A Theory of Reference Point Formation
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1 A Theory of Reference Point Formation Ozgur Kibris Yusufcan Masatlioglu Elchin Suleymanov Sabanci Maryland Michigan Motivation Model Examples Behavioral Foundation Identification PC-SER References 0/47
2 Reference Dependence Markowitz [1952], Kahneman and Tversky [1979], and Tversky and Kahneman [1991] The idea of reference-dependence has played a very significant role in economics Motivation Model Examples Behavioral Foundation Identification PC-SER References 1/47
3 Reference Dependence Explain observed behavior such as pension and insurance choice, selection of internet privacy, organ donation Attitudes towards risk, equity premium puzzle, annuitization puzzle, disposition effect in financial markets and in housing markets golf players, poker players, cab drivers, physicians, fishermen, deer hunters, drivers,... Samuelson and Zeckhauser [1988], Kahneman Tversky [1984], Banford et al. [1979], Heberlein and Bishop [1985], Raymond and Hartman [1991], Boyce et al. [1992], Duborg et al. [1994], Kahneman et.al. [1990], Knetsch and Sinden [1984], Singh, [1991], Shogren et al. [1994], Morrison [1997], Coursey et al. [1987], Bateman et al. [1997], Johnson et al. [1993], Madrian and Shea [2001], Johnson et al. [2000], Johnson and Goldstein [2003],... Thaler and Benartzi [2004], Sydnor [2010], Johnson et al [2002], Johnson-Goldstein [2003], Pope and Schweitzer [2011], Eil and Lien [2014], Camerer et al [1997], Rizzo and Zeckhauser [2003], Rabin [2000], Wakker [2010], Benartzi and Thaler [1995], Benartzi et al. [2011], Odean [1998], Genesove and Mayer [2001]... Motivation Model Examples Behavioral Foundation Identification PC-SER References 2/47
4 What is the reference point? Motivation Model Examples Behavioral Foundation Identification PC-SER References 3/47
5 What is the reference point? Markowitz [1952] It would be convenient if I had a formula [for the reference point]... But I do not have such a rule and formula. Tversky and Kahneman [1991] The question of the origin and the determinants of the reference state lies beyond the scope of the present article. Motivation Model Examples Behavioral Foundation Identification PC-SER References 3/47
6 What is the issue? Wakker [2010] argues that If too much liberty is left concerning the choice of reference points, then the theory becomes too general and is almost impossible to refute empirically. Motivation Model Examples Behavioral Foundation Identification PC-SER References 4/47
7 A General Model S r(s) max x S U r(s)(x) c(s) S and c(s) are observable r(s) and {U ρ} are not observable Motivation Model Examples Behavioral Foundation Identification PC-SER References 5/47
8 A General Model S r(s) max x S U r(s)(x) c(s) S and c(s) are observable r(s) and {U ρ} are not observable Take r(s) = c(s) and U ρ(ρ) > U ρ(x) for all x X \ ρ any choice can be rationalizable without any structure, there is no empirical content!!! reference point formation is the key Motivation Model Examples Behavioral Foundation Identification PC-SER References 5/47
9 Most Salient Alternative Most salient alternative as the reference point Brickman, Coates, and Janoff-Bulman [1978], Samuelson and Zeckhauser [1988], Pratkanis [2007], DellaVigna [2009], Larrick and Wu [2012], Bhatia and Golman [2015], Bhatia [2017] Bhatia and Golman [2015]...reference points are merely options that are especially salient to the decision maker. Motivation Model Examples Behavioral Foundation Identification PC-SER References 6/47
10 Our Aim We provide a simple theory of reference point formation How the reference point endogenously determined How it affects choices Based on the idea of most salient alternative Motivation Model Examples Behavioral Foundation Identification PC-SER References 7/47
11 Our Model Choice Set Reference Point Reference- Dependent Utility Reference-Dependent Utility Maximization Choice Choice Set Most Salient Alternative Reference-Dependent Utility Maximization Choice Choice Motivation Model Examples Behavioral Foundation Identification PC-SER References 8/47
12 Our Model Choice Set Reference Point Reference- Dependent Utility Reference-Dependent Utility Maximization Choice Choice Set Most Salient Alternative Reference-Dependent Utility Maximization Choice : salience ranking r(s): the highest ranked alternative in S w.r.t. Salience based Endogenous Reference Model (SER) Choice Motivation Model Examples Behavioral Foundation Identification PC-SER References 9/47
13 Salience Ranking Salience ranking a reflection of what grabs the decision maker s attention subjective unobservable Motivation Model Examples Behavioral Foundation Identification PC-SER References 10/47
