Why Do We Avoid Doctors? The View from Behavioral Economics Standpoint

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1 Why Do We Avoid Doctors? The View from Behavioral Economics Standpoint Ksenia Panidi 20 February 2008 Abstract Some people visit doctors very rarely because of a fear to receive negative results of medical inspection, others prefer to resort to medical services in order to prevent any diseases. Recent research in the eld of Behavioral Economics suggests that human's preferences may be signicantly inuenced by the choice of a reference point. It seems natural to think that the same is true for health consumption. This paper considers a model with reference-dependent utility that allows to characterize how people choose their health care strategy, namely, the frequency of visiting doctors. The study focuses on the eect of loss aversion as potential factor that may lead to considerable delays in seeking medical advice. The model constructed in the paper shows that loss-avers agents may have incentives to avoid visiting the doctor under high risk of illness and when the net benets of treatment are suciently low. Keywords: loss aversion, health anxiety, reference-dependent preferences, anticipation, preference for uncertainty JEL Classication: D81, D84, I19 I gratefully acknowledge constructive suggestions of my academic advisor Prof. Georg Kirchsteiger. Also I would like to thank my advisors from the New Economic School (Moscow, Russia) Prof. Andrei Bremzen and Prof. Anton Suvorov who helped me a lot at the rst stage of writing this work. Doctoral student at Universit e Libre de Bruxelles (ECARES), Brussels, Belgium 1 Electronic copy available at:

2 I. Introduction Study of health care behavior deals to a large extent with the psychological attitude of people to their health and health risks. As we may observe in our everyday life, attitude to health is likely to be dierent from the attitude to the majority of other consumption goods. For example, health could be regarded as an asset that could not be bought easily despite the availability of an adequate medical service in case of illness. Also, persons' attitude to health risk problems seems to have some specics, compared to their attitude to standard risk and uncertainty situations that involve monetary outcomes. For instance, people may be more willing to sacrice a sum of money in order to maintain certain level of health than to sacrice their health in order to obtain the same sum of money. The indirect experimental evidence for this could be found in Viscusi et al. (1987). Here the experiment is described where the agents had to choose, rst, the amount of money they will be ready to sacrice to eliminate partially health risk. Second, the respondents were asked to state the sum of money they would demand for accepting the increase in the level of heath risk by the same degree as it was reduced in the rst case. The results of this experiment showed that the majority of people was ready to pay for health risk reduction. However at the same time the subjects completely refused to "sell" their health (in terms of increased health risks) for any sum of money. As the example above shows, the process of health-related decision making may be largely aected by humans' feelings and emotions about health. One of the problems that arise in this eld is that people could make unhealthy decisions due to experiencing dierent kinds of emotions. In other words, health care behavior of people could violate the assumption of rationality in many possible ways. The present paper will focus on the analysis of the following issue. Many studies in the eld of human health care behavior indicate that people tend to avoid visiting doctors because of their fear to learn negative results of medical inspection. Caplin and Leahy (2001) refer to the empirical evidence of Kash et al. (1992) to illustrate the fact with the patients' avoidant behavior among women with a family history of breast cancer. Koszegi (2002) stresses that the 1 Electronic copy available at:

3 acknowledgment of the problem of unhealthy medical decisions appears both among academic researches and in mass-media. Caplan (1995) and Bowen et al. (1999) indicate that people tend to delay visiting doctors longer when the probability of illness seems to be rather high, or when symptoms of an illness are more obvious. Such behavior may seem to be irrational. It seems better to visit a doctor at an earlier stage of illness, because treatment in this case is less costly and probably more ecient. However, preventive behavior appears to be a less frequently observed phenomenon than the opposite situation. In this paper we ask for possible explanations of this behavior. One of the most wide-spread explanations for described phenomenon is the fact that people experience the sense of anxiety about their health level. Caplin and Leahy (2001) present a quote from the glossary of the Diagnostic and Statistical Manual of Mental Disorders that denes the sense of anxiety, or worry, as "apprehension, tension, or uneasiness that stems from the anticipation of danger". According to many studies in Psychology and Medicine, anxiety is responsible for keeping people away from visiting doctors. Recent researches stress that people often experience the sense of fear, which is a negative emotion, prior to the moment of visiting a doctor. Hence, it seems reasonable to suggest that people act in the way that decreases the possibility of experiencing fear. One obvious way to avoid this fear is just avoid visiting doctors. Although many researchers recognize the importance of anxiety for the process of decision-making, little has been made to investigate this issue theoretically. However, several papers provide models of anxiety, and some of them apply it to health care behavior. In the majority of these models the central role is played by the beliefs of people about the states of the world rather than by the actual states. As pointed out in Eliaz and Spiegler (2005), the existing models of decision-making fall into two groups: those in which agent's belief is a parameter in his or her utility function, and those in which agents choose their beliefs, or in other words, manipulate them to increase their expected utility. One example of the former category is Caplin and Leahy (2001), where the so-called model of psychological expected utility is developed. The example of the latter is Akerlof and Dickens (1982) that studies the phenomenon of cognitive dissonance, which originates from 2

