VI Lecture
Stable demand curves with arbitrary
preferences
Wrap up of the previous lecture
• Formal definition of preferences, utility and rationality.
• Behavioral foundation and empirical hypothesis of
preferences exogeneity to choices.
• Evidence of a recursive causal relation between
preferences and choices.
• Metrical problem: do past choices influence utility or
do they bias the subjective estimation of utility?
Introduction
• Stable demand curves are assumed to reflect
individuals fundamental valuations of goods.
• Empirical
evidence
of
preferences
responsiveness to the cue dimension of the
external stimuli.
• Stable demand curves might reflect arbitrary
preferences.
Standard comparative statics
• Down-ward sloping demand curves trace back to
agents’ “true” valuations.
• Indirect measure of value attribution through changes
in the environment and institutional rules (i.e.
restrictions on the budget line) to test the consistency of
behavior with theoretical predictions (Smith 1994).
• Individuals adapt their choices to the external changes
(i.e. new constraints on the budget line) but their
preferences are assumed to remain stable: preferences
are consistent across equilibria.
Limitation
• Comparative statics is a necessary but not
sufficient condition for the inference of
individuals’ fundamental valuations.
• The downward sloping shape of demand curves
are not exclusively produced by individuals’
fundamental valuations.
• Random choices produce downward sloping
demand curves by virtue of the scarcity constraint
alone (Becker 1971).
Problem of coherent arbitrariness
• Individuals’ fundamental valuations of a good are
highly sensitive to normatively irrelevant factors
(i.e. framing, anchor).
• Individuals’ relative valuations of different
amounts of the good come to be orderly; they
satisfy axioms of rationality.
• Individuals might exhibit patterns of coherent
arbitrary preferences that support downward
sloping demand curves.
Hypothetical explanation
• Valuations are initially malleable by both
normatively irrelevant stimuli.
• Valuation become imprinted once the subject is
asked to make upon an initial decision.
• In repeated choices relative valuations become
logically coherent.
Experiment 1: Coherent arbitrariness
with ordinary products
•
Test of the anchoring effect on
participants’ fundamental valuations.
•
Anchoring effect: the valuation of an
auctioned good is influenced by an
unrelated stimulus (i.e. last two digits
of SSN).
•
55 students of MIT are shown 6
ordinary products without mentioning
market prices (computer accessories,
Belgian chocolate, wine bottles and
books).
•
Subject are asked to whether they
would buy each good for a dollar
figure equal to the last two digits of
their social security number (SSN).
•
Subjects were asked to state their
maximum WTP through an individual
pricing procedure.
•
A random device decided if the good
would be sold on the basis of the first
or second response (BDM).
•
Subjects know that both responses
have a chance to be decisive for the
purchase. They were eligible to
purchase one product at most.
Results
• Significance of the impact of the SSN on the subjects’
WTP in spite of the realism of the products.
• Subjects with above median SSN stated a values from
57% to 107% greater than did subjects with belowmedian prices.
• Fundamental valuations volatility is compatible with a
marked stability of relative preferences: i.e. the
majority of subjects value the cordless keyboard more
than the trackball.
Results
Explanation
• When individuals face a new decision problem they are not
endowed with a well-defined structure of preferences.
• Individuals face new decision problems with a range of acceptable
values.
• If the value of an item falls within the range, so that no choice is
determined, then individuals’ choices are largely malleable.
• These foundational choices become part of one’s stock of decisional
precedents that restricts the range of acceptable values for similar
choice problems (Gilboa and Schmeidler 1995).
Example
• Subject with a SSN ending with 25 and an a priori WTP
range (5$, 30$) for the average wine, and (10$, 50$) for the
rare wine.
• Both wines might or might not be purchased for 25$.
• A subject expresses a WTP for the average wine of 25$. He
is willing to purchase the rare wine for the same price.
• Restriction on the choice problem: both prices should range
starting from 25$.
Implications
• In decision problems without precedents the sensitivity to
the cue dimension is higher.
• Initial choices have a disproportionate normative influence
on subsequent choices.
• In repeated similar interactions individuals exhibit orderly
pattern of choices with respect to numerical parameters.
• But consistency does not necessarily reveal true
preferences. (Is the assumption of true preferences
surreptitiously implied?)
Broadening the inference from past
experiences
• Willingness to accept money for an annoying sound
elicited through BDM. Results: significance of the
impact of the anchoring effect.
• The experiment is replicated with stakes ten times
higher than those ones of the previous experiment and
the results points to a higher significance of the impact
of the anchoring effect on WTA.
• Notice that high anchor condition lead subject to overprice the annoying sound such to experience higher
losses with respect to subjects with low anchor.
Experiment 4: coherent arbitrary
valuations in the market
• Auction of an annoying sound in two logically equivalent markets.
• Listening to the sound in increasing condition (10, 20, 30 seconds)
for three times or decreasing condition (30, 20, 10 seconds) for three
times.
• Anchoring treatments: high anchor 1$; low anchor 10 cents.
• Elicitation of WTA values through a multi-person auction: the three
lowest bids win the auction and get paid with the fourth lowest bid
(triangulation method).
• Subjects experience the sounds for 30 seconds before the auction
starts.
Methodological justification of the interactive
structure and auctioned good
• The interactive structure is simple, incentive
compatible and guarantees of interactive learning
(Binmore 1999).
• The auctioned good avoids field price censoring,
affiliated beliefs of field prices, affiliated beliefs about
the commodity quality (Harrison et al. 2004):
Individuals’ WTA valuations are independent.
• The price is a reliable basis to infer subjects’
preferences
Predictive hypotheses
• DPH-based predictions: if arbitrariness reduces then we will
observe a reduction of the mean bids variance between
markets: equality of the mean bids value between auctions.
• PCH-based predictions: we will observe a reduction of the
mean bids variance within auctions and an increase of the
mean bids variance between markets.
• Operational hypothesis: market forces do not reduce bias
but prices converge towards market specific values.
Results
• Average bids in Low anchor conditions: 24, 38, 67 (cents)
respectively for 10, 20, 30 sec of the sound; High anchor
conditions 47 cents, 1.32$, 2.11$
• WTAla < WTAha
• The mean payment is $ .59 in high anchor condition and $
.08 in low anchor condition.
• Bids and auction prices do not converge towards a common
value; bids within each group converge toward an arbitrary
value: coherent arbitrariness is robust with respect to market
forces.
Illustration
Problem
• The non-convergence is an empirical evidence
supporting the Becker’s statement about the
downward sloping shape of demand curves even
with random and biased choices.
• The non-convergence is not supportive of the
DPH-based predictions.
• However, non-convergence is simply compatible
with PCH-based prediction but not supportive: the
metrical problem persists.
Conclusions
• Willingness to accept exhibits the pattern of coherent
arbitrariness.
• Coherence: people respond in a robust fashion to change in
the relevant variables.
• Arbitrariness: these response occur around a base level that
is normatively arbitrary.
• The metrical problem remain because anchoring effect does
not distinguishes between the possibility of a biased
estimation of utility and the shaping of utility.