Behavioural Economics - Topics 3, 4 & 5 Flashcards
Topic 3.1 L - What is expected utility theory?
a Normative model of rational choice that has dominated most of economic analysis as the standard theory of choice under uncertainty risk. It is assumed that all reasonable people obey the axioms most of the time. It is worth noting that in several choice problems, it has been observed that preferences systematically violate the axioms.
Topic 3.1 L - What is a prospect (with formula)?
A prospect denoted by (x1,p1, … ; xn,pn), is a contract that yields outcome xi with probability pu where p1 + p2 + … + pn = 1.
We omit null outcomes and use (x, p) to denote the prospect (x, p; 0, 1 - p) that yields x with probability p and 0 with probability 1 - p.
A riskless prospect that yields x with certainty is denoted by (x).
Topic 3.1 L - What words are analogous to prospect?
Lottery and game.
Topic 3.1 L - Expected Value (EV) of a prospect?
The value of each possible outcome * the probability of that outcome.
Topic 3.1 L - What can be deduced about expected values and utilities and the preference of individuals?
People seek to maximise expected utility, not expected value.
Topic 3.1 L - Expected Utility formula?
E(u) = p1 * o1 + … + Pn * On.
The utility of each outcome multiplied by the probability of each outcome.
Topic 3.1 L - What is the difference between EV and EU?
Expected Value is the probability weighted average of the monetary value.
Expected Utility is the probability weighted average of the utility from the potential monetary values.
Topic 3.1 L - How do endowments play into expected utility?
Utility will be derived from the current endowment + the utility from the gain or loss. ‘w’ is the current endowment.
Topic 3.1 L - Expected Utility Theory: What are the three tenets that relies on?
- Expectations.
- Asset Integration.
- Risk Aversion
Topic 3.1 L - Expected Utility Theory - Expectations?
The overall utility of a prospect, denoted by U, is the expected utility of its outcomes.
People choose the risky item which yields a higher expected utility than others.
U(x1; p1; … ; xn; pn) = p1u(x1) + p2u(x2) + … + pnu(xn)
Topic 3.1 L - Expected Utility Theory - Asset Integration?
A prospect is acceptable if
the utility resulting from integrating the prospect with
one’s assets exceeds the utility of those assets alone.
(x1; p1; … ; xn; pn) is acceptable at asset position w if
U(w + x1; p1; … ;w + xn, pn) > u(w)
Topic 3.1 L - Expected Utility Theory - Risk Aversion?
u is concave (u’’ < 0).
Topic 3.1 L - Risk Aversion?
A preference set that results in E(U) < E(V). The degree of risk aversion is represented by the concavity of the utility function of an individual.
Topic 3.1 L - What can be said about someone who is risk neutral?
They have a constant marginal utility of wealth, hence , a utility function linear in wealth. Maximising expected value is the same as maximising the expected utility.
Topic 3.1 L - How will marginal utility change for a risk loving person?
A risk loving person will have a convex utility function has increasing marginal utility of wealth. Each additional dollar provides greater additional happiness that the dollar before it.
Topic 3.1 L - What can the Expected Utility theory be called? What is some information about this name?
The von Neumann-Morgenstern (vNM) utility. They characterised the 4 expected utility axioms: completeness, transitivity, continuity and independence.
Topic 3.1 L - Continuity Definition?
Very small changes in probabilities do not change the preference ordering between lotteries.
Topic 3.1 L - EUT Independence Definition?
If we mix two lotteries with a third one, the preference ordering of the two pictures will not change and is independent of the particular third lottery used.
Topic 3.1 L - What is Independence sometimes called and what is the requirement?
The substitution axiom.
Independence requires that pA + (1 - p)C > pB + (1 - p)C
Topic 3.1 L - Who originally described the pattern of violation in EUT in which:
B > A then it should be that D > C
In practice, most people answer B > A and C > D? What principle is violated in particular?
The Allais Paradox. It is a model that works on utility. The principle of EUT that is violated is the Expectation Principle.
Topic 3.1 L - Explain the Certainty Effect?
AKA the Allais paradox. People overnight outcomes that are considered certain relative to outcomes which are merely probable. This violates EUT.
Topic 3.1 L - What is implied by the reflection effect? Intuitive understanding?
Risk aversion in the positive domain and risk seeking in the negative domain.
“Overweighting of certainty” favours risk aversion in the domain of gains and risk seeking in the domain of losses.
In the positive domain, the certainty effect contributes to a risk averse preference for a sure gain over a larger gain that is merely probable.
In the negative domain, the same effect leads to a risk seeking preference for a loss that is merely probable over a smaller loss that is certain.
