Elsevier Editorial System(tm) for Journal of Economic Psychology Manuscript Draft Manuscript Number: JOEP-D-15-00353 Title: Sunk-Cost Fallacy and Cognitive Ability in Individual DecisionMaking Article Type: Research Paper Keywords: cognitive ability, cognitive dissonance, sunk-cost fallacy, loss aversion Corresponding Author: Dr. Corina Haita-Falah, Ph.D. Corresponding Author's Institution: University of Hamburg First Author: Corina Haita-Falah, Ph.D. Order of Authors: Corina Haita-Falah, Ph.D. Abstract: This paper reports on a laboratory experiment aiming at documenting the sunk-cost fallacy in individual decision-making and at identifying the role of the cognitive ability in its manifestation. For this purpose, the design rules out loss aversion and cognitive dissonance, identified by the literature as being the main psychological drivers of the bias. The sunk-cost fallacy is identified by comparing a low and a high sunk-cost treatment, respectively, against a control group that does not incur a sunk cost. There is evidence of a weak manifestation of the sunk-cost fallacy, which is statistically significant only for the high sunk-cost treatment. However, strong evidence of the fallacy was found among the high-cognitive-ability subjects. Finally, although cognitive ability is predictive of status-quo bias, it was not found to reduce the sunk-cost bias.
Cover Letter
Corina Haita-Falah, Ph.D. Hamburg University Von-Melle-Park 5 20146-Hamburg, Germany Tel.: +49-(0)40-42838-8049 Fax: +49-(0)40-42838-3243 September 6, 2015
Dear Editor, I am sending attached my manuscript “Sunk-Cost Fallacy and Cognitive Ability in Individual Decision-Making” to be considered for publication in the “Journal of Economic Psychology”. The paper reports on a laboratory experiment aiming at documenting the sunk-cost fallacy in individual decision-making, and at investigating the role of the cognitive ability in its manifestation. The experimental data was collected in the laboratory of the Faculty of Economics and Social Science of the University of Hamburg. I confirm that this manuscript has not been published elsewhere and it is not under consideration by another journal. Please address all the correspondence to
[email protected], the postal address and phone numbers provided in the header of this letter. Thank you very much for your consideration and I am looking forward to your decision. Sincerely, Corina Haita-Falah, Ph.D.
*Highlights (for review)
Sunk-Cost Fallacy and Cognitive Ability in Individual Decision-Making
Highlights • Laboratory experiment documenting the sunk-cost fallacy • Cognitive dissonance and loss aversion are made impotent • The larger the sunk cost, the stronger the bias • Cognitive ability does not alleviate the bias • Sunk cost fallacy found within the high-cognitive-ability subjects
1
*Title page with author details
Sunk-Cost Fallacy and Cognitive Ability in Individual Decision-Making Corina Haita-Falaha a
University of Hamburg Von-Melle-Park 5, 20146-Hamburg, Germany E-mail:
[email protected] Phone: +49-(0)1523-6709-877
1
*Manuscript without author identifiers Click here to view linked References
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Sunk-Cost Fallacy and Cognitive Ability in Individual Decision-Making
Abstract This paper reports on a laboratory experiment aiming at documenting the sunkcost fallacy in individual decision-making and at identifying the role of the cognitive ability in its manifestation. For this purpose, the design rules out loss aversion and cognitive dissonance, identified by the literature as being the main psychological drivers of the bias. The sunk-cost fallacy is identified by comparing a low and a high sunk-cost treatment, respectively, against a control group that does not incur a sunk cost. There is evidence of a weak manifestation of the sunk-cost fallacy, which is statistically significant only for the high sunk-cost treatment. However, strong evidence of the fallacy was found among the high-cognitive-ability subjects. Finally, although cognitive ability is predictive of status-quo bias, it was not found to reduce the sunk-cost bias. Keywords: cognitive ability, cognitive dissonance, sunk-cost fallacy, loss aversion JEL Clasification: C91, D03, D11, M41
1
Introduction
Normative economic theory indicates that costs incurred in the past are irrelevant for future marginal payoffs, i.e. sunk costs must be ignored. Nevertheless, there is evidence that the actual human behavior violates this normative prescription and people tend to account for historical costs. In common language, the sunk-cost fallacy (bias) is the irrational behavior of ”throwing good money after bad,” i.e. once found on a course of action to which they committed an investment (e.g. time, money, effort), people continue to stay on that course of action and invest even more resources despite it being unprofitable.
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
As Thaler (1980) points out, efforts of identifying the sunk-cost fallacy from field data are often hindered by a selection bias. Therefore, evidence of the sunk-cost fallacy has, thus far, been limited to hypothetical scenarios and field experiments, while efforts for documenting it in laboratory are still surprisingly scarce and provide mixed evidence (Ashraf et al., 2010). On the one hand, hypothetical questions lack salience since subjects are asked to imagine decision scenarios and state their decisions. On the other hand, field experiments are most of the time contextual and use real commodities (Harrison and List, 2004), which limits the validity of the findings to the particular context. Moreover, decisions in the field interfere with subjects’ unobserved prior beliefs and experience in relation to the particular experimental context. At the same time, it is conceivable that (consumption) decisions in the field do not elicit individual, but rather group decisions, being, thus contaminated by the relative bargaining power within the group.1 The latter, however, remains unobserved to the experimenter. Therefore, more controlled laboratory experiments can provide cleaner evidence for the manifestation of the fallacy in individual decision making and help identifying the roots of the bias. In the sunk-cost fallacy literature, two main psychological mechanisms have been made responsible for the manifestation of the bias. First, Staw (1976) argues that the state of cognitive dissonance between one’s actions and the cognition of rational behavior creates a state of mental discomfort. One common mechanism that reduces this discomfort is a post-hoc rationalization of past decisions, i.e. self-justification of past decisions. In the context of the sunk costs, the best way one can justify past decisions is by continuing to pour resources into a failing course of action. Supporting this argument, the author finds that people are more committed to a previously chosen alternative if made responsible for that decision at an earlier point in time. Similarly, Bazerman et al. (1984) find that being made responsible for the existence of a sunk cost increases the amount of resources allocated for the continuation of a project. Arkes and Blumer (1985) 1
See, for example, Ashraf et al. (2010) which studies consumption decisions at household level.
