Ostrich Effect in Health Care Decisions: Theory and Empirical Evidence Ksenia Panidi∗† Job Market Paper

Abstract In this paper I study the link between loss aversion and the frequently observed tendency to avoid useful but negative information (the ostrich effect). In the context of preventive health care choices, I obtain several novel results. First, I construct a theoretical model showing that high loss aversion decreases the frequency of preventive testing due to the fear of a bad diagnosis. Second, I show that under certain conditions, increasing risk of illness discourages testing for a highly loss-averse agent. Third, I use a representative sample of the Dutch population to provide empirical evidence supporting these predictions. The main findings confirm that loss aversion, as measured by lottery choices in terms of life expectancy, is significantly and negatively associated with the decision to participate in preventive testing for hypertension, diabetes and lung disease. Higher loss aversion also leads to lower frequency of self-tests for cancer among women. Finally, the effect is more pronounced in magnitude for people with higher subjective risk of illness. 1

JEL Classification: D80 Keywords: health anxiety, loss aversion, information aversion

∗ Doctoral

student at Université Libre de Bruxelles (ECARES), Aspirant FNRS, Brussels, Belgium am grateful to Georg Kirchsteiger, Peter Kooreman, Katie Carman, Jan Potters, Peter Wakker, Johannes Binswanger, Wieland Müller, Reyer Gerlagh, Ernan Haruvy, Martin Hellwig, Eric Bonsang, Miguel Carvalho, Oleg Shibanov, Fangfang Tan, Patric Hullegie, Markus Fels, and the participants of the workshops and seminars at Université catholique de Louvain, Tilburg University, Max Planck Institute for Research on Collective Goods in Bonn, ENTER Jamboree and MESS Workshop in Oisterwijk for 1 valuable comments and discussion. I would like to thank the researchers at the CentERdata unit in Tilburg University, especially Tom de Groot, for their excellent organization of empirical work. 1 This paper draws on data of the LISS panel of CentERdata. †I

1. Introduction The present paper studies the so-called "ostrich effect", in which an individual prefers not to obtain information about her state of affairs because of the fear that she may receive bad news, despite the prospect of making better decisions based on this information. Although the ostrich effect may arise in many different situations the present study addresses it in the context of health care decision-making. It provides theoretical and empirical support for the link between loss aversion and the frequency of preventive health tests2 . More frequent testing for many diseases is desirable because earlier diagnosis usually allows for less costly and more efficient treatment. However, empirical evidence suggests that many people avoid visiting doctors because of their fear of receiving negative medical results3 . Studies of lung disease and cancer screening show that symptomatic patients delay visiting doctors longer when the probability of being ill is high or when symptoms of an illness are more obvious (Basnet et al. (2009), Caplan (1995), Bowen et al. (1999)). Women with a family history of breast cancer often experience higher anxiety about the results of a mammogram (an X-ray of the breast to identify potentially malignant cell masses), which becomes a barrier to regular screening for breast cancer (Kash et al. (1992), Andersen et al. (2003)). In Calder et al. (2000), the time that passes between noticing tuberculosis symptoms and deciding to consult a doctor about them is shown to be associated with a fear of learning one’s diagnosis. The study contributes to the research on the issue in several ways. First, it presents a behavioral economic model with reference-dependent preferences explaining the choice of preventive test frequency. The model establishes a negative relationship be2 The

term "ostrich effect" has been used in studies of financial decision-making, where it signifies investors’ willingness to "avoid risky financial situations by pretending that they do not exist" (Galai and Sade(2003)). Karlsson et al. (2009) finds empirical support for investors’ tendency to pay more attention to positive rather than negative financial information. 3 The word "negative" here means "indicating a health problem" contrary to its usual meaning in medicine.

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tween the frequency of health tests and the degree of loss aversion for agents with no particular symptoms of a disease. Moreover, the model demonstrates that under certain conditions increasing risk of illness discourages testing. Second, this is the first study that provides empirical support for the effect of loss aversion on the uptake of preventive testing among the non-symptomatic undiagnosed population in a broad range of conditions such as hypertension, diabetes, chronic lung disease and cancer. Finally, the link between loss aversion and the ostrich effect is supported based on a general population questionnaire study. This feature distinguishes the study from other empirical works on loss aversion in the health domain, which are typically based on non-representative population samples (such as students or very small groups of individuals). The theoretical explanation of the link between loss aversion and testing frequency is based on the assumption of reference-dependent preferences with respect to health status. A person may have some beliefs about her level of health (i.e. a reference point) and be afraid to learn that her actual health is lower than this perceived level. An agent may expect to experience a sense of loss after a doctor visit and prefer to avoid it (in other words, to maintain the status quo). In each period of a two-period model, the agent decides whether she wants to undergo a test and receive treatment in case an illness is detected. If the agent did not undergo a test in the first period, she can choose to do so in the second period. However, she has to keep in mind that if an illness has already developed, the situation may become worse if it is left untreated. Treatment in the second period will be more costly in this case. Will the agent choose to learn potentially unpleasant news more frequently (e.g., in every period) with the benefit of cheaper treatment, or to test only once or not test at all, thus, reducing emotional distress but potentially suffering a worse health outcome? The answer that the model gives depends on the degree of loss aversion. When loss aversion is lower than a certain threshold, testing in every period is preferred. However, as loss aversion increases, the

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agent first switches to testing only once and, then, to not testing at all for very high loss aversion. Under certain conditions on the model parameters, a highly loss-averse person is even more likely to avoid testing when her risk of illness increases. Yet, if the agent’s loss aversion is sufficiently small, then increasing risk will lead to more frequent testing. This modeling approach is different from the well-known Kreps-Porteus type of preferences for delayed resolution of uncertainty (Kreps and Porteus (1978)). The latter implies that a person cannot take action to improve the outcome of a future lottery; she may only choose whether to reveal it now or later. Note that revealing the health state early in my model also means reducing the likelihood that health will worsen in the future. The present model also differs from other theoretical studies using reference-dependent preferences to model health anxiety. For example, Kőszegi (2003) aims to explain individuals’ tendency to delay visiting doctors based on psychological expected utility (Caplin and Leahy (2001)) and derives the conditions under which such delays are most likely to occur. Although this model explains doctor avoidance in case of bad symptoms, it crucially depends on the assumption that the set of treatment possibilities available to an agent coincides with that of a doctor. This assumption seems questionable for many serious illnesses, and if it is not satisfied, a person will always prefer to visit the doctor. We will see that this is not the case in my model. Empirical analysis of the link between loss aversion and the ostrich effect is based on a specially designed survey administered to a representative sample of the Dutch population. Respondents answered a series of gain-loss lottery choice questions that elicit a proxy for the degree of loss aversion. To make this measure more relevant to the health domain, the lotteries were formulated in terms of gains and losses of life years with a 50-50 chance. Each lottery was a gain-loss lottery with a clearly stated reference point, i.e., the respondent’s current life expectancy. Each lottery had an identical

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amount of gains (10 additional years of life), and losses varied from 0 to 10 years of life. The largest loss that an individual accepted in return for 10 additional years of life at a 50-50 chance provided a proxy for loss aversion. Additionally, respondents had to indicate their frequency of performing various health tests, such as tests for high blood pressure and high blood sugar level, X-rays to detect lung disease and medical cancer tests, and self-tests for cancer. Because a large part of the population (25-75 percent) never performs any of these tests, I use a two-part modeling approach. I first determine whether loss aversion influences the decision to test (participation decision) and then determine whether it affects the frequency of tests for those who have chosen to test. The results indicate that the loss aversion proxy is significantly and negatively correlated with the decision to test in all cases except cancer screening. For a person with average characteristics, the difference between the highest and lowest degrees of loss aversion translates roughly into a 10-percentage-point difference in the probability of participation in testing. Loss aversion is also found to decrease the frequency of cancer self-tests significantly for women. Finally, the loss-aversion effect is consistently larger in magnitude for people who judge themselves to be at above-average risk, although the difference from the below-average risk group is not statistically significant. The paper is structured as follows. Section 2 presents the theoretical model. Section 3 presents the details of data collection. The empirical strategy and estimation results are presented in Section 4. Section 5 concludes.

2. The Model 2.1 Assumptions and structure I consider a two-period model. Prior to period 1, an individual enjoys perfect health of level H > 0. At period 1, the agent’s health may change. The change in health is a discrete 4

random variable4 that takes the value zero with probability p and −a (where a > 0) with probability (1 − p):      0, ∆H1 =     −a,

with prob. p;

(1)

with prob. (1 − p),

with p > 1/2. In other words, an agent’s health may either become worse or remain the same in the first period, and illness occurs with a probability less than 50% 5 . The change in health is not observable. The agent observes a signal that contains some information about the underlying health change. The signal can be either negative (equal to -1), or zero which corresponds to observing or not observing the symptoms of an illness, respectively. The distribution of the first-period signal conditional on ∆H1 is the following:

P r(s1 = 0|∆H1 = 0) = 1; P r(s1 = 0|∆H1 = −a) = 1 − q; P r(s1 = −1|∆H1 = 0) = 0; P r(s1 = −1|∆H1 = −a) = q, with q > 1/2. These assumptions imply that zero health change cannot produce a negative signal. A negative signal is informative (i.e., indicates a negative health change correctly in more than 50% of cases) and revealing (i.e., it cannot appear if there is no health change). A zero signal is informative, yet not fully revealing. 4 The model is solvable and generates qualitatively similar results when the health change is continuous, but because it involves tedious computations, a discrete version is presented here for ease of exposition. 5 This assumption is not very restrictive because most illnesses to which this study is related typically have incidence rates lower than 50%.

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After observing the signal the agent may decide whether to do a medical test that accurately reveals the health condition. If an illness is detected (∆H1 < 0), the agent receives a costly treatment that restores her health back to level H. The costs of treatment are proportional to the health change and are equal to C · a with6 C < 1. Note that costs of treatment may include not only monetary expenses but also any physical discomfort from medical procedures. In the second period, the agent’s health may change further. The agent observes signal s2 and decides whether to undergo a test. Again, if an illness is detected, she pays the costs of treatment. The distribution of the second-period change depends on whether testing was chosen in period 1. If the agent has chosen to test, then her health level prior to the signal in period 2 is H. The distribution of an unobservable health change ∆H2 is identical to that of period 1 (defined by equation (1)). Therefore, her health state prior to testing in period 2 may be either H or H − a with probability p and (1 − p), respectively. If no test was taken, then her health level at the beginning of period 2 may be either H or H − a and is not known. If no illness happened during period 1, she again faces the same distribution of health change as ∆H1 . If an illness has occurred, then her health worsens in the second period with probability 1 and becomes H − ka (i.e., ∆H2 = −(k − 1)a). In other words, if an illness was left undetected and untreated in period 1, it worsens by a factor of k in the second period. The observed signal s2 is distributed similarly to s1 :

P r(s2 = 0|∆H2 = 0) = 1; P r(s2 = 0|∆H2 = −a) = P r(s2 = 0|∆H2 = −ka) = 1 − q; P r(s2 = −1|∆H2 = 0) = 0; 6 In

the case of C > 1, the agent never chooses to perform any test in both periods. Therefore, this case is uninteresting for analysis.

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P r(s2 = −1|∆H2 = −a) = q, with q > 1/2. The assumption that P r(s2 = 0|∆H2 = −a) = P r(s2 = 0|∆H2 = −ka) is not crucial for the results of the model. It generates identical results if the probability of observing a neutral signal decreases with worsening health. Note here that a negative signal is not fully revealing (unlike in period 1). It may indicate a health change of either −a or −ka. The costs of treatment can be either 0, Ca or Cka depending on the detected health change.

2.2 Utility function Define t ∈ {1, 2} to be the period index, St to be the set of signals available to the agent in period t, and At to be the action taken in period t. Note that S1 = {s1 }, S2 = {s1 , s2 }, and At ∈ {Vt , N Vt } where Vt and N Vt stand for "visit" and "no visit" to the doctor in period t respectively. The agent’s utility function consists of two parts - emotional, which is referencedependent, and physical, which corresponds to physical outcomes7 . To represent the reference-dependent part of the utility function, I use the approach developed in Kahneman and Tversky (1979). Namely, the emotional reaction of the agent to the news about her health level is determined as a gain-loss utility. In this case, good news about the agent’s health is equivalent to obtaining information that her current health state is better than her expected health level. Analogously, the agent gets bad news when she learns that her actual health is worse than expected. The reference point here is defined as the agent’s expectation of health after observing the signal. The reference point may change after new information arrives. Therefore, I define it, depending on the period, as: 7 The

idea of separating physical and emotional outcomes has been employed in several previous studies. See, for example, Kőszegi and Rabin (2006,2007,2009).

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HR,1 = H + E(∆H1 |S1 ) HR,2 = H + E(∆H2 |S2 , A1 ) In each period, the agent decides whether to undergo a health test. I first define a one-period utility that she gets from testing. This utility has an emotional part, which is a linear value function with a kink at reference point HR,t and a loss aversion coefficient equal to λ > 1. This form of emotional utility has been proposed in Köbberling and Wakker (2005). The physical part includes costs of treatment and utility of health H:     if (H + ∆Ht ) > HR,t  (H + ∆Ht − HR,t ) + C∆Ht + H, Ut (Vt ) =     λ(H + ∆Ht − HR,t ) + C∆Ht + H, if (H + ∆Ht ) < HR,t

(gains).

