Weeks 4 and 5
Intertemporal choice
Standard model - Exponential Discounted Utility (EDU) Model
Intro
• Samuelson (1937) proposed a discounted utility (DU) model
• The EDU has been accepted as a standard for public policy
Timeperiods te 0.1.2 tl
of
Temporalp rofile consumption C co ci
u tility
Discounted
É
at
uated discount
inI.n
instantaneous
We discount due to:
• Impatience
• Uncertainty about the future
• Memory utility- consuming sooner yields a longer time getting utility from memories
EDU
Discount
functionDlt 1,1 St
discount
disjoint factor
P 98 Ipresentvalue
Ucc
IIstop oh go gg
Properties:
• Constant discount rate
◦ The MRS between two periods t and t’ is DAY
Dlt
egDan S
Dct
• Integration of new alternatives into existing plans
◦ Suppose there are two consumption pro les C and C’
◦ The EDU maximiser will choose C over C’ i
UC Stuka StuG UIC
◦ Integration implies that a consumption choice is not evaluated in isolation, but against how it
would change consumption in all periods
• Utility independence
◦ Utility is the sum of all the discounted future utilities
◦ Individuals seek to maximise U(C)
◦ Therefore the time path of utility is irrelevant if the discounted sum is the same
• Consumption independence
◦ An individual's welfare in a time period is independent of consumption in any other period
◦ This rules out habit formation
• Stationarity
at ilytee a as gist
◦ ie. ranking of temporal payments depends only on the time distance and payment distance
between options
, ◦ This rules out changing tastes
• Time/ dynamic consistency
◦ The ranking of outcome-time pairs does not change depending on the the time period they
are asked in
Evidence against EDU
Declining discount rates
Plans made for the future tend to re ect more patience than choices made for the present
• Thaler, 1981 (1)
◦ One apple today two apples tomorrow
7
◦ One apple in 100 days two apples in 101 days
• Thaler, 1981 (2)
◦ Asked subjects to specify the amount of money they would require at various points in the
future to make them indi erent to receiving $15 now
◦ Median responses were $20 in 1 month, $50 in 1 year, $100 in 10 years
◦ By continuously compounding discount rates, he found median responses imply annual
discount rates of
‣ 345% for one month horizon
‣ 120% one year
‣ 19% ten year
• Friedrick et al, 2002
Preference reversal, dynamic inconsistency
1) Read et al., 1999
• Subjects asked to choose what lm to watch in 24hrs: high brow or low brow
• Advanced choices
◦ Day 1: 56% low brow
◦ Day 2: 37% low brow
◦ Day 3: 29% low brow
• Immediate choices
◦ Day 1: 58% low brow
◦ Day 2: 53% low brow
◦ Day 3: 56% low brow
• This shows time inconsistency, when the optimal decision at one point in time is no longer the
optimal choice at another point in time, causing preference reversals
◦ Reversed preferences because of a change in opportunity set rather than the passage of time
is not time inconsistency
Intertemporal choice
Standard model - Exponential Discounted Utility (EDU) Model
Intro
• Samuelson (1937) proposed a discounted utility (DU) model
• The EDU has been accepted as a standard for public policy
Timeperiods te 0.1.2 tl
of
Temporalp rofile consumption C co ci
u tility
Discounted
É
at
uated discount
inI.n
instantaneous
We discount due to:
• Impatience
• Uncertainty about the future
• Memory utility- consuming sooner yields a longer time getting utility from memories
EDU
Discount
functionDlt 1,1 St
discount
disjoint factor
P 98 Ipresentvalue
Ucc
IIstop oh go gg
Properties:
• Constant discount rate
◦ The MRS between two periods t and t’ is DAY
Dlt
egDan S
Dct
• Integration of new alternatives into existing plans
◦ Suppose there are two consumption pro les C and C’
◦ The EDU maximiser will choose C over C’ i
UC Stuka StuG UIC
◦ Integration implies that a consumption choice is not evaluated in isolation, but against how it
would change consumption in all periods
• Utility independence
◦ Utility is the sum of all the discounted future utilities
◦ Individuals seek to maximise U(C)
◦ Therefore the time path of utility is irrelevant if the discounted sum is the same
• Consumption independence
◦ An individual's welfare in a time period is independent of consumption in any other period
◦ This rules out habit formation
• Stationarity
at ilytee a as gist
◦ ie. ranking of temporal payments depends only on the time distance and payment distance
between options
, ◦ This rules out changing tastes
• Time/ dynamic consistency
◦ The ranking of outcome-time pairs does not change depending on the the time period they
are asked in
Evidence against EDU
Declining discount rates
Plans made for the future tend to re ect more patience than choices made for the present
• Thaler, 1981 (1)
◦ One apple today two apples tomorrow
7
◦ One apple in 100 days two apples in 101 days
• Thaler, 1981 (2)
◦ Asked subjects to specify the amount of money they would require at various points in the
future to make them indi erent to receiving $15 now
◦ Median responses were $20 in 1 month, $50 in 1 year, $100 in 10 years
◦ By continuously compounding discount rates, he found median responses imply annual
discount rates of
‣ 345% for one month horizon
‣ 120% one year
‣ 19% ten year
• Friedrick et al, 2002
Preference reversal, dynamic inconsistency
1) Read et al., 1999
• Subjects asked to choose what lm to watch in 24hrs: high brow or low brow
• Advanced choices
◦ Day 1: 56% low brow
◦ Day 2: 37% low brow
◦ Day 3: 29% low brow
• Immediate choices
◦ Day 1: 58% low brow
◦ Day 2: 53% low brow
◦ Day 3: 56% low brow
• This shows time inconsistency, when the optimal decision at one point in time is no longer the
optimal choice at another point in time, causing preference reversals
◦ Reversed preferences because of a change in opportunity set rather than the passage of time
is not time inconsistency