Topic 3.1 L - The Asian Disease Example?
An example by Tversky and Kahneman (1981) in which the same question was asked to doctors (with statistical knowledge) but from the perspective of the gains in life and the losses of life. One choice has certainty of death/ life and the other had a framing effect of a probability of death/ life. Despite the outcomes being identical, When preventing deaths, the doctors chose the chance of saving deaths(the probability), whereas when framed in terms of how many people will live, the majority changed to picking the certainty option.
Topic 3.1 L - What is the Major Difference between Prospect Theory and Expected Utility Theory?
Prospect Theory is the reference-dependence with loss aversion. With EUT, we need to know the state of wealth. In Prospect theory, you also need to know the reference state. Kahneman and Tversky introduced prospect theory in 1979.
Topic 3.2 L - Why was prospect theory formalised?
To accommodate systematic violations of the standard expected utility theory.
Topic 3.2 L - What is the symbol used for the overall value of an edited prospected, what is it expressed in terms of?
V.
It is expressed in terms of two scales, v and π
Topic 3.2 L - Prospect Theory: first scale, v?
The first scale, v, assigns to each outcome x a number. v(x), which reflects the subjective value of that outcome. Outcomes are described relative to a reference point, which serves as the zero point of the value scale.
Topic 3.2 L - Prospect Theory: The second scale, π?
The second scale, π, associates with each probability p a decision weight π(p), which reflects the impact of p on the overall value of the prospect.
Topic 3.2 L - For prospects of the form (x, p; y, q), when would the prospect be strictly positive?
if x,y > 0 and p + q = 1.
So if all outcomes are strictly positive. p+q will always equal 1.
Topic 3.2 L - For prospects of the form (x, p; y, q), when would the prospect be strictly negative?
If all outcomes are negative. x,y < 0 and p,q = 1
So if the outcomes are less than 0.
Topic 3.2 L - If (x, p; y, q) is a regular prospect, what will V(x, p; y, q) equal?
V(x, p; y, q) = π(p)v(x) + π(q)v(y)
Topic 3.2 L - Prospect Theory - For V(x, p; y, q) = π(p)v(x) + π(q)v(y), what is the difference between V and v
V is defined on prospects, while v is defined on outcomes.
Topic 3.2 L - Prospect Theory - For V(x, p; y, q) = π(p)v(x) + π(q)v(y), when will V and v coincide?
At V(x,1) or V(y,1)
These are sure prospects.
Topic 3.2 L - Prospect Theory - How does V(x, p; y, q) = π(p)v(x) + π(q)v(y) generalise EUT?
It relaxes the expectation principle.
Topic 3.2 L - For Regular Prospects, V is defined on prospects, while v is defined on outcomes. When would the two concede? (formula)
V(x,p; y,q)= π(p)v(x) + π(q)v(y)
Where v(0) = 0, π(0) = 0 and π(1) = 1
Known as the general form for regular prospects.
Topic 3.2 L - General Form for Strictly positive and strictly negative prospects: What is the process and explain?
These prospects are separated into two components:
- The Risk-less Component i.e. the minimum gain or loss which is certain to be obtained or paid.
- The Risky Component i.e. the additional gain or loss which is actually at stake.
For example, (400; 0:25; 100; 0:75) is naturally decomposed into a sure gain of 100 and the risky prospect (300, 0.25).
Topic 3.2 L - General Form for Strictly positive and strictly negative prospects: What is the equation for strictly positive and strictly negative prospects? How would you explain this equation? Example?
If p + q = 1 and either
a) x > y > 0 [Strictly positive] or
b) x < y < 0 [Strictly Negative], then
V (x,p; y, q) = v(y) + π(p)[v(x) - v(y)]
The decision weight is applied to the value-different [v(x) - v(y)], representing the risky component of the prospect. v(y) is the risk-less component.
V (400, .25; 100; .75) = v(100) + π(.25)[v(400) - v(100)]
Topic 3.2 L - What are the main elements of prospect theory?
- Reference Points
- Diminishing Marginal Sensitivity.
- Loss-Aversion
- Decision-Weighting.
These general forms represent all of these.
Topic 3.2 L - Prospect Theory Elements: 1. Reference Points?
Changes are measured relative to reference points, serving as a zero point of the value scale (has a 0 value).
The carriers of value are changes in wealth or welfare, rather than final states.
“v” measures the value of deviations from the reference point.
EXTRA: We often assume that the relevant reference point of evaluating gains and losses is the current status of wealth or welfare, but the reference point may be the outcome that you expect or feel entitled to.
Topic 3.2 L - Value Functions in Prospect Theory: What would be the y-axis and x-axis?