4 people adjusting their beliefs about the probability of negative events. The work most closely related to the present paper is Koszegi (2002). This work aims to explain the tendency of individuals to delay visiting doctors and derives the conditions under which such delays are most likely to occur. The basis of the work is the psychological expected utility, constructed in Caplin and Leahy (2001). Koszegi builds up a two-period model where the agent obtains utility from the expectations about his future health state. The agent has two variants to choose between. He may consult the doctor, who will determine an adequate treatment for the patient. The alternative is not to reveal the actual health state and to choose the treatment himself. But the agent has to take into account that inadequate treatment will bring him some disutility, or loss. The central nding presented in the paper is that people will avoid visiting doctors only in case of rather bad symptoms, that is when the probability to hear bad news about health and get upset is high. However, once bad diagnosis is set they will prefer to visit one more specialist to verify it. Although the model of Koszegi (2002) provides rather intuitive results, the approach used in this work faces some critique in Eliaz and Speigler (2005). They emphasize that the modeling practice, in which agents maximize their utility from expectations as outcomes, fails to explain anomalous attitude to information in several cases. For example, preference patterns introduced by Koszegi and Caplin and Leahy will lead to the fact that people with dierent preferences over information acquisition will demonstrate the same behavior and, hence, will be behaviorally indistinguishable. Our analysis of the issue will be based on some ndings in the eld of Behavioral Economics. Recent research suggests that human's preferences may be signicantly inuenced by the choice of a reference-point. Kahnemann and Tversky (1979) presents the theory of decision-making which states that carriers of agent's utility are not absolute values of wealth, but its changes relative to some reference level. It also states that agent's are in general characterized by loss-aversion. This means that their disutility of a loss relative to a reference point is higher in absolute value than utility from a gain of equal size. Therefore, agent's gain-loss utility can be presented as an S- shaped value-function, the slope of which in the domain of losses is larger 3

5 than that in the domain of gains. Behavioral pattern with loss-aversion has been observed in the consumption of goods and was responsible for the endowment eect and a status-quo bias (see, for example, Kahnemann, Knetch, Thaler (1991)). We suppose that this might also be true for health consumption. A person may have some beliefs about his or her level of health and be afraid to learn that the actual health status is much lower than this perceived level. An agent may expect to experience the sense of loss after a visit to a doctor and would prefer to avoid it (in other words, maintain his status-quo). Introducing reference-dependent preferences is one more way to model health anxiety. It is worth noting that the approach to the analysis of the problem presented in this paper diers from that of Koszegi (2002) in two essential ways. First, as was mentioned earlier, Koszegi (2002) assumes that the expectations of the next period's health state enter the agent's utility function, and the agent chooses his actions in the way that maximizes this utility. The better are the expectations, the higher is the utility. This assumption is central for the formalization of health anxiety. In the present paper the anxiety about health is modeled in terms of possible gains and losses from good or bad news about health state. Second, Koszegi (2002) introduces the concepts of information-averse and information-loving agents depending respectively on the concavity or convexity of the utility function from expectations. This implies that the agent is supposed to have some special utility function for making health-related decisions, and this function could be essentially dierent from that used to make other consumer decisions. In the present paper we do not suppose that agents are of two types - with convex or concave utility function. What we do is that we apply a more general concept of reference-dependent preferences to the analysis of a more narrow issue of health care decision-making, while what the work of Koszegi does is that it broadens the concept of classical utility allowing it to be convex. One consequence of the Koszegi's approach is that it unies the attitude of people to dierent kinds of illnesses. If the agent turns to be an information-lover, he will be seeking information and visiting doctors independently of what illness he thinks about. The concept of reference-dependent preferences allows us to analyze the way the attitude 4

6 of people may dier for dierent illnesses and emphasizes the role treatment costs (both physical and emotional) may play in the process of decisionmaking. In presented model the agent may be information-averse as well as information-lover depending on many circumstances: the costs of treatment, the likelihood of falling ill, the current belief of the agent about his level of health and his emotional reaction to good and bad news from the doctor. This means that in some circumstances the agent will be seeking information, while in other situations he will be demonstrating information-aversion and avoid visiting doctors. In other words, in the present work informationaversion is more the way a person behaves in a particular situation, while in Koszegi (2002) it is the characteristic of a person himself. Moreover, the reference-dependent model of health behavior provides microfoundations for the explanation of the phenomenon of information-aversion and informationloving. The paper is structured as follows. In section II we present assumptions and general structure of the model. Section III provides the main results. Concluding remarks and discussion are presented in Section IV. II. The Model In this section we develop the model of health behavior based on the implication of the idea of reference-dependent preferences. First, we formulate the model in the general form. Then we consider a particular specication in order to explore it in more detail. 1. Assumptions and Structure The model is based on the following assumptions. At period zero an agent under consideration has some level of health H, which is observed and constant. At period 1 the agent's health level could change with some probability. The change in health level H is a stochastic variable distributed conditional on the actual health level with the density function f( H H) symmetric with respect to zero. The variable H could take positive as well as negative values. Negative values of H correspond to worsening of agent's health, 5