2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
also discuss the cognitive dissonance theory as being related to the manifestation of the sunk-cost bias, but conclude that this explanation is insufficient for understanding the bias. Instead, the authors advocate loss aversion (Kahneman and Tversky, 1979) as a suitable explanation for the sunk-cost fallacy. In fact, the connection between loss aversion and the sunk-cost fallacy was firstly noted by Thaler (1980) starting right from the experiments conducted by Kahneman and Tversky (1979). The author explains that the convexity of the utility function in the domain of losses, i.e. risk-seeking behavior, is responsible for the escalation on an initial investment. In this paper I use a laboratory experiment in which the above-mentioned psychological drivers of the sunk-cost fallacy are made impotent. Hence, the first endeavor of this study is to show that the two psychological channels of the sunk-cost fallacy are not necessary for the bias to manifest itself. Second, I investigate the potential of the cognitive ability to alleviate the bias. Cognitive ability was found to reduce several biases such as conjunction fallacy, base rate fallacy, conservatism bias and overconfidence (Oechssler et al., 2009; Hoppe and Kusterer, 2011). However, virtually all the evidence relating the sunk-cost fallacy to the cognitive ability is supplied by the psychology literature (see Section 2). Although subjects in psychological experiments are paid for their participation, they are not paid in accordance to their decisions. In fact, these experiments use hypothetical-scenario tasks without economic consequences for the participants and, therefore, they do not guarantee actual behavior. Economic experiments, on the other hand, are likely to provide a more accurate measure of people’s actual behavior in an economic environment. Nevertheless, I am not aware of any economic experiment in a controlled laboratory setting which investigates the relationship between cognitive ability and the decision to ignore sunk costs. I take up this endeavor in the experiment reported here. For this, I use the Cognitive Reflection Test (CRT) developed by Frederick (2005), together with three mathematical questions from Benjamin et al. (2006), as a measure of cognitive ability.
3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
The experimental manipulation consists of one control and two treatment groups. The participants in the control group are endowed with a number of units of an asset A and an amount of cash, whereas the participants in the two treatment groups are endowed with cash and offered the possibility to purchase the same number of units of asset A as the control group. The two treatment conditions differ with respect to the price of asset A, a low sunk-cost and a high sunk-cost treatment, respectively, in order to test whether the sunk-cost fallacy is related to the size of the investment. In a subsequent stage, all participants have the possibility to trade their holdings of asset A and buy an alternative asset B that has the same redemption value but a lower ask price than asset A. For this reason, selling all the endowment of asset A is the profit-maximizing decision, though the selling price of asset A is lower than the initial purchase price, i.e. part of the initial investment remains sunk. Comparing trades in this second stage allows to identify a sunk-cost bias if participants in the treatment groups sell fewer units of asset A than those in the control group. The experimental data indicates behavior consistent with the manifestation of the sunk-cost fallacy. The non-parametric analysis confirms the existence of a statistically significant trend across the three experimental groups, though two-by-two comparisons show a significant difference only between the control group and the high sunk-cost treatment. Similarly, regression analysis shows a significant treatment effect only for the high sunk-cost treatment. While the treatment effect in the case of the high sunk cost survives controlling for cognitive ability, the interaction between the treatment dummy and the measure of cognitive ability does not confirm an effect of the latter on the sunk-cost bias. However, cognitive ability appears to be responsible for a status-quo bias. The paper proceeds as follows. In the next section I review the existing evidence of the sunk-cost fallacy. In Section 3 I present the experimental design and I discuss how it relates to the psychological causes of the fallacy. Section 4 presents the experimental
4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
results, while Section 5 includes a discussion of the results and the limitations of the study. Section 6 summarizes the findings and concludes.
2
Existing Literature
It appears that most of the experimental literature investigating the sunk-cost fallacy makes use of contexts and situations, particularly in field studies where real goods are used. For this reason, the results are rather confined to the context, the particular commodity used or the population treated. Along these lines, Tan and Yates (1995) shows that the decision to escalate on an initial course of action is sensitive to the context in which the problem is formulated. Using hypothetical scenario questions, the authors show that students who had prior instructions in sunk-cost principles did ignore it when the context of the problem was similar to the textbook examples. However, they failed to do so when the decision reflected a real-life situation. Probably the most prominent study documenting the sunk-cost fallacy is the field experiment conducted by Arkes and Blumer (1985). The authors are able to capture differences in behavior among three groups of theater season tickets buyers, who were randomly chosen to pay different prices: full price and two levels of discounted prices. The experiment shows that those who paid the full price of the ticket visited the theater more often during the season than those who paid a discounted price. Considered to be the second field experiment investigating the sunk-cost fallacy, Ashraf et al. (2010) employ a randomized control trial in Zambia to test whether higher prices induce more product use. Their experimental design is able to isolate the sunkcost effect from the self-selection effect, but they find no evidence of the sunk-cost effect, at least in the domain of health products used in their study. Their experimental manipulation is inspired by the unexpected random discount in the offer price manipulated by Arkes and Blumer (1985). However, unlike Arkes and Blumer (1985) and similar to my
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
design, they include a treatment with zero transaction price. Using this treatment the authors test the hypothesis of paying a positive price versus paying zero price and find a sunk-cost effect, although not statistically significant. Interestingly, Ashraf et al. (2010) find evidence of the sunk-cost effect in households’ answers to hypothetical questions, which is, however, inconsistent with households’ actual behavior. This result seems to undermine the reliability of the findings from previous studies based on hypothetical questions, and reinforces the need for laboratory experiments in order to clarify the mixed evidence. I am aware of only two economic experiments that explicitly investigate the sunkcost fallacy in the laboratory. First, using lottery valuations as a measure of escalation of commitment, Phillips et al. (1991) show that when the sunk costs are made more transparent, they are more likely to be ignored. Nearly half of their subjects failed to ignore the sunk cost when this was not explicitly paid, but was only a verbal commitment. However, only 19% of their subjects exhibited the bias when the sunk cost was made more salient through the physical act of paying the lottery ticket (the sunk cost in their experiment). Second, Friedman et al. (2007) devised a computer game to isolate factors which determine the sunk-cost fallacy. Precisely, their design eliminates rational motives for the manifestation of the fallacy, but can identify the effects of the cognitive dissonance and loss aversion on the bias. The authors report surprisingly small and inconsistent evidence of the sunk-cost fallacy, while the psychological drivers manipulated by their study also have a small and inconsistent impact on the manifestation of the fallacy. The experimental psychology literature points to cognitive ability as a candidate to explaining the sunk-cost fallacy, though the evidence from these experiments is rather mixed. For example, Larrick et al. (1993) find some correlation between subjects’ recognition of economists’ position with respect to sunk costs and the Scholastic Assessment Test (SAT) verbal score, which is their measure of cognitive ability. However, the SAT score did not correlate with subjects’ own reported behavior. Similarly, Strough et al.
