Week 1 – Uncertainty and Time
Risk Aversion and Incentive Effects (Holt and Laury, 2002)
Risk aversion is a significant element to consider when creating theories on decision-making, e.g., on
insurances, asset valuations, auctions, and lottery choices. An assumption in auctions is that relative
risk aversion remains constant when increasing payoffs, whether this is true is tested in this article.
When analyzing risk aversion, it is important to consider whether the choice concerns buying (risk-
aversion) or selling (risk-seeking), because subjects (tend to) estimate a higher price when selling
something already owned and a lower price on something not yet in possession, due to willingness to
pay.
→ Individuals tend to exhibit increasing risk aversion when payoffs increase. → In contrast,
behaviour is largely unaffected when hypothetical payoffs are scaled up.
A change in behaviour when payoffs are scaled up is inconsistent with constant relative risk aversion,
which can be backed by the fact that the safe option will be chosen more often when the payoff is
scaled up. In other words, the increase of risk-aversion by choosing the safe over the risky, low-
probability option is inconsistent with the assumption of a constant RRA. Risk-aversion effects are
often controversial or ignored, but the results of increasing risk aversion (even with a low real payoff)
clearly show how inaccurate it might be to analyse behaviour while assuming risk neutrality or even
while completely ignoring risk aversion.
Psychology and Economics: Evidence from the Field (DellaVigna, 2009)
The standard model and theory of consumption over time imply that rational decision-makers have
equal preferences of future consumption at different points in time, implying that there are time-
consistent preferences. It assumes a discount factor (δ) between any two time periods, that is
independent of when the utility is evaluated. However, research has provided evidence against this
assumption, showing individuals’ deviations from the standard model.
→ Discounting is steeper in the close future than in the far future. Preferences for immediate
consumption instead of future earnings concern self-control problems.
→ While looking at the future, people are patient and make ambitious plans (e.g., to eat healthier or
to stop smoking). However, when this future becomes the present, the discounting becomes steeper
and preferences with these features induce time inconsistency (they start to eat unhealthy again or
continue to smoke). These are self-control problems, so not fulfilling what an individual had in mind.
(β, δ) model:The model is meant to show that, compared to actual consumption, an individual
overestimates investment-good consumption while underestimating leisure-good consumption,
leading to incorrect predictions.
The overall utility at time t (Ut) of this model is given by the following formula:
Ut =ut +(βδut+1)+(βδ2ut+2)+(βδ3ut+3)+(βδxut+x):
Here ut = the per-period utility, β = the parameter for the self-control problems; δ = the discount
factor.
When β < 1, the discounting between the present and the future is higher than between any future
time periods.
When β = 1, this is the standard model (there are no self-control problems).
In the model, β is the true / actual level of bias and β^ is the expected level.
1
,The (β, δ) model also includes expectations about future time preferences. Here, the agent is
partially naive about future self-control problems. Functioning of the model: take a good with
immediate payoff (b1) at t = 1 and delayed payoff (b2) at t = 2.
Investment good → Exercising is an example of an investment good, which has the features b 1 < 0
and b2 > 0, because the good requires effort now, but delivers a reward in the future.
Leisure good → Watching tv is an example of a leisure good: it has the features b 1 > 0 and b2 < 0,
because it gives a reward now, but costs something in the future.
The agent consumes too little investment good (b 2 > 0) and too much leisure good (b2 < 0). An aware,
sophisticated agent would look for commitment devices to avoid this from happening and to gain
protection from overspending. The difference in desired and expected utility determines the
willingness to pay for these devices.
The utility function of the future period t + s for a partially naive agent in this model is:
Ût+s = ut+s + (βˆ δut+s+1) + (βˆ δ2ut+s+2) + (βˆ δ3ut+s+3 + (βˆ δxut+s+x)
βˆ ≥ β means that an individual agent overestimates consumption of the investment good (b 2 > 0)
and underestimates consumption of the leisure good (b 2 < 0).
βˆ = β = 1: there is no overestimation and no biases.
