年纪和决策

1 Aging and Decision Making: A broad comparative study of decision behavior in neurologically healthy elderly and young individuals Stephanie Kovalchika,1, Colin F. Camererb, David M. Gretherb, Charles R. Plottb, and John M. Allmanc aCalifornia Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91126 bDivision of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA. c Division of Biology, California Institute of Technology, Pasadena, CA. Abstract We investigate behavior in a series of economic decisions with two populations, one of healthy elderly individuals (with average age 82) and one of younger students (average age 20). We examine confidence, gambling, the endowment effect, 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 decision behaviors suggest that the elderly individuals are less biased than the younger individuals. (1) There is a greater prevalence of overconfident behavior in the younger population. (2) Choice over lotteries do not reflect the age differences previously reported in the psychology and biology literature. (3) Both populations perform similarly on the beauty contest task, although there is a modest indication of a higher incidence of confused behavior in the older adults in this task. (4) Our results show no support for a theory of an endowment effect in either population. Keywords: Age, overconfidence, endowment effect, theory of mind, game theory, risk- taking Classification: D00, D80, D81 Aging and Decision Making: A broad comparative study of decision behavior in neurologically healthy elderly and young individuals 1 Corresponding author, MSC 323 California Institute of Technology, Pasadena, CA 91126. stephk@caltech.edu 2 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 primarily on data from student populations. While this could be the result of subject availability, the narrow exploration in this area may also reflect a common belief among researchers of decision behavior-- that decision making ability declines with aging (Peters 2000). Despite the pervasiveness, even among scientists, of this view of aging, it remains an unsubstantiated notion. Many older individuals are productive and intellectually viable throughout their lives. Still, it is true that others are vulnerable to dementia and neurodegenerative illnesses, such as Alzheimer's disease. For these reasons, our objective in the pilot study was to begin to characterize the decision behavior associated with normal aging, with an emphasis on economic choices. The recent book edited by Stern and Carstenson (2000) presents advances in understanding cognition of older individuals and suggests an agenda for future research. 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. Older people also are more likely to vote than young people are, so they may have disproportionate political influence. Meanwhile, both long-term trends (increased longevity) and short-term trends (baby booms) mean that increasing proportions of the population are older and retired. 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 how the increasing segment of wealthy, experienced older people will behave. 3 The decisions we chose to study are a first cut at addressing the robustness of regularities that are well-established in younger populations. The tasks also were chosen because common observation suggests older people may behave differently from young people on some of these tasks. One feature of wisdom, which presumably is acquired over a lifetime, is meta-knowledge—knowing what one knows, and what one is good at. We measure meta-knowledge by self-reported confidence in trivia questions. A common stereotype of older people is that they are “conservative, dislike taking risk, are “set in their ways”, and have regular rituals and practices that they are reluctant to abandon. We ask if such tendencies might manifest in decisions under uncertainty. We conduct experiments with choices over monetary gambles similar to those preformed by psychologists and biologists. While these experiments are not the one’s that are suggested by the economic theory of risk taking behavior, they are experiments that have been conducted many times and can thus serve as a baseline for finding elements of age differences in behavior. The monetary gambles include incomplete and complete information (i.e., where probabilities are known ex ante or unknown). The final group of experiments explores possible differences in willingness to pay and willingness to accept. In these experiments the choices involve gambles for everyday objects (a coffee mug). One body of theory suggests that observed differences are due to an asymmetry of preferences between losses and gains, which might be exacerbated by age. An alternative theory suggests that the phenomena are due to experimental procedures and subject misconceptions. The plan of the paper is as follows: sections on each of the decisions will include a brief introduction, a discussion of methodology, and a presentation of the results. We conclude with a general discussion regarding our findings. 4 Subject Population and General Experimental Design In our comparative investigation, we performed interviews with two age groups: a young population (ages 18-26, 51% female) and elderly population (ages 70-95, 70% female). 2 The older subjects (N=50) serve as controls for the Alzheimer's Disease Research Center (ADRC) at the University of Southern California (USC). Based on annual cognitive and behavioral testing, the older individuals are considered neurologically healthy, with no history of dementia or mental illness. The student population (N=51) consisted of healthy undergraduates from a junior college near Caltech. 