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.