βˆ = β: the agent is fully aware and acknowledged of the self-control problem; sophisticated,
correctly predicting how preferences change over time and knowing that present bias problems are
present.
β^ = 1 > β (or 1 > β^ > β > 0): partially naïve; being aware that future preferences will differ and that
self-control problems are present, but misinterpreting the magnitude.
βˆ = 1: fully naïve; belief that future preferences will be identical to current preferences.
If an individual could set consumption a period in advance: b 1 + δ b2 ≥ 0.
Reality (actual consumption): b1 + β δ b2 ≥ 0 (too little investment good, too much leisure good).
Debating Climate Economics: The Stern Review vs. Its Critics (Ackerman,
2007)
Stern is considered to be much more sensible than his critics, even though he is unsuccessful in
providing solutions to the problems. Stern concluded that climate change presented a serious danger
for the world, and that it demanded urgent global response. His strong opinion was that the benefits
of cutting carbon outweighed the costs. Stern stated that the damage to ecosystems caused by
businesses should be reduced through introducing higher emission taxes or a maximum level of
emission. He presented concerning numbers, which were way higher than estimates from other
economists.
Criticism: The criticism on Stern (invalidation) consists of three principal points:
The discount rate is too low.
The treatment of risk and uncertainty is inappropriate.
The calculation and comparison of costs and benefits was not performed correctly.
The critics state that these three point make Stern’s statement of benefits being way bigger than the
costs invalid.
The discount rate: Future amounts are discounted into the present value to be able to make a good
comparison between current and future costs and benefits. Since the impact of actions undertaken
today on climate change only shows far into the future, choosing a discount rate is very significant to
make a good analysis.
2
, A low discount rate makes the future look more significant today and, therefore, supports
investments for a better future. The discount rate consists of two elements: the rate of pure time
preference and a wealth-based component.
→ The wealth-based component reflects the assumption that if future generations will be richer than
we are, then there is less need for us to invest today in order to help them protect themselves.
→ This gives the following formula (Stern notation): r = δ + η * g.
Here, δ is the rate of pure time preference, g is the growth rate of per capita consumption, and η
determines how strongly economic growth affects the discount rate. If the first discount rate
component, which applies if all present and future generations have equal resources, is equal to 0,
then welfare is treated as equally important among all generations àδ = 0 (rate of pure time
preference).
If growth rate g = 0, implying a constant per capita consumption, then r = δ (because eta η * 0 = 0). A
larger η value implies a larger r, and therefore less need to provide for the future. Stern noted that
the η value is equal to 1. Stern believed in philosophical arguments stating all generations to be
equal, which would suggest δ to be zero (delta δ = 0). However, time preferences shown by actions
affecting the future (e.g., saving) show that δ needs to be higher than zero, otherwise we would save
way more for future generations. Stern addresses how future generations may not exist, and sets this
probability of mass extinction to 0.1%, therefore making δ = 0.1%.
In an ‘abstractly perfect market economy’ with rationality and perfect information, Nordhaus claims
that the discount rate should be way higher. Nordhaus argues that the discount rate should match
market interest rates or rates of return on capital, with a rate that exceeds inflation with 5%. In his
calculations, the social cost of carbon is way lower than in Stern’s calculations.
Ethical-based discounting: According to Dasgupta, δ is a measure of the trade-off between present
and future, independent of wealth differences, and η is a measure of the trade-off between rich and
poor, independent of time differences. In this aspect:
η = 0 means every pound is of equal value regardless of who receives it.
η = 1 means every 1% increase in a person’s income is of equal value, regardless of the
wealth
η > 1 means a 1% increase in income is of greater value to a poorer person.
Dasgupta agrees with Stern on a δ close to zero, but states that equity is way more concerning for
the poor and this needs to be reflected in a larger η, even in the present generation. A larger η leads
to a higher discount rate, which then indirectly leads to less investment in the future. This paradox is
the result of economists’ assumption that future generations will be better off than we are. In the
same way, if we believe future generations will be much worse off than us, the discount rate should
be lower or should even become negative.