3 The younger population, being students at a community college, have between 12 and 16 years of formal education. The older population is highly educated relative to their age group4— 78% have more than 12 years of education and 60% have 16 or more years. Other populations of older adults may be more difficult to study (e.g. individuals with Parkinson disease or other aliments or people in assisted living arrangements). We chose a population of healthy high functioning individuals for our first attempt to study decision making in the elderly. Each subject participating in the study completed an individually administered interview, involving a written questionnaire and several interactive tasks. On average subjects of both populations took fifty minutes to complete the interview. For all areas of the investigation involving monetary rewards, real cash was awarded to the subjects. This 3 These populations are not representative of their age groups, though they are reasonably well matched on education level. Representative sampling would be a natural next step but would require a much more complex design. 4 Note that college education only became widespread in the years following World War II, rising from 1.5 percent in 1950 to 5 percent in 1980 (U.S. Government (2001),Walton and Rockoff (1998)). So our older subjects, who were born around 1920 on average, are much more likely than their peers to have graduated from high school or gone to college. 5 method of collecting data is expensive. 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 (i.e., the younger subjects were interviewed one-at-a-time also) to avoid confounding age with the method of data acquisition. Confidence We examined confidence using a meta-knowledge task, which tests the accuracy of an individual’s assessment of his or her own knowledge. Previous work in this area has shown 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). Overconfidence is a subject of intense debate among decision theorists (Ayton and McClelland 1997). Three prominent explanations of overconfidence 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 seem to believe that the correct answer is New York, and are quite confident, even though that answer is incorrect (but not by much). 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 1994). Others argue that it is a cognitive bias activated during the evaluation of information 6 (Kahneman 1996), due to anchoring on an intuitive answer or snap judgment, and adjusting insufficiently for the ways in which the answer could be wrong. More recent studies designed to separate these explanations have generally shown that overconfidence persists even when questions are sampled randomly (Soll, 1996) and responses are adjusted for random error (Wallsten 1994). An important qualification is that many expert populations e.g. weather forecasters (Murphy, 1984), blackjack dealers and others (Camerer, 1995, pp. 590-592), and highly experienced subjects in repeated games (Camerer, Ho and Chong, 2002) do not show the overconfidence that normal populations do. In this study, we investigated confidence by providing subjects with twenty trivia questions on diverse subjects (see Appendix 1). Each of the subjects interviewed was provided the same set of twenty general knowledge questions with binary answer choices. Subjects were instructed to select an answer choice and then provide a confidence assessment (100%-50%) about their choice. Older subjects did somewhat better answering 74.1% of the questions correctly, while 66.1% of answers given by the younger subjects were correct. To study calibration, for each group 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 in an assessment category should match that assessment (e.g., on questions where subjects said they were 80% right, they should be right about 80% of time). Figure 1 compares those confidence assessments with the associated accuracy rates. Nonparametric median analysis shows that the older subjects' assessments are significantly more accurate at 60% (p<0.05) and 70% (p<0.01) reported degrees of 7 confidence. The older subjects do exhibit overconfidence when the reported degrees of confidence are at the 80% and 90% levels (17% of their total responses), but younger subjects are overconfident at all the intermediate levels of reported confidence (48% of their total responses). Behavior between 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% confidence (in calibration terms, their assessments had “higher resolution”). While older subjects reported a confidence of 100% significantly more often than the younger subjects (p<0.025), they made substantially fewer selections with 60%-80% confidence (p<.05 for each group). The percentage of correct responses when reporting 100% confidence was about the same for the two groups (94% correct for the older population and 92% for the younger subjects). One way to interpret these results is that older subjects look like domain experts often do— they make more extreme responses of “don’t know” (50%) or “I’m sure” (100%) and they are not as overconfident in much of the middle range of reports. Much as domain experts like weather forecasters learn to temper their overconfidence over time, by making hundreds or thousands of daily forecasts, perhaps the older subjects have learned to become more