4. Choice and Time Flashcards
What is individual dynamic choice?
When there is extended time between determination of outcome and receipt of outcome or in the outcome itself
What is sequential choice?
When a choice is made at more than one point or uncertainty resolved at more than one point or resolution of uncertainty precedes choice
What is the orthodox economic answer to lifelong trade offs that individuals make between outcomes at different dates
Discounted utility model
What are the components of the discounted utility model?
Ut = w(t+j)u(Ct+j)
Where u(.) is instantaneous utility function
Where w(.) is weighting function, giving weights on utility in different periods viewed from period t w(t+j) = d^j where d is a discount parameter
Features of discounted utility model
-Additive separability of Ut
-Instantaneous utility function isn’t time dependent
-Weighting function isn’t time dependent or consumption dependent
-W(t+j) declines exponentially as j rises
-relative weight w(t+j+k)/w(t+j) is d^k
-for given d, it depends only incremental delay on k and is independent of baseline delay j
Is the discount rate constant in the data?
Studies suggest discount rate declines as j rises.
Evidence of sharp discounting of near future relative to present but less sharp discounting to very distant future relative to not quite as distant future. Think of this as diminishing marginal sensitivity to delay
How do people choose between smaller-sooner and larger-later options and which paper shows this?
Tendency to prefer smaller-sooner option when there is little/no baseline delay, but larger-later when there is a baseline delay
Keren & Roelofsma 1995
Components of hyperbolic discontinuing Loewenstein-Prelec form
W(t+j)= 1/(1+alpha x j)^(y/alpha)
Absolute weighted decline with j
Relative weight is increasing in baseline delay j and decreasing in incremental delay k. These fall sharply but then flatten out compared to exponential discounting
What are the two key features of quasi hyperbolic discounting?
Immediate future can be weighted much less than present
Discount rate declined progressively with baseline delay
Describe Laibsons quasi hyperbolic discounting model
Captures phenomenon of present bias without postulating a steadily declining discount rate. Very simple functional form which nests standard exponential model and is sometimes known as B-d preferences
What are the different psychological intuitions behind Laibsons quasi hyperbolic discounting?
Visceral attraction of present rather than diminishing marginal sensitivity to delay. Only the present is certain
Describe the quasi hyperbolic present bias model
Reduces to exponential model if beta =1.
Beta<1 reduces weight on all future periods by constant factor relative to exponential model with same discount rate
Relative weight is Bd^k when j=0 and d^k when j>0
Beta is an extra discount factor applying to future but only affecting comparisons involving the present
What is a possible welfare implication of the present bias model?
Decisions about allocation of expenditure between periods t and t+x should be taken before t arrives in order to avoid influence of present bias. This is an argument in favour of commitment strategies
Dynamic consistency
An agent sticks to and executes the plan she forms at the start
Forward looking consequential rationality
An agent is forward looking consequential if at each point she evaluates the remaining options
-treating bygones as bygones
-treating all feasible plans as possible choices and evaluating them by their outcomes
How do non exponential discounting models do when looking at consequential rationality and dynamic consistency
They permit conflict between forward looking consequential rationality and dynamic consistency
Resolution
Form best plan for whole problem at the start and stick to it
Myopia/naivety
At each choice act in accordance with current view of best plan for remainder of problem
Sophistication
At each choice, act in accordance with current view of plan that is the best for remainder of problem taking as given that will also do this at every remaining choice
Is sophistication dynamically consistent and forward looking consequential rational?
Dynamically consistent but violates forward looking consequential rationality by treating future revisions as constraints on current plans
What is Rabin &O’Donoghue 1999?
Paper comparing agents with and without present bias. And agents with present bias who don’t foresee their own self control problems.
Time consistents, myopic naifs, sophisticates
Have to miss the movies one weekend in 4
How does present bias affect costs and pleasure for naifs and sophisticates in Rabin and O’Donoghue 1999?
Present bias leads to procrastination of costs and acceleration of pleasure. If true long term welfare is measured by present bias free preferences then present bias has a welfare cost
What are the conceptual problems associated with discounting and which papers point then out?
There are problems with attempts to infer:
-discount parameter without taking account of shape of u(.). Anderson 2008
-preferences over consumption streams from preferences over income streams. Cubitt & Read 2018
-a single discount parameter for an individual applicable to all their decisions. Cubitt, McDonald, Read 2018
What is a consumption stream?
It assigns consequences by dates
