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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.
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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.
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.
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.