7 while positive H means health improvement. The distribution of H is xed for every known health level H. We assume that the agent does not observe the change in health level, but receives a signal that may indicate whether this change was positive or negative. Formally, after the change in health has occurred the agent receives the signal s which could of one of three types: - positive (s = 1); - negative (s = 1); - neutral (s = 0). We assume that the signal of each type could appear with some probability depending on the change in health H. Namely, if the agent's health has improved, the agent receives positive signal with probability P (s = 1 H) 1 and neutral signal with probability P (s = 0 H) = 1 P (s = 1 H). In this case negative signal is assumed to come with zero probability, since its natural to suppose that health improvement cannot generate any negative signal. Analogously, if the health has deteriorated, the agent receives either negative signal (e.g. observes the symptoms of an illness) with probability P (s = 1 H) or a neutral one (e.g. does not observe any symptoms) with probability P (s = 0 H) = 1 P (s = 1 H), and positive signal comes with zero probability. Therefore, neutral signal may be observed in both cases - after a positive as well as negative change in health and, hence, does not give any information about the change under the assumption that density of distribution f( H H) is symmetric 2. The probability of observing a signal of a certain type increases in the value of H. This seems to be intuitive - the larger the change in health, the more probable it is to observe a signal that indicates that this change has occurred, and the less probable it is to receive an uninformative neutral signal. We also assume that the probability of observing a positive signal after a positive health change is equal to the probability of observing a negative 1Here we assume for simplicity that the probability of observing a certain signal does not depend on the health level H, which might not be the case in reality. 2In case this density function is not symmetric, for example, skewed towards positive changes, after the neutral signal the agent would attach higher weight to positive changes, since they are more likely. 6

8 signal after an equal negative change. As follows from this assumption, the probability of observing a neutral signal is a function of H symmetric with respect to the y-axis. After the signal has been received, the agent accounts for this new information using Bayesian updating of his knowledge about the distribution of health change and about his current health level (after the change). At this moment the agents forms his reference point, which we consider below, and makes the decision whether to visit the doctor now or not. The doctor is able to nd out the current health level of the agent and the change that has occurred. The decision is made on the basis of comparing the agent's expected utility from visiting the doctor and utility from not visiting. 2. Reference Point Here we formalize the idea of a reference point. Reference point is the agent's expected level of health based on the information about health available to the agent. At period 1 the this information consists of the agent's observed level of health H and the signal about the change in health received by the agent. Having observed the signal of a certain type the agent now updates his beliefs about the health changes using the Bayes rule and nds out what change was most likely to occur. The posterior density of distribution of H is given by: a = f 1 ( H H, s = i) = b a P (s = i H)f( H H) (1) P (s = i H)f( H H)d( H), where i takes values of 1, 0 or -1 according to the observed signal. Parameters a and b take values of 0 or ± depending on the observed signal: { 0, for s = 1;, for s = 0, 1. and b = { +, for s = 0, 1; 0, for s = 1. According to this posterior distribution density the most likely change in health state that could have occurred, that is the expected value of H, 7

9 could be calculated as follows: E( H H, s = i) = b a Hf 1 ( H H, s = i)d( H) (2) Since the agent does not observe the change in health, but only the signal, he corrects his perception of health by the expectation of the change. This new perceived level of health becomes his reference point. Therefore, we can calculate the reference point after all three types of signal. Reference point after a positive signal is determined as: R + = H + E( H H, s = 1). (3) After a bad signal it is calculated according to the following expression: R = H + E( H H, s = 1), (4) where E( H H, s = 1) < 0. Finally, neutral signal generates the reference point equal to 3 : R 0 = H + E( H H, s = 0) = H (5) The latter result is quite natural. In case of neutral signal the agent does not receive any supplementary information on his health and, therefore, cannot update his perceived health level. This is the consequence of the symmetry of density function for health changes. 3. Utility Function and Decision-Making We consider the agent's utility function consisting of two parts - emotional part, which is reference-dependent, and physical part, which corresponds to physical outcomes. To represent the reference-dependence part of the utility function we use the approach developed by D. Kahnemann and A. Tversky. Namely, the emotional reaction of the agent on the news about his health level is determined as a gain-loss utility. In this case "good news" about health is equivalent to obtaining the information that agent's current health state is higher than his reference point, that is higher than he expected health to be. 3For the formal proof of the latter equality refer to Appendix 1. 8

10 Analogously, the agent gets "bad news" when he learns that his actual health is worse than he expected, i.e. lower than his reference point. Intuitively, the agent will experience a gain from good news and a loss from bad news, and the value of these gains and losses will depend on the reference point. Formally, the gain-loss utility is represented as a linear value function with a kink and the loss-aversion coecient equal to η > 1 4. The physical part of the agent's utility function corresponds to costs and benets associated with treatment, if it is prescribed. Finally, taking into consideration all the assumptions made we could consider the utility of visiting the doctor in the following form: { η(h d R) Costs + Benefits, if H d < R (losses); U(H d R) = (6) H d R Costs + Benefits, if H d > R (gains). Here H d is the actual level of health revealed by the doctor and R is the agent's reference point. The rst term in each expression corresponds to the emotional part of the utility from visiting the doctor, while the second part accounts for costs and benets of treatment in case it is necessary. We will now consider the decision-making procedure of the agent regarding visiting or not visiting the doctor. Since the agent's reference point depends on the signal that he observes his utility from visiting the doctor also depends on the signal. Positive signal indicates that the change in health is positive and therefore no treatment will be prescribed. Positive signal indicates that the change in health is positive and therefore no treatment will be prescribed.hence, the costs and benets of treatment in the agent's utility function will be equal to zero and the function will take the following form: { η(h d R + ), if H d < R + ; U + = (7) H d R +, if H d > R +. Here R + is the reference point after a positive signal. We assume that the doctor can determine the actual health change that has occurred. Therefore, 4One could also include the case η = 1. However, we do not consider it, since gain-loss utility without a kink is of less interest. 9