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
(2008) find small or insignificant correlations between the sunk-cost fallacy and the scores of various cognitive tests. On the other hand, using the self-reported SAT scores as a measure of cognitive ability, Stanovich and West (2008) find a significant effect of the cognitive ability on the manifestation of the sunk-cost fallacy across the cognitive groups (low and high). However, the interaction of the cognitive ability with their measure of the sunk-cost fallacy was not found significant, suggesting that sunk-cost fallacy is not attenuated by cognitive ability. Parker and Fischhoff (2005) measure the correlation between knowledge and reasoning, as proxies for cognitive ability, and the resistance to sunk costs. The authors find a weak and overall statistically insignificant correlation between the sunk-cost fallacy index and their measure of cognitive ability. Extending the scale of the sunk-cost questions of Parker and Fischhoff (2005) and using a much larger sample of adults, Bruine de Bruin et al. (2007) find similar small correlations between the resistance to sunk cost and the two measures of cognitive ability, i.e. knowledge and reasoning. As in my study, Toplak et al. (2011) use the CRT to measure cognitive ability and find that the test results correlate significantly with their measure of rational-thinking which contains a sunk-cost task. However, the authors do not report a separate correlation between the CRT and the performance on the sunk cost task itself, which is one of the endeavors of the present paper.
3 3.1
Experimental Design Theoretical setup
Consider a situation in which, at the time of receiving new information, a decision maker has already made an investment into a course of action towards achieving a certain goal. At this point she learns that, for achieving the goal, a cheaper alternative course of action becomes available and that she has the possibility to partially recoup the initial investment. The reversible nature of the initial investment should provide a nudge to-
7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
wards abandoning the initial course of action when this is no longer profitable. Failure to abandon the initial course of action is interpreted as sunk-cost fallacy. Under the design of this experiment the abandonment of the initial course of action is a continuous rather than a dichotomous variable. Therefore, the fallacy can manifest in various degrees, depending on how much the decision maker adopts the alternative course of action. More specifically, let us assume that there are two types of assets in the economy: asset A and asset B. Next, let us suppose that the decision maker has initially invested in q0A units of asset A at the price pA 0 per unit. Once the investment is completed she learns that (i) asset B is also available for the price pB per unit while asset A can be A traded (bought and sold) for the price pA 1 per unit, (ii) she must accumulate Q > q0
units of assets A and B in any combination of the two, (iii) each of the Q units has the same final value p, regardless of being of type A or B. Thus, at the time of receiving this A A information the total investment in asset A, i.e. pA 0 q0 is sunk. Let q1 be the number of
units of asset A she decides to sell (q1A ≤ 0) or buy (q1A ≥ 0) and q B ≥ 0 the number of units of asset B she decides to buy. Thus, q1A and, equivalently, q B measure the degree to which the decision maker reverts from or escalates on the initial course of action, which is represented by asset A. The final payoff of the decision maker is given by the revenue from holding the Q units of assets minus the cost of buying asset B, minus the cost (plus the revenue) from trading asset A and minus the sunk cost. A rational decision maker chooses q1A and q B to maximize this payoff. Formally, this writes: A A A max Π =pQ − pB q B − pA 1 q1 − p0 q0
q1A , q B
such that Q
=q0A
+
q1A
+q
(1) B
q1A ≥ − q0A and q B ≥ 0
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
A A B Two cases should be analyzed. First, if pB ≥ pA 1 , then q1 = Q − q0 and q = 0. Second, A A B = Q. The former case implies that if asset A is if pB < pA 1 , then q1 = −q0 and q
cheaper than asset B, then it is optimal for the decision maker to keep the initial units of asset A and buy more units of the same asset to complete the Q units. However, only the latter case allows for the identification of the sunk-cost fallacy because it predicts the total abandonment of the initial investment. Therefore, the experimental parameters are chosen to generate this situation. In addition, the re-sale price of asset A is chosen A to be below the initial purchase price, pA 1 < p0 , such that part of the initial investment
remains sunk. The experimental parameters are presented in Table A.1 for each of the treatment conditions described below.
3.2
Treatments and hypothesis
The experimental manipulation consists of three treatment conditions which differ with respect to the unit price pA 0 of the initial investment in asset A: one control (CT) group and two sunk-cost treatments. Considering two sunk-cost treatments, a low sunk cost (LSC) and a high sunk cost (HSC) respectively, the aim is to investigate whether the size of the sunk cost has any effect on the manifestation of the fallacy. The CT group received a free endowment of 20 units of asset A (pA 0 = 0) and 200 Experimental Euro (EE). The LSC subjects received cash endowments of 1000 EE and were offered to invest in q0A = 20 units of asset A for a unit price of pA 0 = 40 EE. The HSC subjects were endowed with 1400 EE and were offered to invest also in q0A = 20 units of asset A for a unit price of pA 0 = 60 EE. Hence, the investment constitutes a sizable amount of the initial cash endowment, which makes the sunk cost sufficiently salient. When offered to invest, all subjects in the treatment groups were informed that if invested, the 20 units of asset A will be redeemed at the end of the experiment for a unit price of p = 70 EE. Therefore, investment was always profitable, which was also emphasized in the experimental instructions. Note that following the investment,
9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
subjects in all treatments had the same financial position: 20 units of asset A and 200 EE, which is identical to the initial endowment in the CT group. This eliminates income effects across the experimental groups. The cash endowment of 200 EE was chosen to allow for the purchase of the extra 10 units of asset A to reach the 30 units, in case a subject chose to fully escalate on the initial course of action. With the experimental design and parameters described above, the sunk-cost fallacy hypothesis can be formulated as follows: Hypothesis 1. The subjects in the control group buy more units of asset B than the subjects in the LSC group, who, in turn, buy more units of asset B than those in the B > qB B HSC group: qCT LSC > qHSC .