3
Risk Aversion and Incentive Effects (Holt and Laury, 2002)
Risk aversion is a significant element to consider when creating theories on decision-making, e.g., on
insurances, asset valuations, auctions, and lottery choices. An assumption in auctions is that relative
risk aversion remains constant when increasing payoffs, whether this is true is tested in this article.
When analyzing risk aversion, it is important to consider whether the choice concerns buying (risk-
aversion) or selling (risk-seeking), because subjects (tend to) estimate a higher price when selling
something already owned and a lower price on something not yet in possession, due to willingness to
pay.
→ Individuals tend to exhibit increasing risk aversion when payoffs increase. → In contrast,
behaviour is largely unaffected when hypothetical payoffs are scaled up.
A change in behaviour when payoffs are scaled up is inconsistent with constant relative risk aversion,
which can be backed by the fact that the safe option will be chosen more often when the payoff is
scaled up. In other words, the increase of risk-aversion by choosing the safe over the risky, low-
probability option is inconsistent with the assumption of a constant RRA. Risk-aversion effects are
often controversial or ignored, but the results of increasing risk aversion (even with a low real payoff)
clearly show how inaccurate it might be to analyse behaviour while assuming risk neutrality or even
while completely ignoring risk aversion.
Psychology and Economics: Evidence from the Field (DellaVigna, 2009)
The standard model and theory of consumption over time imply that rational decision-makers have
equal preferences of future consumption at different points in time, implying that there are time-
consistent preferences. It assumes a discount factor (δ) between any two time periods, that is
independent of when the utility is evaluated. However, research has provided evidence against this
assumption, showing individuals’ deviations from the standard model.
→ Discounting is steeper in the close future than in the far future. Preferences for immediate
consumption instead of future earnings concern self-control problems.
→ While looking at the future, people are patient and make ambitious plans (e.g., to eat healthier or
to stop smoking). However, when this future becomes the present, the discounting becomes steeper
and preferences with these features induce time inconsistency (they start to eat unhealthy again or
continue to smoke). These are self-control problems, so not fulfilling what an individual had in mind.
(β, δ) model:The model is meant to show that, compared to actual consumption, an individual
overestimates investment-good consumption while underestimating leisure-good consumption,
leading to incorrect predictions.
The overall utility at time t (Ut) of this model is given by the following formula:
Ut =ut +(βδut+1)+(βδ2ut+2)+(βδ3ut+3)+(βδxut+x):
Here ut = the per-period utility, β = the parameter for the self-control problems; δ = the discount
factor.
When β < 1, the discounting between the present and the future is higher than between any future
time periods.
When β = 1, this is the standard model (there are no self-control problems).
In the model, β is the true / actual level of bias and β^ is the expected level.
1
,The (β, δ) model also includes expectations about future time preferences. Here, the agent is
partially naive about future self-control problems. Functioning of the model: take a good with
immediate payoff (b1) at t = 1 and delayed payoff (b2) at t = 2.
Investment good → Exercising is an example of an investment good, which has the features b 1 < 0
and b2 > 0, because the good requires effort now, but delivers a reward in the future.
Leisure good → Watching tv is an example of a leisure good: it has the features b 1 > 0 and b2 < 0,
because it gives a reward now, but costs something in the future.
The agent consumes too little investment good (b 2 > 0) and too much leisure good (b2 < 0). An aware,
sophisticated agent would look for commitment devices to avoid this from happening and to gain
protection from overspending. The difference in desired and expected utility determines the
willingness to pay for these devices.
The utility function of the future period t + s for a partially naive agent in this model is:
Ût+s = ut+s + (βˆ δut+s+1) + (βˆ δ2ut+s+2) + (βˆ δ3ut+s+3 + (βˆ δxut+s+x)
βˆ ≥ β means that an individual agent overestimates consumption of the investment good (b 2 > 0)
and underestimates consumption of the leisure good (b 2 < 0).
βˆ = β = 1: there is no overestimation and no biases.