11 the revealed health level is represented by the health level H, which is known, and its correction by the health change H observed by the doctor. In other words, we assume that: H d = H + H. Taking into consideration the formula (3) for the reference point after a positive signal we come to the following expression for the utility from visiting the doctor in this case: { η( H E( H H, s = 1)), if H < E( H H, s = 1); U + = H E( H H, s = 1), otherwise If the observed signal was negative, then the agent knows that the change in health was denitely nonpositive, and the doctor would prescribe an adequate treatment. The costs are proportional to the degree of health deterioration - the more serious an illness is, the more costly 5 its treatment is. The costs of treatment are represented in the form C H, where C > 0. Here we abstract from xed costs of visiting the doctor in terms of time spent and payment for the consultation. The long-run benets of treatment are represented by the expression D H, where D > C. Therefore, the utility of visiting the doctor after a negative signal will be equal to: { η(h d R ) (D C) H, if H d < R, U = (9) H d R (D C) H, if H d > R, where H < 0. Analogously to the previous case we can develop this expression and obtain the following form: U = { η( H E( H H, s = 1)) (D C) H, (8) if H < E( H H, s = 1); H E( H H, s = 1) (D C) H, otherwise (10) As was mentioned above, the reference point in case of neutral signal equals the actual health level before the change has occurred. Hence, two variants are possible. In case the negative change has occurred the agent would be prescribed a treatment. On the other hand, if no change of health 5We may consider the costs of treatment both in terms of money and in terms of disutility of treatment (unpleasant medical procedures, opportunity costs of time spent in the queues in a hospital, etc.), which may also be proportional to the seriousness of the illness. 10

12 has taken place then the utility of visiting the doctor will be equal simply H, which will constitute a dierence between actual and perceived level of health. Overall, the utility from a visit to the doctor after a neutral signal is: { η H (D C) H, if H < 0; U 0 = (11) H, if H > 0. In order to decide whether to visit the doctor or not, the agent calculates his expected utility from visiting the doctor and compares it to zero, which is the utility from not visiting. Consider the expected utility after a positive signal: E(U + ) = H<E( H H,s=1) η( H E( H H, s = 1))f 1 ( H H, s = 1)d( H)+ + ( H E( H H, s = 1))f 1 ( H H, s = 1)d( H) (12) H>E( H H,s=1) The expected utility after a negative signal equals: E(U ) = is: H<E( H H,s= 1) η( H E( H H, s = 1))f 1 ( H H, s = 1)d( H)+ + H>E( H H,s= 1) ( H E( H H, s = 1))f 1( H H, s = 1)d( H) (D C)E( H H, s = 1). (13) Finally, the expected utility from visiting a doctor after a neutral signal E(U 0 ) = H>0 Hf 1 ( H H, s = 0)d( H)+ + (η H (D C) H)f 1 ( H H, s = 0)d( H). (14) H<0 11

13 III. General Results Given the structure of the model described in previous sections we will now consider the decision of the agent for all three cases: after positive, neutral and negative signal. We start with the case of a positive signal. The analysis of the agent's utility function in this case leads to proposition 1. Proposition 1. The agent's utility from visiting the doctor after a positive signal is negative for all values of model parameters. This proposition can be proved for the general formulation of the model presented in section 3 of the present paper 6.The result stated in this proposition is quite intuitive. If the agent observes positive signal, which denitely indicates the increase in his health level, then there is no necessity for him to visit the doctor. In terms of the developed model, after a positive signal the agent has high reference point and his chances to learn something bad about his health become higher, because now the set of health states regarded as "bad" outcomes, i.e. those lower than the reference point, widens. Therefore, the potential emotional "costs" of visiting the doctor increase, which discourages the agent from going for inspection. Now let us turn to the consideration of the agent's behavior after a neutral signal. Proposition 2. If the posterior density function for H is symmetric with respect to zero, the agent will visit the doctor after a neutral signal if η 1 < D C, and will not in the opposite case. The formal proof of this proposition is presented in Appendix 4. This result is quite intuitive. The condition stated in the proposition implies the comparison between the degree of loss-aversion of the agent measured by η 1 and the net benets of possible treatment expressed by D C. When the loss-aversion of the agent is relatively high, the emotional costs of visiting 6The formal proof of Proposition 1 can be found in Appendix 3. 12