expert over a lifetime of making assessments. Decision Making Under Uncertainty Psychologists and biologists have studied behavior in the context of a gambling paradigm. Because the background research is extensive and because results have been 8 interpreted as related to the physiology and health of the brain the environment lends itself to an inquiry about the possible effects of age. The psychology and biology literature refer to their work as reflecting attitudes toward risk but we will not use such interpretations because the experimental setting does not support the interpretation of risk attitudes as developed in the theory of risk as found in economics. While these differences will become clear as the discussion proceeds, the reader will see that the experiments are more focused on the propensity of subjects to exhibit preferences that respond to the statistical properties of the lotteries . Two gambling tasks are employed. The first task is a modified version of the card-deck gambling task of Bechara et al. (2000) in which there is incomplete information about the probability of prospects. 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 ten cards and the other deck (B) had an overall gain of $2.50 every ten cards. All the cards in deck A gave a $1.00 on every turn but were occasionally accompanied with high 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 2); they had to learn as they went along. Subjects were instructed that they always had to select the top card of one of the decks, but they could switch between decks at any time during the task. Each subject selected 50 cards one at a time, but were not informed in advance about the total number of draws. In mean-variance terms deck A is dominated by deck B because it has a lower mean payoff and a greater variance.5 5 Note that choosing deck B is utility-maximizing if a person is sufficiently risk-preferring, so that higher variance is preferrable (a risk-preferrer will sacrifice mean payoff to get more variance). The 9 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 learn to choose from the more advantageous deck A (with the higher mean payoff and lower variance). 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 A in comparison to control subjects (Damasio 1994). Denburg et al. (1999) administered this task with a population of healthy older adults and argue that the older individuals behave similarly to the frontal-lobe-damaged subjects . This suggestion that age influences behavior in ways similar to brain damage leads naturally to a more systematic investigation under a wider range of tests such as those reported here. Consistent with the results of the Bechara study, our findings show that subjects decide quickly that deck B is more preferred. The beginning phase of the task is a learning period in which both populations sample each deck equally. By the third 10- draw interval of selections, the subjects begin to have a preference for deck B and this preference increases for the final ten cards selected (Fig. 2). Interestingly, the older and younger subject populations choose roughly the same decks for the first forty cards. In the final ten cards a suggestive difference appears. The younger subjects show a slightly more extreme preference for deck B in the final 10 cards, which is not significant at conventional levels (p=0.14). Replication and more trials are needed to determine whether or not this difference is a robust property of aging and decision-making. As a complement to this first task, we conducted a second, gambling procedure that allowed impressions about relative attitudes toward risk by removing the need for neuroscientific literature, however, uniformly treats the deck B choice as a mistake rather than an expression of risk preference. 10 subjects to learn about possible payoffs. In these experiments, unlike the earlier one, subjects had complete information about the probabilities of prospects. Their task was again to select one of two decks (see Appendix 2). Unlike in Bechara’s incomplete information design, subjects saw the money payoffs from each of the ten cards in each deck before making their selection. Once they decided which deck they wanted, the ten cards were shuffled and the subjects selected one card. Risky decks had the highest individual gains and losses (larger variance) and an expected payoff that was zero or negative. The less risky decks had lower individual gains and losses, (and smaller variances) and positive expected values. Thus the risky deck had a lower mean and a higher variance than the less risky deck. A total of six choices, with reshuffling after each draw, were given to 36 of the older subjects and 51 of the student subjects. In contrast to the gambling task with incomplete information, when subjects predominantly learned to choose the deck with the highest expected return, in this complete information task the individuals in both groups tend to prefer the higher risk decks, with no difference across age groups. Among older subjects, 58% selected four or more risky decks out of the six choices, while 59% of the younger subjects select four or more risky decks (Fig. 3) (and the proportions were similar across age groups for each of the six different deck pairs). An interesting difference between the groups is that the elderly individuals were more likely to mix their choices among risky and less-risky decks. In contrast, younger subjects were more likely to choice the riskier deck all six times (22% of younge