As discussed in Section 1, the previous literature argued that cognitive dissonance and loss aversion are the leading explanations for the manifestation of the sunk-cost fallacy. In order to examine the role of the cognitive ability in the manifestation of the bias, the experimental design rules out these psychological explanations. To see this, first note that when faced with the decision to invest in asset A, the subjects of my experiment knew the exact consequences of the investment, i.e. the sure profit resulted from the difference between the redemption value and the purchase price. Since there is no deception in the experiment, the decision to invest is both ex ante and ex post optimal. Hence, in this experiment investing does not have negative consequences and, therefore, cannot create a need for self-justification. This rules out cognitive dissonance as an explanation for the sunk-cost bias in this experiment. Next, loss aversion cannot explain why subjects in this experiment escalate on the initial commitment, i.e. hold on asset A or even buy more units of asset A when a cheaper alternative is available. Note that the key condition for loss aversion to explain this escalation is that the decision-maker is in the domain of losses.2 Quite the opposite, the 2 Loss aversion predicts risk seeking in the domain of losses, due to the convexity of the psychological value associated with losses. This means that after an unsuccessful investment the decision-maker is willing to take further risks in the hope of an eventual gain.
10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
investment decision in my experiment is always profitable since p > pA 0 , for all treatment conditions. In fact, the decision to invest increases subjects’ financial positions, such that they are in the domain of gains. After ruling out the psychological factors explaining the sunk-cost bias, cognitive ability remains one factor that could play a role in its manifestation. To measure cognitive ability I use the CRT developed by Frederick (2005) and three mathematics questions selected from Benjamin et al. (2006). The CRT is a three-item test that requires reflection that leads to the correct answer, but at the same time calls for the temptation to give an intuitive, but wrong answer. The mathematics questions had the purpose of collecting information about subjects’ numeracy skills, particularly the ability to perform arithmetic operations and compare numbers. In line with the evidence from the psychology literature, the second hypothesis of this study can be formulate: Hypothesis 2. High cognitive-ability subjects are less prone to the sunk-cost fallacy than the low cognitive-ability subjects.
3.3
Procedure
Six experimental sessions (two per treatment) were run in the experimental laboratory of the School of Business, Economics and Social Sciences of the University of Hamburg in July 2014. A total of 138 subjects, recruited online through the hroot system (Bock et al., 2012), participated in the experiment. The participants were mostly undergraduate students from both social and natural sciences. No subject participated in more than one session. Each experimental session lasted approximately 45 minutes. The interface of the experiment was programmed in z-Tree (Fischbacher, 2007). Each experimental session consisted of two parts: the main sunk-cost experiment described above, and a cognitive ability test. Both parts of the experiment were monetaryincentivized. In particular, every correct answer in the cognitive ability test was worth 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
50 EE. The sum of the earnings was converted into Euros at the exchange rate of 200 EE for 1 Euro and paid out in private at the end of the session. Per subject earnings ranged between 5 and 13.90 Euro, with an average of 12.35 Euro. Before the experiment started, the instructions reproduced in Appendix C were read aloud. The general part of the instructions informed the subjects about the two parts of the experiment and the calculation of the final payoff. Subsequently, the instructions described the main sunk-cost experiment. These instructions were meant to provide an overview of the experiment and to familiarize the subjects with the sequence of decisions, without introducing the parameters. The subjects learned the specific parameters only on the experimental screens as proceeding through the sequence of decisions. Snapshots of the experimental screens are presented in Appendix D. Before the actual experiment, all subjects answered a set of control questions. In the case of an incorrect answer, the next screen provided the correct answer along with an explanation.3 The stages of the main sunk-cost experiment are as follows. After the initial endowment stage, the LSC and HSC groups where offered the possibility to invest in asset A (the Investment stage). The subjects who chose not to invest could keep their cash endowment and were asked to wait in their seats for the second part of the experiment.4 Those subjects who chose to invest proceeded to the Trade stage of the experiment. In the case of the control group, this stage followed immediately after the initial endowment. At the Trade stage, subjects in all groups could actively trade, i.e. buy or sell units of asset A and buy units of asset B under the constraint of holding exactly 30 units of asset A and/or B. Since there was no room for speculation in this experiment and in order to eliminate confusion, the experimental interface did not allow subjects to buy and sell units of asset A at the same time (see Figure D.4). Moreover, as there was only 3 The control questions verified subjects’ understanding of the exchange mechanism between the two assets, the rules of the trade and the fact that the two assets had the same redemption value. 4 Not only was it obvious that investment was more profitable than the outside option of keeping the endowment, but also the screen instructions at the Investment stage of the experiment stressed that one’s final payoffs cannot be lower than the initial cash endowment, regardless of further decisions.
12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
one round of trade, the subjects were asked to confirm their trading choice before this became effective (see Figure D.5). After the completion of the main sunk-cost experiment, all subjects present in the laboratory solved the CRT and three mathematics questions. The two types of questions were shuffled and presented to the subjects in the order shown in Appendix E, where questions 1, 4 and 6 constitute the CRT. The experiment ended with a final questionnaire in which all subjects answered demographic questions.
4
Results
The following analysis is based on the sample composed of all subjects in the control group and those in the treatment groups who invested in asset A and, thus, continued the experiment with further decisions.5 The summary statistics of the treatment groups are presented in Table A.2. The last column in the table shows the p-values of the Kruskal-Wallis equality-of-populations rank test, which tests whether at least two of the three treatment groups differ significantly from each other. Apart from slightly more males in the LSC group, the three treatment conditions do not exhibit statistically significant differences. Most importantly, they are the same with respect to the score of the cognitive ability quiz, both overall and on its two components, the CRT and the mathematics questions. The variable of interest for testing Hypothesis 1 is the number of units of asset B bought by the subjects. This measures the degree to which the subjects recognized the optimality of adopting the alternative course of action and acted accordingly. The possible values of this variable range from 0 units, indicating full escalation of commitment, to 30 units, meaning full abandonment of the initial course of action. Any value below 30 is interpreted as evidence of the sunk-cost fallacy and the lower this value, the higher 5
11 out of the 96 subjects who were offered to invest chose not to do so. A discussion of the potential selection effect due to these subjects is deferred to Section 5.
13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
the manifestation of the fallacy. Hence, in this experiment subjects can manifest the sunk-cost bias in a continuous manner.