14 An Illustration Consider a decision maker with a salient ranking z x y and reference-dependent utility functions U z(y) > U z(z) > U z(x) and U x(x) > U x(y) Motivation Model Examples Behavioral Foundation Identification PC-SER References 11/47
15 An Illustration Consider a decision maker with a salient ranking z x y and reference-dependent utility functions U z(y) > U z(z) > U z(x) and U x(x) > U x(y) Implied choices Motivation Model Examples Behavioral Foundation Identification PC-SER References 12/47
16 An Illustration Consider a decision maker with a salient ranking z x y and reference-dependent utility functions Implied choices U z(y) > U z(z) > U z(x) and U x(x) > U x(y) S r(s) c(s) {x, y, z} z y {x, y} x x {y, z} z y {x, z} z z Motivation Model Examples Behavioral Foundation Identification PC-SER References 12/47
17 Behavioral Patterns SER accommodates Cyclical behavior Attraction Effect Compromise Effect More... Motivation Model Examples Behavioral Foundation Identification PC-SER References 13/47
18 Attraction Effect An inferior product increases the attractiveness of dominating another Huber, Payne, and Puto [1982] more than 7300 Google scholar articles Motivation Model Examples Behavioral Foundation Identification PC-SER References 14/47
19 Attraction Effect An inferior product increases the attractiveness of dominating another Huber, Payne, and Puto [1982] more than 7300 Google scholar articles Motivation Model Examples Behavioral Foundation Identification PC-SER References 14/47
![Attraction Effect An inferior product increases the attractiveness of dominating another Huber, Payne, and Puto [1982] more than 7300](/docs-images/89/97968694/images/20-0.jpg "Google scholar articles c(a, B) = B and c(a, B, a) = A Motivation Model Examples Behavioral Foundation Identification PC-SER References")
20 Attraction Effect An inferior product increases the attractiveness of dominating another Huber, Payne, and Puto [1982] more than 7300 Google scholar articles c(a, B) = B and c(a, B, a) = A Motivation Model Examples Behavioral Foundation Identification PC-SER References 14/47
21 Attraction Effect 4-alternative version of AE c(a, B, a) = A and c(a, B, b) = B Motivation Model Examples Behavioral Foundation Identification PC-SER References 15/47
22 Attraction Effect 4-alternative version of AE c(a, B, a) = A and c(a, B, b) = B Motivation Model Examples Behavioral Foundation Identification PC-SER References 16/47
23 Compromise Effect Tendency to choose the middle option Simonson [1989], Simonson and Tversky [1992] more than 2200 Google scholar articles Motivation Model Examples Behavioral Foundation Identification PC-SER References 17/47
24 Compromise Effect Tendency to choose the middle option Simonson [1989], Simonson and Tversky [1992] more than 2200 Google scholar articles c(a, B, C) = B Motivation Model Examples Behavioral Foundation Identification PC-SER References 17/47
25 Compromise Effect 4-alternative version of CE c(a, B, C) = B and c(b, C, D) = C Motivation Model Examples Behavioral Foundation Identification PC-SER References 18/47
26 Compromise Effect c(a, B, C) = B and c(b, C, D) = C Motivation Model Examples Behavioral Foundation Identification PC-SER References 19/47
27 Prediction Power Is the model too general? Motivation Model Examples Behavioral Foundation Identification PC-SER References 20/47
28 Prediction Power Is the model too general? SER can be falsified. Motivation Model Examples Behavioral Foundation Identification PC-SER References 20/47
29 Prediction Power Is the model too general? SER can be falsified. For example, the following c is outside of the model. S {x, y, z} {x, y} {y, z} {x, z} c(s) y x z x Motivation Model Examples Behavioral Foundation Identification PC-SER References 20/47
30 Behavioral Foundation Motivation Model Examples Behavioral Foundation Identification PC-SER References 21/47
31 Behavioral Foundation Single Reversal Axiom: For each S, T and distinct x, y with {x, y} S T, if x c(s) c(s \ x) and c(t ) y then c(t \ y) = c(t ). Motivation Model Examples Behavioral Foundation Identification PC-SER References 21/47
32 Single Reversal Axiom Motivation Model Examples Behavioral Foundation Identification PC-SER References 22/47
33 Single Reversal Axiom Motivation Model Examples Behavioral Foundation Identification PC-SER References 23/47
34 Single Reversal Axiom Motivation Model Examples Behavioral Foundation Identification PC-SER References 24/47
35 Single Reversal Axiom Motivation Model Examples Behavioral Foundation Identification PC-SER References 25/47
36 Single Reversal Axiom Motivation Model Examples Behavioral Foundation Identification PC-SER References 26/47