Y-Axis: Value
X-Axis: Gains/ Losses.
Topic 3.2 L -Prospect Theory Elements: 1. Diminishing Marginal Sensitivity? How would we prove this theory?
The value function for changes of wealth is concave above the reference point (v’‘(x) < 0, for x > 0) and convex below the reference point (v’‘(x) > 0, for x <0). This can be proved through the following scenario:
Prospects (6000; .25) <18%> or (4000; .25; 2000; .25) <82%>
vs
Prospects (-6000; .25) <70%> or (-4000; .25;-2000; .25) <30%>
The frequency of responses to a study is show with percentages within <>.
We can see that people tend to take the more risky option with losses and less risky option with gains. This example is meant to show diminishing marginal sensitivity though?
Topic 3.2 L - Prospect Theory Elements: 3. Loss Aversion? What conclusion can we make?
Pleasure of gaining money is less than the pain of losing money, so symmetrical bets of an equal chance winning 50 an equal chance of the losing 50 are unattractive.
Moreover, there is an aversiveness of symmetry bets when the stake increases [for x>y≥0 , (y, .5; -y, .5) is preferred to (x, .5; -x,.5]
We conclude that v(x) < -v(-x) for x > 0 and
the value function for losses:
v’(x) < v’(-x)
[value is lost at a greater rate than a the same and opposite change in gains]
Topic 3.2 L - Prospect Theory Elements: 3. Loss Aversion - How would you measure the extent of loss aversion and what is the typical gain that would be required to offset the chance of a loss.
What is the smallest gain that is needed to balance an equal change to lose, say £100?
The typical answer is £200, but the LOSS AVERSION RATION typically has a range between 1.5 and 2.5
Topic 3.2 L - Prospect Theory Elements: 3. Loss Aversion - What are the implications (2 effects)?
The Endowment Effect: The difference between what potential buyers are wiling to pay (WTP) for goods and what potential sellers are willing to accept (WTA) for the same goods.
The Disposition Effect: Investors tend to hold on to stocks that have lost value (relative to their purchase price) too long, while being eager to sell stocks that have risen in price.
Topic 3.2 L - Value Functions: What properties describe the most commonly used value function?
v(x) = { x^α. If x ≥ 0
{ -𝛌(-x)^β If x < 0
Where α: coefficient of diminishing marginal sensitivity for gains. β: coefficient of DMS for losses. 𝛌: coefficient of loss-aversion x: gain/loss
Topic 3.2 L - Value Function: Why does an individuals preference to integrate or segregate gains and losses matter?
Due to the value function being concave in the domain for gains and convex in the domain for losses, it matters how outcomes are bundled.
Gains and losses can be segregated or Integrated.
Integrated: You have gained a total of £75, translating to v(75) in value terms.
Segregated: You have won £25 and then £50, translating in value terms to v(25) + v(50)
Topic 3.2 L - Value Functions: What would the implications be for the following game:
You buy two lottery tickets at a charity event, and you win £25 on the first and £50 on the second. How does prospect theory differ to the standard theory?
Think of the implications of each and how it each would look on a graph.
a) Integrated: You have gained a total of £75, translating to v(75) in value terms.
b) Segregated: You have won £25 and then £50, translating in value terms to v(25) + v(50)
According to standard theory, no matter how you describe the various outcomes, you end up with an additional £75. PT said that BUNDLING MATTERS.
People value two gains more when they are segregated than when they are integrated.
See Brainscape Assistant. 1.
Topic 3.2 L - Prospect Theory 4 - Decision Weighting: How does weighting effect outcome? What is the formula and how does it differ?
The value of each outcome is multiple by a decision weight.
V(prospect) = π(p)v(x) + π(q)v(y)
NOT
pv(x) + qv(y)
Decision weights [π(p,q)] measure the impact of events on the desirability of prospects, not merely the perceived likelihood of these events.
Topic 3.2 L - Prospect Theory 4 - Decision Weighting:: When does the perceived likelihood and decision weights value coincide. What is an important distinction between the two?
If π(p) = p. If the expectation principle holds.
Decision weights are not probabilities so do not obey probability axioms.
Topic 3.2 L - What are the first 3 main properties of the decision weighting function?
- π(0) = 0 and π(1)=1
- π is an increasing function of p, which means that the value of π increases as the probability increases.
- Very low probabilities are generally overweighted, that is, π(p) > p for small p. [but, THIS IS NOT THE SAME AS OVERESTIMATION - overestimation regress to the wrong assessment of the probability of rare events]
Topic 3.2 L - What is fourth main property of the decision weighting function? (function required)
Subcertainty
π(p) + π(1-p) < 1 for all p not equal to 1
[so not just for small p]
See Brainscape Assistant 2.
