Abstract
This paper addresses two major topics concerning the role of expectations in the formation of reference points. First, we show that when expectations are present, they have a significant impact on reference point formation. Second, we find that decision-makers employ expected values when forming reference points (integrated mechanism) as opposed to single possible outcomes (segregated mechanism). Despite the importance of reference points in prospect theory, to date, there is no standard method of examining these. We develop a new experimental design that employs an indirect approach and extends an existing direct approach. Our findings are consistent across the two approaches.
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Notes
We follow Köszegi and Rabin (2006, 2007) and consider those expectations held in the “recent” past (t = 1) about current outcomes (t = 2). As they point out, this should not mean that beliefs are slow to adjust to new information but that preferences do not instantaneously change when beliefs do. They give the following example for this setting: “When somebody finds out 5 min ahead of time that she will for sure not receive a long-expected $100, she would presumably immediately adjust her expectations to the new situation, but she will still 5 min later assess not getting the money as a loss” (Köszegi and Rabin 2006, footnote 9).
Note that in contrast to Fig. 1, there is no actual outcome P1 in t = 1 when the lotteries are announced. This intermediate outcome P1 will become meaningful in Experiment 2.
The higher willingness of those participants in the experimental treatments to take risks, even if not significant, could first be due to the “hot hand effect” (Rabin and Vayanos 2010; Croson and Sundali 2005). Participants in the experimental treatments won the higher amount of money during the first lottery and thus might believe in a run of good luck. Second, the higher willingness could be due to the more pronounced “house-money effect” (Thaler and Johnson 1990) as participants in the experimental treatments received a higher amount of money (8 CHF or 12 CHF) compared with those in the control treatment (4 CHF).
As we asked participants to reveal their expectations about the current stock price, we are able to statistically compare this information for both treatments. The mean reported expectations in the control treatment with 39.16€ are approximately the same size as those in the base treatment A (B) with 38.54€ (39.55€). Statistical comparisons show no significant differences (A: Mann–Whitney-U = 4,161.50; p = 0.663; B: Mann–Whitney-U = 1,992.5; p = 0.324).
Reference point adaptation high treatment A (7.88€) minus reference point adaptation base treatment A (5.69€).
Reference point adaptation base treatment A (5.69€) minus reference point adaptation low treatment A (4.09€).
A statistical comparison of the squared differences in reference point adaptation compared with the base treatment for treatments low and high A confirms the differences on a significant level (U = 1,866.00; p = 0.046). This is not true for the comparison between treatments low and high B (U = 2,269.00; p = 0.943).
For a possible range effect, see, for example, Curley and Yates (1985).
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Acknowledgments
This research was supported by the Deutsche Forschungsgemeinschaft (DFG) awarded to Frauke von Bieberstein. We gratefully acknowledge support from the Volkswagen Foundation, Grant no. 85 487.
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Appendices
Appendix 1: Instructions for the experiment (treatment 1)
Welcome to this experiment! Please read these instructions carefully. All decisions you make in this experiment are anonymous. At the end of the experiment you will also be paid out anonymously. During the experiment no communication is allowed.
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1.
Personal information
How old are you?; What is your field of study?; Please indicate your gender.
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2.
General information
We will be playing two lotteries with you where you can win real money.
To do so we have divided all participants into two groups: Group A and Group B.
You are part of: Group A.
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3.
Lottery One
The first lottery has the following payoffs:
Win 4 CHF with 50 % probability/Win 8 CHF with 50 % probability
We will now toss a coin. Your payoff will be calculated in the following way:
“Heads”: Group A wins 4 CHF, Group B wins 8 CHF/
“Tails”: Group A wins 8 CHF, Group B wins 4 CHF.
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4.
Lottery Two
The table below shows in each row two alternatives. You can choose in each row between participation in a lottery (Alternative 1) or a safe payment (Alternative 2).
Please fill in the table below as follows: Start with the first row and move down from row to row. In each row, you have to decide between Alternative 1 and 2. Alternative 1 is the same in each row. Only the safe payment in Alternative 2 increases with each row.
After you have made your choices, we will select one of the rows by chance. This row will determine your payment: If you have selected Alternative 1 in this row, we will play the lottery with you. If you have selected Alternative 2 in this row, you will receive the safe payment.
Please mark in each row only one alternative with a cross (all in all 17 crosses):
Row | Alternative 1 | Alternative 2 |
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1 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 0 CHF for sure |
2 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 0.50 CHF for sure |
3 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 1 CHF for sure |
4 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 1.50 CHF for sure |
5 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 2 CHF for sure |
6 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 2.50 CHF for sure |
7 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 3 CHF for sure |
8 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 3.50 CHF for sure |
9 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 4 CHF for sure |
10 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 4.50 CHF for sure |
11 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 5 CHF for sure |
12 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 5.50 CHF for sure |
13 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 6 CHF for sure |
14 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 6.50 CHF for sure |
15 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 7 CHF for sure |
16 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 7.50 CHF for sure |
17 | 10 CHF with probability of 50 %, 0 CHF with probability of 50 % | 8 CHF for sure |
Appendix 2: Instructions for the questionnaire study
Thank you for participating in our short questionnaire study!
Please complete the following questionnaire. Take your time and carefully read the questions. There are no right or wrong answers in the second and third part of the questionnaire. We are only interested in your personal assessment. All answers will be made anonymous.
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1.
Personal information
How old are you?; What is your field of study?; Please indicate your gender.
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2.
Personal assessment
Please imagine the following situation:
“Two months ago, you bought a stock for 30€ per share. One month ago, you were delighted to learn the stock was trading higher—at 36€ per share. [Only in experimental treatments: One month ago you also learned that this month’s stock price is expected to range between x and y€, with each price within this interval being equally likely.]
This month, you decide to check the stock’s price again. At what price would the stock need to trade today to make you just as happy with the stock’s price this month as you were when you learned the stock had risen from 30 to 36€ last month?”
Please indicate the stock price that would make you just as happy here:
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3.
Further information
Please indicate what stock price you had expected when answering the question on the previous page on “the stock price that would make you just as happy”.
Please indicate the stock price that you had expected here:
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Hack, A., von Bieberstein, F. How expectations affect reference point formation: an experimental investigation. Rev Manag Sci 9, 33–59 (2015). https://doi.org/10.1007/s11846-014-0121-0
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DOI: https://doi.org/10.1007/s11846-014-0121-0