37 Behavioral Foundation Theorem A choice function c admits a SER representation if and only if it satisfies Single Reversal. Motivation Model Examples Behavioral Foundation Identification PC-SER References 27/47
38 Uniqueness / Identification a choice reversal the reference point Motivation Model Examples Behavioral Foundation Identification PC-SER References 28/47
39 Uniqueness / Identification a choice reversal the reference point x R y if there is S {x, y} such that x c(s) c(s \ x) Motivation Model Examples Behavioral Foundation Identification PC-SER References 28/47
40 Uniqueness / Identification a choice reversal the reference point x R y if there is S {x, y} such that x c(s) c(s \ x) Proposition (Revealed Salience) Suppose c admits a SER representation. Then x is revealed to be more salient than y if and only if x R y. Motivation Model Examples Behavioral Foundation Identification PC-SER References 28/47
41 Uniqueness / Identification How to reveal preference between x and y when the reference point is z? Motivation Model Examples Behavioral Foundation Identification PC-SER References 29/47
42 Uniqueness / Identification How to reveal preference between x and y when the reference point is z? Find a choice problem such that x, y, z are feasible z is the reference point x is chosen Motivation Model Examples Behavioral Foundation Identification PC-SER References 29/47
43 Uniqueness / Identification How to reveal preference between x and y when the reference point z? xp zy if there are S T {x, y, z} s.t. (i) z c(s) c(s \ z) (ii) x = c(t ). Motivation Model Examples Behavioral Foundation Identification PC-SER References 30/47
44 Uniqueness / Identification How to reveal preference between x and y when the reference point z? xp zy if there are S T {x, y, z} s.t. (i) z c(s) c(s \ z) (ii) x = c(t ). Proposition (Revealed Preference) Suppose c admits a SER representation. Then x is revealed to be preferred to y under reference point z if and only if xp zy. Motivation Model Examples Behavioral Foundation Identification PC-SER References 30/47
45 Summary Choice Set Reference Point Reference- Dependent Utility Reference-Dependent Utility Maximization Choice Choice Set Most Salient Alternative Reference-Dependent Utility Maximization Choice an intuitive reference formation simple model simple axiomatization Choice Motivation Model Examples Behavioral Foundation Identification PC-SER References 31/47
46 Psychological Constrained Model Motivation Model Examples Behavioral Foundation Identification PC-SER References 32/47
47 Psychological Constrained Model A new underlying reference dependent choice (Masatlioglu and Ok [2014]) S r(s) max x S Q(r(S)) U(x) c(s) Motivation Model Examples Behavioral Foundation Identification PC-SER References 32/47
48 Psychological Constrained Model A new underlying reference dependent choice (Masatlioglu and Ok [2014]) S r(s) max x S Q(r(S)) U(x) c(s) r(s): the most salient alternative in S U: reference-free Enable welfare analysis Psychological Constrained SER (PC-SER) Motivation Model Examples Behavioral Foundation Identification PC-SER References 32/47
49 Behavioral Foundation Motivation Model Examples Behavioral Foundation Identification PC-SER References 33/47
50 Behavioral Foundation Consistency: For each S X, there is x S such that if {x, z} T T, z c(t ) c(t \ z) and x = c(x, z), then either c(t ) = x or c(t ) / S. Motivation Model Examples Behavioral Foundation Identification PC-SER References 33/47
51 Behavioral Foundation Theorem A choice function c admits a PC-SER representation if and only if it satisfies Single Reversal and Consistency. Motivation Model Examples Behavioral Foundation Identification PC-SER References 34/47
52 Uniqueness / Identification For any x, y, z such that x y, we define xp y if S, T with {x, y, z} T S such that (i) z c(s) c(s \ z), (ii) c(y, z) = y, and (iii) x = c(t ). Motivation Model Examples Behavioral Foundation Identification PC-SER References 35/47
53 Uniqueness / Identification For any x, y, z such that x y, we define xp y if S, T with {x, y, z} T S such that (i) z c(s) c(s \ z), (ii) c(y, z) = y, and (iii) x = c(t ). Let P T be the transitive closure of P. Proposition (Revealed Preference) Suppose c admits a PC-SER representation. Then x is revealed to be preferred to y if and only if xp T y. Motivation Model Examples Behavioral Foundation Identification PC-SER References 35/47
54 Uniqueness / Identification Q M (x) = {y X S T {x, y} s.t. x c(s) c(s \ x) and y = c(t )} Motivation Model Examples Behavioral Foundation Identification PC-SER References 36/47
