My reference point, not yours

Journal of Economic Behavior and Organization 171 (2020) 297–311

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Journal of Economic Behavior and Organization journal homepage: www.elsevier.com/locate/jebo

My reference point, not yours Joy A. Buchanan1 Brock School of Business, Samford University, 800 Lakeshore Drive, Birmingham, AL, USA

a r t i c l e

i n f o

Article history: Received 8 August 2019 Revised 16 January 2020 Accepted 21 January 2020

JEL classification: C91 D84 D91 Keywords: Reference points Beliefs Experiments Expectations

a b s t r a c t Reference points formed by initial endowments influence individual decisions. This experiment tests whether an individual can predict the behavior of other people who have different reference points. Despite financial incentives for being correct, players fail to imagine themselves in another person’s shoes. A low endowment player generally cannot predict the behavior of those who were assigned high endowments, and vice versa, when asked about group behavior. Instead of considering the perspectives of others, a low endowment player predicts that all others will act as if they all had low endowments. This controlled experiment helps explain why it is difficult to understand the perspectives of other people, while also demonstrating that it is possible when a player is specifically prompted to consider an individual in a different circumstance. © 2020 Elsevier B.V. All rights reserved.

1. Introduction It is said that in order to understand another person, you must “walk a mile in their shoes”. People do not usually make the conscious effort to think about the perspective of other people, even if it means, as this experiment demonstrates, leaving money on the table. In a large diverse society, people often fail to act on information about others that is readily available. Often we simply expect others to act the way that we do ourselves, as if their experiences were like our own. This can lead to missed opportunities in markets and talking past each other in political conversations.2 To avoid losses, people will sometimes make choices that do not maximize the expected value of their monetary outcomes. One example is the resistance to selling a house for less than the nominal purchase price (Genesove and Mayer, 2001). Many experiments have demonstrated this tendency.3 Each person has a different life experience, providing him or her with a unique reference point from which to evaluate gains and losses. Although loss averse behavior is ubiquitous, is it common to anticipate that other people are likewise loss averse with respect to their own unique reference points?4

E-mail address: [email protected] I thank Noah Leatham for research assistance. The paper was improved by conversations with Greg Leo, Cary Deck, Kevin McCabe and participants at the Southern Economic Association meeting. Funding was provided by Samford University. 2 Catapano et al. (2019) study how taking the perspective of someone with an opposing political view affects the polarization of American politics. 3 Kahneman and Tversky (1979), Kahneman et al. (1990), Abeler et al. (2011) and others provide evidence of loss averse behavior. The reason for the observed behavioral anomalies was questioned by Plott and Zeiler (2005). Goette et al. (2018) recently found evidence that more than half of the subjects they sampled display loss aversion in an exchange setting. 4 People appear aware of their own foibles, including their own loss aversion. Imas et al. (2016) document that people who are more loss averse prefer a contract that will ensure they work hard to avoid a loss. The interpretation is that people anticipate their own future distaste for losses and use the 1

https://doi.org/10.1016/j.jebo.2020.01.023 0167-2681/© 2020 Elsevier B.V. All rights reserved.

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J.A. Buchanan / Journal of Economic Behavior and Organization 171 (2020) 297–311

To answer that question, we designed an experiment in which participants make decisions and then predict what other participants chose. A controlled experiment allows the unique opportunity to observe how exogenous starting points affect predictions. In the first stage of the experiment, participants are randomly assigned an initial endowment amount and then make investment decisions that could involve losses. The reference point of the participant (i.e. the amount of this initial endowment) affects their decisions, as expected. This phase of the experiment confirmed and quantified this effect for the pool of participants. In the second stage, participants earn money for making accurate predictions about the choices of other participants. The amount of money available in the two stages of the experiment was roughly equal, so subjects have an incentive to think about the decisions of others. Participants know that several reference points are uniformly distributed among other subjects. Instead of relying on this objective fact, their own experience informs their predictions. Subjects also tend to project their own level of loss aversion onto others. The finding from this experiment is not that subjects don’t expect other people to be loss averse, but rather that they expect others to act as if they all started from the same initial endowment level as their own. In some cases, high performance on a cognitive reflection test (CRT) indicates that a person is less subject to bias. In our experiment, we test whether a higher CRT score is associated with less biased predictions. Neither high CRT scores nor additional comprehension quiz questions result in participants correctly taking the objective distribution of endowments into account. However, when prompted to think about one endowment assigned to others, subjects make accurate predictions about behavior, perhaps because empathy toward a single individual enables a Theory of Mind. The following section describes additional related research. We present our design in Section 3 and hypotheses in Section 4. Results are in Section 5, followed by our conclusion. 2. Related literature Our study relates to many strategic games in the economics literature. For example, the Ultimatum Game allows a responder to reject the offer of a first mover, if the first mover disappoints or violates the expectations of the responder (Güth and Kocher (2014) review Ultimatum Game literature). Xiao and Houser (2005) suggest that the rejection by responders is motivated by anger towards the first mover. In a similar way, the first mover in a Gift Exchange Game (Fehr et al., 1993) will only succeed if they can anticipate the way that their offer affects the responder. Implicitly, the first mover should know the reference points that responders measure the offer against. Economists infer from the heterogeneity in responses that there is a distribution of reference points in the population. The innovation in our study is to gain control over the reference point of individuals through random assignment of initial endowments.5 This sort of investigation into how empathy works in relation to a distribution of types was suggested by Singer and Fehr (2005). We show that subjects are fairly accurate when thinking about an individual, which is the normal function of empathy. However, when they try to make predictions for a group, they are both inaccurate and heavily biased toward guessing as if all other people had the endowment that they themselves had. Rubinstein and Salant (2016) conducted an experiment in which subjects play a strategic game and then predict how others behaved in the same experiment. The reported beliefs appeared to be influenced by self-similarity, meaning that a player thinks that others made the same choice that he himself made. Bose and Sgroi (2019) found that subjects tend to project their own characteristics (i.e. degree of extroversion) onto an anonymous opponent which affects play in a strategic game. Our experiment allows us to test own reference point as an explanation for self-similarity, which has not been done before to our knowledge. People who live in groups must, to some extent, be able to anticipate how their neighbors will act. Before writing The Wealth of Nations, Smith (1976) wrote extensively on how people perceive their neighbors.6 3. Experimental design Subjects are assigned an initial endowment by a die roll that is called “earnings”. The endowment can be $1, $2, $3, $4, $5, or $6 with equal probability. After the endowment is assigned, subjects make 6 choices. Table 1 presents the choices in a menu, however they were each presented on a separate screen to subjects.7 Option A is to keep the initial endowment that was determined by the initial die roll. Option B is to enter a binary lottery, as shown in Table 1. Option B always has an expected value that is positive and greater than the value of Option A. In many cases, Option B could result in a loss relative to the initial endowment. For example, if a subject initially rolled a 5, then they earn $5 for certain with Option A. If they picked Option B on Choice #1, then they earn either $10 or $1. Final earnings are determined by a second electronic die roll to select one choice for payment (the other five choices were not paid). If the subject picked Option B, a computerized coin flip determines the lottery outcome. contract as a commitment device to work hard. Similarly, a sophisticated person might avoid a store where they know their future self will be tempted to make an impulsive purchase. The new question addressed in this paper is whether people expect loss aversion in others. 5 This is a difference from related work on the false consensus effect by Engelmann and Strobel (2012). 6 Smith and Wilson (2018) apply Smith’s idea of ‘fellow feeling’ to the observation that subjects in two-player sequential games can successfully anticipate the resentment or gratitude that their behavior will elicit from their counterpart in controlled experiments. Our study indicates that fellow feeling is naturally generated by considering an individual in a particular circumstance. However, it is not produced by a composite group of others. 7 Brown and Healy (2018) suggest separate screens to avoid artificial menu effects.