(2)

(losses);

Note that costs of treatment may arise in both cases. If the agent’s actual health has worsened less then she expected, this will constitute an emotional gain, but she will have to pay costs of treatment anyway. If the agent rejects the opportunity to undergo a test (and, hence, does not resolve the uncertainty about her health), she receives a one-period utility from her expected health level:

Ut (N Vt ) = HR,t

(3)

Because the agent does not live more than two periods, her choice of action in period 2 results only from comparison of expressions (2) and (3). In period 1, the agent makes the decision by taking into account not only the first-period utility but also the consequences of her decision for her second-period outcomes. Therefore, her overall utility from visiting the doctor in period 1 is defined as the sum of the first-period

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utility from undergoing a test and the expectation of her second-period utility:

U12 (V1 ) = U1 (V1 ) + E(U2 (A2 )|S2 , V1 ),

(4)

where A2 denotes the action that the agent expects to take in period 2 after observing the second-period signal. Analogously, her overall utility from not visiting the doctor in period 1 equals:

U12 (N V1 ) = U1 (N V1 ) + E(U2 (A2 )|S2 , N V1 ).

(5)

2.3 Choice of testing frequency Because this study focuses on the preventive behavior of non-symptomatic individuals, the model is considered for the cases s1 = 0 and s2 = 0. Figure 1 presents the game tree. The agent is first confronted with the choice between visiting and not visiting the doctor after she observes a zero signal in the first period. Next, in period 2, she observes either a zero or a negative signal. Four cases are possible depending on the first-period choice and second-period signal. Each case represents a decision node, which is denoted as Ii with i ∈ {1, 2, 3, 4}. To solve the model I use the concept of the subgame perfect equilibrium. The model is solved by backward induction. First, the agent decides on her optimal strategy in period 2. A second-period strategy is defined as a four-element set W = {w1 , w2 , w3 , w4 } where wi ∈ {V2 , N V2 } represents the agent’s choice in each of the four decision nodes of period 2. In every decision node she makes her choice based on the posterior distribution of her health state. The latter is calculated using the Bayes rule based on the history of signals and the first-period action. Consider, for example, decision node I1 . In this node, both signals are zero, and the agent has chosen to visit the doctor in period 1. In this case, the conditional prob-

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abilities of the second health change are independent of the first-period signal. The probability that the second-period health change is zero is recalculated in the following way:

P r(∆H2 = 0|I1 ) =

=

P r(s2 = 0|∆H2 = 0) · P r(∆H2 = 0) P r(s2 = 0|∆H2 = 0) · P r(∆H2 = 0) + P r(s2 = 0|∆H2 = −a) · P r(∆H2 = −a)

Therefore this probability is P r(∆H2 = 0|I1 ) = probability is P r(∆H2 = −a|I1 ) =

p p+(1−p)(1−q)

(6)

and the complementary

(1−p)(1−q) . p+(1−p)(1−q)

Next, the agent computes her reference point in node I1 , which is her expected level of health given the posterior distribution of a health change:

∆H 2 (I1 ) = −a ·

(1 − p)(1 − q) p + (1 − p)(1 − q)

(7)

Observing a negative health change after a doctor visit constitutes an emotional loss compared to the reference point, whereas observing a zero health change constitutes a gain. The agent computes her expected utility from visiting the doctor taking into account the probabilities of a gain and a loss derived above. Note that the expectation of emotional utility is always negative, independent of the probability weights assigned to losses and gains. This utility part depends linearly on loss aversion (or more precisely on (λ − 1)). The agent’s expected utility from visiting a doctor in this case is8 : 8 The

details of this computation can be found in the Appendix.

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E(U2 (V2 )|I1 ) =

(8)

= −(λ − 1) · a · P r(∆H2 = −a|I1 ) · P r(∆H2 = −a|I1 ) − C · a · P r(∆H2 = −a|I1 ) + H Finally, her expected utility of not visiting the doctor is calculated by the following:

E(U2 (N V2 )|I1 ) = H − a · P r(∆H2 = −a|I1 )

(9)

Comparing equations (8) and (9), the agent chooses whether to undergo a test. Her choice in this case is determined by the following inequality for loss aversion (substituting for computed probabilities):

(λ − 1) <

(1 − C)(p + (1 − q)(1 − p)) p

(10)

This inequality provides a threshold for loss aversion that defines whether the agent will undergo a test. If loss aversion is below this threshold, the agent will choose to test, and she will choose not to test otherwise. Similar thresholds are obtained for the choice in other decision nodes. The computations for each node can be found in the Appendix. In the node I2 , a negative signal perfectly reveals the health change. The distribution of the second-period signal after visiting the doctor coincides with that of the first period. Observing s2 = −1, the agent knows for sure that her health change is negative (because a negative signal can only appear in case of a negative health change) and equals −a. In this case her health state revealed by the doctor coincides with her reference point. As a result, her emotional costs are equal to zero, and loss aversion does not influence her choice (she always chooses to visit the doctor). Therefore, only the thresholds from nodes I1 , I3 and I4

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determine the agent’s choices in the second period. The corresponding thresholds are denoted as T1 , T3 and T4 . These thresholds define four intervals for loss aversion. Depending on the considered interval the agent’s optimal behavior is characterized by one of the four strategies described in the following lemma:

Lemma: There exist thresholds 0 < T1 < T3 < T4 such that the agent’s optimal second-period strategy depends on loss aversion in the following way: (1) for (λ − 1) ∈ (0, T1 ) the agent chooses to test in all four decision nodes (i.e. W ∗ = {V2 , V2 , V2 , V2 }); (2) for (λ − 1) ∈ (T1 , T3 ) the agent chooses not to test in node I1 and to test in all other nodes (i.e. W ∗ = {N V2 , V2 , V2 , V2 }); (3) for (λ − 1) ∈ (T3 , T4 ) the agent chooses not to test in node I1 and I3 and to test in all other nodes (i.e. W ∗ = {N V2 , V2 , N V2 , V2 }); (4) for (λ−1) ∈ (T4 , +∞) the agent chooses to test only in node I2 (i.e. W ∗ = {N V2 , V2 , N V2 , N V2 }).

To understand the intuition behind this lemma, consider the emotional costs of the agent. These emotional costs depend on the reference point, which determines the sizes of gains and losses from learning the diagnosis. The reference point in turn depends on the second-period signal and on the previously taken action. In node I1 , the reference point is the highest among the four nodes. The agent has visited a doctor in the first period and, hence, should not expect a large health change given the neutral signal. In node I2 , the agent receives a negative signal, which shifts her reference point downwards. In node I3 , the reference point is even lower. Although the agent observes a neutral signal, she is in a more uncertain situation: her expected health change may be larger because an undetected illness from period 1 may have progressed. Finally, the lowest reference point is in node I4 . Here, the negative signal definitely means worsening of health, possibly as large as −ka.

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As the reference point decreases from one node to another, the expected emotional costs decrease as well. When the reference point becomes lower, the outcome above it provides more of a gain and the outcome below it brings less of a loss (holding loss aversion constant). The loss aversion coefficient may then be interpreted as the sensitivity of the agent’s decision to changes in her emotional costs. When emotional costs are large (as in node I1 ), a small increase in loss aversion produces a large increase in emotional costs and, hence, leads the agent to switch from testing to not testing. When the reference point decreases, a larger change in loss aversion is needed to make the agent switch. Hence, the threshold defining refusal to test increases when moving from one node to another. This is exactly what is described in the Lemma. The agent’s problem is analogously solved in period 1 for each agent’s secondperiod optimal strategy. The agent observes a zero first-period signal and computes the overall expected utility from visiting and not visiting the doctor in period 1. As stated in equations (4) and (5), this utility consists of two components: expected utility of the first and second periods, respectively. The first part is defined by equation (2). To compute the expected second-period utility, the agent first calculates the probability of getting into every decision node of period 2 given her action and the first-period signal. Then, she multiplies these probabilities by the utility that she expects to obtain in every decision node given her second-period strategy. Because the agent may have four different strategies in period 2, the solution to her problem then generates four cases. Analogously to period 2, the agent’s first-period decision depends on loss aversion. This gives four first-period thresholds that determine whether the agent chooses to test. Combining these thresholds with those obtained in period 2, I derive the intervals for loss aversion in which the agent chooses to test in both periods, in one period or not at all. The following proposition holds9 : 9 See

the Appendix for a detailed calculation.

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Proposition 1: In the subgame perfect equilibrium given that s1 = 0, C < 1 and p, q > 1/2 there always exist thresholds 0 < L1 < L2 such that: (1) for (λ − 1) ∈ (0, L1 ) the agent chooses testing in both periods; (2) for (λ − 1) ∈ (L1 , L2 ) the agent chooses testing only in period 1; (3) for (λ − 1) ∈ (L2 , +∞) the agent chooses not to test in any period.

This proposition states that the frequency of testing decreases with loss aversion. Let us consider the intuition behind this result. The agent makes a choice in period 1, taking into account her expected utility of period 2. Her trade-off involves not only current emotional costs and utility of treatment, but also the possibility to avoid larger physical costs in the future. This choice is again characterized by a threshold. If loss aversion is lower than the minimum between the first-period threshold and T1 , the agent will undergo testing in both periods. When loss aversion increases beyond this level, the agent rejects testing in the second period. This happens because the second period is the last one, and testing does not bring additional future benefits (e.g., avoiding a large health loss in the future). Finally, when loss aversion is above threshold L2 , the agent’s emotional costs in the first period become so large that they override future benefits of testing. As a result, the agent decides not to test in any period when loss aversion is large enough. I analyze the behavior of thresholds L1 and L2 with respect to the risk of illness as determined by the probability (1 − p). The following proposition holds10 :

Proposition 2: (1) The agent is more likely to choose testing in both periods versus testing only in one period when the probability of being ill (1 − p) increases (i.e., the threshold L1 decreases in p); (2) There exist parameter values of k and q such that the agent is less likely to choose testing 10 See

Appendix for the proof.

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in one period versus not testing at all when the probability of being ill (1 − p) increases (i.e., there exist functions f1 (q) and f2 (q), monotonously decreasing and increasing in q, respectively, and such that for any f1 (q) < k < f2 (q), the threshold L2 increases in p).

Suppose that loss aversion is below L2 , and the agent has chosen to test in the first period. The threshold L1 determines whether the agent will choose to test in period 2. The first part of the proposition means that the frequency of testing depends positively on the risk of illness. When the risk of illness increases, the agent becomes more likely to test twice rather than once. An increase in the risk of illness has several effects on the agent’s utility. First, it reduces the expected health of the second period, which increases the expected physical benefits of treatment. The expected costs of treatment increase as well, but because C < 1, the net benefits of treatment rise. Second, the larger risk of illness reduces the agent’s reference point. This effect reduces the emotional costs of testing by increasing gains and reducing losses relative to this reference point. Finally, an increased risk of illness lowers the posterior probability of ∆H2 = 0 after observing a zero signal. The first two effects make testing in the second period more attractive. The third effect works in the opposite direction. However, because, by assumption, p, q > 1/2, the overall effect of an increase in the risk of illness is to encourage the agent to test more often. Because this happens for any value of loss aversion, the threshold L1 increases with risk. The second part of the proposition describes the choice between testing only in period 1 and not testing at all. Here, the agent knows that her loss aversion is large enough to make her reject testing in the second period. However, if loss aversion is smaller than L2 , she may still choose to test in the first period. An increase in the probability of illness will diminish the emotional costs of testing due to the same effect described above. However, a higher risk of illness may have the opposite effect on the second-period expected utility. When the agent makes a decision to test in the first

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period, she does not know which signal she will observe in period 2. Therefore, she has to compare the expected utility that she may obtain in period 2 after testing early versus not testing. If she chooses not to test, she runs the risk of a large decrease in health due to the factor k > 1 if an illness is left untreated. This, in turn, lowers the reference point in the second period. As a result, when the risk of illness rises, the agent may prefer to delay testing until she observes symptoms in period 2. This enables her to save emotional costs in the first period and reduce them in the second period by allowing her reference point to adjust downwards. The direction in which the threshold L2 moves in response to the increase in risk depends on which of the opposing effects dominates. When k is not very large, the gains of delaying the test until symptoms are observed will override the potential higher costs of treatment. Hence, L2 will depend negatively on the risk of illness (i.e., increase in p) when k is not too large. Propositions 1 and 2 allow us to derive the following testable predictions: Hypothesis 1: The frequency of preventive checkups for people who do not observe any symptoms of an illness and are not diagnosed with it depends negatively on their level of loss aversion. Hypothesis 2: The negative effect of loss aversion on the frequency of tests is larger for people with higher subjective risk. In the remainder of the paper I provide empirical support for these hypotheses.

