Summary
Summary for exam, inlcuding lecture notes + articles - Advanced Behavioural Economics
- Course
- Institution
Summary for exam, inlcuding lecture notes articles - Advanced Behavioural Economics
[Show more]
Seller
Follow
Carlijn18
Reviews received
Content preview
Short Summary ABEWeek 1: lecture 1+2: Introduction, Choice under Risk – Expected Utility
“Explaining the Characteristcs of the Power (CRRA) Utlity amilyy
The power family contains functons of the form U(x)=xr; and is also known in the economic literature
as the family of constant relatie risk aiersion (CRRA).
The functon U(x)=b+ axr is equivalent to U(x)=xr for any a > 0 and b ϵ R.
Unlike the intercept and the slope, the curvature of U does have empirical meaning for interval
scales.
Changing units of inputs
For the power functons, no empirical implicaton is aaected if all inputs are multplied by a common
positve factor.
In general, if we multply all inputs by a factor σ > 0, then, for r≠0; all utlites x r or -xr are multplied by
σ r (homogeneity of degree r).
It is due to Assumpton 3.1 U is unique up to unit and level, i.e. it can be multplied by any positve
factor and any constant can be added without aaectng any relevant empirical aspect (U is an
interial scale).
Changing the leiels of inputs
Unlike changes of the unit of the inputs, changes of the level of the inputs, through substtutons x
x + τ; are empirically relevant.
For interval scales, neither the level (intercept) nor the unit (slope) is relevant, but the degree of
curvedness is relevant.
=> Several papers independently observed the importance of the concavity index to capture
curvedness:
-U’’(x)/U’(x)
The concavity index is ofen called the Arrow–Prat index or the index of absolute risk aversion. The
index is constant for the exponental ((ARA) family of utlity.
together we conclude that the Prat-Arrow
concavity index for the power family is (1-r)/x
for all r.
THIS MEANS (RRA.
- The degree of concavity decreases in
r; with a natural smooth transiton at r = 0: It confirms that the curvature of x r converges to that of
ln(x) for r tending to 0 both from above and from below.
- The concavity index also shows that the concavity of power functons becomes less extreme
for large inputs x. DE(REASING ABSOLUTE RISK AVERSION.
-
Back to Example 4.2 it illustrated this phenomenon. The (absolute) risk aversion generated for
outcomes from [200;400] by r = 0.94 was similar there to the risk aversion generated for outcomes
,from [100 200; 100 400]by r= -19. The concavity index (1-r)/x; with midpoints of intervals taken for x;
indeed confirms that (1-0.94)/300=0.0002 ≈ (1-(-19))/100300= 0.000199; which explains the
numerical results of Example 4.2.
The concavity index illustrates once more that interpretng r as an ant-index of concavity (or ‘risk
aversion’) without specifying the domain of inputs can be misleading, and we should be careful when
comparing values of r derived from diaerent domains of inputs.
LECTURE 1:
Behaiioural economics:
- Improving economic predictons: making more realistc assumptons about behavior, while keeping
the models tractable.
- Infuencing behavior: -changes in laws (forbidding certain behavior), - changes in financial incentves
(increasing the financial costs of certain behavior), -nudging
This course;
• Why are some people more risk averse than others? Is it because of the way they perceive
and evaluate outcomes? Or is it because of the way they perceive and evaluate probabilites?
• How can we empirically assess which types of people are more risk averse?
Later on;
Intertemporal choice:
• Why are some people more willing to invest in the future than others? Is it because of the
way they perceive and evaluate future outcomes? Or is it because of the way they perceive
and evaluate tme?
• Are people aware of their self-control problems or not? And what does this mean for
behavior?
Last weeks;
Decisions in a social context:
• Why do some people seem more fair than others? Are they truly fair or are they just
strategic? And if they are fair, is it because they care about final outcomes or about the
procedure by which these final outcomes are achieved?
NOW choice under risk-expected utlity:
Diaerences with risk (known probabilites) and uncertainty (unkown prob) today: risk
A first assumpton: monotonicity: If, no mater what happens, L1 always gives more than L2, then L1
is preferred to L2.
,FIRST: Expected Value
St petersburg paradox:
I fip a fair coin repeatedly untl we get head. If head comes at throw number n, then you earn 2 n.
Expected Value is infinite so you are willing to pay and infinite amount unlogical
problem with EV:
EV means that an increase in our wealth of 100 feels the same no mater whether we earn 1000
per month or 9000 per month. (of course 100 have more impact on poor person than on rich
person).
Soluton (Bernoulli, 1738): first translate monetary amounts into utlites, or subjectve values, of
monetary amounts. IMPORTANT: first transfer outcomes in utlites before calculaton Expected
Utlity.
NOW: Expected Utlity
Our example: P = (50% : 4; 50% : 16)
EV = 0.5*4+0.5*16 =10
(E = certainty equiialent of the prospect P
= outcome that makes person indiaerent between receiving the prospect or receiving (E for
sure: U((E) = EU(P)
As EU(P)<U(10) Risk Averse.
Risk premium= amount of money you are willing to give up in order to avoid the risk.
for risk loverthis amount is negatve.
The coefcient of absolute risk aversion is a measure of concavity. r(x)= -U’’(x)/u’(x)
risk premium for Peter is larger than the risk premium for John if and only if r(x) for Peter is larger
than r(x) for John
, Maybe more plausible than (ARA: higher income means lower risk aversion, i.e. decreasing absolute
risk aversion ''
We get r*(x)= x r( x )=−x u ( x ) = coefcient of relatve risk aversion
u' ( x )
• If we keep r*(x) constant, then a higher income x means a lower absolute risk aversion.
• (RRA implies decreasing absolute risk aversion.
Wakker (2008) gives characteristcs of (RRA utlity, which are sometmes overlooked in empirical
applicatons.
• Important: When r = 0 we do not have xr = x0 = 1, but ln(x).
• Wakker (example 2.1) shows that you should not overlook the negatve powers r < 0.
SOME PROPERTIES OF (RRA UTILITY
• When x = 0, (RRA utlity is not always well-defined:
ln(0) (when r=0) and 0r (when r < 0) do not exist
→ this is no problem if your analysis only considers x > 0.
• When x > 0, but close to zero, (RRA utlity can generate extreme behavior:
example 4.1 of Wakker (2008)
→ this is no problem if your analysis only considers large x.
What drives diaerences in risk attudes if everybody satsfies expected utlity?
A. differences in eialuatons of outcomes
B. diaerences in evaluatons of probabilites
(. diaerences in evaluatons of outcomes or probabilites
they all face the same lotery, utlity functon deals with how we deal with outcomes, not
probabilites.
First additonal readings:
Wakker, Peter, and Daniel Deneffe (1996), “Elicitng ion NeumannMorgenstern Utlites when
Probabilites are Distorted or Unknown,y Management Science, 42, 1131-1150
The certainty-equivalent method and the probability- equivalent method require precise knowledge
of probabilites.
the "gamble-tradeoa method," or "tradeoa method" for short. The main advantage of the
tradeoa method is that it minimizes the role of probabilites while preserving full validity when used
in the expected utlity criterion.
Summary of fndings:
Our experiments have confirmed the general finding of diminishing marginal utlity both for life years
and for money.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Carlijn18. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.69. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67232 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now