Nội dung

Journal of Economic Behavior & Organization Vol. xxx (2004) xxx–xxx Aging and decision making: a comparison between neurologically healthy elderly and young individuals Stephanie Kovalchika,1 , Colin F. Camererb,2 , David M. Gretherb,∗ , Charles R. Plottb,3 , John M. Allmanc,4 a b c California Institute of Technology, MSC 323, Pasadena, CA 91125, USA California Institute of Technology, MSC 228-77, Pasadena, CA 91125, USA California Institute of Technology, MSC 216-76, Pasadena, CA 91125, USA Received 17 March 2003; accepted 15 December 2003 Abstract We report the results of experiments on economic decisions with two populations, one of healthy elderly individuals (average age 82) and one of younger students (average age 20). We examine confidence, decisions under uncertainty, differences between willingness to pay and willingness to accept and the theory of mind (strategic thinking). Our findings indicate that the older adults’ decision behavior is similar to that of young adults, contrary to the notion that economic decision making is impaired with age. Moreover, some of the demonstrated decision behaviors suggest that the elderly individuals are less biased than the younger individuals. © 2004 Elsevier B.V. All rights reserved. JEL classification: D00; D80; D81 Keywords: Age; Overconfidence; Willingness to pay/accept; Endowment effect; Theory of mind; Game theory; Risk-taking ∗ Corresponding author. Tel.: +1 626 395 4068; fax: +1 626 405 9841. E-mail addresses: stephk@caltech.edul (S. Kovalchik), camerer@hss.caltech.edu (C.F. Camerer), dmg@hss.caltech.edu (D.M. Grether), cplott@hss.caltech.edu (C.R. Plott), cebus@caltech.edu (J.M. Allman). 1 Tel.: +1 626 395 6800; fax: +1 626 795 1547. 2 Tel.: +1 626 395 4054; fax: +1 626 405 9841. 3 Tel.: +1 626 395 4209; fax: +1 626 793 8580. 4 Tel.: +1 626 395 6805. 0167-2681/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jebo.2003.12.001 2 S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx 1. Overview Though it is widely recognized that the population of the United States is aging, much of our current understanding in the field of individual decision making is based on data from student populations. While this could be a consequence of subject availability, it may reflect a common though largely unsubstantiated belief that decision making ability declines with aging (Peters et al., 2000). Many older individuals are productive and intellectually viable throughout their lives. Still, others are vulnerable to dementia and neurodegenerative illnesses, such as Alzheimer’s disease. Our objective in this study is to begin to characterize the relationship between economic decision behavior and aging. How well older people make economic decisions is an important issue for social policy. Since wealth tends to accumulate over one’s lifetime, a large portion is in the hands of older people. Both long-term trends (increased longevity) and short-term trends (baby booms) mean that increasing proportions of the population are older and retired. Also, older people are more likely to vote than young people are, so they may have disproportionate political influence. It is conceivable that our scientific model of economic decision making, so heavily rooted in studies of 20-year-old students, is a misleading guide to the behavior of older people. We studied four types of decisions with a potential for age effects. One feature of wisdom, which presumably is acquired over a lifetime, is meta-knowledge, accurately knowing one’s own knowledge and abilities. We assessed this through self-reported confidence on answers to trivia questions. A common stereotype of older people is that they are “conservative, dislike taking risk, and are set in their ways”. We tested this stereotype using choices over monetary gambles similar to those performed by psychologists and biologists; the monetary gambles include incomplete and complete information designs (i.e., where probabilities are known ex ante or unknown). A third group of experiments explored possible differences in willingness to pay and willingness to accept. In these experiments, the choices involved valuations of everyday objects (e.g. a coffee mug). It has been suggested that observed differences are due to an asymmetry of preferences between losses and gains that might be exacerbated by age. Finally, both younger and older subjects participated in beauty contest games, in which strategic thinking plays a central role. In each case, the experiments were taken from the literature allowing us to focus on age differences rather than on theories behind the experiments. 2. Subject population and general experimental design We interviewed two age groups: a young population (ages 18–26, 51 percent female) and an elderly population (ages 70–95, 70 percent female). The older subjects (N = 50) serve as controls for the Alzheimer’s Disease Research Center at the University of Southern California. Based on annual cognitive and behavioral testing, the older individuals are considered neurologically healthy having no history of dementia or mental illness. The student population (N = 51) consisted of healthy undergraduates from a junior college near California Institute of Technology. The younger participants have between 12 and 16 years of formal education. The older population is highly educated relative to their age group, 78 S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx 3 percent have more than 12 years of education and 60 percent have 16 or more years. As other populations of older adults (e.g. individuals with Parkinson disease or other ailments or people in assisted living arrangements) may be more difficult to study, we chose a population of healthy high-functioning individuals for our first attempt to study decision making in the elderly. Each subject completed an individually administered interview, involving a written questionnaire and several interactive tasks. On average, subjects of both populations took 50 min to complete the interview. For all areas of the investigation involving monetary rewards, real cash was used. This method of collecting data is expensive, but for many populations of older adults living outside of retirement communities, individual interviews may be a necessary burden. The same method was used for all subjects to avoid confounding age with the method of data acquisition. 