3. Data 3.1 Data sources The data used in this paper were collected by means of a questionnaire study specifically designed for this purpose. The questionnaire study was conducted in August 2010 as a separate study within the Longitudinal Internet Studies for the Social Sci-

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ences (LISS) panel11 of the CentERdata (Institute for Data Collection and Research at Tilburg University, Netherlands). The data on loss aversion were obtained in a separate wave in March 2011. The questionnaire was administered to a representative sample of the Dutch population above 40 years old. It was conducted by internet. In the LISS panel the respondents who do not have internet access are provided with a device allowing them to access and complete the survey via their television set. The total number of respondents who completed both questionnaires is12 3006. The socio-economic characteristics of the respondents are available for all participants of the LISS panel and did not require collection by means of a questionnaire. Table 2 in Appendix B3 presents summary statistics and sample composition for those characteristics. Since 2007, participants of the LISS panel are invited to complete an annual core study that contains a separate health-related module. I use some of the variables in this module (measured in 2009 (wave 3)) as additional control variables. In this study I focus on several conditions and illnesses for which taking preventive measures is particularly important because a long delay can significantly worsen the long-term prognosis. These include hypertension (which increases the risk of a heart attack and stroke), high blood sugar level (which is associated with diabetes), chronic lung disease (such as chronic bronchitis or emphysema), and cancer. The questionnaire began by asking whether the respondent has experienced the symptoms of the conditions of interest. For every disease, the respondents were asked 11 Further

information on the structure and functioning of this panel is available at www.liss.nl total number of respondents who received an invitation to complete the main survey (without the loss aversion section) was 4640. The response rate was 80.3% (3725 respondents), and a total of 3702 completed questionnaires were received. The wave measuring loss aversion was sent to a sample of 4252 people and completed by 3465 (81.5%) respondents, most of whom also participated in the first wave. The second sample does not completely match the first one. Members of the LISS panel are restricted in the number of questionnaires they can complete during a month (they usually receive approximately 4-5 questionnaires). Hence, some people from the first wave did not appear in the second wave because they had already completed the maximum number of questionnaires for that month. In addition, the second wave contains respondents who did not participate in the first wave for the same reason. 12 The

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a Yes/No question about whether they have ever thought that they might be developing it. Next, they were presented with lists of symptoms typical for each of the four conditions (high blood pressure/hypertension, high sugar level/diabetes, chronic lung disease, any type of cancer) and asked to indicate whether they had ever experienced any of those symptoms on a regular basis (i.e., Yes/No for every group of symptoms). Table 1 presents the lists of symptoms given to the respondents. Next, they were asked whether those symptoms were still present, whether they had ever consulted a doctor about them and whether they had been diagnosed with a disease (and if so, when). This information filters out the group of non-symptomatic undiagnosed respondents, who are the primary interest in this study. The prevalence rate of the symptoms that are mentioned in Table 1 and the diagnosis rates in the sample (both as reported by the participants of the study) are presented in Table 2 (see Appendix B3). This table also provides summary statistics of the background variables for the subsamples of undiagnosed non-symptomatic individuals. Two specific main variables that are interesting are the frequency of preventive tests for these respondents and the individual degree of loss aversion. In addition, a measure of subjective risk is elicited to test the second hypothesis. Below, I describe the procedures used to obtain these variables. 3.2 Measuring frequency of preventive tests Preventive measures correspond to the four conditions in the following way: - high blood pressure/hypertension: blood pressure test; - high blood sugar level/diabetes: blood test to determine the blood glucose level; - chronic lung disease: chest X-ray; - cancer: any non-invasive procedure for cancer screening (such as mammogram, Pap smear test, blood test, any kind of screening, etc.). I explore separately the frequency of cancer tests performed in a hospital and

18

the frequency of self-tests for cancer. Examples of self-tests for cancer include selfexamination of the breasts for breast cancer, detecting the presence of blood in the stool for colon cancer, self-examination of the cervix for cervical cancer, visual inspection of the mouth for signs of oral cancer, etc. The respondents had to indicate how often they performed tests for the 4 conditions described above. The frequencies of blood pressure tests and sugar level tests were measured as categorical variables, with answers falling into one of 8 categories: (1) Never; (2) Every few years; (3) Once a year; (4) 2 times a year; (5) 3-4 times a year; (6) Every 2 months; (7) Once a month; (8) Once a week or more often. To assess the frequency of lung disease tests and cancer screening, the respondents had to indicate how often they had undergone the relevant tests in the past 10 years. The frequency of self-tests for cancer was measured in the same way as the frequencies of blood pressure and sugar level tests. 3.3 Measuring loss aversion The standard procedures for eliciting loss aversion have mostly been applied in the monetary domain. Studies eliciting risk preferences, and particularly loss aversion in health care, are scarce. The study by Abellan-Prepinan et al. (2009) exploring risk preferences in health outcomes adopts the estimates of the loss aversion coefficient obtained for the monetary domain in Tversky and Kahneman (1992). In Stalmeier and Bezembinder (1999), the loss aversion coefficient is estimated for the choice between

19

some impaired health state as a status quo and a gamble with possible improvement or worsening of health. Bleichrodt and Pinto (2002) estimates the significance of the loss aversion phenomenon in the domain of health using riskless choice questions. One important problem that arises in eliciting loss aversion is separating the risk preferences stemming from the utility curvature (risk aversion) from those evoked by the disproportional weight put on losses compared to gains (loss aversion).13 . Several studies have filtered out different components of risk preferences. These techniques usually imply stating indifference in a series of choices comparing two lotteries with changing outcomes or probabilities (Booij and van de Kuilen(2009), Wakker and Deneffe (1996)). These procedures often result in a high non-response rates in general population studies because the task becomes too complicated for many people. Stating indifference in lotteries presented in terms of health outcomes may be even less accessible for the respondents than when the lotteries are presented in terms of money. On the other hand, employing a less complicated elicitation procedure may not deliver enough information to derive a good measure of loss aversion. In this study, I aim to balance these conflicting issues. To preserve the representativeness of the sample and yet obtain a reasonable proxy for loss aversion in a series of acceptance/rejection questions, I elicit indifference between the lotteries in life expectancy and a fixed reference outcome. The reference outcome is fixed at the respondent’s perceived life expectancy. The respondent is presented with a series of binary choice questions (accepting or rejecting a lottery). Each lottery is a 50-50 probability lottery with a positive outcome being an increase in life expectancy by 10 years. The negative outcome is varied from the loss of 0 years of the current life expectancy up to 10 years14 . The value of loss aversion is recorded from the midpoint between the last 13 According

to prospect theory, probability weighting may also influence risk preferences: people are generally found to overstate large and understate small probabilities. In this study, respondents face 5050 lotteries. Empirical evidence suggests that probability distortions are minimized around the middle of the probability scale (Gonzalez and Wu(1999), Wu and Gonzalez(1996)). 14 The examples of the questions for this procedure can be found in Appendix B2.

20

accepted lottery and the rejected lottery. Loss aversion is computed according to the following formula: LA = 10/(n−3/2), where n is an index of the rejected lottery. For example, if the respondent rejects the lottery offering (+10, -4) but accepts all preceding lotteries, his/her loss aversion coefficient is recorded as 2.86 (because this is the fifth lottery in the sequence). People who answer "Yes" to all 11 lotteries are assigned loss aversion equal to 1. Respondents who rejected the very first, "harmless", lottery with the negative outcome being zero are assigned loss aversion of15 58. Although this procedure does not allow me to perfectly separate loss aversion (in the sense of relatively heavier losses versus gains) from the utility curvature, I argue that the choice in this task is to a large extent driven by loss aversion. First, the respondents face lotteries with a clearly stated reference point. Positive and negative outcomes here are unambiguously coded with respect to a given point of comparison, which is the perceived life expectancy. Previous studies have shown that loss aversion is typically more pronounced in choices with a clearly stated reference point. For example, Hjorth and Fosgerau (2011) find more evident loss aversion in cases when the reference point is more firmly established. In Ritov and Baron (1993), manipulating the salience of the reference point leads to changes in the subjects’ behavior in risky choices: when the status quo is more salient fewer subjects demonstrate indifference in choices between risky options. Koop and Johnson (2010) argues that salience may be an important condition for an outcome to become a reference point. Second, many studies find that the status quo, the respondent’s expectation of the outcome, or the respondent’s aspiration level of the outcome usually serve as points of comparison evoking loss aversion. Several studies support the status quo bias in the domains of goods and money (Knetsch (1989), Schweitzer (1994)). Koszegi and Rabin 15 Formally,

it is impossible to derive loss aversion for this group of respondents because there is no midpoint. In other words, their loss aversion can be infinitely large. However, it is desirable to assign a certain value for them, and this value should be on the same "scale" as all other values. To do this, I build a curve that connects all 11 points representing the loss aversion values. I then approximate it with a polynomial of degree 6 (which appears to be an optimum) and find that the value predicted by this polynomial is approximately 58.

21

(2006) argue that the status quo may also be interpreted in terms of expectation if a person does not expect her status quo to change. Van Osch et al. (2006) finds that a sure outcome presented in the lottery choices involving life expectancy serves as a reference point for the majority of subjects. Harinck et al. (2007) lists several studies confirming that loss aversion is more relevant for anticipated rather than experienced outcomes. Neuman and Neuman (2008) uses a discrete-choice experiment to confirm that loss aversion arises with respect to the status-quo scenario given to the subjects. It is easy to see that perceived life expectancy used as a point of comparison in the present study satisfies all mentioned definitions of a reference point. Life expectancy by definition is an individual’s expected length of life. It may indicate an aspiration of life duration. At the same time, it is also presented as a status-quo scenario as the respondents do not have any better estimate of their life duration than their perceived life expectancy. All of this makes perceived life expectancy a likely candidate for the reference point in this study. Finally, to derive a proxy for loss aversion, I use mixed gambles, i.e., gambles involving both gains and losses. This makes the concept of loss aversion particularly relevant. If the lotteries offered to the respondents were framed solely in terms of gains or losses, then loss aversion would not be able to explain observed lottery choices (Wakker (2010)). Brooks and Zank (2004) find that once a loss outcome is introduced to a pure gain lottery, most subjects shift in the direction of loss aversion. Several points should be made regarding the use of this proxy for loss aversion in regressions. First, loss aversion is normalized to the interval from 0 to 1, with the first-lottery rejecters receiving the value 3. Table 3 (in Appendix B4) presents the list of loss aversion values with their corresponding frequencies in the sample. Normalized loss aversion gives an objectively better fit of the data compared to the logarithm of non-normalized loss aversion: in the regressions with identical numbers of observations and sets of ex-

22

planatory variables, it produces a higher pseudo R-squared and higher likelihood ratio and higher significance of loss aversion itself. Second, as a robustness check, I present regression results excluding respondents who have rejected the "harmless" lottery (with zero loss in health). People may be rejecting this lottery for various reasons not directly related to loss aversion. For example, they may have an aversion to any kind of medical procedure or may not be able to imagine a treatment with no side effects. Such beliefs may decrease the frequency of testing without relation to loss aversion. Finally, the group of respondents who answered "Yes" to all loss aversion questions is not included in the sample. Although this group constitutes only 2-3% of the sample in regressions (depending on the illness), it has a disproportional influence on the estimated effect of loss aversion and on its statistical significance. For example, inclusion of these observations in the regression for sugar level tests (only 2.5% of the sample) increases the p-value for loss aversion almost threefold. In the empirical analysis literature, such observations are typically called "fringeliers", i.e., observations that do not greatly stand out in the sample (usually approximately 3 standard deviations from the mean) and yet "occur more often than seldom" (Wainer (1976)). It has been found that inclusion of the fringeliers may significantly increase the error variance and reduce the power of statistical tests (Osborne and Overbay (2004)). Deleting these observations is recommended as one potential way of dealing with them (Hancock (2010), p.62). I follow this practice when presenting the main results of the study, but the results of regressions, including the fringeliers, are also presented in the Appendix as a robustness check16 . 16 Note that the respondents may be assigned to this group just by answering "Yes" to every loss aversion question without careful consideration. A suggestive fact is that the average time spent per question by the respondents in this group is 14 seconds, which is much lower than the average of 63 seconds for the rest of the sample. Another reason for such responses may be the acquiescence bias (so-called "yeah-saying"; Fischhoff and Manski (2000)).

23

3.4 Measuring subjective risk To measure subjective risk of illness, respondents were asked to indicate how likely they believe it is that they will develop an illness in their lifetime. They were asked to state this likelihood using a number between 0 and 100. However, this measure does not give any information on whether a respondent views this risk as high, low or average. In addition, as previous general population studies have shown, the stated probability of being ill may be far from its epidemiological estimates (see Carman and Kooreman (2011)). To address this problem, I ask the respondents to indicate the number of people out of 100 from the same socio-economic group who they estimate will develop an illness in their lifetime. The ratio of these two measures allows me to classify respondents into three groups. If this ratio is larger than 1, a person belongs to the above-average risk group; if it is smaller than 1, to the below-average risk group; and if it is exactly 1, to the average-risk group. For example, if an individual estimates her own risk to be 10% but states that only 5 people out of 100 will develop an illness, then she is classified as a subjectively high-risk person.

