5. Choice, Time, and Risk Flashcards
In this topic how do we review the relationship between orthodox sequential choice principles and expected utility theory?
Using a dynamic form of common ratio effect and a simplified version of framework from Cubitt, Starmer & Sugden 1998
Frame independence
The agent makes the same decision in any two decision problems with the same decision tree regardless of how the decision is framed
Separability
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’
Equivalence
Making the same choice between up and down in each tree
Timing independence
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
If an agent violated EUT by having CRE preferences in sequential choice problems what must they violate
Separability or timing independence or reduction principle of compound lotteries or frame independence principle
What are the most famous ways to extend non-EU models
By dropping separability (e.g. Machina 1989) or frame independence (e.g. T & K 1979)
What does CSS 1998 find is violated?
Timing independence
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?
Behavioural preference models pose issues of intra-personal conflict in sequential decision problems
Whet causes indifference curves to kink?
Loss aversion- how preferences are affected by reference- point bundle
What do Kozegi & Rabin 2006 model?
How Time, uncertainty, reference points inter-relate in environment in which reference points are endogenous
What do Kozegi & Rabin 2006 argue determines the reference point?
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
What are the two components of utility?
Consumption utility- depends on level of consumption of goods
Gain-loss utility- depends on deviation of actual consumption- utility from reference level
In the stripped down version of the Kozegi & Rabin 2006 model, what is overall utility a sum of
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))
3 core ideas of Kozegi & Rabin 2006 model
-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
What are the steps towards an equilibrium between consumption and reference point?
- Agent learns probability distribution over set Beta of possible budget sets
- Agent predicts own consumption bundle. Let predicted bundle be (x^e, y^e)
- Agent sets reference level of consumption for each good rx= x^e, ry= y^e
- Agent learns actual budget set B
- Agent sets actual consumption bundle (x,y)
What is optimal consumption levels given by?
X= x(B, rx, ry)
Y* = y*(B, rx, ry)
What is a personal equilibrium?
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)))
How do you find out if two bundles are a personal equilibrium?
-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
What is Kozegi & Rabins equilibrium selection criterion?
Preferred personal equilibrium- the personal equilibrium that yields the highest expected overall utility
Under conditions of certainty whet can be said about preferred personal equilibrium?
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
Under certainty what is gain loss utility in every personal equilibrium?
Gain loss utility = 0
What are the interpretations of behaviour in preferred personal equilibrium being the same as when there is no reference dependence in preference?
- Uncertainty about budget set is crucial for reference dependence to matter in consumer choice
- Result specific to PPE, which requires agent to optimise over equilibria
- Model relies on particular view of reference point that is formed by optimal forward looking forecast of own behaviour but there are others
How do kinked indifference curves impact the substitution effect compared to smooth indifference curves?
Because of the reference dependent effect the kinked indifference curves reduce the substitution effect compared to smooth indifference curves