3. Confidence Research suggests that non-expert individuals are typically overconfident; they overestimate the quality of their own abilities or knowledge (Svenson, 1981; Weinstein, 1980) and state extreme probabilities more often than they should. Work in economic theory, particularly with business-related forecasting, has provided further support for this behavioral phenomenon (Camerer and Lovallo, 1999). The reasons for overconfidence when answering trivia questions are a subject of intense debate among decision theorists (Ayton and McClelland, 1997). Three prominent explanations have emerged. One argument is that it is an illusion created by asymmetrically misleading items in investigation methods (Juslin, 1994; Gigerenzer et al., 1991). For example, one question used was: which city is farther north Rome or New York? Most Americans claim that the correct answer is New York, and are quite confident, even though that answer is incorrect. Soll (1996) found that overconfidence persists even when questions are sampled randomly. Some contend that overconfidence results from subjects basing their answers on a reasonable probability but responding with error, which biases their reported probabilities in the direction of overconfidence (Erev et al., 1994). Wallsten and Gonzales-Vallejo (1994) found overconfidence after adjusting for this source of bias. A third explanation is that overconfidence is a cognitive bias due to anchoring on an intuitive answer or snap judgment and adjusting insufficiently for the ways in which the answer could be wrong (Kahneman and Tversky, 1996). An important qualification is that many expert populations such as weather forecasters (Murphy and Winkler, 1984), blackjack dealers and others (Camerer, 1995, pp. 590–592), and highly experienced subjects in repeated games do not show overconfidence in their fields of expertise. We investigated confidence by providing subjects with 20 trivia questions on diverse subjects (appendices will be available on the JEBO website). Each subject answered the same set of 20 general knowledge questions. All questions had two possible answers. Subjects were instructed to select an answer and then provide a confidence assessment (50, 60, 70, 80, 90 or 100 percent) of their choice. Older subjects did somewhat better, answering 74.1 percent of the questions correctly, while 66.1 percent of answers given by the younger subjects were correct. 4 S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx Fig. 1. Proportion of correct responses (±standard error of mean (S.E.M.)) for a given confidence level out of the total responses with that confidence. The width of each bubble reflects the percentage of responses that were given at each confidence level out of the total responses. Exact percentages for response distribution are labeled next to bubbles for each population. * The hypothesis that the proportions correct are the same is rejected at P < 0.05. ** The hypothesis that the proportions choosing this response are the same is rejected at P < 0.05. For both groups we combined all the answers in which subjects gave the same confidence assessment and calculated how often they were right. Good calibration means that the fraction of correct answers should be about equal to the stated confidence level. For example, on questions where subjects said they were 80 percent confident, they should be right about 80 percent of time. If subjects are well calibrated, then a graph of the percent correct against the confidence levels should lie near a 45◦ line. Points below the line would represent overconfidence and points above would show underconfidence. Fig. 1 contains these scatters for both older and younger subjects, along with standard errors and significance tests for differences in accuracy and in distribution of responses. Both groups of subjects display overconfidence at some levels, and neither group shows underconfidence at any level. Older subjects’ assessments are significantly more accurate at 60 percent (P < 0.05) and 70 percent (P < 0.01) reported degrees of confidence. The older subjects do exhibit overconfidence when reporting confidence levels of 80 and 90 percent (17 percent of their total responses), but younger subjects are overconfident at all the intermediate levels of reported confidence (48 percent of their total responses). One interpretation of these results is that older subjects have learned through experience to temper their overconfidence and, thus, look more like experts. The groups also differed in their response distributions. The younger subjects spread out their responses across the confidence levels: half of their selections were evenly distributed among the intermediate confidence levels. In the older subjects, the majority of the responses were given with either 100 or 50 percent confidence (in calibration terms, their assessments had “higher resolution”). While older subjects reported a confidence of S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx 5 100 percent significantly more often than the younger subjects (P < 0.025), they made substantially fewer selections with 60–80 percent confidence (P < 0.05 for each group). The percentage of correct responses when reporting 100 percent confidence was about the same for the two groups (94 percent correct for the older population and 92 percent for the younger subjects). 