4. Empirical Results For every particular illness, I focus on people who report that they have never had any of the mentioned symptoms on a regular basis and have never been diagnosed with it. The analysis of the stated frequencies of preventive testing reveals that many people choose not to undergo any tests at all. Tables 4-8 present the distributions of stated testing frequencies for each disease. The first two columns show the number of respondents and their fraction in the whole sample, and columns 3 and 4 show the same information in the subsample of non-symptomatic undiagnosed respondents. For cancer screening, the breakdown of answers for men and women is combined. We observe that from 25 to 75% of the population report a zero frequency of tests depending on the illness. For cancer screening, this number goes up to 85% for men 24

and 65% for women17 . Therefore, I separately study the factors that influence the decision to participate in preventive testing and those that determine the frequency of testing among participants. For this purpose, I employ a two-part model (Leung and Yu (1996)). For each disease, I first run a probit regression with a binary dependent variable equal to zero if a person does not undergo a relevant test and 1 if he/she chooses any positive frequency of testing. Next, I run either an ordinary logit or an OLS regression (depending on the way frequency is measured) with the dependent variable being the frequency of tests. These regressions are restricted to the sample of those who reported a non-zero frequency18 . For each regression, I present both the long and the short versions (i.e., excluding nonsignificant regressors). First, consider blood pressure and sugar level tests (Tables 9 and 10). The first and second columns of these tables present the estimation results for the probit model. The estimation results show that loss aversion is a statistically significant factor that discourages people from preventive testing. The decision to participate in testing is positively influenced by such factors as age, body mass index (BMI), having a family history of a disease, visiting a family physician more often and worrying about a disease19 . Increased smoking and alcohol consumption are associated with a lower probability of preventive testing (although not significantly for alcohol). Variables showing how many cigarettes a person smokes and how much alcohol she consumes may be indicative of a more general attitude towards health. People in whom these levels are high may be less likely to care about their own health and, therefore, less inclined to adopt preventive measures. 17 This

difference is likely due to the existence in the Netherlands of publicly funded programs for breast cancer and cervical cancer screening for women, but no cancer screening program for men. 18 An alternative way to perform this analysis would be by means of the Heckman selection model. However, a commonly indicated distinction between the two is that the Heckman model is more appropriate when one needs to predict values of the outcome as if there was no selection. The two-part model is more suitable for the situation when one needs to analyze the actual outcome (see, for example, Leung and Yu (1996) for a discussion). The latter is closer to the present case. 19 Table 28 contains a detailed description of all control variables.

25

Columns 3 and 4 of the same tables contain estimation results for the frequency of preventive check-ups among those respondents who have decided to undergo a test. Regressions are ordered logit because the dependent variable (frequency of tests) is categorical. The set of regressors does not change because the same factors may influence testing frequency. Loss aversion is not significant. Other factors contributing to more frequent testing are older age, visiting a family physician and worrying about a disease more often. Table 11 shows similar results for lung disease testing. Regressions for lung disease do not contain variables from the LISS core study of 2009 because the period for which the frequency of lung disease tests is measured extends to 10 years. Hence, the variables from 2009 are irrelevant for earlier decisions to test. However, I add other variables that may influence this decision. These are the number of times a person has had the flu, the number of times she received a flu shot and a binary variable indicating whether the respondent gets colds easily. All of these factors may increase adherence to preventive testing. I expect the effect of flu shots to be positive because a person who receives flu shots frequently may either be more conscious about his/her health or have some underlying condition that makes him/her susceptible to both flu and lung disease. The results for lung disease are similar to those for blood pressure and sugar level testing. Loss aversion is found to be a significant and negative factor in the decision to undergo a test for lung disease. However, it is not significant for the choice of testing frequency above zero. The effect of loss aversion on cancer screening is explored in two different dimensions: cancer screenings in hospitals and self-tests for cancer. In the Netherlands, screening programs for female-specific types of cancer are publicly funded for women in certain age groups: the government provides breast cancer screening every 2 years for women between 50 and 75 years old, and cervical cancer screening is funded ev-

26

ery five years for women between 30 and 60 years old. There is no cancer screening program for men. Therefore, one might expect that the decision to participate in preventive screening and the effect of loss aversion on this decision would differ between men and women. To account for this possibility, loss aversion is multiplied by the dummy variables for gender. In addition to the standard control variables, I include the average number of screening programs for which a person was eligible during the past ten years20 . I find that the discouraging effect of loss aversion on the participation decision is not significant for either gender (Table 12). Worrying about cancer, having a family history and eligibility to enter a screening program are the most important factors in this decision. The influence of loss aversion on the frequency of medical tests is not statistically significant, but the size of the effect is larger for men than for women. Table 13 shows that loss aversion is marginally significant in the decision to participate in testing and significant at the 10% level for the frequency of testing for women. However, no significant effect is observed for men. The set of control variables is the same as for medical cancer tests. Although self-tests by definition do not require a visit to the hospital, the average number of accessible screening programs is still included for the simple reason that a woman undergoing a medical test for cancer also has more access to information on self-testing. As Table 13 shows, the number of available programs is indeed a significant positive factor. For the regressions where loss aversion is significant, I perform two robustness checks (Tables 14-17). First, I examine how the results change when the respondents with the highest loss aversion are excluded (group 1). Second, I present the estimation results when the group of loss-neutral individuals (group 12) is included in the regressions. We observe that exclusion of people with the highest loss aversion does 20 For men, this variable is always zero.

For women, this variable can be 0, 1 or 2. I compute a weighted average, taking into account the number of years out of the past ten that a woman has been eligible for each of these screenings. An example of this computation can be found in Table 20.

27

not change the sign of the loss aversion effect for blood pressure, blood sugar and lung disease testing. For blood pressure and lung disease testing, the effect is also most stable in terms of statistical significance. Loss aversion is a significant and positive predictor of cancer self-test frequency among men. However, only 125 men remained in this subsample, which may not be enough to obtain a correct estimate of the effect. For women, the effect on self-test frequency seems to be driven by the excluded individuals. This situation may reflect the fact that women who have a greater aversion to medical procedures also reject the harmless lottery more often. Finally, as mentioned earlier, the inclusion of loss-neutral individuals greatly reduces the significance and size of the loss aversion estimates, although this group constitutes only 2 to 3% of the sample. This result is consistent with the view of these observations as "fringeliers". Tables 18-22 present the estimates of the marginal effects in the main regressions. For brevity, I consider only regressions without nonsignificant parameters. I present marginal effects for a unitary and a one-standard-deviation change in each regressor, keeping other variables at their mean levels. From marginal effects for the probit model, I find that an increase of the loss aversion logarithm by one increases the probability of non-participation in testing by 1.4-1.8 percentage points. For blood pressure, blood sugar and lung disease, the size of the loss aversion effect is similar to or larger than the effect of obtaining one additional level of education21 . The effect for selftesting for cancer for women is in a similar range. As explained earlier, loss aversion is not significant in the probit regression for medical cancer tests, but it produces a large effect on testing frequency among both men and women who have decided to undergo testing. Because the logarithm of loss aversion may be not very intuitive for interpretation, I also consider the predicted probability of participation in testing given different lot21 Note,

however, that the influence of education on the decision to test may be positive or negative. On the one hand, education may increase awareness of the benefits of testing, exerting a negative effect on the probability of non-testing. On the other hand, more educated people are less likely to engage in health-worsening activities, which may increase the probability of non-testing (Chen and Lange (2008)).

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tery rejection choices (which correspond to different loss aversion values) and mean values of other variables. Table 23 presents the results. The difference in the predicted probability of testing between a person rejecting the first lottery (and therefore having the highest possible loss aversion) and a person accepting all lotteries except the last one can be as large as 10 to 13 percentage points. In other words, being willing to sacrifice one additional year of life expectancy with a 50 percent chance of winning 10 additional years of life expectancy is associated with an increase of roughly 1.1-1.3 percentage points in the probability of testing. Finally, I analyze whether the effect of loss aversion differs in various risk groups. Tables 24-27 present the results. In these regressions, the low-risk group is taken as a benchmark. The first row shows the effect of loss aversion in this benchmark group, and the other two estimates indicate how much the effect differs from this benchmark. We observe that, for the blood pressure, blood sugar and lung disease tests, the absolute loss aversion effect is consistently larger in the high-risk group. People who consider themselves to be at higher-than-average risk are more influenced by loss aversion in their decision to test for these illnesses. The same pattern is observed for the frequency of self-tests for cancer among women22 . The difference between the groups is not statistically significant, possibly because both loss aversion and the risk ratio appear to be very noisy measures.

5. Conclusions The theoretical and empirical analysis in this paper helps to establish a link between two important phenomena: loss aversion and information aversion in the context of health care decision making. It is shown that loss aversion is a significant contributor to infrequent preventive testing among non-symptomatic people. A person has to 22 In the case of cancer testing, the average- and high-risk groups have been merged together because the average-risk group becomes too small.

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make a choice about his/her frequency of preventive check-ups, which constitutes a trade-off. On the one hand, learning health information more frequently allows a person to detect an illness earlier and, hence, to receive a less costly treatment. On the other hand, learning a bad diagnosis is emotionally distressing, and a person may prefer to avoid it. The model shows that the frequency of testing depends negatively on loss aversion, which is the main driving force behind health anxiety. Empirical analysis supports this theoretical prediction. I construct an individual proxy for loss aversion, measured by the lottery choice questions with respect to life expectancy, and relate it to the frequency of tests for four illnesses: hypertension, diabetes, chronic lung disease and cancer. Although these conditions differ in their controllability and consequences for life duration, the loss aversion effect is quite stable across all of them. The size of the effect is statistically and economically significant. Moreover, the negative effect of loss aversion is higher in magnitude for people who consider themselves to be at above-average risk of illness. The policy implications that can be derived from this analysis relate to the methods of encouraging people to use preventive testing. One of these methods involves distributing messages and informational booklets about the importance of preventive testing. It has been found that framing of those messages in terms of either gains or losses may influence their efficiency. For example, it is often argued that loss-framed messages may induce an instinct to avoid losses, leading to a higher uptake of prevention (Rothman et al. (2006)). The results of the present study, however, suggest that this strategy may give rise to the ostrich effect, thus generating the opposite behavior, especially in a high-risk population. A more efficient measure in this case would be to increase the perceived effectiveness of treatment. In the present model, it is assumed that treatment allows the individual to restore his/her health to its initial level. In reality, this may not be the case. If a person thinks that her health may only be restored to some low level, then her likelihood of testing will be decreased. Therefore, informing

30

the population about cases of successful treatment or high disease controllability may outweigh the ostrich effect, at least for some people.

31

Appendix A A1. Game tree: Visit (V2)

S2=0 Visit (V1)

I1

No Visit (NV2) Visit (V2)

S2=-1 S1=0

No Visit (NV2)

I2

Visit (V2)

S2=0 No Visit (NV1)

I3

No Visit (NV2) Visit (V2)

S2=-1

I4

Period 1

No Visit (NV2)

Period 2

Figure 1. Game tree. A2. Proof of Lemma: I consider the four decision nodes of the second period and derive the optimal strategy in each of them. Each decision node is characterized by the action taken in the previous period and the signal observed in period 2. I assume that the first-period signal is equal to zero. (1) Decision node I1 : (s1 = 0, s2 = 0, V1 ) First, the posterior probability of the health change being equal to zero is computed according to the following formula: 32

P r(∆H2 = 0|I1 ) =

P r(s2 =0|∆H2 =0)·P r(∆H2 =0) P r(s2 =0|∆H2 =0)·P r(∆H2 =0)+P r(s2 =0|∆H2 =−a)·P r(∆H2 =−a)

Therefore, the posterior probabilities of the possible health changes in this node are the following:

p p + (1 − p)(1 − q) (1 − q)(1 − p) P r(∆H2 = −a|I1 ) = p + (1 − p)(1 − q) P r(∆H2 = 0|I1 ) =

(11) (12) (13)

Next, the expected health level in node I1 is: ∆H 2 (I1 ) = −a ·

(1 − p)(1 − q) p + (1 − p)(1 − q)

(14)

Because, in this decision node, only two health changes are possible, the larger of them brings a gain and the smaller brings a loss with respect to the reference point. This allows me to compute the agent’s emotional utility Em2 in case she decides to undergo a test:

( ) (1 − q)(1 − p) p + λ −a − ∆H 2 (I1 ) = p + (1 − p)(1 − q) p + (1 − p)(1 − q) p(1 − q)(1 − p) = −(λ − 1)a (15) (p + (1 − p)(1 − q))2

E(Em2 |I1 ) = (0 − ∆H 2 (I1 ))

The total utility of visiting the doctor in node I1 according to equation (8) is:

EU (V2 |I1 ) = −(λ − 1)a

p(1 − q)(1 − p) (1 − q)(1 − p) − Ca +H p + (1 − p)(1 − q) (p + (1 − p)(1 − q))2

The utility of not visiting the doctor in this node is: 33

(16)

EU (N V2 |I1 ) = H − a ·

(1 − q)(1 − p) p + (1 − p)(1 − q)

(17)

Comparing equations (16) and (17) the agent chooses testing when loss aversion is lower than the following threshold:

(λ − 1) <

(1 − C)(p + (1 − p)(1 − q)) = T1 p

(18)

(2) Decision node I2 : (s1 = 0, s2 = −1, V1 ) In this node, the agent observes a negative signal. Because a negative signal appears only when the health change is equal to −a, it is revealing. The posterior probability of ∆H2 = 0 equals zero while P r(∆H2 = −a|I2 ) = 1. Therefore, ∆H 2 (I2 ) = −a. Because the signal in this node is revealing, the agent’s emotional utility is equal to zero. The agent always chooses to test independently of loss aversion (because the utility of testing −Ca + H is always larger than utility in case of no test, which is equal to H − a).