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Table 1 Choices in the first task. Option A

Choice Choice Choice Choice Choice Choice

#1 #2 #3 #4 #5 #6

Keep Keep Keep Keep Keep Keep

your your your your your your

Option B

earnings earnings earnings earnings earnings earnings

50% chance of Heads

50% chance of Tails

Double Double Double Double Double Double

$1 $2 $3 $4 $5 $6

your your your your your your

earnings earnings earnings earnings earnings earnings

Note: Option A is referred to as the ‘Keep’ decision throughout the paper.

In the second task, subjects make incentivized guesses about what other subjects chose in the first task.8 The instructions explicitly state that other participants had the same instructions and other participants could have different initial endowments based on the first random die roll. The instructions for university students read as follows: Other participants at this university have completed this experiment. Their instructions were exactly the same as yours on every page. Thus, they could experience a different die roll or coin flip outcome than you did. The main treatment variable is the random assignment of initial endowments. The experiment was run with two different populations and with a small change in the instructions for the purpose of a robustness check. The primary sample is 97 students at a private US university who participated in a computer lab.9 Their behavior was replicated with 144 participants from the online crowdsourcing platform Mechanical Turk (MTurk). In the original version, University, 80 university students reported incentivized beliefs about other university students. In the next version, MTurk, 63 MTurk workers made guesses about other MTurkers. Subjects understood that other participants had experienced the same instructions and had received a die roll outcome. However, subjects might originate their own subjective belief about the distribution of initial die roll outcomes. Incorrect beliefs about the distribution of initial die roll outcomes could lead to results that look like the main effect we are trying to measure. To ensure that the main results are not a result of confusion or false beliefs about the distribution of die roll outcomes, we implemented two additional versions, University Pool and MTurk Pool, with 17 and 81 subjects respectively. In those versions, the incentives were identical to the previous versions. In the pool version, instead of guessing what “other” previous participants had done, subjects made guesses about the choices made by a pool of 30 other participants who had participated in the same university (for MTurk, the pool was others from MTurk). Each of the 6 possible endowment levels had been experienced by 5 people in the pool of 30. This ensured that beliefs about choices were not distorted by an incorrect subjective belief about the process that produced the starting reference points. MTurk workers (MTurkers) were paid in tokens. Two tokens converted to $1. Thus, the payout from doing the experiment on MTurk was about half of what university students received (which is high for Mechanical Turk). MTurkers received a $1.50 show-up fee. University students received a $5 show-up fee. The instructions for all versions were identical in the first stage. There are slight differences in wording for the second prediction stage. The first 80 University students made guesses for “other participants”. In the additional Pool version of the instructions, the following true statement was added to the MTurk Pool instructions: 30 people have been selected who completed the experiment on Mechanical Turk. You will be making predictions about what choices those people made. Within that group, 5 people had an initial die roll of 1, and 5 people had an initial die roll of 2, and so on. The group was selected by taking the 30 people who completed the experiment most recently, such that all of the possible starting die rolls are represented in this group in an equal number. The possible starting die rolls are 1,2,3,4,5, and 6. In addition to extra instructions explaining the pool, a quiz was added. One quiz question read: Of the 30 people I am making predictions for, a. None of them started the experiment with a roll of 6 b. 5 started the experiment with a roll of 6 c. All of them started the experiment with a roll of 6

8 A group of university students seeded the experiment. Their data are not included because their payment was delayed and all other participants received immediate payment. They made predictions about what each other did and they were paid a week after they participated. Their incentives were the same as subsequent participants. Subsequent experiments compared the predictions of current subjects to the behavior of previous subjects. Subjects knew that previous participants had been recruited in the same way from the same population. 9 University students were recruited through flyers and emails. The experiment interface was programmed with oTree by Chen et al. (2016).