14 the doctor might appear to be higher than the net benets of treatment in case the negative change is revealed. As a result, the agent will be avoiding carrying these excessive costs and will refuse to go the doctor. In the opposite situation, when the net benets overweigh the agent's disutility from bad news, the medical inspection will be preferable for the agent. Note that this result is valid only under condition of a symmetric posterior density function for H. Due to this condition it does not depend on the specication of the model. In other words, it holds no matter what the parameters of the H posterior density function are. For example, the variance of possible health changes does not play any role here. If positive and negative health changes are equally probable then the agent cannot gure out what change has occurred and his best guess would be zero. As was mentioned earlier, if the agent does not receive any new information on his health, he has no incentive to update his perception of the current state. This means that the current state of the agent does not appear in his decision and that he needs to compare the expected emotional and physical costs and benets of two possible outcomes - positive or negative health change. Since in the probabilistic sense these two outcomes are identical, the only thing that matters for the agent is their relative costs and benets. The weight of the net emotional costs of visiting the doctor equals 7 η 1, where η is the weight of bad news and 1 is that of good news. Analogously, the weight of net physical benet of positive change is zero (since a positive change does not imply any treatment), while the coecient for net benet implied by a negative change is D C. The agent comes to the decision by comparing these two expressions. Naturally, if the costs appear to have higher weight than corresponding benets, the agent will refuse to visit the doctor. Let us now consider the case of a negative signal. The expected utility in this case is given by expression (13). Adding and subtracting 1 from coecient η and developing further this expression, we get: E(U ) = (η 1) H<E( H H,s= 1) ( H E( H H, s = 1)) 7We will call this value "relative loss-aversion", since it measures the slope of the agent's value function in the negative domain relative to that of the positive domain. 13

15 f 1 ( H H, s = 1)d( H) (D C)E( H H, s = 1). (15) Note that E( H H, s = 1) is always negative, since by our assumption the negative signal can be generated only by a negative H. The rst term of expression (15) is negative as well, as follows from the fact that we integrate H E( H H, s = 1) in the domain of integration where it is below zero and η > 1. Therefore, the exact sign of the expected utility depends on the values of parameters η, D and C and on the specication of functions that determine the expected value of H in this case. We will now consider this issue in a more detail using a particular specication of the model. In the general framework described above, the distribution of possible health changes is conditional on H. In this specication in order to simplify further calculations we assume that this distribution is identical for all health states and takes the following symmetric form: { 1 2 f( H H) = f( H) = e H, if H > 0, (16) 1 2 e H, if H < 0, where is a positive constant. The expectation of health change for its positive values is E( H H > 0) = 1 2 and for negative values E( H H > 0) = 2. 1 The higher is, the lower are the expected positive and negative changes in health state. This parameter also inuences the variance of the distribution. The variance of the exponential distribution is 1, that is it decreases in. Therefore, higher 2 means that the signal gives more precise information about the health change. This parameter also can be interpreted as a health-stability indicator: the higher is the lower is the variance and the absolute value of the expected change prior to the observation of a signal. We also specify the probability of observing a signal of each type in the following form. The probability of observing a positive signal is: { 1 e H, if H > 0, P (s = 1 H) = (17) 0, if H 0, As could be seen from this specication, this probability equals zero for negative health shocks, that is positive changes in health could not generate 14

16 negative signals.the probability of a good signal increases in H in the positive range and tends to 1 in innity.as was mentioned above, observing good signal after a positive change is more likely, the larger was the positive change. Analogously, the probability of observing a negative signal after health deterioration equals: { 0, if H 0, P (s = 1 H) = (18) 1 e H, if H < 0, The probability of observing neutral signal, therefore, is symmetric and takes the following form: { e H, if H 0, P (s = 0 H) = (19) e H, if H < 0, The calculation of this specication of the model yields the following results. The posterior density function after a negative signal has the form 8 : f 1 ( H H, s = 1) = (1 + )[e H e (+1) H ] (20) In our specication of the model the expected utility after negative signal takes the form 9 : E(U ) = (η 1)e 2+1 (+1) ) (e 2+1 (+1) (C D) ( + 1) (21) Using this formula we can analyze the inuence of model parameters on the decision of the agent after a negative signal. First, we consider the inuence of the dierence between the costs and benets of treatment C D by the derivative of the function with respect to this dierence (for a shorter notation we use E(U ) = F): F C D = ( + 1). (22) Since parameter is always positive, this derivative is always strictly negative. This means that the expected utility of the agent decreases in 8For all calculations see Appendix 2. 9For all calculations see Appendix 5. 15