(3) Decision node I3 : (s1 = 0, s2 = 0, N V1 ) In node I3 the agent did not visit the doctor in the previous period. She does not know whether an illness started to develop in period 1. Hence, she faces three possible values for the second-period health change: zero, −a or −ka. The posterior probabilities for each of these values are computed in the following way:

34

P r(∆H2 = 0|I3 ) = P r(∆H2 = 0|I3 , ∆H1 = 0)P r(∆H1 = 0|I3 )+ +P r(∆H2 = 0|I3 , ∆H1 = −a)P r(∆H1 = −a|I3 ) =

p2 P r(s1 = 0, s2 = 0, N V1 )

(19)

P r(∆H2 = −a|I3 ) = P r(∆H2 = −a|I3 , ∆H1 = 0)P r(∆H1 = 0|I3 )+ +P r(∆H2 = −a|I3 , ∆H1 = −a)P r(∆H1 = −a|I3 ) =

p(1 − q)(1 − p) P r(s1 = 0, s2 = 0, N V1 )

(20)

P r(∆H2 = −ka|I3 ) = P r(∆H2 = −ka|I3 , ∆H1 = 0)P r(∆H1 = 0|I3 )+ +P r(∆H2 = −ka|I3 , ∆H1 = −a)P r(∆H1 = −a|I3 ) =

(1 − q)2 (1 − p) P r(s1 = 0, s2 = 0, N V1 )

(21)

Finally, P r(s1 = 0, s2 = 0, N V1 ) = p2 + p(1 − q)(1 − p) + (1 − q)2 (1 − p). The expected health level in node I3 is: −ap(1 − q)(1 − p) − ka(1 − q)2 (1 − p) ∆H 2 (I3 ) = 2 p + p(1 − q)(1 − p) + (1 − q)2 (1 − p)

(22)

The maximum (∆H2 = 0) and minimum (∆H2 = −ka) outcomes of the second-period health change constitute a gain and a loss, respectively, relative to the reference point. The outcome ∆H2 = −a may be a gain or a loss depending on the parameter values. For brevity, I consider the case of k <

p2 (1−q)2 (1−p)

+ 1 when ∆H2 = −a constitutes a loss.

Therefore, the expected emotional utility in node I3 is:

35

ap(1 − q)(1 − p) + ka(1 − q)2 (1 − p) p2 E(Em2 |I3 ) = 2 × + p + p(1 − q)(1 − p) + (1 − q)2 (1 − p) P r(s1 = 0, s2 = 0, N V1 ) ( ) ap(1 − q)(1 − p) + ka(1 − q)2 (1 − p) p(1 − q)(1 − p) +λ −a + 2 × + P r(s1 = 0, s2 = 0, N V1 ) p + p(1 − q)(1 − p) + (1 − q)2 (1 − p) ( ) ap(1 − q)(1 − p) + ka(1 − q)2 (1 − p) (1 − q)2 (1 − p) +λ −ka + 2 × , P r(s1 = 0, s2 = 0, N V1 ) p + p(1 − q)(1 − p) + (1 − q)2 (1 − p)

(23)

where P r(s1 = 0, s2 = 0, N V1 ) is defined above. The agent’s expected utility of visiting the doctor is:

EU (V2 |I3 ) = E(Em2 |I3 ) − C∆H 2 (I3 ) + H

(24)

The expected utility of not visiting the doctor in this node is:

EU (N V2 |I3 ) = H − ∆H 2 (I3 )

(25)

Comparing these two expected utilities, the agent chooses to undergo a test when her loss aversion satisfies the following inequality:

(1 − C)(p2 + p(1 − q)(1 − p) + (1 − q)2 (1 − p)) (λ − 1) < = T3 p2

(26)

(4) Decision node I4 : (s1 = 0, s2 = −1, N V1 ) In node I4 the agent may experience two values of the second-period health change: ∆H2 = −a and ∆H2 = −ka. Since the agent observes a negative signal she knows that 36

her health change has reduced. However, the agent does not know exactly the size of this reduction. The posterior probabilities of these values are:

P r(∆H2 = −a|I4 ) = P r(∆H2 = −a|I4 , ∆H1 = 0)P r(∆H1 = 0|I4 )+ +P r(∆H2 = −a|I4 , ∆H1 = −a)P r(∆H1 = −a|I4 ) =

q(1 − p)p P r(s1 = 0, s2 = −1, N V1 )

(27)

P r(∆H2 = −ka|I4 ) = P r(∆H2 = −ka|I4 , ∆H1 = 0)P r(∆H1 = 0|I4 )+ +P r(∆H2 = −ka|I4 , ∆H1 = −a)P r(∆H1 = −a|I4 ) =

(1 − q)q(1 − p) P r(s1 = 0, s2 = −1, N V1 )

(28)

Finally, P r(s1 = 0, s2 = −1, N V1 ) = q(1 − p)p + q(1 − q)(1 − p). The expected health change is then:

∆H 2 (I4 ) =

−aq(1 − p)p − ka(1 − q)q(1 − p) q(1 − p)p + q(1 − q)(1 − p)

(29)

The expected emotional utility in this node is:

(

) aq(1 − p)p + ka(1 − q)q(1 − p) q(1 − p)p E(Em2 |I3 ) = −a + × + q(1 − p)p + q(1 − q)(1 − p) P r(s1 = 0, s2 = −1, N V1 ) ( ) −aq(1 − p)p − ka(1 − q)q(1 − p) (1 − q)q(1 − p) +λ −ka + × = q(1 − p)p + q(1 − q)(1 − p) P r(s1 = 0, s2 = −1, N V1 ) ) ( (1 − q)q(1 − p) −aq(1 − p)p − ka(1 − q)q(1 − p) × , = (λ − 1) −ka + q(1 − p)p + q(1 − q)(1 − p) P r(s1 = 0, s2 = −1, N V1 )

(30)

where P r(s1 = 0, s2 = −1, N V1 ) is defined above. The utilities of visiting and not visiting the doctor are derived similarly to cases already considered. The agent chooses to perform a test in node I4 when the following

37

inequality holds:

(λ − 1) <

(1 − C)(p + k(1 − q))(p + (1 − q)) = T4 (k − 1)p(1 − q)

(31)

I now compare the thresholds T1 , T3 and T4 . First, it is easy to see that threshold T1 is lower than T4 . After some simplification of the inequality, we obtain: (1−C)(p+(1−q)(1−p)) p

<

(1−C)(p+k(1−q))(p+(1−q)) ; (k−1)p(1−q)

⇒ −p(1 − q) − kp(1 − q)2 − (1 − q)2 (1 − p) < p2 + p(1 − q) The latter is true since the left-hand side is always negative, whereas the right-hand side is positive. A similar procedure yields the following comparison for thresholds T1 and T3 : (1−C)(p2 +(1−q)(1−p)p+(1−q)2 (1−p)) ; p2 ⇒ p2 + p(1 − q)(1 − p) < p2 + (1 − q)(1 − p)p + (1 − q)2 (1 − p) (1−C)(p+(1−q)(1−p)) p

<

The latter holds since 0 < (1 − q)2 (1 − p). Finally, I compare T3 and T4 : (1−C)(p2 +(1−q)(1−p)p+(1−q)2 (1−p)) (1−C)(p+k(1−q))(p+(1−q)) ; < (k−1)p(1−q) p2 ⇒ k(p2 (1 − q) + (1 − q)2 (1 − p)(p + (1 − q)) − p(1 − q)(p + (1 − q))) < p2 (1 − q) + (1 − q)2 (1 −

p)(p + (1 − q)) + p2 (p + (1 − q)). The right-hand side of this inequality is positive. Compare the left-hand side to zero: p2 (1 − q) + (1 − q)2 (1 − p)(p + (1 − q)) − p(1 − q)(p + (1 − q)) < 0; ⇒ (1 − q)(1 − p) < p2 ; The latter holds since given that p, q > 1/2, (1 − q)(1 − p) < 1/4 and p2 > 1/4. Therefore, the threshold T3 is always smaller than T4 . Hence, we obtain that 0 < T1 < T3 < T4 . These thresholds allow us to define the optimal strategy of the agent in period 2 for any loss aversion interval as stated in the Lemma. Q.E.D. 38

A3. Proof of Proposition 1:

To prove Proposition 1, I consider each of the four intervals for loss aversion obtained in the Lemma. In each interval, the agent’s first-period problem is solved. Combining this solution with the optimal second-period strategy, I obtain the equilibrium for each loss aversion value. In the first period, the agent compares the overall utility of visiting the doctor and the overall utility of not visiting the doctor. The overall utility takes into account not only the first-period utility, but also the expectation of the second-period utility given the action taken in the first period. In period 1, the agent does not know which signal she will observe in period 2. She computes the probability of observing a zero or negative signal, given that she will visit the doctor in period 1, in the following way:

P r(s2 = 0|s1 = 0, V1 ) = P r(s2 = 0|V1 ) = P r(s2 = 0|∆H2 = 0, V1 )P r(∆H2 = 0|V1 )+ +P r(s2 = 0|∆H2 = −a, V1 )P r(∆H2 = −a|V1 ) = p + (1 − q)(1 − p)

(32)

P r(s2 = −1|s1 = 0, V1 ) = P r(s2 = −1|V1 ) = P r(s2 = −1|∆H2 = 0, V1 )P r(∆H2 = 0|V1 )+ +P r(s2 = −1|∆H2 = −a, V1 )P r(∆H2 = −a|V1 ) = 0 + q(1 − p) Analogously, the probabilities of signals after not visiting in period 1 equal:

(1 − q)2 (1 − p) p + (1 − q)(1 − p) q(1 − p)(p + (1 − q)) P r(s2 = −1|s1 = 0, N V1 ) = p + (1 − q)(1 − p) P r(s2 = 0|s1 = 0, N V1 ) = p +

(1) Consider first the interval (λ − 1) ∈ (0, T1 ):

39

(33)

In this interval, the optimal strategy in period 2 is to visit the doctor in every decision node. The utilities of visiting the doctor in every node are defined in the proof of the Lemma above. By weighting them with the probabilities (32) and (33) and combining them with the first-period utilities of visiting and not visiting the doctor, respectively, I obtain the overall utilities of visiting and not visiting the doctor. Note that the first-period utility given s1 = 0 always coincides with that of the second period in node I1 defined in the Lemma. The overall expected utility of visiting the doctor in period 1 is:

(

) (1 − q)(1 − p) p(1 − q)(1 − p) + (p + (1 − q)(1 − p))× EU12 (V1 ) = H − Ca − (λ − 1)a p + (1 − q)(1 − p) (p + (1 − q)(1 − p))2 ( ) (1 − q)(1 − p) p(1 − q)(1 − p) × H − Ca + q(1 − p)(H − Ca) (34) − (λ − 1)a p + (1 − q)(1 − p) (p + (1 − q)(1 − p))2 Analogously, the overall expected utility of not visiting equals:

) p2 + (1 − q)(1 − p)p + (1 − q)2 (1 − p) (1 − q)(1 − p) + EU12 (N V1 ) = H − a · p + (1 − q)(1 − p) p + (1 − q)(1 − p) (

(

ap(1 − q)(1 − p) + ka(1 − q)2 (1 − p) (λ − 1)p2 (ap(1 − q)(1 − p) + ka(1 − q)2 (1 − p)) · H −C 2 − p + (1 − q)(1 − p)p + (1 − q)2 (1 − p) (p2 + (1 − q)(1 − p)p + (1 − q)2 (1 − p))2 ( q(1 − p)(p + (1 − q)) aq(1 − p)p + kaq(1 − q)(1 − p) H −C + + p + (1 − q)(1 − p) q(1 − p)p + q(1 − p)(1 − q) ) apq(1 − p) − kaqp(1 − p) +(λ − 1) q(1 − q)(1 − p) (35) (q(1 − p)p + q(1 − p)(1 − q))2 Comparing the inequalities (34) and (35), I find that the agent chooses to undergo a test in period 1 if her loss aversion is lower than the following threshold S1 :

40

)

(λ − 1) <

(1 − C) + C(k − 1 + p) p p+q(1−p)

p3 +p2 (1−q)k

+ p − p2 +(1−q)(1−p)p+(1−q)2 (1−p) −

qp(k−1) p+1−q

(36)

Now I compare this expression with threshold T1 obtained in the proof of the Lemma (inequality (18)). Note that threshold S1 increases in k. Therefore, its minimum is reached at k = 1 (since k > 1) and is equal to:

S1(min) =

(1 − C) + Cp p p+q(1−p)

p3 +p2 (1−q)

+ p − p2 +(1−q)(1−p)p+(1−q)2 (1−p) −

Note that 1 − C + pC > 1 − C, and p <

p3 +p2 (1−q) p2 +(1−q)(1−p)p+(1−q)2 (1−p)

qp(k−1) p+1−q

iff p2 + (1 − q)(1 − p)p +

(1 − q)2 (1 − p) < p2 + p(1 − q), or (1 − q)2 (1 − p)p2 (1 − p), (1 − q)(1 − p) < p2 . The latter holds since p, q > 1/2. Therefore, the minimum of S1 is larger than T1 . This means that in the interval (λ−1) ∈ (0, T1 ) the equilibrium when s1 = 0 and s2 = 0 is to test in both periods. (2) Consider the interval (λ − 1) ∈ (T1 , T3 ): In this interval, the agent’s optimal strategy in period 2 is to visit the doctor in nodes I2 , I3 and I4 and not visit in node I1 . Following the same logic as in the previously considered case I obtain that the agent’s overall expected utility of visiting the doctor is:

( ) p(1 − q)(1 − p) (1 − q)(1 − p) − (λ − 1) EU12 (V1 ) = H − Ca + p + (1 − q)(1 − p) (p + (1 − q)(1 − p))2 ) ( (1 − q)(1 − p) + q(1 − p)(H − Ca) +(p + (1 − q)(1 − p)) H − a p + (1 − q)(1 − p) The overall expected utility of not visiting is: 41

(37)

