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 below-median 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$.
Implications
• In decision problems without precedents the sensitivity to the cue dimension is higher.
• Initial choices have a disproportionate normative influence on subsequent choices.
• In repeated similar interactions individuals exhibit orderly pattern of choices with respect to numerical parameters.
• But consistency does not necessarily reveal true preferences. (Is the assumption of true preferences surreptitiously implied?)
Broadening the inference from past experiences
• Willingness to accept money for an annoying sound elicited through BDM. Results: significance of the impact of the anchoring effect.
• The experiment is replicated with stakes ten times higher than those ones of the previous experiment and the results points to a higher significance of the impact of the anchoring effect on WTA.
• Notice that high anchor condition lead subject to over-price the annoying sound such to experience higher losses with respect to subjects with low anchor.
Experiment 4: coherent arbitrary valuations in the market
• Auction of an annoying sound in two logically equivalent markets.
• Listening to the sound in increasing condition (10, 20, 30 seconds) for three times or decreasing condition (30, 20, 10 seconds) for three times.
• Anchoring treatments: high anchor 1$; 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.
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