17 (C D). The more costs of treatment overweight its benets the lower is the agent's expected utility of visiting the doctor after negative signal keeping all other parameters constant. The intuition here is straightforward: higher relative costs of treatment imply higher physical costs of visiting the doctor. Notice that observation of negative signal means negative health change, for which an adequate treatment will be prescribed by the doctor. The derivative of function F with respect to loss-aversion coecient η is the following: F η = e ) (e 2+1 (+1) (23) As it is shown in Appendix 6, this derivative is negative. The intuition for this result is similar to the that described above for parameters C and D with the distinction that the increase in loss-aversion coecient increases emotional costs of visiting the doctor. The higher is η, the more painfully the agent perceives bad news related to his health and, hence, more discouraged he will be to go to the doctor after a negative signal. This analysis shows how the model parameters can inuence the agent's expected utility. However, agent's decision to visit the doctor or to avoid it depends on the comparison of utilities that he gets from these options. We assume the utility from not visiting the doctor to be equal to zero. Let us refer to the expression (21) and call its rst term "emotional costs", while the second one will represent "physical costs" of visiting the doctor. Since both these terms depend on parameter the nal decision of the agent will also be determined by it, given some xed values of η, C and D. For our future analysis we will denote emotional costs by function g 1 () and physical costs by function g 2 (), where: g 1 () = (η 1)e 2+1 (+1) ) (e 2+1 (+1) g 2 () = (C D) ( + 1), (24) and F () = g 1 () g 2 (). Notice that both functions g 1 () and g 2 () are negative. 16

18 Proposition 3. If condition D C < 2(η 1)e 2 holds then function g 1 () lies below g 2 () (F () is negative) for all > 0. If D C > (η 1)e 1 holds then function g 1 () is always above g 2 () (F () is positive) for all > 0. If 2(η 1) e 2 < D C < (η 1)e 1 then function g 1 () is below g 2 () for small values of and above for large ones. The proof of this proposition is presented in Appendix 7. The proposition shows that the agent's behavior after negative signal depends on the combination of all parameters: loss-aversion coecient, costs and benets of treatment and the indicator of health-stability. If the dierence between benets and costs of treatment is much smaller 10 than the agent's relative loss-aversion (namely, if D C is smaller than 2(η 1)e 2 ) the agent never goes to a doctor independently of. In this case net physical benets of treatment that the doctor will prescribe are smaller than emotional losses of possible bad news and their dierence is not compensated even for large, which implies small expected health change. Consider the second situation where D C > (η 1)e 1. Here net benets of treatment overweight emotional losses of bad news. As a result the agent visits the doctor independently of. Note that the mentioned condition can be divided into two parts: D C > η 1 and (η 1)e 1 < D C < (η 1). In the rst part net physical benets are higher than emotional costs and hence the decision of the agent is obvious. However, as second part shows, the benets need not to be higher than costs to make the agent go to the doctor. What is needed is that their dierence is not too large. The most interesting case of Proposition 3. is the third one. Here the relationship between the costs and benets of supposed treatment is such that the agent's decision depends on the parameter. In this case neither costs (emotional or physical) nor benets of visiting the doctor can prevail to the extent when the agent's decision becomes the same independently of a possible health change. The behavior of the agent diers for high and for 10Note that since 2 e is smaller than 1, D C appear to be strictly smaller than η 1. In the third case of Proposition 3 2 this condition holds as well (since 1 e < 1). Therefore, it makes sense to say that under the rst condition D C is "much smaller" than η 1, meaning that under the second one it is still smaller than η 1 but not that much. 17

19 low. However, it is not determined for being in the medium range of its values. Since the functions g 1 () and g 2 () are continuous, the condition stated in this proposition implies that they intersect at least ones. Therefore, there exists at least one value of for which the agent is indierent between visiting and not visiting the doctor. However, Proposition 3 reveals that the agent's behavior is determined for being suciently high or suciently low. Remember that we interpret as a health stability parameter. Consequently, the proposition states that, in the third case, if the risk of getting seriously ill is low (health stability expressed by is high) the agent will decide to visit the doctor. This is natural since in this case the emotional costs of visiting the doctor are not expected to be high (the risk that the actual health level after the change is far below the agent's reference point is small). In other words, if the possibility of a serious illness is small the agent has nothing to be afraid of. On the other hand, if the parameter is low the agent will avoid visiting a doctor. Low implies high expected absolute value of a health change, which transforms to a possible serious health deterioration, if the agent observes negative signal. From the point of view of intuition this means that if the agent knows in advance that he is at high risk of being seriously ill (e.g. when he is known to have bad health inheritance) he will refuse to consult a doctor after having observed bad symptoms. The reason for this is increased health anxiety in the situation when net benets of treatment are not overwhelmingly high compared to agent's loss aversion. IV. Conclusions and Discussion As the model considered in this paper shows, people may expect to learn bad news about their actual level of health, and this may discourage them from going to a doctor. The behavior of agents may dier in three situations: when the agent observes health improvement, when he observes health deterioration and, nally, when he does not notice any change at all. The model predicts that the agent will always refuse to visit the doctor in the rst case. In two other cases his decision will depend on emotional and physical costs and benets of a visit to the doctor. Here we have obtained two interesting results. The rst one refers to the willingness of the agent to undergo a pre- 18