(

) ( ) (1 − q)(1 − p) (1 − q)2 (1 − p) EU12 (N V1 ) = H − a + p+ × p + (1 − q)(1 − p) p + (1 − q)(1 − p) ( ap(1 − p)(1 − q) + ka(1 − q)2 (1 − p) × H −C 2 − (λ − 1)· p + (1 − q)(1 − p)p + (1 − q)2 (1 − p) ) ap(1 − p)(1 − q) + ka(1 − q)2 (1 − p) 2 q(1 − p)(p + (1 − q)) · 2 p + × 2 2 p + (1 − q)(1 − p) (p + (1 − q)(1 − p)p + (1 − q) (1 − p))

( ) aq(1 − p)p + kaq(1 − q)(1 − p) apq(1 − p) − kaqp(1 − p) × H −C + (λ − 1) q(1 − q)(1 − p) q(1 − p)p + q(1 − q)(1 − p) (q(1 − p)p + q(1 − q)(1 − p))2 (38) Rewriting and comparing the expressions (37) and (38), we find that the agent chooses to test in period 1 when the following inequality holds:

( (1 − q)(1 − p)p((k − 1)q − 1) a(1 − q)(1 − p)p2 (λ − 1) a + · p + (1 − q)(1 − p) (p + (1 − q)(1 − p))2 ) p + k(1 − q) · 2 < p + (1 − q)(1 − p)p + (1 − q)2 (1 − p) < (1 − C)

k(1 − q)(1 − p) − (1 − p)2 (1 − q)(1 + q) k(1 − p)(1 − q) − (1 − p)2 (1 − q) − p + (1 − q)(1 − p) p + (1 − q)(1 − p)

Consider the left-hand side (LHS) of this inequality:

( ) p(1 − p)(1 − q) p2 + kp(1 − q) 1 LHS = − − p + (1 − q)(1 − p) p + (1 − q)(1 − p) p2 + (1 − q)(1 − p)p + (1 − q)2 (1 − p) =−

p(1 − p)(1 − q) (1 − p)((1 − q)(p + 1 − q) − qp2 − kp(1 − p)(1 − q + pq)) p + (1 − q)(1 − p) (p + (1 − q)(1 − p))(p2 + (1 − q)(1 − p)p + (1 − q)2 (1 − p))

(39)

This expression is positive when (1 − q)(p + 1 − q) − qp2 − kp(1 − q + pq) < 0. Then the following chain of inequalities holds: kp(1 − q + pq) − (1 − q)2 − p(1 − q − pq) > p(1 − q + pq) − (1 − q)2 − p(1 − q − pq) = 2qp2 − (1 − q)2 > 0. From the latter inequality, 42

it follows that the LHS is always positive. The right-hand side of the main inequality is negative because the first ratio is smaller than the second. Therefore, in the considered loss aversion interval, the agent chooses to test in the first period and chooses not to test in the second observing zero second-period signal. This result guarantees the existence of threshold L1 of the Proposition (i.e. L1 = T1 ). (3) Consider the interval (λ − 1) ∈ (T3 , T4 ): The agent’s overall expected utility of visiting the doctor in this interval is:

(

) (1 − q)(1 − p) p(1 − q)(1 − p) + EU12 (V1 ) = H − Ca − (λ − 1)a p + (1 − q)(1 − p) (p + (1 − q)(1 − p))2 ( ) (1 − q)(1 − p) +(p + (1 − q)(1 − p)) H − a + q(1 − p)(H − Ca) p + (1 − q)(1 − p)

(40)

The overall expected utility of not visiting the doctor is:

) ( (1 − q)(1 − p) (1 − q)2 (1 − p) × EU12 (N V1 ) = H − a + p+ p + (1 − q)(1 − p) p + (1 − q)(1 − p) ( ) ap(1 − p)(1 − q) + ka(1 − q)2 (1 − p) × H− 2 + p + (1 − p)(1 − q)p + (1 − q)2 (1 − p) ) ( ( q(1 − p)(p + (1 − q)) aq(1 − p)p + kaq(1 − q)(1 − p) × H −C + + (λ − 1)· p + (1 − q)(1 − p) q(1 − p)p + q(1 − q)(1 − p) apq(1 − p) − kaqp(1 − p) · q(1 − q)(1 − p) (q(1 − p)p + q(1 − q)(1 − p))2

(41)

Simplifying and comparing expressions (40) and (41) we find that the agent chooses to test in period 1 independently of loss aversion when k > q(1 − q), since this restriction guarantees that the left-hand side is always positive while the right-hand side is negative. When k < q(1 − q), the agent chooses to test in period 1 if her loss aversion is smaller than threshold S3 , defined as: 43

(λ − 1) <

(1 − p)(1 − q)(k + p − 1 − (1 − C)(kq − q(1 − p) − 1)) ( ) p(1−p)(1−q) (k−1)p (p + (1 − p)(1 − q)) (p+(1−p)(1−q))2 − q(1−p)(p−q+1)2

(42)

Analogously, the threshold S4 can be computed from the case of (λ − 1) ∈ (T4 , +∞). Several situations are possible: (a) S3 < T3 . In this case, in equilibrium, the agent chooses not to test at all immediately above threshold T3 and onwards, and tests only in period 1 below T3 in the corresponding interval; (b) T3 < S3 < T4 . In this case, the agent tests only in period 1 when loss aversion is below S3 and chooses not to test at all from S3 onwards; (c) S3 > T4 . In this case, threshold S3 is not binding for the agent in the interval (λ − 1) ∈ (T3 , T4 ). The agent tests only in the first period until max(T4 , S4 ). This is the case when k > q(1 − q). Combining all of the above, we find that there always exist thresholds 0 < L1 < L2 such that the statement in Proposition 1 holds. Q.E.D.

A4. Proof of Proposition 2:

Consider the first threshold L1 = T1 =

(1−C)(p+(1−q)(1−p)) p

= (1 − C)(1 + (1 − q)( p1 − 1)).

Obviously, this expression decreases in p. Consider the threshold L2 . From the proof of Proposition 2 it follows that when (1−C)(p+k(1−q))(p+(1−q))

k > q(1 − q) = f1 (q), either L2 = T4 or L2 = S4 . Threshold T4 = . The (k−1)p(1−q) ( ) k(1−q)2 4 derivative of T4 with respect to p is dT . The function T4 (p) reaches its dp = 1 − p2 √ minimum at p∗ = k(1 − q). Consider the threshold S4 : 1 2 2 1−q (p(1 − q(1 − q) − Cq ) + k(1 − q) + q(1 − q) − C(1 − q ))(1 + q − 1 + (1 − q)/p) (1−q)(k(1−q)+q(1−q)−C(1−q2 )) 1 2 + const), 1−q (pq(1 − q(1 − q) − Cq ) + p

S4 =

44

=

where const does not depend on p. Note that 1 − q(1 − q) − Cq2 = 1 − q + q2 (1 − C) > 0. Hence, the function S4 (p) reaches its minimum when: 1−q

q(1 − q + q2 (1 − C)) = p2 (k(1 − q) + q(1 − q) − C(1 − q2 )) = √ k+q−C(1+q) ∗∗ when p = (1 − q) q(1−q+q2 (1−C)) .

(1−q)2 (k p2

+ q − C(1 + q)), i.e.

If both p∗ and p∗∗ are below 1/2 (since we consider only p > 1/2) then for any p from the considered interval both thresholds increase in p. In other words, threshold L2 increases in p when two conditions hold:

k(1 − q)2 < 1/4 1 k(1 − q)2 < q(1 − q + q2 (1 − C)) − (q − C(1 + q))(1 − q)2 4 Consider the difference between the right-hand sides of the inequalities: ( 3 ) q 3q 7q2 3q3 1 1 1 2 2 2 4 q(1−q+q (1−C))−(1−q) (q−C(1+q))− 4 = − 4 + 4 − 4 − 4 −C 4 + (1 − q) (1 + q) . Note that

7q2 4

<

3q 3q3 1 4 + 4 +4

since 7q2 −3q−1−3q2 = (1−q)(−1−4q+3q2 ) = (1−q)(3q2 −

4q − 1) < 0. Therefore, the right-hand side of the second condition is always smaller than 1/4. Hence, only the second restriction on parameters is active. Function f1 (q) = q(1 − q) monotonously decreases in q and function f2 (q) = monotonously increases in q for q > 1/2. Q.E.D.

45

1 2 2 4 q(1−q+q (1−C))−(q−C(1+q))(1−q) 2 (1−q)

Appendix B

B1 List of symptoms Disease

Symptoms dizziness, morning headaches,

High blood pressure/hypertension

ringing or buzzing in ears, fatigue changes of vision, nose bleeds always being hungry, always being thirsty, dry mouth, constantly

High blood sugar level/diabetes

having to urinate, dry itchy skin, fatigue or extreme tiredness, blurred vision, slow healing of wounds shortness of breath, especially during physical activity, wheezing,

Chronic lung disease

chest tightness, a chronic cough that produces yellowish sputum, frequent respiratory infections unexpected weight loss, constant fatigue, persistent cough or blood-tinged saliva,

Cancer

hoarseness, breast lump, pain in breast, vaginal bleeding, painful urination, blood in stool, abdominal pain, continuous diarrhea Table 1: List of symptoms

46

B2 Example of loss aversion questions Suppose you could undergo a treatment that is successful with probability 50%. If the treatment is successful, you can expect to live 10 years longer (compared to how long you currently expect to live). If the treatment is unsuccessful it will not affect your current life expectancy. Would you like to undergo the treatment? (Yes/No) If the answer is "Yes", the next question is: Suppose you could undergo a treatment that is successful with probability 50%. If the treatment is successful, you can expect to live 10 years longer (compared to how long you currently expect to live). If the treatment is unsuccessful it will decrease your life expectancy by 1 year. Would you like to undergo the treatment? (Yes/No) If the answer is "Yes", the next question is the same except the loss in life expectancy is increased to 2 years. If the answer is "No", the procedure stops.

47

B3 Summary statistics Variable

All sample

Non-symptomatic and not diagnosed with: High blood High sugar Lung disease Cancer pressure/hyper level/Diabetes tension

Gender men women

1456 1550

48% 52%

765 789

49% 51%

1187 1347

47% 53%

1230 1322

48% 52%

1334 1340

50% 50%

41-50 725 51-60 924 61-70 894 71-80 371 >80 92 Mean: 59.34 Median: 59 Std. Deviation: 10.71 Min: 41 Max: 97 Education Basic (1) 318 vmbo/havo/vwo (2) 1,200 599 mbo (3) hbo/vo(4) 882 Mean: 2.68 Median: 2 Std. Deviation: 1.01 Min: 1 Max: 4 Paid job Yes 1228 No 1778 Net monthly income, euro 0-1000 702 1001-1500 580 1501-2000 627 2001-2500 368 2501-3000 204 3001-3500 87 >3500 81 Mean: 1710 Median: 1568 2398 Std. Deviation: Min: 60 Max: 114303

24% 31% 30% 12% 3%

494 495 408 132 25 56.91 57 10.28 41 97

32% 32% 26% 8% 2%

685 796 700 285 68 58.47 58 10.71 41 97

27% 31% 28% 11% 3%

661 799 743 291 58 58.64 58 10.5 41 92

26% 31% 29% 11% 2%

692 837 768 301 76 58.74 58 10.67 41 97

26% 31% 29% 11% 3%

11% 40% 20% 29%

124 607 325 495 2.77 3 0.99 1 4

8% 39% 21% 32%

230 970 532 795 2.75 3 1 1 4

9% 38% 21% 31%

245 988 530 782 2.73 3 1 1 4

10% 39% 21% 31%

273 1033 551 811 2.71 3 1.01 1 4

10% 39% 21% 30%

41% 59%

500 949

35% 65%

922 1453

39% 61%

959 1442

40% 60%

995 1524

39% 61%

27% 22% 24% 14% 8% 3% 3%

319 258 297 194 111 41 43 1718 1606 968 60 10000

25% 20% 24% 15% 9% 3% 3%

548 446 494 311 154 73 68 1737 1600 2651 60 114303

26% 21% 24% 15% 7% 3% 3%

536 449 497 307 176 73 74 1765 1600 2654 60 114303

25% 21% 24% 15% 8% 3% 4%

569 479 526 328 177 77 73 1749 1600 2589 60 114303

26% 21% 24% 15% 8% 3% 3%

Age

(Continued on the next page)

48

Symptoms occurance rate: Blood pressure/Hypertentio n 872 29% Diabetes 389 13% Lung disease 446 14% Cancer 236 8% Note: fraction of the respondents who reported experiencing (some of) mentioned symptoms of a disease Diagnosis rate: Blood pressure/Hypertentio 992 33% n Diabetes 289 10% Lung disease 303 10% Cancer 227 8% Note: fraction of the respondents who reported being diagnosed with a disease

Table 2. Summary statistics for the whole sample and for undiagnosed non-symptomatic respondents (by disease).

49

B4 Loss aversion values

Index of rejected lottery 1 2 3 4 5 6 7 8 9 10 11 All “yes” Mean: Median: Std. deviation:

Loss aversion 58 20 6.67 4.00 2.86 2.22 1.82 1.54 1.33 1.18 1.05 1.00 25.38 20 23.11

Loss aversion (normalized) 3 1 0.298 0.158 0.098 0.064 0.043 0.028 0.018 0.009 0.003 0 1.28 1 1.21

Number of respondents

% of the sample

947 830 356 303 187 121 97 30 12 15 15 93

31.50 27.61 11.84 10.08 6.22 4.03 3.23 1.00 0.40 0.50 0.50 3.09

Table 3. Distribution of loss aversion values.