4. Decision making under uncertainty Two gambling tasks are employed. The first task is a modified version of the card-deck gambling task of Bechara et al. (2000) that has been used extensively in the biology and psychology literature. In the modified gambling task, subjects selected cards from one of two decks to earn cash. The cards were pre-organized so that one deck (A) had an overall loss of $2.50 every 10 cards and the other deck (B) had an overall gain of $2.50 every 10 cards. All the cards in deck A gave $1.00 on every turn but were occasionally accompanied with losses, $7.50 for example (for a net loss of $6.50). The other deck B gave a smaller gain for each card, +$0.50 but had smaller occasional losses. Subjects did not know the composition of the decks (given in Appendix B). Subjects were instructed to select the top card of one of the decks, and that they could switch between decks at any time during the task. Each subject selected 50 cards one at a time, but was not informed in advance about the total number of draws. Deck A has a lower mean payoff and higher variance than deck B. Since subjects do not know the composition of the decks, there is no optimal strategy. In the neuroscience literature the choice of deck A is treated as a mistake. Bechara et al. conducted their gambling task with a population of healthy adults and a population of individuals with damage to the ventromedial prefrontal cortex (VM). They found that the VM patients, unlike the healthy adults, did not gradually shift their choices to the more advantageous deck B. Other studies employing Bechara’s design have found that individuals with damaged orbitofrontal cortex have an impaired ability at adapting their deck preferences to deck B in comparison to control subjects (Damasio, 1994). Denburg et al. (1999) administered this task with a population of healthy older adults and argued that the older individuals behave similarly to the frontal-lobe-damaged subjects. Our results do not confirm this finding. Consistent with the results of the Bechara study, our subjects gradually concentrated their choices on deck B (Fig. 2). The beginning phase of the task was an exploratory period in which both populations sampled each deck equally. For the next 20 draws subjects shifted towards deck B drawing on average 8 of the 20 cards from deck A. In the final 10 draws both groups largely abandoned deck A: on average the younger subjects chose deck A two times of 10 and the older subjects chose deck A three times of 10. In summary both populations appear to have adapted the same way to the payoffs. In our second gambling experiment, subjects were asked to make six choices. For each choice subjects had to select one of two decks of 10 cards. Unlike the Bechara et al. experiment, subjects saw the payoffs from each of the 10 cards in the pair of decks before making their selection. Once they decided which deck they wanted, the 10 cards were 6 S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx Fig. 2. The plot indicates the results for the median number of cards selected from deck A, the deck with high variance and negative expected value (−$2.50 per interval). Selections from deck B would simply be 10 minus those of deck A. Subjects with no switching behavior were removed from the data pool. The difference in the number of choices in the final 10 draws is not significant (P-value 0.14). shuffled and the subjects selected one card. In all six choices one of the two decks had a positive mean payoff, and the other deck had a non-positive payoff. The deck with the positive average payoff had a smaller variance. A total of six choices were given to 36 of the older subjects (this task was added after the first 14 interviews were completed) and 51 of the student subjects. The decks used are shown in Appendix B. We do not see significant differences in behavior of the younger and older subjects. Somewhat surprisingly subjects more often than not chose the lower average payoff decks. Among older subjects, 58 percent chose the lower payoff decks on four or more of the six choices, while 59 percent of the younger subjects did so (Table 1 and Fig. 3). The proportions were similar across age groups for each of the six different deck pairs. Older women were significantly more likely than older men to choose the lower mean, higher variance decks (Fig. 4). Of the 54 choices made by the older male subjects, 17 were of the lower average payoff decks while the older females chose those decks on 96 of their 162 choices. This is the only significant gender effect we found in any of the tasks studied. We tested whether there were any order effects of previous winning or losing draws, but found no significant effects. Table 1 Percentage of subjects preferring low payoff deck Lotteries Older subjects Young subjects (N = 51) 1 2 3 4 5 6 64 (N = 50) 55 56 (N = 50) 67 66 (N = 50) 63 53 (N = 36) 73 53 (N = 36) 61 36 (N = 36) 47 The table