20 ventive medical inspection. In other words, the question is - will the agent visit the doctor if he does not observe any symptoms of an illness. The answer that the model gives is that in this case the agent might be discouraged if his loss-aversion is high. He may prefer uncertainty about the magnitude of the actual health change to the possibility of receiving bad news about it. However, the fear of getting upset might be overweighed by high physical benets of treatment or its costs being low relative to these benets. The second obtained result answers the question whether the agent will visit the doctor if he notices health deterioration. Our model predicts that here emotional costs might as well be demotivating. High degree of loss-aversion compared to the net benets of treatment may prevent the agent from a visit to the doctor. In the opposite case, if visiting the doctor is helpful and not very costly, while the agent is not extremely loss-avers, he will decide to go for a medical inspection independently of how serious the illness might be. In the in-between situation the decision of the agent depends how much he is prone to a serious health-change. If he does not expect any serious illness to occur he is not likely to receive bad news from the doctor, and, hence, has nothing to be afraid of (emotional costs are low). If the probability to get seriously ill is known to be high, the agent will prefer the uncertainty. These results are intuitive. First, they show that not all people are ready to go for preventive inspections, but only those whose loss-aversion is overweighed by the net benets of treatment. Second, the predictions of the model are in line with the results of the surveys highlighted in the beginning of the present paper. Patients who have bad health inherence (e.g. those who have an increased risk of cancer or other serious diseases) are less willing to go to the doctor than those who do not have such risk. Finally, notice that in our model we consider costs of treatment not only in terms of monetary costs but also as unpleasantness of medical procedures. In this sense, the perspective of a less unpleasant treatment may be encouraging for a patient. Decreased monetary costs also make the visit to the doctor more likely. The latter in practice means that better functioning of the health insurance programs and larger parts of treatment costs being covered by insurance companies may lead to more people willing to undergo preventive medical inspections. These results show that applying the concept of reference-dependent pref- 19

21 erences for the understanding of human health-related decision-making might be fruitful. The model presented in this paper has some limitations that could also serve as the directions for its further development. First, we assume here that the doctor has a perfect ability to determine the patient's diagnosis. Also, the doctor in this model cannot choose which amount of information should be disclosed to the patient. Elimination of these assumptions raises a set of interesting questions. How the possibility to get a wrong diagnosis inuences the decision of the agent? To what extent the doctor should inform the patient about the severity of an illness and the consequences of treatment. Is providing less information a more favorable strategy to diminish health anxiety and encourage patients to resort to medical services more often? How can the doctor manipulate the beliefs of the patient about the real health state? Some of these issues have been already considered in Koszegi(2002). However, the reference-dependence approach, used in the present paper might be helpful in shedding light on the patient's decisionmaking in these problems as well. Another eld of research concerns the way the patient himself could choose the beliefs about health. Namely, what does the reference point depend on and could it be the case that patients choose their own beliefs about health in a way that changes their reference point to maximize their utility. Finally, a one-period model does not allow to analyze how the agent's decision changes with time. Namely, how long the agent is willing to delay visiting the doctor and on what parameters it would depend on. 20

22 appendix Appendix 1. Consider the posterior density of distribution of H after the neutral signal: f 1 ( H H, s = 0) = + P (s = 0 H)f( H H) P (s = 0 H)f( H H)d( H), The value of denominator is a constant for all values of H and a given value of H. By assumption, the function f( H H) is symmetric as well as the function P (s = 0 H). Therefore, the values of the numerator for H and for H are equal. Hence, the function f 1 ( H H, s = 0) is symmetric with respect to y-axis.in this case the expectation of H after a neutral signal is equal to zero for all values of H: E( H H, s = 0) = 0 Hf 1( H H, s = 0)d( H) Hf 1 ( H H, s = 0)d( H) = = E( H H, s = 0, H > 0) + E( H H, s = 0, H < 0) = = E( H H, s = 0, H > 0) E( H H, s = 0, H > 0) = 0. Q.E.D. Appendix 2. Calculations for the case of negative signal (s=1). We should calculate the density function for the posterior distribution of health shocks after the negative signal according to formula (1). We calculate the denominator 0 as follows: P ( H s = 1)f( H)d( H) = (1 e H )e H d( H) = = 1 2 ( 1 ) 1 +1 = 1 2(+1). 21

23 Hence, the posterior density function will be: f 1 ( H H, s = 1) = 1 2 (e H e (+1) H ) 1 2(+1) = (1 + )(e H e (+1) H ). The expectation of health change for this posterior distribution is: E( H s = 1) = 0 H(1 + )(e H e (+1) H )d( H) = = (1 + ) (1 + ) 2 (1+) = (1+) The reference point then according to (3) is: R = H + E( H s = 1) = H (1+). 2+1 Appendix 3. Proof of proposition 1. Consider expression (12) for expected utility from visiting the doctor after a positive signal. It could be rewritten the following way: E(U + ) = H<E( H H,s=1) (η 1)( H E( H H, s = 1))f 1( H H, s = 1)d( H) + + ( H E( H H, s = 1))f 1( H H, s = 1)d( H). By assumption η > 1. Taking into consideration the condition under which the rst integral is calculated we observe that the rst term of the expression above is always negative. Consider the second term of this expression. By denition of the mathematical expectation and the formulation of the model we get that: + Hf 1( H H, s = 1)d( H) = E( H H, s = 1). Taking into account that E( H H, s = 1) is constant in H and that by denition of the density function + f 1( H H, s = 1)d( H) = 1 we come to the fact that the second term of the expected utility function in this case is equal to zero. Hence, the expected utility after a positive signal is always negative. 22