B5 Distribution of testing frequencies

   Frequency of tests Never Once a year 2 times a year 3-4 times a year Once in 2 months Once a month 2-3 times a month Once a week or more Total:

Blood pressure testing All respondents Undiagnosed non-symptomatic N. % N. % 747 24.91 541 36.11 878 29.28 548 36.58 397 13.24 163 10.88 543 18.11 148 9.88 168 5.60 48 3.20 140 4.67 26 1.74 78 2.60 18 1.20 48 1.60 6 0.40 2999* 100 1498 100

*Note: 7 observations are missing from the original sample due to non-response Table 4. Distribution of blood pressure test frequency.

50

   Frequency of tests Never Once a year 2 times a year 3-4 times a year Once in 2 months Once a month 2-3 times a month Once a week or more Total:

Sugar level testing All respondents Undiagnosed non-symptomatic N. % N. % 1521 50.72 1375 56.42 989 32.98 840 34.47 180 6.00 133 5.46 158 5.27 63 2.59 32 1.07 16 0.66 33 1.10 8 0.33 23 0.77 2 0.08 63 2.10 0 0.00 2999* 100 2437 100

*Note: 7 observations are missing from the original sample due to non-response Table 5. Distribution of blood sugar level test frequency.

   Frequency of tests 0 1 2 3 4 5 6 7 8 9 10 >10 Total:

Lung disease tests All respondents Undiagnosed non-symptomatic N. % N. % 2103 70.12 1901 76.93 374 12.47 251 10.16 202 6.74 141 5.71 93 3.10 55 2.23 51 1.70 27 1.09 84 2.80 53 2.14 24 0.80 13 0.53 5 0.17 3 0.12 5 0.17 4 0.16 2 0.07 0 0.00 25 0.83 13 0.53 31 1.03 10 0.40 2999* 100 2471 100

*Note: 7 observations are missing from the original sample due to non-response Table 6. Distribution of lung disease test frequency. 51

Medical tests for cancer Undiagnosed non-symptomatic women men women N. % N. % N. % 922 59.6 1124 86.59 848 65.48 170 10.99 84 6.47 134 10.35 113 7.3 35 2.7 85 6.56 65 4.2 14 1.08 47 3.63 49 3.17 9 0.69 37 2.86 121 7.82 12 0.92 97 7.49 15 0.97 5 0.39 9 0.69 6 0.39 2 0.15 4 0.31 18 1.16 1 0.08 10 0.77 3 0.19 1 0.08 2 0.15 37 2.39 7 0.54 14 1.08 28 1.8 4 0.32 8 0.62 1547 100 1298 100 1295 100

All respondents

   Frequency of tests

men N. % 0 1191 82.02 1 105 7.23 2 50 3.44 3 17 1.17 4 12 0.83 5 16 1.1 6 10 0.69 7 6 0.41 8 5 0.34 9 1 0.07 10 12 0.83 >10 27 1.88 Total: 1452 100 Note: 7 observations are missing from the original sample due to non-response

Table 7. Distribution of cancer test frequency.

   Frequency of tests Never Once a year 2 times a year 3-4 times a year Once in 2 months Once a month 2-3 times a month Once a week or more Total:

Self-test for cancer All respondents Undiagnosed non-symptomatic men women men women N. % N. % N. % N. % 1230 84.71 544 35.16 1125 86.67 479 36.99 139 9.57 278 17.97 119 9.17 242 18.69 36 2.48 119 7.69 26 2.00 97 7.49 16 1.10 184 11.89 6 0.46 154 11.89 5 0.34 118 7.63 4 0.31 92 7.10 15 1.03 205 13.25 9 0.69 159 12.28 4 0.28 53 3.43 3 0.23 38 2.93 7 0.48 46 2.97 6 0.46 34 2.63 1452 100 1547 100 1298 100 1295 100

Note: 7 observations are missing from the original sample due to non-response

Table 8. Distribution of cancer self-test frequency.

52

B6 Estimation results

Sample: Dependent variable : Log of loss aversion

Blood pressure tests Excludes loss aversion group 12 Excludes loss aversion group 12 Decision to test (binary) Frequency of tests (categorical) -0.048** -0.049** -0.050 -0.050 (0.024)

Gender Age Edu Paid job Long-stand. disease BMI Smoking Alcohol Fam. physician Med. specialist Worry Family history

(0.041)

(0.041)

-0.098

(0.024)

-0.291**

-0.32**

(0.075)

(0.140)

(0.138)

0.018***

0.016***

0.028***

0.021***

(0.005)

(0.004)

(0.009)

(0.007)

0.051

0.061*

0.029

0.033

(0.038)

(0.037)

(0.069)

(0.066)

0.104

0.266

(0.093)

(0.171)

0.061

0.175

(0.088)

(0.149)

0.022***

0.024***

0.012

0.013

(0.010)

(0.010)

(0.020)

(0.019)

-0.13**

-0.118*

0.028

(0.064)

(0.064)

(0.127)

-0.025

-0.03*

0.001

(0.017)

(0.017)

(0.032)

0.105***

0.105***

0.059**

0.074***

(0.022)

(0.020)

(0.035)

(0.031)

0.009

0.020

(0.024)

(0.039)

0.277***

0.278***

0.182

0.189*

(0.066)

(0.065)

(0.115)

(0.112)

0.133*

0.122*

0.166

0.159

(0.073)

(0.073)

(0.138)

(0.137)

Regression type: probit probit ordered logit ordered logit N. of observations: 1440 1440 920 920 LR-test (prob.>chi^2): 0.000 0.000 0.000 0.000 Pseudo R-squared: 0.06 0.06 0.017 0.015 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; robust standard errors in parentheses. Loss aversion group 12 contains individuals who responded “Yes” to all lottery questions.

Table 9. Estimation results for two-part model: blood pressure tests.

53

Sample: Dependent variable :

Log of loss aversion

Sugar level tests Excludes loss aversion group 12 Excludes loss aversion group 12 Decision to test (binary) Frequency of tests (categorial) -0.037** -0.038** 0.001 0.006 (0.018)

Gender

-0.216

(0.057)

(0.163)

0.019***

Edu

(0.029)

Long-stand. disease BMI

(0.050)

-0.133**

Age

Paid job

(0.018)

(0.050)

0.019***

0.016

(0.003)

(0.003)

(0.010)

-0.025

-0.011

0.101

0.078

(0.028)

(0.080)

(0.076)

0.059

0.152

(0.072)

(0.202)

0.061

0.307*

0.380**

(0.061)

(0.165)

(0.156)

0.008

0.008

0.013

0.014

(0.006)

(0.006)

(0.013)

(0.015)

Smoking

-0.140***

-0.13**

0.131

(0.053)

(0.053)

(0.169)

Alcohol

-0.011

-0.016

0.046

(0.013)

(0.012)

(0.037)

0.047***

0.047***

0.026

(0.013)

(0.012)

(0.021)

Fam. physician Med. specialist

0.005

0.005

(0.012)

Worry Family history

(0.024)

0.585***

0.576***

0.303**

0.304**

(0.063)

(0.062)

(0.148)

(0.141)

0.075

0.074

0.199

(0.064)

(0.064)

(0.174)

Regression type: probit probit ordered logit ordered logit N. of observations: 2354 2354 1029 1029 LR-test (prob.>chi^2): 0.000 0.000 0.085 0.024 Pseudo R-squared: 0.070 0.067 0.014 0.009 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; robust standard errors in parentheses. Loss aversion group 12 contains individuals who responded “Yes” to all lottery questions.

Table 10. Estimation results for two-part model: blood sugar level tests.

54

Sample: Dependent variable : Log of loss aversion

Gender Age Edu BMI Smoking Alcohol

Lung disease tests Excludes loss aversion group 12 Excludes loss aversion group 12 Decision to test (binary) Frequency of tests (continuous) -0.052*** -0.052*** -0.035 -0.048 (0.020)

(0.020)

(0.073)

(0.076)

0.108*

0.100*

0.859***

0.769*** (0.236)

(0.061)

(0.060)

(0.230)

0.016***

0.016***

0.017

0.017

(0.003)

(0.003)

(0.013)

(0.013)

-0.067**

-0.070**

-0.101

(0.031)

(0.030)

(0.120)

0.007

0.013

(0.006)

(0.027)

0.093

0.090

0.184

(0.061)

(0.061)

(0.243)

-0.005

-0.075

(0.013)

Worry Family history Flu frequency Flu shots Immunity

(0.054)

0.239***

0.248***

(0.070)

(0.070)

-0.077 (0.050)

0.102

-0.482*

-0.470**

(0.077)

(0.258)

(0.243)

0.128***

0.128***

0.146

(0.026)

(0.026)

(0.120)

0.051**

0.053***

0.126*

0.120*

(0.015)

(0.015)

(0.069)

(0.069)

-0.189**

-0.198**

0.325

(0.089)

(0.088)

(0.330)

Regression type: probit probit OLS OLS N. of observations: 2384 2384 554 554 (1) LR-test (prob.>chi^2): 0.000 0.000 0.000 0.000(1) (Pseudo) R-squared: 0.064 0.063 0.057 0.043 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; robust standard errors in parentheses. Loss aversion group 12 contains individuals who responded “Yes” to all lottery questions. (1) F-test for OLS regression

Table 11. Estimation results for two-part model: lung disease tests.

55

Sample: Dependent variable : Log loss aversion x dummy(female)

Log loss aversion x dummy(male)

Medical tests for cancer Excludes loss aversion group 12 Excludes loss aversion group 12 Decision to test (binary) Frequency of tests (continuous) -0.005 -0.005 -0.079 -0.090 (0.025)

(0.025)

(0.085)

(0.083)

0.014

0.012

-0.308

-0.316

(0.029)

(0.029)

(0.369)

(0.364)

Age

0.014***

0.014***

0.042***

0.041***

(0.003)

(0.003)

(0.013)

(0.013)

Edu

0.056*

0.053*

-0.064

(0.030)

(0.030)

(0.121)

BMI

0.007

Smoking Alcohol Worry Family history Avg. number of programs

-0.004

(0.005)

(0.012)

-0.076

-0.142

(0.061)

(0.225)

0.012

0.124*

0.128**

(0.013)

(0.065)

(0.066)

0.284***

0.280***

0.226

(0.045)

(0.045)

(0.259)

0.129**

0.125**

-0.034

(0.058)

(0.058)

(0.263)

0.490***

0.496***

0.541**

0.565***

(0.042)

(0.042)

(0.233)

(0.225)

Regression type: OLS OLS probit probit N. of observations: 2502 2502 606 609 LR-test (prob.>chi^2): 0.000 0.000 0.000(1) 0.000(1) Pseudo R-squared: 0.083 0.081 0.037 0.034 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; robust standard errors in parentheses. Loss aversion group 12 contains individuals who responded “Yes” to all lottery questions. (1) F-test for OLS regression

Table 12. Estimation results for two-part model: medical tests for cancer.

56

Sample: Dependent variable : Log loss aversion x dummy(female)

Self-tests for cancer Excludes loss aversion group 12 Excludes loss aversion group 12 Decision to test (binary) Frequency of tests (categorical) -0.040m -0.039m -0.072* -0.075* (0.026)

(0.026)

(0.043)

(0.042)

Log loss aversion x dummy(male)

-0.003

-0.003

0.099

0.102

(0.028)

(0.028)

(0.112)

(0.111)

Age

0.0002

0.005

(0.003)

(0.006)

0.010

-0.046

(0.030)

(0.062)

Edu BMI Smoking Alcohol Worry Family history Avg. number of programs

0.002

0.008

(0.005)

(0.020)

-0.127**

-0.130**

0.049

(0.057)

(0.056)

(0.131)

0.002

0.069**

0.070***

(0.013)

(0.030)

(0.028)

0.350***

0.350***

0.224**

0.199*

(0.049)

(0.048)

(0.110)

(0.108)

0.097*

0.095*

-0.038

(0.058)

(0.057)

(0.120)

0.923***

0.922***

0.653***

0.650***

(0.044)

(0.043)

(0.107)

(0.105)

Regression type: probit probit ordered logit ordered logit N. of observations: 2502 2502 957 957 LR-test (prob.>chi^2): 0.000 0.000 0.000 0.000 Pseudo R-squared: 0.206 0.206 0.021 0.020 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; m — marginal significance (p-value<0.15); robust standard errors in parentheses. Loss aversion group 12 contains individuals who responded “Yes” to all lottery questions.

Table 13. Estimation results for two-part model: self-tests for cancer.