4.1
Treatment effects
Figure B.1 presents the kernel density estimates of the distribution of the number of units of asset B bought by the experimental subjects in each of the treatment conditions. The upper tails of the distributions (11 to 30 units of asset B) correspond to the region in which subjects sold at least half of their holdings of asset A - the region of highest rational behavior. Consistent with the manifestation of the sunk-cost fallacy, this region features the lowest frequency among the HSC group (the dotted line) followed by the LSC (the dashed line), with the CT group (the continuous line) exhibiting the highest frequency. The lower tails of the distributions (0 to 10 units of asset B) correspond to the region in which the experimental subjects retained the entire 20 initial units of asset A to which they added more units of asset A towards the completion of the required 30 units of assets. This is the region of lowest rational behavior. Again, consistent with committing the sunk-cost fallacy, the lowest frequency of this type of behavior is manifested by the CT group, followed by the LSC and HSC groups, respectively. I further analyze the treatment differences using non-parametric analysis. Table A.3 shows the treatment averages and the standard errors for the units purchased from asset B, along with the number of units of asset A bought or sold.6 In both sunk-cost treatments the subjects recognized less the optimality of switching to the cheaper asset B than in the CT group. However, the difference in behavior is statistically significant only between the CT and the HSC group (p = .01).7 Nevertheless, a test of the joint B > qB B hypothesis that qCT LSC > qHSC , which is the hypothesis of this study, confirms the
existence of a trend across the treatments with respect to the number of units of asset 6
Note that while all these variables are measures of the sunk-cost fallacy, the latter two are mutually exclusive by design. 7 Unless otherwise specified, all the reported p-values are 1-sided, Mann-Whitney-Wilcoxon test.
14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
B bought (Jonckheere-Terpstra trend test, 1-sided p = .01). The above results are also confirmed by the regression analysis presented in Table A.4. Column (1) shows the treatment effects in which the control group is the baseline category. Thus, the constant shows the average number of units of asset B bought by the control group: 22 out of the maximum possible of 30 units. Indeed, the coefficients on LSC and HSC (the treatment effects) have signs consistent with the manifestation of the sunk-cost bias, but they are statistically significant only for the HSC group. A subject in the HSC treatment bought, on average, 5 to 6 units of asset B less than a subjects in the CT group. Hence, the sunk-cost hypothesis of this study is only partially confirmed: Result 1. Subjects’ behavior in the experiment is consistent with the manifestation of the sunk-cost fallacy, but this behavior is statistically significant only for the HSC group.
4.2
Cognitive ability
In order to investigate the causal relationship between cognitive ability and the sunkcost bias, I add the two measures of the cognitive ability (CRT and Math) as covariates to the regression from column (1) of Table A.4. Both measures are standardized. The results are presented in column (2). The treatment effects remain unchanged, both in magnitude and statistical significance. The coefficient on Math is both economically small and statistically insignificant, but the CRT test score is strongly predictive of behavior consistent with rationality.8 Specifically, a subject in the CT group with a CRT score of one standard deviation above the mean bought 4 more units of asset B as compared to a subject who had an average CRT score. 8 The reason for the lack of significance of the mathematics test is the very small variation with respect to this dimension of the cognitive ability (s.d. = 0.4, average 2.84). In fact, 99% of the subjects answered correctly at least two out of the three mathematics questions and no subject gave zero correct answers. By contrast, the proportion of correct answers for the CRT was only 45%, 60% and 68%, respectively, for each of the three questions comprising the test. These proportions are in line with those obtained by Oechssler et al. (2009) and Hoppe and Kusterer (2011).
15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Column (3) includes the variable Stock market which indicates familiarity with the stock-market trading and stock-market news, as reported by the subjects in the final questionnaire.9 Holding the treatment and the CRT test score constant, a subject who reported reading financial newspapers and following the stock market bought on average 5 more units of asset B than a subject who reported not having this habit. However, the inclusion of this variable did not affect the results on the treatment effects and the CRT score established in the regression from column (2). Next, since the mathematics score was not found significant, I further investigate the effect of the cognitive ability on the sunk-cost fallacy using only the CRT score. To this end I interact the treatment dummies with the standardized CRT score. The results are presented in column (4). Compared to the previous specifications, the treatment effects remain unchanged, both in magnitude and significance level. However, the CRT score has no effect on the manifestation of the sunk-cost fallacy, as the interaction coefficients are statistically insignificant. This is summarized in the following result: Result 2. Cognitive ability has no effect on the manifestation of the sunk-cost fallacy. Hence, Hypothesis 2 of this study is not confirmed. This result adds to the findings of Hoppe and Kusterer (2011) who could not confirm an effect of the CRT test on the endowment effect, and concluded that the CRT has predictive power only for biases that arise due to errors in reasoning and for which analytical skills are helpful in deriving the correct solution. As a final exercise I split the experimental sample into a high and a low-cognitive ability group, according to the number of correct answers in the CRT. Precisely, a score of 2 or 3 correct answers belongs to the high-cognitive-ability group (76 subjects) and a score of 0 or 1 correct answers belongs to the low-cognitive-ability group (51 subjects). Figure B.2 presents the treatment averages of the number of units of asset B by cognitive 9 While gender, field of study and years of education where also reported in the final questionnaire, they were not found significant in the regression.
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
ability group. For each of the treatment conditions, the high-cognitive-ability subjects bought significantly more units of asset B than the low-ability subjects (LSC: p = .06, HSC: p = .012, CT: p = .006). In fact, the average of the low-cognitive-ability CT group is below that of the high-cognitive-ability HSC group, though not statistically significant (p = .22). This indicates that the low-cognitive-ability subjects are affected by a status-quo bias. Therefore, I also conducted a non-parametric analysis of the treatment differences within the group of high-cognitive-ability subjects only. Statistically significant differences in the number of units of asset B are, indeed, confirmed between the CT group and the LSC group (p = .075) and between the CT group and the HSC group (p = .039), but not between the two sunk-cost group (p = .306). Hence, the following result can be established: Result 3. There is evidence of the sunk-cost fallacy within the group of high-cognitiveability subjects, which is, however, independent of the size of the sunk cost.