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Subjects had to select the correct answer (b) before continuing. The fact that some versions had extra comprehension checks allows us to see if the pattern of behavior in the University version is simply due to confusion. Full instructions are available. This experiment is designed to investigate how personal experience affects beliefs about the general population. Subjects made predictions about what percent of the other subjects decided to keep (Option A) in each of the 6 choices in the first task. Then they guessed what percent of other subjects decided to keep (Option A) in all of the 6 choices in the first task. Finally, subjects made guesses about the behavior of a subset of the pool who all had a single specified endowment. The question about the percent of others who decided to keep in a single choice solicits an estimate of the average behavior of other participants. Asking for the percent of others who always picked keep gets at beliefs about types within the population. The scoring rule used to elicit incentivized predictions awarded 1$ for an answer that is within 5% of the true value.10 An answer within 15% of the true value (but further than 5%) earned $0.50. Every prediction was paid. The reward was in tokens in Mechanical Turk. The most money a subject can earn in the lottery choice is $12. There is also up to $12 that can be earned for correct guesses about the choices of others. Subjects ought to pay as much attention to the prediction task as the initial lottery choices. Subjects read instructions and answered questions. They had to answer quiz questions correctly to proceed. At the end, there was a questionnaire. 4. Theoretical considerations and hypotheses If people maximize expected value in the first stage (see Table 1), then the choice is obvious. The expected value, for a player with endowment e, of the investment choice (Option B) with a Tails payoff of l > 0 is

EV [Invest[l]] = 0.5(l ) + 0.5(2e ) The investment reduces to

EV [Invest[l]] = 0.5(l ) + e ˝ which is always higher than keeping e (Option A). Following Kahneman and Tversky (1979) and Koszegi and Rabin (2006), we assume that reference points affect decisions.11 Option A might be preferred over the chance of ending up in the loss domain. Unless they begin the experiment with the lowest endowment, plausible levels of loss aversion will prevent most subjects from accepting the first investment in Choice #1. The first investment will, half the time, mean getting only $1. If a player had $6 guaranteed and they perceive a loss to be twice as important as gains, then the fall from $6 to $1 would have the negative impact to utility of 2∗ (-$5)= -$10. That potential negative impact would outweigh the positive event of rising from $6 to $12, and thus they would reject the first investment. According to the principle that “losses loom larger than gains” (Kahneman and Tversky, 1979), we expect that people with larger endowments are less likely to accept investments because, for them, more of the investments involve losses. People with large endowments have the most to gain in absolute terms by doubling their original amount, but for many (not all, due to heterogeneity in loss aversion) that will not be attractive enough for them to maximize expected value. See Appendix B for a discussion of the role of risk aversion in decision making. Regarding the first stage: Hypothesis 1. People with higher endowments will reject more investments. In the second stage, players predict what other people picked. They know that other people were assigned initial endowments by a die roll, so they are informed that there is a uniform distribution of the 6 possible endowments. Additionally, in the Pool versions of the experiment, they are explicitly told and tested on the fact that there is an even distribution of endowments among the group. 10 We infer beliefs from predictions. The decision to use this incentivized belief elicitation was based on several factors. Paying for close answers and making the interval for any payment wide (30 percentage points) serves a purpose. Subjects believe that they will earn money in the prediction stage of the experiment. An approach that specifically elicits the mode of the subjective distribution used by Dufwenberg et al. (2011) has the advantage of precision; however we did not want subjects who have a flatter belief distribution to become discouraged, in our experiment. Our tiered payment structure is meant to elicit the center of the 10% modal bin of the subjective beliefs, like Charness and Dufwenberg (2006). Distortion can occur if a subject has a belief distribution with a mode of 100%, or near the extreme bounds of the distribution, or due to risk aversion. A tendency to shade reported beliefs toward 50% in a strategic attempt to capture either the large or small payment would work against finding a significant effect of own endowment on beliefs. See Hossain and Okui (2013) and Harrison et al. (2017) for discussions of proper scoring rules. In our design for this paper, we did not want to introduce a stochastic scoring rule because the subjects are already asked to process the distribution of endowments and we want to reduce the possibility of confusion due to complexity. 11 Specifically, we assume that the reference point is equal to the subject’s initial endowment, which is empirically supported by Baillon et al. (forthcoming). They identify which reference points are most commonly used in choices under risk. The most common reference points in their experiment were the status quo and the maximin payoff. In our experiment, the status quo is the initial endowment, and the endowment is the maximin payoff in choices that involve risk.

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Fig. 1. Actual decisions in Choice #1, n=50.