24 Note that in this proof no particular specication of the distribution functions was used. Therefore, the obtained result holds for a general formulation of the model. Q.E.D. Appendix 4. Utility after a neutral signal. Consider expression (14) for the expected utility from visiting the doctor after a neutral signal. We can develop it in the following way: E(U 0 ) = + 0 Hf 1 ( H H, s = 0)d( H)+ + 0 (η D + C) Hf 1( H H, s = 0)d( H). Adding and subtracting 1 from the expression in (η D + C) we get that: E(U 0 ) = + Hf 1( H H, s = 0)d( H)+ + 0 (η 1 (D C)) Hf 1( H H, s = 0)d( H). The rst term of this expression is equal to the mathematical expectation of the change in health H after a neutral signal. Hence, given the condition that the posterior density function of H under neutral signal is symmetric with respect to zero (for the proof of this statement see Appendix 1.), this mathematical expectation is equal to zero. Now consider the second term of this expression. The function f 1 ( H) H, s = 0) is always positive and we integrate H across the interval where H < 0. This implies that the integral (excluding the constant) is always negative. Therefore, the decision of the agent in this case depends only on the sign of the constant (η 1 (D C)). If this constant is positive, that is when η 1 > D C, the expected utility from visiting the doctor after neutral signal is negative, and the agent refuses to undergo a medical inspection. In the opposite situation, when (η 1 (D C)) is negative, the expected utility is positive and the agent decides to visit the doctor. Q.E.D. 23

25 Appendix 5. Calculation of expected utility after negative signal. In our specication we can calculate the expected utility after negative signal the following way (for a shorter notation we will substitute A = 2+1 (+1)): E(U ) = A [η( H + A) + (C D) H]f 1( H s = 1)d( H)+ + 0 A [ H + A + (C D) H]f 1( H s = 1)d( H) We can take out of both integrals the part that corresponds to coecient C D. This part will be equal to: (C D) 0 Hf 1( H s = 1)d( H) = = (C D) 0 H(1 + )[e H e (+1) H ]d( H). The integral here represents the expected value of H conditional on the negative signal. It is calculated in Appendix 2. Hence, the initial equality can be continued as follows: E(U ) = (η 1) A ( H + A)f 1( H s = 1)d( H) (C D)A. Further we separate the integral in this expression into three parts and calculate each of them separately. A ( H + A)f 1( H s = 1)d( H) = = ( + 1)[ A He H d( H) A He(+1) H d( H)+ + A A(e H e (+1) H )d( H)]. A Using the rule of integration by parts we obtain the following results: A He H d( H) = e A (A + 1). He(+1) H d( H) = (+1) e A(+1) [A( + 1) + 1]. 2 24

26 [ A A(e H e (+1) H e )d( H)] = A A ] e A(+1) +1. Substituting these three expressions into the corresponding formula for the expected utility we get: ( ) E(U ) = (η 1)e A e A (C D)A. Replacing A with 2+1 (+1) we get exactly expression (21). Q.E.D. Appendix 6. Derivative of function F with respect to η. Consider expression (23) for the derivative of expected utility with respect to parameter η. In this expression the exponent outside the brackets is always positive. Hence, the sign of the derivative depends solely on the sign of the rest its part. By the sequence of equivalent transformations (for positive ) we can show that this part is negative. Since the power of the exponent is negative, the following comparison holds: Hence, 2 e 2+1 (+1) < 2 < e 2+1 (+1) < ( + 1) 2. 1 Multiplying both parts of the comparison by (+1), we get that: Consequently, and F η is negative. Q.E.D. e 2+1 (+1) + 1 < + 1. e 2+1 (+1) < 0 25

27 Appendix 7. Proof of Proposition 3. Consider the 1st-order Tailor series of function F () taken for 0: F () = (η 1)e We can rewrite this expression as follows: (C D) ( + 1) + o ( 1 F () = 1 ((η 1)e 1 + (C D)) (η 1)e 1 C D o ) ( ) 1. Since the constant term (η 1)e 1 and the ratio C D +1 belong to o ( 1 following equality holds: Hence, F () = 1 ((η 1)e 1 + (C D)) + o lim (g 1() g 2 ()) = Const 1, 0 ( ) 1. ), the where Const 1 = (η 1)e 1 + (C D). Since is always positive, the behavior of the dierence between g 1 () and g 2 () around zero depends only on the sign of the constant Const 1. If Const 1 > 0 (that is when D C < ((η 1)e 1 )) function g 1 () lies below g 2 () around zero. In other words, if Const 1 > 0 then 0 > 0 g 1 () < g 2 () < 0. The reverse holds for the case Const 1 < 0. Now consider the 1st-order Tailor series of function F () for : ( F () = (η 1) e 2 + e (+1) + O ( ) ) [ ) +1 (1 2 +(1+) 2 2 (1+) e (+1) + +1 O ( ) We can develop part of this expression in the following way: +1 (1 2 +(1+) 2 2 (1+) 2 e 2+1 (+1) ) + +1 O ( 1 2 ) +1 = = (1+) 2 (+1) 3 e 2+1 (+1) + +1 O ( 1 2 ) +1 = = 2+1 (+1) 2 (1+) O ( ) 1 = 2 26 ] (C D) 2+1 (+1).