5
Discussion and Caveats
Although statistically significant evidence of the sunk-cost fallacy was found only for the HSC treatment, the sign of the treatment effect for the LSC group is also consistent with the fallacy. These treatment differences survived in a regression controlling for cognitive ability and socio-demographic variables. Moreover, the statistically significant test of a trend across the three experimental groups supports the sunk-cost fallacy hypothesis. These results are surprising in light of the obvious character and the simplicity of the experimental design, but suggest that sunk-cost fallacy could manifest itself even in the absence of the psychological roots usually discussed in the literature, i.e. loss aversion and cognitive dissonance. In this experiment, the sunk-cost fallacy was identified by the reluctance of giving up on the initial holdings of asset A for a lower price than the purchase price. An expla-
17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
nation for this reluctance can be adapted from the realization utility theory developed by Barberis and Xiong (2012). According to the authors, people feel a burst of pleasure when a gain is realized and a burst of pain when a loss is realized, right in the moment of its realization. In other words, people derive utility not only from consumption of goods and services, as economic models often assume, but also from the mere act of selling an asset at a gain, right in the moment of executing the sale.10 This line of argument seems to also explain the reluctance of the subjects to part with asset A when offered a price below the purchase price.11 There were significantly fewer subjects in the HSC treatment as compared to both the CT group and the LSC treatment who sold at least 1 unit of asset A (37% compared to 86% and 70% in the CT and LSC groups, respectively). Hence, despite recognizing the optimality of selling the inventories of asset A, the subjects in the sunk-cost treatments failed to do so completely and only chose to sell intermediate amounts of their inventories. This is consistent with subjects being willing to experience the pain from the realization of a loss only up to a point, i.e. the existence of a threshold for the realization utility. The surprising evidence of the sunk-cost fallacy is, however, weakened by the presence of a high degree of status-quo bias among the experimental subjects. Indeed, a postestimation coefficients test shows that the constant in the regressions from Table A.4 is significantly different from 30, the number of units corresponding to rational behavior. The regressions from Table A.4 suggest that the status-quo bias is attributed to cognitive ability. The strong status-quo bias exhibited by the group of low-cognitive-ability subjects (see Figure B.2), which represents about 40% of the experimental sample, partially explains the low treatment differences between the CT group and the sunk-cost groups. Therefore, I conjecture that had the status-quo bias been less severe, the sunk-cost bias 10
This theory was confirmed by Frydman et al. (2012) using an experimental stock market in which they scanned subjects’ brain activity at the moment of submitting their trading decisions. 11 Realization utility has also been proven suitable for explaining the closely related, but different, disposition effect (Barberis and Xiong, 2012). While the disposition effect explains the greater propensity to selling ”winning” stocks rather than ”losing” stocks, the sunk-cost fallacy is a phenomenon that accounts for the size of the loss.
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
would have been more pronounced. Status-quo bias was also observed at the Investment stage of the experiment. From the total of 96 subjects who were offered to invest (the sunk-cost treatments), 3 subjects in the LSC group and 8 subjects in the HSC group chose to keep the initial cash endowment. This choice occurred despite the fact that the experimental parameters guaranteed that investing was always profitable and despite the experimental instructions emphasizing the benefit of investing. This situation raises worries of self-selection bias.12 However, the decision to invest in asset A is, in this experiment, solely motivated by the sure profit resulting from the difference between the purchase price and the redemption value. Hence, investing as opposed to not investing is the rational payoffmaximizing choice in both sunk-cost treatments and it is therefore, not driven by selfselection. Moreover, those subjects who chose not to invest were asked to remain in the laboratory for the second part of the experiment, which also excludes the opportunity cost of time as an explain for their decision. It is, nevertheless important to asses the extent to which the self-selection could affect the results. For this, note that cognitive ability is the main difference (p = .04) between the subjects who invested and the 11 attriters. This difference is driven by the CRT (p = .02) and it is also confirmed by the Probit regression presented in Table A.5 (column (1)). Apart from the CRT score, the decision to invest is not explained by any of the co-variates collected via the final questionnaire (column (2)). Therefore, the refusal to engage in the cognitive effort entailed by the continuation of the experiment appears to be the most pertinent explanation for these subjects’ attrition. This is, in turn, predictive of status-quo bias. Moreover, the irrational behavior they exhibited at the Investment stage is an indicator of potential further irrational behavior with respect to sunk costs. Therefore, had they been forced to invest the 11 subjects would have, in fact, increased the gap between the CT group and the two treatment groups, thus 12
Self-selection is an issue in identifying the sunk-cost fallacy because those subjects who choose to buy an asset do so because they are also more likely to use it.
19
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
strengthening the evidence for sunk-cost fallacy.
6
Conclusions
This paper presents a laboratory experiment to test for the manifestation of the sunkcost fallacy. The experimental manipulation consists of two groups which differ with respect to the size of the sunk cost, low and high, and an additional control group which incurs no sunk cost. Despite the obviousness of the optimal course of action and the absence of the psychological drivers of the bias, the data shows behavior consistent with the manifestation of the sunk-cost fallacy. However, this behavior is statistically significant only for the high-sunk cost treatment. This result survives controlling for other covariates in a regression analysis. Therefore, the first result of this study is that sunk-cost fallacy may manifest itself even in the absence of the typical psychological mechanisms that explain it. The second goal of this experiment was to understand the relationship between cognitive ability and sunk-cost fallacy. First, the CRT score was found to account for the status quo bias, but had no effect on the sunk-cost bias. Second, non-parametric analysis of treatment differences confirms the sunk-cost fallacy hypothesis for the group of high-cognitive-ability subject, who were also less status-quo biased.
Acknowledgments This research was funded by Hamburg University Cluster of Excellence ”Integrated Climate System Analysis and Prediction” (CliSAP). The funding source has no involvement in the collection, analysis and interpretation of the data or in the writing of the paper.