All players are trying to predict the same estimates, and they earn extra money for accuracy. It is worth noting here that all subjects experienced the same instructions before the prediction stage.12 Hypothesis 2. Since the distribution of endowments is common knowledge, people with high endowments will not systematically differ in their predictions from people with low endowments. Unlike the distribution of endowments, the distribution of loss averse tendencies in the sample is not known with certainty. Players might assume that other people are like themselves. Hypothesis 3. People who exhibit loss aversion might predict that others reject more investments. More loss averse subjects will predict a higher rate of keeping among other subjects. 5. Results A key finding is an emphatic rejection of the null Hypothesis 2. This experiment indicates that people are heavily biased by their own past experience. 5.1. Choices over players’ own earnings First, subjects appear loss averse and confirm Hypothesis 1. This result merely replicates what other experiments have found. Result 1. High-endowment subjects reject more investments. Fig. 1 presents data from both university students and MTurkers. The height of the bar (with standard errors) shows the percent of subjects who keep (Option A) in Choice #1. There are 50 observations because this represents the subjects who did not experience the Pool version of the instructions and it only includes subjects who were assigned the extreme endowments of either $1 or $6. MTurkers with the highest endowment of $6 closely resemble high-endowment university students. About 75% choose to keep and the remaining quarter are willing to invest. Almost all of the subjects with the lowest endowment of $1 are willing to invest.13 12 They experienced nearly the same instructions in the prediction stage. The small differences are between the original version and the Pool version, not between subjects who had different endowments. 13 MTurkers all make the rational decision to invest when there is nothing to lose. MTurk workers had experience with the computer format and the university subjects were inexperienced. Several university students reject the investment even when they cannot get less than their assigned $1 in Option

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J.A. Buchanan / Journal of Economic Behavior and Organization 171 (2020) 297–311 Table 2 Logit for probability of keeping and linear regression for predictions. Dependent variable: Actual Choice #1, Logit

Predict Choice #1, OLS

Predict Always Invest, OLS

(1)

(2)

(3)

(4)

(5)

(6)

0.632∗∗∗ (0.092)

6.813∗∗∗ (1.236)

-5.975∗∗∗ (0.930)

20.516∗∗∗ (4.832)

6.865∗∗∗ (1.243) -2.452 (5.760) -4.320 (5.396) -4.313 (9.132) 22.732∗∗∗ (5.676)

58.236∗∗∗ (3.639)

-5.999∗∗∗ (0.936) 2.442 (4.335) 2.493 (4.061) -2.874 (6.874) 57.045∗∗∗ (4.272)

241

241

241

241

0.113 34.023

0.115 34.188

0.147 25.621

0.151 25.732

Constant

-2.119∗∗∗ (0.344)

0.637∗∗∗ (0.093) 0.264 (0.383) 0.484 (0.365) -0.362 (0.632) -2.343∗∗∗ (0.414)

Observations Log Likelihood R2 Residual Std. Err.

241 -136.933

241 -135.509

Endowment MTurk MTurk Pool Uni. Pool

Standard errors in parentheses. ∗ p < 0.1; ∗∗ p < 0.05; ∗∗∗ p < 0.01. Note: Endowment ranges from 1 to 6. The version indicators are dummy variables.

Intermediate-endowment subjects who are not pictured in Fig. 1 fall between the extremes. Table A.1 shows the proportions of keeping for each endowment level and version. On average, including all endowment levels, half of subjects choose to keep in Choice #1. Table 2 contains results for data from all participants, including all six possible endowments and four versions. A higher endowment increases the likelihood of keeping. The version does not have a significant effect on choices, as shown with version controls in column (2). ‘Uni. Pool’ refers to the sample of university students who were making predictions for a pool of 30 students who had participated previously that represented all endowment types in equal numbers. A logit model is used because to keep or not is a binary decision (Keep = 1 and Invest = 0). The positive coefficient on Endowment in columns (1) and (2) indicates that the probability of keeping in Choice #1 increases for participants with larger endowments. Specifically, the model predicts that a subject with the lowest endowment ($1) will keep 18% of the time while a subject with the highest endowment ($6) has an 84% chance of keeping. 5.2. Predictions for Choice #1 Using the same sample as Fig. 1, Fig. 2 shows the average prediction of the percentage of other subjects who decided to keep in Choice #1. Although all of the (incentivized) predictions are of the same statistic, there is a large difference between the guesses of low-endowment subjects and high-endowment subjects. Result 2. The predictions of average group behavior are dramatically affected by the individual initial endowment. Columns (3) and (4) of Table 2 show that the effect of endowment on predictions was large and significant. An increase by one in the endowment is associated with an increase of more than 6 percentage points of expecting others to keep. Going from the lowest to highest initial endowment is associated with a 266% increase in the prediction. This effect is robust to platform (traditional lab and internet) and the representation of the uniform distribution of endowments for others. Columns (3) and (4) of Table 2 only shows results for predictions about behavior in Choice #1, since this leads to the most divergent predictions. The difference between endowments disappears for predictions about behavior on Choice #6. The later choices are not affected as much by endowment, so it is not surprising that the predictions are not significantly affected by endowment. The accuracy of the predictions varies with endowments. Subjects with high endowments are more accurate when predicting the decisions made by others in Choice #1. The low-endowment subjects struggle to imagine that many people will turn down investments, and thus they do worse in predictions for Choice #1. 5.3. Predictions for investing in all six choices Columns (5) and (6) of Table 2 show how endowment affects the prediction about types within the population. Subjects estimate the percent of others who invested (chose Option B) in all 6 choices. A high-endowment subject predicts that less other people invested every time. Going from the lowest to highest initial endowment is associated with a 48% decrease in B. The most plausible reason for the low-endowment university students who did not invest is confusion. University subjects might have an underlying aversion to investing, although the word “invest” is never used in the instructions. Regardless of the reason for those few decisions that are hard to rationalize, the next result on predictions is striking because the bias seems to affect the MTurkers even more than the university students.

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Fig. 2. Predicted decisions in Choice #1, n=50.