55 Uniqueness / Identification Q M (x) = {y X S T {x, y} s.t. x c(s) c(s \ x) and y = c(t )} Proposition (Revealed Psychological Constraint) Suppose c admits a PC-SER representation. Then (i) x is revealed to be in the psychological constraint set of y iff x Q M (y), (ii) x is revealed to be outside the psychological constraint set of y if and only if xp T y and c(x, y) = y. Motivation Model Examples Behavioral Foundation Identification PC-SER References 36/47
56 Uniqueness / Identification For any x y x R y if (i) (ii) S {x, y} such that x c(s) c(s \ x), or yp T x and x = c(x, y). Let T R stand for the transitive closure of R. Motivation Model Examples Behavioral Foundation Identification PC-SER References 37/47
57 Uniqueness / Identification For any x y x R y if (i) (ii) S {x, y} such that x c(s) c(s \ x), or yp T x and x = c(x, y). Let T R stand for the transitive closure of R. Proposition (Revealed Salience) Suppose c admits a PC-SER representation. If x T R y then x is revealed to be more salient than y. Motivation Model Examples Behavioral Foundation Identification PC-SER References 37/47
58 Existing Literature Motivation Model Examples Behavioral Foundation Identification PC-SER References 38/47
59 Existing Literature Motivation Model Examples Behavioral Foundation Identification PC-SER References 39/47
60 Existing Literature Motivation Model Examples Behavioral Foundation Identification PC-SER References 40/47
61 Existing Literature Motivation Model Examples Behavioral Foundation Identification PC-SER References 41/47
62 Existing Literature Motivation Model Examples Behavioral Foundation Identification PC-SER References 42/47
63 A Comparison Consider riskless outcomes The constant loss aversion as the underlying reference-dependent model Consider two different reference point formations: PPE (Koszegi and Rabin 2006) Salience Based (This paper) Motivation Model Examples Behavioral Foundation Identification PC-SER References 43/47
64 A Comparison The constant loss aversion model as the underlying reference-dependent model Consider two different reference point formations: PPE (Koszegi and Rabin 2006) Salience Based (This paper) Motivation Model Examples Behavioral Foundation Identification PC-SER References 44/47
65 A Comparison The constant loss aversion model as the underlying reference-dependent model Consider two different reference point formations: PPE (Koszegi and Rabin 2006) Salience Based (This paper) Answers WARP (hence No Compromise or Attraction Effects) (KR, 2006 Prop. 3) Motivation Model Examples Behavioral Foundation Identification PC-SER References 44/47
66 A Comparison The constant loss aversion model as the underlying reference-dependent model Consider two different reference point formations: PPE (Koszegi and Rabin 2006) Salience Based (This paper) Answers WARP (hence No Compromise or Attraction Effects) (KR, 2006 Prop. 3) accommodates both Compromise and Attraction Effects Motivation Model Examples Behavioral Foundation Identification PC-SER References 44/47
67 A Comparison Motivation Model Examples Behavioral Foundation Identification PC-SER References 45/47
68 Conclusion Motivation Model Examples Behavioral Foundation Identification PC-SER References 46/47
69 THANK YOU Motivation Model Examples Behavioral Foundation Identification PC-SER References 47/47
70 S. Bhatia. Comparing theories of reference-dependent choice. Journal of Experimental Psychology: Learning, Memory, and Cognition, 43(9):1490, S. Bhatia and R. Golman. Attention and reference dependence. Working Paper, P. Brickman, D. Coates, and R. Janoff-Bulman. Lottery winners and accident victims: Is happiness relative?. Journal of Personality and Social Psychology, 36(8): , ISSN S. DellaVigna. Psychology and economics: Evidence from the field. Journal of Economic Literature, 47(2):315 72, D. Kahneman and A. Tversky. Prospect theory: An analysis of decision under risk. Econometrica, 47(2): , R. P. Larrick and G. Wu. Risk in negotiation: Judgments of likelihood and value. Oxford University Press, H. Markowitz. The utility of wealth. Journal of Political Economy, 60(2): , A. R. Pratkanis. Social influence analysis: An index of tactics. The Science of Social Influence: Advances and Future Progress, pages 17 82, W. Samuelson and R. Zeckhauser. Status quo bias in decision making. Journal of Risk and Uncertainty, 1(1):7 59, Motivation Model Examples Behavioral Foundation Identification PC-SER References 47/47
71 A. Tversky and D. Kahneman. Loss aversion in riskless choice: A reference-dependent model. Quarterly Journal of Economics, 106(4): , P. P. Wakker. Prospect Theory: For Risk and Ambiguity. Cambridge University Press, Motivation Model Examples Behavioral Foundation Identification PC-SER References 47/47
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