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
References Arkes, H. R. and Blumer, C. (1985), ‘The psychology of sunk cost’, Organizational Behavior and Human Decision Processes 35(1), 124–140. Ashraf, N., Berry, J. and Shapiro, J. M. (2010), ‘Can higher prices stimulate product use? Evidence from a field experiment in Zambia’, American Economic Review 100, 2383– 2413. Barberis, N. and Xiong, W. (2012), ‘Realization utility’, Journal of Financial Economics 104, 251–271. Bazerman, M. H., Giuliano, T. and Appelman, A. (1984), ‘Escalation of commitment in individual and group decision making’, Organizational Behavior and Human Performance 33(2), 141–152. Benjamin, D. J., Brown, S. A. and Shapiro, J. M. (2006), ‘Who is ’Behavioral’ ? Cognitive ability and anomalous preferences’, Working paper, Harvard University . Bock, O., Nicklisch, A. and Baetge, I. (2012), ‘hroot: Hamburg registration and organization online tool.’, WiSo-HH Working Paper Series No. 1. . Bruine de Bruin, W., Parker, A. M. and Fischhoff, B. (2007), ‘Individual differences in adult decision-making competence’, Journal of Personality and Social Psychology 92(5), 938–956. Fischbacher, U. (2007), ‘z-Tree: Zurich Toolbox for Ready-made Economic Experiments’, Experimental Economics 10(2), 171–178. Frederick, S. (2005), ‘Cognitive Reflection and Decision Making’, Journal of Economic Perspectives 19(4), 25–42. Friedman, D., Pommerenke, K., Lukose, R., Milam, G. and Huberman, B. A. (2007), ‘Searching for the sunk cost fallacy’, Experimental Economics 10(1), 79–104. Frydman, C., Barberis, N., Camerer, C., Bossaerts, P. and Rangel, A. (2012), ‘Using neural data to test a theory of investor behavior: An application to realization utility’, Yale ICF Working Paper No. 12-30 . Harrison, G. W. and List, J. A. (2004), ‘Field Experiments’, Journal of Economic Literature XLII, 1009–1055. Hoppe, E. I. and Kusterer, D. J. (2011), ‘Behavioral biases and cognitive reflection’, Economic Letters 110(2), 97–100. Kahneman, D. and Tversky, A. (1979), ‘Prospect theory: An analysis of decisions under risk’, Econometrica 47(2), 263–291.
21
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Larrick, R. P., Nisbett, R. E. and Morgan, J. N. (1993), ‘Who uses the cost-benefit rules of choice? implication for the normative statues of microeconomics theory’, Organizational Behavior and Human Decision Processes 56, 331–347. Oechssler, J., Roider, A. and Schmitz, P. W. (2009), ‘Cognitive abilities and behavioral biases’, Journal of Economic Behavior and Organization 72, 147–152. Parker, A. M. and Fischhoff, B. (2005), ‘Decision-making competence: External validation through an individual-differences approach’, Journal of Behavioral Decision Making 18, 1–27. Phillips, Q. R., Battalio, R. C. and Kogut, C. A. (1991), ‘Sunk and opportunity costs in valuation and bidding’, Southern Economic Journal 58(1), 112–128. Stanovich, K. E. and West, R. F. (2008), ‘On the relative independence of thinking biases and cognitive ability’, Journal of Personality and Social Psychology 94(4), 672–695. Staw, B. M. (1976), ‘Knee-deep in the big muddy: A study of escalating commitment to a chosen course of action’, Organizational Behavior and Human Performance 16, 27–44. Strough, J., Mehta, C. M., McFall, J. P. and Schuller, K. L. (2008), ‘Are older adults less subject to the sunk-cost fallacy than younger adults?’, Association for Psychological Science 19(7), 650–652. Tan, H.-T. and Yates, J. F. (1995), ‘Sunk cost effects: The influences of instructions and future return estimates’, Organizational Behavior and Human Decision Processes 63(3), 311–319. Thaler, R. (1980), ‘Toward a positive theory of consumer choice’, Journal of Economic Behavior and Organization 1, 39–60. Toplak, M. E., West, R. F. and Stanovich, K. E. (2011), ‘The cognitive reflection test as a predictor of performance on heuristics-and-biases tasks’, Memory and Cognition 39, 1275–1289.
22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Appendix A
Tables Table A.1: Experimental parameters Treatment pA 0 (EE) Initial cash (EE) A0 (units) Q (units) pA 1 (EE) pB (EE) p (EE)
CT LSC HSC 0 40 60 200 1000 1400 20 0 0 30 30 30 uniform in [16, 20] 10 10 10 70 70 70
Table A.2: Descriptive statistics: means by treatment Treatment
LSC 43 .58 (.076)
HSC 42 .33 (.073)
p-value
N Males
Control 42 .45 (.077)
Cognitive score
4.62 (.187)
4.65 (.182)
4.45 (.174)
.64
CRT score
1.76 (.163)
1.79 (.154)
1.64 (.155)
.75
Math score
2.85 (.055)
2.86 (.063)
2.81 (.061)
.66
Behav. Econ.
.17 (.058)
.16 (.057)
.12 (0.50)
.79
Stock market
.29 (.070)
.19 (.060)
.17 (.058)
.36
.07
Note: Standard errors in parentheses. “Behav. Econ.” and “Stock market” are self-reported variables indicating whether the subject attended a Behavioral Economics course and reads financial newspapers or follows the stock market, respectively. p-value is reported from the Kruksal-Wallis equality-of-populations rank test.
23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Table A.3: Decision variables (averages)
Control LSC HSC
N 42 43 42
Purchases of Asset B (1) 21.83 (1.49) 19.18 (1.59) 16.26 (1.67)
Sales of Asset A (2) 12.43 (1.31) 10.47 (1.29) 8.09 (1.31)
Purchases of Asset A (3) .59 (.35) 1.28 (.50) 1.83 (.57)
Note: Standard errors in parentheses
Table A.4: GLS regression results Dependent variable:
Units of asset B (2) (3)
(1) Constant LSC HSC
21.956 (1.479)*** -2.075 (2.154) -5.635 (2.229)**
21.494 (1.408)*** -2.254 (1.985) -5.058 (2.060)** 4.158 (0.872)*** 0.745 (0.844)
20.063 (1.480)*** -1.905 (1.98) -4.432 (2.009)** 4.336 (0.860)*** 0.654 (0.838) 4.815 (2.013)**
127
127
127
CRT Math Stock market LSC X CRT HSC X CRT N
(4) 20.186 (1.488)*** -2.052 (2.008) -4.509 (2.016)** 3.331 (1.377)** 0.703 (0.844) 4.772 (2.047)** 1.199 (2.038) 1.997 (2.03) 127
Note: Heteroskedastic standard errors in parenthesis. The control group is the baseline category. ”CRT” and ”Math” are the standardized scores for the CRT and the numeracy questions, respectively. ”Stock market”is a dummy of whether the subject reported to read financial newspapers or follow the stock market. ***p < .01, **p < .05, *p < .10
24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Table A.5: The investment decision Dependent variable: CRT score Math score
Invest (1 if invested, 0 if not invested) (1) 0.404 (0.162)** -0.239 (0.408)
Male (1 if male, 0 if female) Read financial newspapers Trimester of study Difficulty of the experimental tasks Constant Number of observations
1.314 (1.163) 96
(2) 0.334 (0.179)* -0.251 (0.434) 0.264 (0.391) 0.354 (0.483) 0.117 (0.147) -0.199 (0.243) 1.405 (1.415) 96
Note: Robust standard errors in parentheses. *p < 0.1; **p < 0.05; ***p < 0.01.