Fig. 3. Predicted types, n=90.

the prediction. This is consistent with the result in column (3) that high-endowment subjects predict that a larger percent of others keep (not invest) in Choice #1. Result 3. The predictions of types within the group are dramatically affected by the individual initial endowment. Predictions about types are fairly accurate on average. However, low-endowment subjects overestimate how many other people invest every time, while high-endowment types underestimate the same statistic. Fig. 3 shows the difference in type predictions between those with the lowest and highest endowments. In all versions, the low endowment subjects predicted that about half of all other subjects invested in all 6 choices. Those with high endowments predicted that the proportion of others was about one quarter. The difference appears larger among MTurkers.

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J.A. Buchanan / Journal of Economic Behavior and Organization 171 (2020) 297–311 Table 3 Linear regression, endowment and choices effect on predictions. Dependent variable: Predicted % of Others who Always Invest

Endowment = 2

(1)

(2)

-3.046 (5.381) -24.145∗∗∗ (5.567) -29.532∗∗∗ (5.909) -27.704∗∗∗ (5.859) -27.077∗∗∗ (5.302)

Constant

55.220∗∗∗ (3.912)

1.064 (5.450) -19.481∗∗∗ (5.754) -23.097∗∗∗ (6.545) -21.018∗∗∗ (6.623) -18.221∗∗∗ (6.515) -12.637∗∗∗ (3.997) 3.751 (5.514) -4.403 (5.637) 5.716 (5.246) -7.339 (6.316) 0.399 (6.146) 56.140∗∗∗ (3.891)

Observations R2 Residual Std. Error

241 0.198 25.052 (df = 235)

241 0.244 24.648 (df = 229)

Endowment = 3 Endowment = 4 Endowment = 5 Endowment = 6 Own Choice #1 Own Choice #2 Own Choice #3 Own Choice #4 Own Choice #5 Own Choice #6

Note: Standard errors in parentheses. ∗ p < 0.1; ∗∗ p < 0.05; ∗∗∗ p < 0.01. Endowments are dummy variables for own endowment. Own choice variables are “1” if the subject chose to keep, and zero otherwise.

Fig. 3 summarizes results for 90 observations. These 90 observations are only the subjects who had either the lowest or highest endowment, in all versions. The difference does not appear smaller among subjects in the Pool version. So, the observed effect is robust to additional quiz questions ensuring that participants acknowledge the information about the true distribution of endowments experienced by others. Is this result merely due to subjects guessing that other people behaved the way that they themselves did? Is there evidence that own choice is biasing predictions more than own endowment? When both own choice and own endowment are entered into a model to explain predictions, both are significant, however own endowment appears more important. The regression is reported in Table 3. Result 4. Subjects who exhibit loss aversion by keeping are more likely to predict that others keep. Table 3 reports the results a linear regression for beliefs about what percent of others always chose to invest. Unlike regressions reported above, here endowments enter as discrete binary inputs instead of as a continuous censored variable. Beliefs for those with an endowment of $2 are not significantly different from those of the lowest endowment. High endowment individuals predict that a much smaller percent of others always invest. This is a further confirmation of Result 2 and Result 3, which state that endowments bias prediction. Table 3 column (2) includes dummy variable for all endowment levels and also the individual choices made by the subject. This is to test whether subjects who invest predict that most others invest. One’s own decision to keep in Choice #1 is associated with a 13% decline in the predicted proportion of others who always invest, controlling for own endowment levels. Put another way, someone who invested on the first choice will assume that 13% more of the rest of the group will always invest. This suggests that own risk aversion does affect predictions about others, controlling for endowment. A test for predictions about the average behavior of others, as opposed to always-invest types, yields the same result. The magnitude of the effect of endowment goes down when controlling for own choice (from column (1) to column (2)), but it only decreases by about 25%. The average effect of starting with $6 goes from -27 to -18. Importantly, the regression results do not indicate that subjects are simply predicting that other people behave the way that they themselves behave. It is clear from comparing Figs. 1 to 2 that players are not predicting that others made the same choice that they themselves made.

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305

Fig. 4. Predicted types if endowment=1, n=90.

5.4. Demographics At the end of the experiment, subjects reported their sex and whether it is true that they “take risks in life”. People who say that they take risks do invest more, but they do not predict that significantly more other people invest. Subjects who self-report being risk-takers do not predict more risk-taking in others. Neither sex nor being on the MTurk platform had an apparent effect on average actual choices for predictions about types in the population. Own endowment remains a strong influence, even when controlling for demographic factors. Results are reported an a regression in the appendix Table A.2. Subjects who perform well on a cognitive reflection test (CRT) are not less prone to biased predictions, as shown in appendix Table A.3.14 This evidence indicates that the main result of this paper is not simply due to confusion. We also demonstrate that performance on the CRT is not evidence of good Theory of Mind skills, confirming the findings of Corgnet et al. (2018). It is possible that subjects who think more about the CRT questions also think more about their own reference point, which influences their predictions about how others behave. 5.5. Predictions for a single specified endowment It appears to be difficult for subjects to think about a distribution. A final prediction task prompted subjects to think about one specific endowment and how the other people with only that endowment would behave. Result 5. If asked to consider other subjects who all have the same endowment, the predictions are not biased by own endowment as much. The second-to-last belief elicitation was for other subjects who had started with an endowment of $1. Everyone guessed that about 75% of the low-endowment others invest every time. The guess is not much biased by own endowment (see Fig. 4). Note that the people with an endowment of $1 made an accurate prediction about how other $1 subjects act. When prompted to think about low-endowment subjects, everyone was correct, on average. This suggests that the large errors in the first prediction tasks were due to endowment bias as opposed to a serious difficulty with thinking about the task. The bias apparent in predictions about the population do not appear as strong when subjects are asked to consider a subset of subjects who all have the same endowment. Fig. 4 shows that the effect of own endowment is much less than it was for the composite group in Fig. 3. 14 The university students had CRT questions borrowed from Frederick (2005) and Toplak et al. (2014). Key nouns were replaced for the MTurkers to create new questions of the same difficulty level.

