrium?

Answer 18

A function f defined on beta such that for all
B is a member of beta, f(B)= (x(B),y(B)) with x(B)= x(B, E(x(B)), E(y(B)))
y(B)= y(B, E(x(B)), E(y(B)))

Question 19

How do you find out if two bundles are a personal equilibrium?

Answer 19

-construct midpoint between the bundles (as each budget set has prob 0.5)
-draw reference dependent indifference curves for this reference bundle
-if they give (x(B1), y(B1)) as optimum in B1 and (x(B2), y(B2)) as optimum in B2 then we have a personal equilibrium

Question 20

What is Kozegi & Rabins equilibrium selection criterion?

Answer 20

Preferred personal equilibrium- the personal equilibrium that yields the highest expected overall utility

Question 21

Under conditions of certainty whet can be said about preferred personal equilibrium?

Answer 21

Behaviour coincides with behaviour when preferences aren’t reference dependent. With certainty, rationally formed expectations are correct. In this case, all personal equilibria have actual consumption = expected consumption

Question 22

Under certainty what is gain loss utility in every personal equilibrium?

Answer 22

Gain loss utility = 0

Question 23

What are the interpretations of behaviour in preferred personal equilibrium being the same as when there is no reference dependence in preference?

Answer 23

1. Uncertainty about budget set is crucial for reference dependence to matter in consumer choice
2. Result specific to PPE, which requires agent to optimise over equilibria
3. Model relies on particular view of reference point that is formed by optimal forward looking forecast of own behaviour but there are others

Question 24

How do kinked indifference curves impact the substitution effect compared to smooth indifference curves?

Answer 24

Because of the reference dependent effect the kinked indifference curves reduce the substitution effect compared to smooth indifference curves