shows the percentage of subjects in each of the populations who chose the lower average payoff deck. Percentages are shown for each of the six lotteries. For each lottery, participants were given the option to randomly select one card from one of two decks, composed of 10 cards of varying monetary reward/loss. In each lottery, one deck had zero or negative expected value and one had positive expected value and smaller variance. Appendix B shows the exact deck compositions that were shown to participants. S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx 7 Fig. 3. Each subject was given six choices. The plot indicates the percentage of subjects against the number of times the deck with a lower average payoff and larger variance was chosen out of the six choices. * Mann–Whitney, P < 0.10. Fig. 4. Choices by elderly men and women. The plot indicates the percentage of subjects against the number of times the lower payoff, higher variance deck was chosen out of the six choices. Mann–Whitney test showed the difference is significant (P < 0.01). 5. Willingness to pay/willingness to accept asymmetry Observed differences between stated willingness to pay (WTP) for an item and willingness to accept payment (WTA) for the same item have been a subject of extensive research. In previous investigations of this behavior, individuals have been divided into two groups: sellers and buyers. The sellers are given an item and told that they are its owners. They are then asked to indicate the minimum they would accept to sell the item, the WTA. Buyers are shown the same item and are asked to indicate the maximum they would be willing to pay for the item, the WTP. The consistent tendency for the WTA to be greater than the WTP is the asymmetry that has attracted the attention of economists. 8 S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx The observed differences between willingness to pay and willingness to accept have been labeled an “endowment effect”, intimating that the phenomena is due to loss-aversion over the domain of choices (Thaler, 1980; Tversky and Kahneman, 1991). The theoretical idea is that an individual who owns a good anticipates a loss from the sale and, thus requires a higher payoff than the individual would pay to acquire the good if it were not owned (Kahneman et al., 1990, 1991; Knetsch, 1989; Knetsch and Sinden, 1984). In other words, the willingness to accept (WTA) exceeds the willingness to pay (WTP). Some recent experiments support a claim that the observed differences between willingness to pay and willingness to accept are related to experimental procedures and have nothing to do with preference asymmetries (Plott and Zeiler, 2003) or are eliminated by trading experience (List, 2004). Older people are often presumed to be more conservative and more likely to avoid risk. If this is true, then it would seem natural to expect loss avoidance to be stronger in the older populations. Alternatively, it may be that older people having experienced the loss of many everyday items have learned that such losses are not that serious and do not show an endowment effect. In either event, by testing for an asymmetry between WTA and WTP using the procedures of Plott and Zeiler to avoid confusion, we are able to test endowment effect theory and to investigate possible preference differences between young and old under circumstances that could exacerbate these differences if endowment theory is correct. In our experiments, subjects were interviewed one at a time and each subject performed in one of two roles: seller or buyer. For each round, sellers were told that they own the item in front of them (buyers were shown the item, but not told that they own it). Each subject was then asked to report his/her value for the item. Each seller was instructed to offer the minimum they would accept to give up the item, while buyers were instructed to offer the maximum they would be willing to pay for the item. The subject’s offer was then compared to a fixed offer. The fixed offer was randomly determined and not based on the actual value of the item (Becker et al., 1964). For sellers, if WTA was less than or equal to the random offer, they gave up their item and received the amount of the random offer. If the WTA was greater, they kept the item. For buyers, if the WTP was greater than or equal to the random offer, they purchased the item for the amount of the random offer. If the WTP was less than the amount of the random offer, they kept their money. Subjects were informed that the fixed offers had been determined by a random method that would be revealed at the end of the interview (Plott and Zeiler, 2003). There were a total of three rounds in the task. The first two were hypothetical and the last was the actual round. A pen and a picture frame were used in the hypothetical situations, and a coffee mug was used for the actual situation. Only the actual round had a real payoff, either the mug or the cash value of the fixed offer. On the third round when each subject had determined their offer, they wrote it on an index card and place it inside an envelope (both items were provided) along with the amount of the WTA or WTP. Each subject was informed that the interviewer would not know his/her offer or outcome. This was done to ensure that the subject’s offer was anonymous and not influenced by the presence of the interviewer. The subjects subsequently received either the mug or the return of their money in the mail. S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx 9 Table 2 Statistics for WTA/WTP [mean, median (S.D.)] Round Older WTA (N = 25) Older WTP (N = 25) Younger WTA (N = 26) Younger WTP (N = 25) Hypothetical 1 (pen) Hypothetical 2 (frame) Actual (mug) 8.84, 3.5 (17.82) 5.13, 3.95 (6.12) 2.2, 1.5 (3.2) 1.62, 1.25 (1.12) 6.61, 7 (3.74) 9.34, 6.5 (6.21) 7.46, 5 (8.63) 4.98, 4 (3.59) 2.48, 2.5 (1.7) 3.25, 2 (3.04) 3.88, 2.38 (4.88) 2.24, 2 (1.75) The data shows the mean, median (standard deviation) for the WTAs (seller offers) and WTPs (buyer offers). Data for each of the three rounds and the items used are given. Only the actual round used real cash. For the actual round the difference between the WTA and WTP prices within each group is not significant (P > 0.25). The data exhibit no significant differences between WTA and WTP in either group (Table 2). Thus, for these findings, endowment effect theory must be rejected. We also conclude that there is no significant difference between the young and the old. Excluding the difference of reference states, the experimental design was identical for both the seller and buyer groups. The median seller price is higher than the median buying price for each sample. In the actual round, the coffee cup round, the median offer price for the sellers in the older population is $2.50, and the median buyer price was $2.00. In the student population, the median seller offer is $2.25, and the median buyer offer was $2.00. These differences are not significant for either group (P > 0.25). Pooling the young and older subjects gives an insignificant difference between WTA and WTP. The median offer price of sellers is slightly higher for the other rounds, excluding the first hypothetical round for the older subjects. Thus, in both groups the results are consistent with those of Plott and Zeiler. 6. Strategic thinking In many situations a decision maker’s outcome does not depend on his or her own choice alone but upon the choices of others. Investing in the stock market, crossing an intersection where there is opposing traffic, and playing poker are all examples. A game known as the “p-beauty-contest” has been widely used in economic studies to examine some of the simplest principles of interdependent decision making (Nagel, 1995; Nagel et al., 1999; Stahl, 2001). In the “p-beauty-contest” game, subjects select a number in the range [0,100], and the winner is the individual whose selection is closest to a proportion of the average of all the numbers selected. In our design, we used p = 2/3. Since the winning number hinges on the average of all the numbers selected, the subject needs to determine the numbers other players will choose, having been told that others are trying to do the same. The simplest strategy is to assume that other people choose randomly and therefore the average will be around 50. In this case the best decision would be to choose a number that is (2/3) 50 or 33, yet whether the subject continues with this rationale he or she will consider that the other subjects may also use this strategy and therefore the average would 10 S. Kovalchik et al. / J. of Economic Behavior & Org. xxx (2004) xxx–xxx decrease, becoming (2/3) 50. In this case, the best strategy is to choose the number that is (2/3)2 50 or 22. This line of strategies can be viewed as progressive steps of reasoning, the strategy of each step being given by 50(2/3)n . In dozens of studies with students, business executives, and individuals responding to newspaper experiments, the evidence has shown that people’s choices are limited to the first, second, and sometimes third steps of iterative reasoning. Formal models that assume an average of 1.5 steps generally predict better than conventional equilibrium concepts when people face a game for the first time (e.g., Camerer et al., in press). Given that thinking steps have been shown to be modestly correlated with the efficiency of working memory (measured by digit span; see Devetag and Warglien, 2003) and aging may reduce working memory or, potentially, some other cognitive process related to strategic reasoning, these changes could lead older subjects to use lower values of n and to choose higher numbers than younger subjects. For the actual task, participants were told that they would be playing with nine other individuals from their research population who had gone through identical procedures before providing their numbers. A written questionnaire was used to outline the game procedures and to inform participants that the winner of the competition would earn 20 dollars, which would be sent as cash by US mail after the winner had been determined (within 2 weeks of interview). Our results show that both the old and young samples behave similarly on this task. The majority of responses are clustered around the first step (50(2/3) = 33) and the second step (50(2/3)2 = 22) of reasoning (Fig. 5). Overall the behavior for this task is very similar Fig. 5. The plot shows the total number of subjects and number selections for the p-beauty contest (theory of mind task). Players try to choose a number close to 2/3 times the average of 10 numbers provided by participating subjects. The values in the left column are the “stems” or the tens digit, and the values on the right list the digits. Each numerical response is therefore 10 times the left column stem plus the middle or right column “leaf” value. For example, the most extreme guesses were 4, given by a younger subject, and an 86 given by an older subject. Values greater than 50 may indicate confused responses. Older subjects were more likely to give a response above 50 (P < 0.07).