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Fig. 5. Predicted types if endowment=3, n=90.

The effect of own endowment is not significant at the 5% level in a regression model explaining predictions for lowest endowment players. By contrast, endowment has a large and highly significant effect on the prediction for how much of the composite group always invests. See Table A4 in the appendix for regression results. The last incentivized prediction is for how many subjects who started with $3 always invest. Among university students there was no significant difference between high and low endowment predictions (see Fig. 5). There was a small endowment effect among MTurkers. Generally it seems that endowment bias is stronger among MTurkers. In a regression (appendix Table A.4), the significant effect of endowment on the $3 prediction is significant but it is half the size of the effect on the composite group prediction. 6. Conclusion In a simple transparent environment, with financial incentives, subjects could not anticipate how other people behave who had a different reference point from themselves. Subjects overwhelmingly make predictions as if everyone began in the same way that they themselves did. It may be that one’s own endowment is more salient than another person’s endowment, unless there is a specific prompt to think about another person (Bordalo et al., 2012). Our inclination is to think about other people as if they had our life experiences. It usually comes as a shock if we are asked to specifically contemplate someone else’s experience, even if the information was already available to us. There is also a tendency to assume that other people share our own level of risk aversion. Historically, humans lived in relatively small homogeneous groups in which most people did indeed share similar life experiences. People in the modern world often misunderstand each other. Many new products fail and political candidates begin campaign bids that are mostly unsuccessful.15 Usually the environment is too complex to measure the precise effect of one’s own starting point on one’s miscalculation about others. This experiment is the first controlled test of that influence. Future research can establish whether this apparent bias survives in competitive environments, and what factors help people to succeed in making composite predictions. Ambuehl et al. (2019) recently found that more patient people impose greater patience on others, when given an opportunity to be paternalistic. A promising area for future research is on the role of experts in correcting this bias. Lawyers can convince people to settle out of court and real estate agents can convince sellers to accept a lower price than they paid for a house. Perhaps this illustrates a role for experts. List (2003) demonstrates in an experiment that experts are not subject to the loss aversion that distorts the decisions of most retail consumers in a field.

15

For example, (Griffin, 1997) found that over 40% of new product introductions were considered failures by their respective firms.

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One way to interpret the results of this experiment is that putting yourself in someone else’s shoes is costly. We often speak of it as a moral obligation, especially to consider the plight of those who are worse off than ourselves. Not only do people usually decline to do this for moral reasons, they fail to do it for money. Additionally, this experiment shows that, if people are prompted to think about a specific past experience that someone else had, then mutual understanding is easier to establish. Declaration of Competing Interest None. Appendix A. Additional results A1. Proportion of subjects who keep Each subject can only fall into one cell of Table A.1. This shows the decision in Choice #1 of the experiment. This is the data used for the logit model in columns (1) and (2) of Table 2. The progression is not always smooth, but the proportion of people choosing to keep increases as the endowment increases. A2. Demographics results and cognitive reflection At the end of the experiment, subjects reported their sex and whether it is true that they “take risks in life”. The phrasing of the self-reported risk measure was modeled from Dohmen et al. (2011). They found that the self-reported risk attitude was a reliable predictor of actual risky behavior in an incentivized experiment. They find, like Eckel and Grossman (2008), that women are more risk averse. Table A.2 shows how self-reported measures relate to own actual choice and predictions about the types of others, along with a control for the MTurk platform. The negative coefficient for Reported Risk indicates that people who “take risks in life” are less likely to keep in Choice #1. Although sex is often related to risk taking, male students are not significantly less likely to keep. The results do not change if we use a logit model for keeping in Choice #1.

Table A.1 Proportion of subjects who keep by endowment and version. Version

University University Pool Mechanical Turk Mechanical Turk Pool

Initial endowment 1

2

3

4

5

6

0.17 0 0 0

0.42 0.17 0.50 0.36

0.43 0.00 0.36 0.64

0.50 0.50 0.67 0.75

0.61 1.00 0.83 0.75

0.75 0.80 0.75 0.90

Table A.2 Linear regression on demographic indicators. Dependent variable: Actual Choice #1 (1) Endowment Male Reported Risk All MTurk Constant Observations R2 Adjusted R2 Residual Std. Error F Statistic

Predict % Others Always Invest (2)

(3)

(4)

0.133∗∗∗ (0.016) -0.050 (0.059) -0.135∗∗ (0.058) 0.080 (0.058) 0.094 (0.079)

-0.057 (0.067) -0.149∗∗ (0.066) 0.099 (0.066) 0.557∗∗∗ (0.065)

-6.044∗∗∗ (0.931) -5.430 (3.463) -0.465 (3.411) 3.690 (3.415) 59.618∗∗∗ (4.670)

-5.106 (3.751) 0.200 (3.693) 2.852 (3.697) 38.559∗∗∗ (3.640)

241 0.262 0.249 0.434 20.896

241 0.039 0.027 0.494 3.212

241 0.160 0.145 25.594 11.205

241 0.009 -0.003 27.728 0.756

Standard errors in parentheses. ∗ p < 0.1; ∗∗ p < 0.05; ∗∗∗ p < 0.01. Note: Endowment ranges from 1 to 6. All other indicators are dummy variables.