25
Figures
Density
0
.01
.02
.03
.04
Appendix B
0
10
20
30
Units of Asset B CT
LSC
HSC
Figure B.1: Distribution of units bought from Asset B
High−cognitive ability group
25
Low−cognitive ability group
24.2
21.25
15
15.33
10
12.16
5
Units of asset B (means)
20
19.65 18.35
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
CT
LSC
HSC
CT
LSC
HSC
Figure B.2: Average units of Asset B by cognitive ability groups
26
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Appendix C
Experimental Instruction (Translation from German) Welcome to the Experiment!
This is an experiment in the economics of decision making. It is very important that you read these instructions carefully. If you follow the instructions and make good decisions, you will earn a considerable amount of money. All earnings on your computer screen are in Experimental Euro (EE) and they will be converted in real euro at the exchange rate: 200 EE = 1 euro. The experimental session consists of two independent parts. Your decisions and earnings from one part do not affect your decisions and earnings of the other part. Everyone in this room will participate in both parts of the experiment. You will first receive instructions for Part 1 and then make your decision at the computer terminal. After this, Part 1 is done. Next, you will receive instructions for Part 2 and again make your decision for Part 2. However, each part will start only after everyone has made their decisions for the current part. Your final earnings will be the sum of your earnings from both parts and they will be privately paid to you in cash at the end of the session. After both parts of the experiment are completed, you will be asked to answer some general questions. Important rules: 1. From my side: NO DECEPTION. I promise that this experiment will be conducted exactly as described in these instructions. This is the rule in economics experiments. Without this rule the results of the research cannot be published. 2. From your side: NO COMMUNICATION. This is an experiment on individual decision making. Your earnings in this experiment are NOT affected by the decisions of any other participant and your decisions do NOT affect the earnings of any other participant in this experiment. Therefore, please do not communicate with other participants during this experiment and take your decisions individually. If you have any question during the experiment, please raise your hand and you will receive assistance. Part 1: General Instructions In this part of the experimental session there are two types of assets, A and B. Your task will be to collect a required number of units of assets, in any combination of A and B that you wish. This means that you can have only asset A or only asset B, or any other combination of the two assets which gives you exactly the required total number of units of assets. You will learn the required number of units you must collect during the experiment. The stages of the experiment proceed as follows. • In the first stage of the experiment you will be endowed with an amount of cash in EE [Control condition: and a number of units of asset A. This number will be lower than the required number of units you must collect.]. [Sunk-cost conditions: You will be offered the possibility to invest part of your cash endowment in order to purchase a certain number of units of asset A. This number will be lower than the required number of units you must collect. If you decide to invest, you will continue the experiment with further decisions. If you decide not to invest, you will keep your cash endowment, but you will be asked to wait quietly in your seat for the next part of the experiment.]
27
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
• [Sunk-cost conditions: If you have purchased asset A in the first stage,] In the next stage, a market will open in which you will have the possibility to trade, i.e. to buy or sell asset A and to buy asset B. You will learn the prices of asset A and asset B once the market opens. At this stage you will see a table like the one below:
Asset A
Asset B
Buy Sell In column ’Asset A’ you can decide how many units of asset A to buy or how many units of asset A to sell by entering a number in the corresponding box. Note that you cannot buy and sell asset A at the same time. Please leave empty or enter 0 in the box you do not want to use. If you want to neither buy nor sell asset A (that is, keep all units you currently hold), please leave empty or enter 0 in both boxes. If you choose to sell, you cannot sell more units of asset A than you hold in your account. If you choose to buy, you cannot buy more units of asset A than the number of units you need in order to have the required total number of units of assets. In column ’Asset B’ you only have the option to buy. Note that you cannot buy more units of asset B than the number of units you need in order to have the required total number of units of assets. If you do not want to buy any unit of asset B, please leave the box empty or enter 0. Regardless how you decide to trade, please make sure that the total number of units of assets you hold at the end equals the required total number of units of assets. Note that regardless of the type of asset you want to buy, you will always have enough cash in your account to buy as many units of assets as you want and are allowed to. • As a result of your trading decision, your account will contain a final amount of cash endowment and the required total number of units of assets. At the end of the session, the experimenter will buy all your collected units at the same redemption value per unit, regardless of the type of assets you hold. Your payoff for this part of the experiment will be calculated as: Payoff = [final cash endowment] + [redemption value]*[required total number of units]. Before the experiment begins, please answer the following questions on your screen to make sure you have a good understanding of the process and the decisions in the experiment.
28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Appendix D
Experimental Screens (Translation from German)
Figure D.1: Initial position screen
Figure D.2: Investment screen
29
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Figure D.3: Investment confirmation screen
Figure D.4: Trade screen
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Figure D.5: Trade screen
Figure D.6: Payoff screen
31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Appendix E
The Cognitive Quiz
Question 1: A bat and a ball cost 1.10 euro in total. The bat costs 1.00 euro more than the ball. How much euro does the ball cost? Question 2: Which number is larger? (A) 250 (B) (800 × 1/2) + (0 × 1/2) Question 3: y and z are two numbers with the following properties: If we subtract two from y, z is obtained and by multiplying y and z, we obtain 48. Which of the following CANNOT be NEITHER y NOR z? (A) 6 (B) 8 (C) 12 (D) -6 (E) -8 Question 4: If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets (in minutes)? Question 5: Which number is larger? (A) 250 (B) (200 × 1/2) + (0 × 1/2) Question 6: On a lake there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake (in days)?
32
.02 .01 0
Density
.03
.04
Figure
0
10
20
30
Units of Asset B CT
LSC
HSC
Figure
25
Low−cognitive ability group
High−cognitive ability group 24.2
21.25
18.35
15
15.33
5
10
12.16
0
Units of asset B (means)
20
19.65
CT
LSC
HSC
CT
LSC
HSC
Figure Click here to download high resolution image
Figure Click here to download high resolution image
Figure Click here to download high resolution image
Figure Click here to download high resolution image
Figure Click here to download high resolution image
Figure Click here to download high resolution image
Figure Click here to download high resolution image
Bib file Click here to download Supplementary Material: papers_exp.bib
LaTeX Source Files Click here to download LaTeX Source Files: JEP_20150906.tex
