VI Lecture Stable demand curves with arbitrary preferences.

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Presentation transcript:

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$, 2.11$ WTA la < WTA ha 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.