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J.A. Buchanan / Journal of Economic Behavior and Organization 171 (2020) 297–311 Table A.3 Beliefs of subjects who answered 2 or 3 CRT questions correctly vs. others. Linear regression dependent variable: Predicted % Always Invest Sample: < 2 Correct CRT

Sample: 2 or 3 Correct CRT

(1)

(2)

(3)

(4)

-5.500∗∗∗ (1.189)

-6.831∗∗∗ (1.492)

60.507∗∗∗ (6.201)

-6.823∗∗∗ (1.514) -2.308 (5.761) 5.297 (7.391) 57.435∗∗∗ (8.337)

77 0.219 0.208 23.408 20.973∗∗∗

77 0.224 0.192 23.639 7.037∗∗∗

Constant

57.081∗∗∗ (4.506)

-5.490∗∗∗ (1.194) 0.588 (4.745) 3.432 (4.480) 55.156∗∗∗ (5.058)

Observations R2 Adjusted R2 Residual Std. Error F Statistic

164 0.117 0.111 26.690 21.391∗∗∗

164 0.121 0.104 26.792 7.332∗∗∗

Endowment Any Pool Any MTurk

Standard errors in parentheses. ∗ p < 0.1; ∗∗ p < 0.05; ∗∗∗ p < 0.01. Note: Endowment ranges from 1 to 6. Other indicators are dummy variables.

Table A.2 suggests that endowment has a large effect, as stated in the paper, and that self-reported demographic factors do not significantly affect predictions. Next, we consider whether performance on a cognitive reflection test (CRT) implies that the main result in the paper is due to confusion. Subjects were asked to answer three questions as part of a CRT that was not incentivized. We made slight nominal changes to the questions for the MTurk workers in order to make it more difficult to Google the answers. This is an example of a question presented to University students, copied from previous research on cognitive reflection: A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost? The CRT is designed to have false but intuitively appealing answers. Only 64 people, or 27%, did not fall for any of the intuitive answers. Many subjects, at least once, read the question quickly and gave the intuitive answer. Subjects had 90 seconds to answer three CRT questions. Subjects who are able to answer CRT questions correctly might be less subject to certain types of bias. If some subjects have biased beliefs, it might be the case that subjects who get CRT questions correct are able to report less biased beliefs. It is also likely that subjects who do well on the CRT test are thinking hard about the experiment generally. Table A.3 shows the effect of own endowment on beliefs for two subsamples. The right two rows in Table A.3 show results for subjects who got 2 or 3 CRT questions correct. Only 77 subjects got more than one CRT question correct, perhaps because of the binding time constraint. We control for the possible effect of both the pool framing and Mechanical Turk. The effect of own endowment on beliefs is not smaller for subjects who did well on the CRT test. The individuals who did well on the CRT test have a highly significant coefficient indicating that for every additional dollar of initial endowment their prediction is smaller by almost 7%. Is the endowment bias of predictions reported in this paper just evidence of lazy thinking? It appears from this analysis that even people who are thinking hard and possess some other types of intelligence are subject to the endowment bias in beliefs. In this environment, it is possible that, the more closely subjects are paying attention to the CRT questions, the more they think about their own endowment. That biased their predictions about the actions of the group. A3. Predictions for a single specified endowment The endowment effect on predicting always-invest types is large in column (1) of Table A.4. Column (1) is the prediction made for the type that always invests within the entire group (the result matches those explained the main paper). That effect diminishes when the predictor is prompted to think about a single endowment level specifically. Column (2) is the prediction made for the proportion of the type that always invests, only for the others in the group who started with the lowest endowment level. The constant coefficient is higher in (2) and the effect of own endowment loses significance. All subjects making predictions, with this prompting, realize that most people with nothing to lose will invest every time. The significant result in column (3) of Table A.4 is driven by the MTurk subjects. The disparity is visible in Fig. 5. Among MTurkers, their own endowment biases their predictions about other people who had an endowment of $3.

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Table A.4 Predictions for a single specified endowment. Linear regression dependent variable:

Endowment Constant Observations R2 Residual Std. Error

Predict Invest, All (1)

Predict Invest, e=1 (2)

Predict Invest, e=3 (3)

-5.975∗∗∗ (0.930) 58.236∗∗∗ (3.639)

-1.890∗ (1.121) 81.821∗∗∗ (4.385)

-2.956∗∗∗ (0.979) 60.163∗∗∗ (3.829)

241 0.147 25.621

241 0.012 30.874

241 0.037 26.957

Note: Standard errors in parentheses. ∗ p < 0.1;

∗∗

p < 0.05;

∗∗∗

p < 0.01.

Appendix B. Risk aversion discussion In this section, we argue that loss aversion is an important determinant of behavior in the experiment. It is likely that many of our subjects are also risk averse and that may also affect their choices in the first stage of the experiment. However, risk aversion alone cannot explain behavior in the experiment. First, consider how risk aversion would cause subjects to evaluate the options to invest or keep, if all payouts from the choice are evaluated by subjects in the gain domain. For the following framework, I borrow notation from Harrison and Swarthout (2016). Assume that the utility of income is defined by

U (x ) =

x(1−r )

(1 − r )

(B.1)

where x is the lottery prize and r = 1 is a risk parameter. For r = 1 assume U (x ) = ln(x ) if needed. Thus r is the coefficient of CRRA: r = 0 corresponds to risk neutrality, r < 0 to risk loving, and r > 0 to risk aversion. Second, consider that subjects may use their endowment, E, as a reference point. An amount of money, m, that is above the reference point is in the gain domain and an outcome that is lower than their reference point is evaluated in the loss domain, following Tversky and Kahneman (1992). A functional form for loss aversion, using a CRRA specification of utility, is as follows:

U (m ) =

m ( 1 −α ) when m ≥ 0 (1 − α )

U (m ) = −λ

(−m )(1−β ) when m < 0 (1 − β )

(B.2)

(B.3)

Without risk aversion (i.e. r = 0), loss aversion can be represented as

U (m ) = m when m ≥ 0

(B.4)

U (m ) = −λ(−m ) when m < 0

(B.5)

A subject who maximizes expected value will never keep. For a subject to choose to keep under risk aversion as defined in Eq. (B.1), in a choice that pays l or 2E from the investment, it must be true that the expected utility of keeping is higher than the expected utility of investing, or

E 1−r 1 (2E )1−r 1 l 1−r > + (1 − r ) 2 1 − r 21−r If E is sufficiently high and l is sufficiently low, then risk aversion alone could account for the decision to keep, without loss aversion. Table B.1 shows the minimum level of risk aversion needed to explain why a high endowment subject would refuse to invest in the choices with the 3 lowest l payouts in our experiment. Note that, in this exercise, we assume that there is no loss aversion and therefore no reference dependence. The threshold level 0.17 in the first row of the table is the solution to 6x = 1/2(12x + 1x ) with r = 1 − x. Risk aversion is a plausible reason for why we observe that some high-endowment subjects keep in Choice #1 when l = 1. Risk aversion alone cannot explain why more than half of high-endowment subjects Keep in Choice #3. Holt and Laury (2002) found that most subjects displayed a risk aversion parameter of less than 0.68, and most subjects are in the 0.3–0.5 range. Using risk aversion alone as an explanation, we would not expect anyone to keep on Choice #3.

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J.A. Buchanan / Journal of Economic Behavior and Organization 171 (2020) 297–311 Table B.1 Threshold levels of risk aversion to explain keeping. Endowment, E

Investment payout, l

6 6 6 5 5 5

1 2 3 1 2 3

Minimum level of risk aversion, r, to explain a decision to keep r >0.17 r >0.48 No solution for r ∈ (0, 1) r >0.22 r >0.65 No solution for r ∈ (0, 1)

Table B.2 Proportion of subjects who keep. Initial Endowment

Choice #1 Choice #2 Choice #3

E =5

E =6

0.70 0.67 0.55

0.82 0.73 0.76

By contrast, loss aversion alone can explain why some subjects keep in Choice #3, if they use their endowment as a reference point. For a subject to keep under loss aversion, for a choice that pays l < E in the investment, it must be true that

0>

1 1 (E ) + λ (l − E ) 2 2

The left side of the inequality is zero because money is evaluated only as a gain or a loss from the starting point of E. A subject with E = 6 considering Choice #3 may consider the outcome of l = 3 to be a loss of 3 relative to E. The upside of doubling their endowment is considered a gain of E. Although there was no reasonable level of risk aversion that could explain why a high endowment subject would keep in Choice #3, the minimum level of loss aversion that would cause a subject with E = 6 to keep in Choice #3 is only λ > 2. The average level of loss aversion is often cited as 2 with reference to experiments by Novemsky and Kahneman (2005). There is usually high variance of loss aversion within a subject population, which was confirmed by Gächter et al. (2007). They report that the interquartile range of loss aversion (for a choice without risk) is [1.33,3]. If our population is similar, then we can attribute some of the keep decisions to loss aversion. The minimum level of loss aversion that would cause a subject with E=5 to keep in Choice #3 is λ > 2.5. Table B.2 shows that half of subjects with E = 5 keep in Choice #3, if we pool all versions. While it is impossible to explain that with only risk aversion, it is reasonable if we assume that most subjects are loss averse (with respect to their initial endowment) as well as risk averse. Heterogeneity in loss aversion explains why some keep but not others. Also, a loss aversion threshold of λ > 2.5 is only slightly higher than the estimate of λ = 2.25 from Tversky and Kahneman (1992). An additional explanation for the decision to keep is the fact that people tend to overweight the worse outcome when the probabilities are 50%-50% λ > 2.5 (Starmer, 20 0 0; Wakker, 2010). The central claim of this paper is that subjects fail to account for the starting point of other subjects. Subjects who start out with high endowments expect other subjects to keep for two reasons. First, they do not expect other subjects to be expected value maximizers. Recall that no subject should keep, if they are maximizing expected value. Second, they make predictions as if they believe that other subjects also have a high initial endowment. The analysis in this appendix indicates that loss aversion is necessary to explain behavior in this experiment. Thus, we can say that subjects fail to account for the reference point of others. Additionally, the predictions of subjects may be affected by their own risk aversion. Even controlling for their own endowments, there is evidence in Table 3 that people who keep in Choice #1 are more likely to predict that others keep. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jebo.2020.01.023. References Abeler, J., Falk, A., Goette, L., Huffman, D., 2011. Reference points and effort provision. Am. Econ. Rev. 101 (2), 470–492. Ambuehl, S., Bernheim, B.D., Ockenfels, A., 2019. Projective paternalism. Natl. Bureau Econ. Res. (w26119). Baillon, A., Bleichrodt, H., Spinu, V., 2020. Searching for the reference point. Manag. Sci. 66 (1), 93–112. Bordalo, P., Gennaioli, N., Shleifer, A., 2012. Salience theory of choice under risk. Q. J. Econ. 127 (3), 1243–1285. Bose, N., Sgroi, D., 2019. Theory of mind and strategic decision-making. Technical Report. Competitive Advantage in the Global Economy (CAGE). Brown, A.L., Healy, P.J., 2018. Separated decisions. Eur. Econ. Rev. 101, 20–34. doi:10.1016/j.euroecorev.2017.09.014.

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