Topic 3.2 L - What are the implications of subcertainty?
Hint:
slope
preferences
The slope of π can be viewed as a measure of the sensitivity of preferences to changes in probability.
It shows that preferences are generally less sensitive to variations of probability than the expectation principle would dictate.
It therefore captures peoples attitudes to uncertain events. Namely, that the sum of the weights associated with complementary events is typically less than the weight associated with the certain event. People are limited in their ability to comprehend and evaluate extreme probabilities.
Topic 3.2 L - Recap, what is the difference, in terms of the formula, for EUT and PT?
Graph?
EUT sets the EU subject to the probability of the outcome and the utility of achieving it.
PT sets a probability weighting function, and instead of the utility, looks at the value of the potential outcome.
For low probabilities, π(x) < x and for high probability π(x) > x.
See Brainscape Companion 3 for the graph.
Topic 3.2 L - Closing remarks on weighting functions?
People are limited in their ability to comprehend and evaluate extreme probabilities.
Highly unlikely events are either ignored or overweighted, and the difference between high probability and certainty is
either neglected or exaggerated.
Consequently, is not well-behaved near the end-points.
Topic 3.2 L - Estimations: Parameters for Prospect Theory - What was the estimated model?
See Brainscape Assistant 4.
Topic 3.2 L - Decision Weights: What can be concluded from the proposed theory of Kahneman and Tversky as well as the estimate results for p*?
The is a p* such that:
- π(p) > p and concave if p < p*
- π(p) < p and convex if p > p*
p8* is generally observed to be less than 0.5. People overstate small probability and understate high probabilities.
Topic 3.2 L - Summary of EUT and PT? Hint: Basis Objects Risk Aversion Loss aversion Probability Estimation Problem Descriptions
EUT:
- The basic objects of preferenences are states of wealth (including non-monetary resources like health care).
- The utility function is risk averse everywhere.
- Loss aversion cannot be defined as EUT does not identifiy a status quo.
- People evaluate probabilities linearly.
- Problem descriptions have no effect as long as the problem is logically the same.
PT:
- The basic objects of preferences are changes from a neutral reference point (gains and losses)
- The value function is risk averse for gains and risk seeking for losses.
- The value function implies loss aversion.
- People evaluate probabilities nonlinearly.
- Problem descriptions can change the reference level; hence the definition of gains and losses can change.
Topic 3.2 L - PT: Probabilistic Insurance?
Two Options:
A) Pay a premium for full coverage.
B) Pay half a premium for coverage on half the days of a year.
Normative theory would suggest that, due to a concave utility function, most people reject B.
P to P/2 is a smaller loss than p/2 to 0 (the certainty effect)
Framing an insurance premium as giving full protection against specific risks makes it more attractive.
Topic 3.2 L - Two Effects highlighted by deal or no deal? Application to EUT?
Break Even Effect: Risk aversion seems to decrease after earlier expectations have been shattered by opening high-value briefcases. (similar to horse racers betting on long shots before they go home to break even.
House-Money Effect: Risk aversion decreases after earlier expectations have been surpassed by opening low-value briefcases. Forecasts that investors are more prone to buy higher risk stocks after a profitable trade.
EUT does not predict this as preferences are assumed to be constant, irrespective of the auth travelled before arriving at the problem.
Topic 3.2 L - Define the Break Even Effect.
Risk aversion seems to decrease after earlier expectations have been shattered by opening high-value briefcases. (similar to horse racers betting on long shots before they go home to break even.
Topic 3.2 L - Define the House Money effect.
House-Money Effect: Risk aversion decreases after earlier expectations have been surpassed by opening low-value briefcases. Forecasts that investors are more prone to buy higher risk stocks after a profitable trade.
Topic 3.2 L - How can the House Money Effect and the Break Even Effect be explained?
By a reference-dependent value function.
Topic 3.2 L - SUMMARY - Prospect theory says that understanding human behaviour requires: (3)
- Separation of prospects into positive and negative.
- Relative to a status quo, rather than considering absolute values.
- Consideration of decision weights rather than just probabilities.
Topic 3.2 L - What are the blindspots of utility theory?
3
Hint
Emotional Responses.
Disappointment
Regret.
- People described by PT are guided by Emotional responses to gains and losses rather than long term prospects of wealth and utility.
- PT cannot deal with disappointment. Failing to win when the chances of winning are high is far more disappointing than failing to win when the chances of winning are low.
- PT cannot deal with regret.
If given the option of potentially winning £1m or taking £50 for sure vs potentially winning £1m or taking £150,000 for sure, the latter case will lead to far more regret.