βˆ = β: the agent is fully aware and acknowledged of the self-control problem; sophisticated,
correctly predicting how preferences change over time and knowing that present bias problems are
present.
β^ = 1 > β (or 1 > β^ > β > 0): partially naïve; being aware that future preferences will differ and that
self-control problems are present, but misinterpreting the magnitude.
βˆ = 1: fully naïve; belief that future preferences will be identical to current preferences.
If an individual could set consumption a period in advance: b 1 + δ b2 ≥ 0.
Reality (actual consumption): b1 + β δ b2 ≥ 0 (too little investment good, too much leisure good).
Debating Climate Economics: The Stern Review vs. Its Critics (Ackerman,
2007)
Stern is considered to be much more sensible than his critics, even though he is unsuccessful in
providing solutions to the problems. Stern concluded that climate change presented a serious danger
for the world, and that it demanded urgent global response. His strong opinion was that the benefits
of cutting carbon outweighed the costs. Stern stated that the damage to ecosystems caused by
businesses should be reduced through introducing higher emission taxes or a maximum level of
emission. He presented concerning numbers, which were way higher than estimates from other
economists.
Criticism: The criticism on Stern (invalidation) consists of three principal points:
The discount rate is too low.
The treatment of risk and uncertainty is inappropriate.
The calculation and comparison of costs and benefits was not performed correctly.
The critics state that these three point make Stern’s statement of benefits being way bigger than the
costs invalid.
The discount rate: Future amounts are discounted into the present value to be able to make a good
comparison between current and future costs and benefits. Since the impact of actions undertaken
today on climate change only shows far into the future, choosing a discount rate is very significant to
make a good analysis.
2
, A low discount rate makes the future look more significant today and, therefore, supports
investments for a better future. The discount rate consists of two elements: the rate of pure time
preference and a wealth-based component.
→ The wealth-based component reflects the assumption that if future generations will be richer than
we are, then there is less need for us to invest today in order to help them protect themselves.
→ This gives the following formula (Stern notation): r = δ + η * g.
Here, δ is the rate of pure time preference, g is the growth rate of per capita consumption, and η
determines how strongly economic growth affects the discount rate. If the first discount rate
component, which applies if all present and future generations have equal resources, is equal to 0,
then welfare is treated as equally important among all generations àδ = 0 (rate of pure time
preference).
If growth rate g = 0, implying a constant per capita consumption, then r = δ (because eta η * 0 = 0). A
larger η value implies a larger r, and therefore less need to provide for the future. Stern noted that
the η value is equal to 1. Stern believed in philosophical arguments stating all generations to be
equal, which would suggest δ to be zero (delta δ = 0). However, time preferences shown by actions
affecting the future (e.g., saving) show that δ needs to be higher than zero, otherwise we would save
way more for future generations. Stern addresses how future generations may not exist, and sets this
probability of mass extinction to 0.1%, therefore making δ = 0.1%.
In an ‘abstractly perfect market economy’ with rationality and perfect information, Nordhaus claims
that the discount rate should be way higher. Nordhaus argues that the discount rate should match
market interest rates or rates of return on capital, with a rate that exceeds inflation with 5%. In his
calculations, the social cost of carbon is way lower than in Stern’s calculations.
Ethical-based discounting: According to Dasgupta, δ is a measure of the trade-off between present
and future, independent of wealth differences, and η is a measure of the trade-off between rich and
poor, independent of time differences. In this aspect:
η = 0 means every pound is of equal value regardless of who receives it.
η = 1 means every 1% increase in a person’s income is of equal value, regardless of the
wealth
η > 1 means a 1% increase in income is of greater value to a poorer person.
Dasgupta agrees with Stern on a δ close to zero, but states that equity is way more concerning for
the poor and this needs to be reflected in a larger η, even in the present generation. A larger η leads
to a higher discount rate, which then indirectly leads to less investment in the future. This paradox is
the result of economists’ assumption that future generations will be better off than we are. In the
same way, if we believe future generations will be much worse off than us, the discount rate should
be lower or should even become negative.
3
