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UNIT 5: TIME PREFERENCESDiscounting
Time inconsistency
˟ Hyperbolic discounting
˟ Quasi-hyperbolic discounting
Application for time preferences
˟ Consumer behaviour
˟ Environmental economics
1. INTRODUCTION
Time is an important dimension in most economic decisions related to behaviour having important reflections
on wealth.
Do you watch the livestream today or later? Do you save for retirement now or later? Do you reduce your energy
consumption now or later?
In order to understand time preferences, we need to look at how people behave when time is a dimension in the
choice.
2. DISCOUNTING
When we talk about time preferences, we talk about discounting. Discounting meaning how much basically
weight you put to the future compare to the present.
We observe that being happy in the present (today, this week, this year) is typically more desirable than the
prospect of being happy in the future (tomorrow, next week, next year) (of course is depending on what you are
looking at).
We can suppose happiness/ utility during a time period (day, week, year) can be measured-
The discount means thereby that you put less weight to future happiness or future utility.
The discount factor: Measures how important is the future for an individual in term of utility compared to his
present utility. It measures how much an individual is impatient.
→ The lower your discount factor (or higher your discount rate), the more important the present is to you
→ The lower your discount factor, the less and less weight you give to the future
→ The lower your discount factor, the more impatient you are (you value the future less than the present)
*Do not confuse discount factor with discount rate as it is basically the opposite interpretation
3. TIME INCONSISTENCY
3.1 HYPERBOLIC DISCOUNTING
In reality, people are impatient over short term but more patient over the long term, i.e., discount factor is
larger for longer time intervals.
Thaler in 1981 stablish a task in which subjects were asked the amount of money they would make them
indifferent to receiving $15 now
TIME AMOUNT OF MONEY ASKED
1 MONTH 20$
1 YEAR 50$
10 YEARS 100$
We can observe that actually, subjects were asking much more to wait 1 month compared to what they were
asked to wait in 10 years (20$ vs 100$).
, This phenomenon is called hyperbolic discounting where your discount factor is larger for longer time periods,
meaning that you are more patient in longer time intervals.
E.g., What do you prefer?
• €100 today or €110 tomorrow? More people would prefer 100€ today
• €100 in 30 days’ time or €110 in 31 days? More people would prefer 110€. As they see both 30 and 131
days too far from today.
This is consistent with hyperbolic discounting.
3.2 QUASI-HYPERBOLIC DISCOUNTING
Now, If I ask you the same question after 30 days do you think your answers will have changed?
After 30 days, people might prefer €100 today rather than €110 tomorrow. This is not consistent with
hyperbolic discounting because the model requires choices to be consistent over time. We would need another
model to illustrate this: Quasi-hyperbolic discounting: According to the discounted utility
approach, intertemporal choices are no different from other choices, except that some consequences are delayed
and hence must be anticipated and discounted (i.e., reweighted to take into account the delay). Given two similar
rewards, humans show a preference for one that arrives sooner rather than later.
You probably noticed that sometimes you plan to do something in the future but subsequently change your mind.
For example, planning to do homework on Saturday but then a Saturday you decide to do it on Monday.
There is time inconsistency this is a situation in which a decision-maker's preferences change over time in such
a way that a preference can become inconsistent at another point in time. This is that they change their decision
when time advance in a way.
Time inconsistency is important in term of welfare and policy because it suggests that people tend to do
something but then end up doing something else.
3.2.1. QUASI-HYPERBOLIC DISCOUNTING: (𝜷, 𝜹)PREFERENCES
A simple model of quasi-hyperbolic discounting is to assume present bias referring to the tendency of people to
give stronger weight to payoffs that are closer to the present time when considering trade-offs between two
future moments
Delta to the power of t-1 multiplied by the utility in each period and that is actually the exponential discounting.
The difference between the exponential discounting and the quasi-hyperbolic discounting is that you have this 𝛽
that measures the extent of present bias (how much you weight the present compared to the future). The smaller
it is the more weight is given to today relative to the future.
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