57

Blood pressure tests: robustness check Sample:

Excludes loss aversion group 1

Includes loss aversion group 12

Dependent variable :

Decision to test (binary) -0.062* -0.059*

Decision to test (binary) -0.042m -0.043*

Loss aversion

(1)

(0.036)

Gender

(0.036)

-0.059 (0.094)

Age Edu Paid job Long-stand. disease

Smoking Alcohol Fam. physician Med. specialist

(0.026)

-0.083

-0.101

(0.074)

(0.073)

0.018***

0.017***

0.018***

0.016***

(0.006)

(0.005)

(0.005)

(0.004)

0.094**

0.099**

0.050

0.052

(0.047)

(0.047)

(0.037)

(0.037)

0.051 (0.117) 0.109

0.104 (0.092)

-0.066

(0.107)

BMI

(0.026)

(0.085)

0.034*** (0.012) -0.147*

0.035***

0.021**

0.022**

(0.013)

(0.010)

(0.010)

-0.138*

-0.138**

-0.135**

(0.081)

(0.081)

(0.062)

(0.062)

-0.014

-0.017

-0.027*

-0.028*

(0.021)

(0.021)

(0.016)

(0.016)

0.111***

0.109***

0.101***

0.110***

(0.027)

(0.024)

(0.021)

(0.020)

-0.009

0.017

(0.022)

(0.021)

Worry

0.235*** (0.078)

(0.076)

(0.065)

(0.065)

Family history

0.177**

0.172**

0.113m

0.112m

(0.091)

(0.090)

(0.072)

(0.072)

0.234***

0.291***

0.294***

Regression type: probit probit probit probit N. of observations: 957 957 1492 1492 LR-test (prob.>chi^2): 0.000 0.000 0.000 0.000 Pseudo R-squared: 0.06 0.06 0.065 0.063 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; m – indicates marginal significance (p-value<0.15); robust standard errors in parentheses. (1) In columns 1 and 2 regressions contain natural log of normalized loss aversion; in columns 3 and 4 regressions contain natural log of non-normalized loss aversion in order to include loss aversion of 1 that becomes zero in case of normalization. Loss aversion group 12 contains individuals who accepted all lotteries (loss neutral). Loss aversion group 1 contains individuals who rejected 'harmless' lottery (extremely loss averse).

Table 14. Robustness checks for high blood pressure/hypertension testing. 58

Sample: Dependent variable :

Loss aversion(1)

Sugar level tests: robustness check Excludes loss aversion group 1 Includes loss aversion group 12 Decision to test (binary) Decision to test (binary) -0.022 -0.021 -0.030m -0.033* (0.026)

(0.026)

Gender

-0.125*

Age

0.021***

0.018***

(0.004)

Edu

-0.015 (0.034)

(0.069)

Paid job Long-stand. disease BMI

(0.020)

(0.020)

-0.122** (0.056)

0.020***

0.019***

(0.003)

(0.003)

(0.003)

0.003

-0.015

(0.034)

(0.028)

0.136

0.063

(0.088)

(0.070)

0.093

-0.052

(0.074)

(0.060)

0.004

0.005

0.007

(0.007)

(0.007)

(0.006)

Smoking

-0.140**

-0.127**

-0.139***

-0.125**

(0.065)

(0.065)

(0.053)

(0.052)

Alcohol

-0.004

-0.009

-0.013

(0.016)

(0.015)

(0.012)

0.030**

0.028**

0.045***

0.047***

(0.015)

(0.013)

(0.013)

(0.011)

Fam. physician Med. specialist

-0.004

0.010

(0.013)

Worry Family history

(0.008)

0.562***

0.549***

0.582***

0.577***

(0.074)

(0.073)

(0.062)

(0.061)

0.028

0.035

0.059

0.064

(0.078)

(0.078)

(0.063)

(0.063)

Regression type: probit probit probit probit N. of observations: 1591 1591 2423 2423 LR-test (prob.>chi^2): 0.000 0.000 0.000 0.000 Pseudo R-squared: 0.057 0.053 0.068 0.064 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; m – indicates marginal significance (p-value<0.15); robust standard errors in parentheses. (1) In columns 1 and 2 regressions contain natural log of normalized loss aversion; in columns 3 and 4 regressions contain natural log of non-normalized loss aversion in order to include loss aversion of 1 that becomes zero in case of normalization. Loss aversion group 12 contains individuals who accepted all lotteries (loss neutral). Loss aversion group 1 contains individuals who rejected 'harmless' lottery (extremely loss averse).

Table 15. Robustness checks for high blood sugar level/diabetes testing.

59

Sample: Dependent variable :

Loss aversion(1)

Lung disease tests: robustness check Excludes loss aversion group 1 Includes loss aversion group 12 Decision to test (binary) Decision to test (binary) -0.069** -0.065** -0.043** -0.040* (0.029)

(0.029)

(0.022)

(0.022)

0.142**

0.125*

0.119**

0.107*

(0.075)

(0.074)

(0.060)

(0.059)

Age

0.016***

0.017***

0.016***

0.015***

(0.004)

(0.004)

(0.003)

(0.003)

Edu

-0.058*

-0.053

-0.067**

-0.077***

(0.037)

(0.036)

(0.030)

(0.029)

BMI

0.02**

0.018**

0.006

(0.009)

(0.009)

(0.005)

Smoking

0.130*

0.129*

0.095

(0.074)

(0.074)

(0.059)

Gender

Alcohol Worry

-0.020

-0.005

(0.017)

(0.013)

0.204**

0.221***

0.228***

0.259***

(0.084)

(0.084)

(0.069)

(0.066)

Family history

0.133

0.144

0.088

(0.095)

(0.094)

(0.077)

Flu frequency

0.127***

0.129***

0.123***

(0.034)

(0.034)

(0.025)

(0.025)

Flu shots

0.059***

0.059***

0.051***

0.050***

(0.019)

(0.019)

(0.014)

(0.014)

Immunity

-0.149

-0.159*

-0.165*

(0.108)

(0.088)

(0.087)

0.123***

Regression type: probit probit probit probit N. of observations: 1599 1599 2461 2461 LR-test (prob.>chi^2): 0.000 0.000 0.000 0.000 Pseudo R-squared: 0.069 0.067 0.061 0.059 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; m – indicates marginal significance (p-value<0.15); robust standard errors in parentheses. (1) In columns 1 and 2 regressions contain natural log of normalized loss aversion; in columns 3 and 4 regressions contain natural log of non-normalized loss aversion in order to include loss aversion of 1 that becomes zero in case of normalization. Loss aversion group 12 contains individuals who accepted all lotteries (loss neutral). Loss aversion group 1 contains individuals who rejected 'harmless' lottery (extremely loss averse).

Table 16. Robustness checks for lung disease testing.

60

Self-tests for cancer: robustness check Sample: Dependent variable : Loss aversion(1) x dummy(female)

Loss aversion(1) x dummy(male) Age Edu BMI

Excludes loss aversion group 1

Includes loss aversion group 12

Frequency of tests(categorical) Frequency of tests(categorical) -0.004 -0.009 0.007 0.005 (0.061)

(0.061)

(0.048)

(0.047)

0.399**

0.387**

-0.493***

-0.491***

(0.175)

(0.174)

(0.102)

(0.102)

-0.003

0.006

(0.008)

(0.006)

-0.039

-0.012

(0.073)

(0.062)

0.023

0.006

(0.018)

(0.017)

Smoking

0.103

0.109

Alcohol

0.067**

0.079**

(0.036)

(0.035)

(0.029)

(0.028)

Worry

0.198m

0.180

0.208*

0.194*

(0.137)

(0.134)

(0.111)

(0.109)

Family history

-0.102

-0.103

0.027

(0.143)

(0.141)

(0.119)

0.516***

0.523***

0.106

0.104

(0.156)

(0.156)

(0.139)

(0.138)

(0.154)

Avg. number of programs

(0.132)

0.054*

0.052**

Regression type: ordered logit ordered logit ordered logit ordered logit N. of observations: 661 661 985 985 LR-test (prob.>chi^2): 0.000 0.000 0.000 0.000 Pseudo R-squared: 0.027 0.023 0.028 0.027 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; m – indicates marginal significance (p-value<0.15); robust standard errors in parentheses. (1) In columns 1 and 2 regressions contain natural log of normalized loss aversion; in columns 3 and 4 regressions contain natural log of non-normalized loss aversion in order to include loss aversion of 1 that becomes zero in case of normalization. Loss aversion group 12 contains individuals who accepted all lotteries (loss neutral). Loss aversion group 1 contains individuals who rejected 'harmless' lottery (extremely loss averse).

Table 17. Robustness checks for self-tests for cancer.

61

B7 Marginal effects

Marginal effects for: Log of loss aversion

Blood pressure testing Participation (probit) Frequency (ordered logit) Unitary change 1 std. dev. Unitary change 1 std. dev. 0.0183 0.0271 0.0123 0.0187

Gender

0.0779

0.0390

Age

-0.0058

-0.0595

-0.0050

-0.0517

Edu

-0.0225

-0.0223

-0.0081

-0.0081

BMI

-0.0087

-0.0428

-0.0032

-0.0171

Smoking

0.0436

0.0236

Alcohol

0.0109

0.0247

Fam. physician

-0.0388

-0.0946

-0.0180

-0.0493

Worry

-0.1027

-0.0601

-0.0460

-0.0284

Family history

-0.0449

-0.0217

-0.0388

-0.0187

Never test 0.3478 1440

Never test 0.3478 1440

Once a year 0.5779 920

Once a year 0.5779 920

Paid job Long-stand. disease

Med. specialist

Predicted outcome: Predicted probability: N. of observations:

Note: columns 1 and 3 show marginal effects (i.e. an absolute change in the predicted probability of a given outcome) for an increase of regressor by 1 (for continuous variables) or a change of regressor from 0 to 1 (for binary variables). Columns 2 and 4 show marginal effects when a regressor changes by one standard deviation. Marginal effects are estimated given the mean values of variables.

Table 18. Marginal effects: blood pressure tests.

62

Marginal effects for: Log of loss aversion

Sugar level testing Participation (probit) Frequency (ordered logit) Unitary change 1 std. dev. Unitary change 1 std. dev. 0.0150 0.0224 -0.0014 -0.0009

Gender Age

-0.0074

-0.0780

Edu

0.0043

0.0043

-0.0128

-0.0127

0.0296

0.0622

-0.0143

-0.0023

-0.0259

-0.0498

Paid job Long-stand. disease BMI

-0.0033

-0.0205

Smoking

0.0501

0.0263

Alcohol

0.0062

0.0140

Fam. physician

-0.0186

-0.0526

Worry

-0.2267

-0.1035

Family history

-0.0293

-0.0127

Med. specialist

Predicted outcome: Never test Never test Once a year Once a year Predicted probability: 0.5658 0.5658 0.7936 0.7936 N. of observations: 2354 2354 1029 1029 Note: columns 1 and 3 show marginal effects (i.e. an absolute change in the predicted probability of a given outcome) for an increase of regressor by 1 (for continuous variables) or a change of regressor from 0 to 1 (for binary variables). Columns 2 and 4 show marginal effects when a regressor changes by one standard deviation. Marginal effects are estimated given the mean values of variables.

Table 19. Marginal effects: blood sugar level tests.

63

Marginal effects for: Log of loss aversion

Lung disease testing Participation (probit) Frequency (OLS) Unitary change 1 std. dev. Unitary change 1 std. dev. 0.0152 0.0224 -0.0353 -0.0550

Gender

-0.0296

-0.0148

0.8557

0.4265

Age

-0.0047

-0.0494

0.0191

0.1890

Edu

0.0207

0.0208

-0.0266

-0.0135 -0.0663

-0.1547

-0.4593

-0.1828

BMI Smoking Alcohol Worry

-0.0734

-0.0303

Family history Flu frequency

-0.0379

-0.0543

0.1435

0.2611

Flu shots

-0.0157

-0.0358

0.1220

0.3048

Immunity

0.0586

0.0187

0.3479

0.1279

Predicted outcome: Never test Never test 2.641 2.641 Predicted probability: 0.7808 0.7808 N. of observations: 2384 2384 554 554 Note: in the first column marginal effects represent absolute change in the predicted probability of outcome given an increase of regressor by 1 (for continuous variables) or a change of regressor from 0 to 1 (for binary variables). In the third column marginal effects represent absolute change in the number of tests during 10 years given a unitary change in regressor. Columns 2 and 4 show marginal effects when a regressor changes by one standard deviation. Marginal effects are estimated given the mean values of regressors. 1 Predicted number of tests during 10 years given the mean values of regressors.

Table 20. Marginal effects: lung disease tests.

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Marginal effects for: Log loss aversion x dummy (female)

Medical tests for cancer Participation (probit) Frequency (OLS) Unitary change 1 std. dev. Unitary change 1 std. dev. 0.0014 0.0015 -0.0903 -0.1141

Log loss aversion x dummy (male)

-0.0035

-0.0037

-0.3159

-0.2511

Age

-0.0041

-0.0436

0.0415

0.4011

Edu

-0.0157

-0.0159

0.1280

0.2986

BMI Smoking Alcohol Worry

-0.0834

-0.0541

Family history

-0.0372

-0.0186

Avg. number of programs

-0.1480

-0.1032

0.5556

0.3775

Never test 0.7778 2502

Never test 0.7778 2502

3.271

3.271

606

606

Predicted outcome: Predicted probability: N. of observations:

Note: in the first column marginal effects represent absolute change in the predicted probability of outcome given an increase of regressor by 1 (for continuous variables) or a change of regressor from 0 to 1 (for binary variables). In the third column marginal effects represent absolute change in the number of tests during 10 years given a unitary change in regressor. Marginal effects are estimated given the mean values of regressors. Columns 2 and 4 show marginal effects when a regressor changes by one standard deviation. Predicted number of tests during 10 years given the mean values of regressors.

1

Table 21. Marginal effects: medical tests for cancer.

65

Marginal effects for: Loss aversion x dummy(female) Loss aversion x dummy(male)

Self-tests for cancer Participation (probit) Frequency (ordered logit) Unitary change 1 std. dev. Unitary change 1 std. dev. 0.0147 0.0158 0.0173 0.0240 0.0012

0.0013

0.0485

0.0252

-0.0233

-0.0155

-0.0160

-0.0358

-0.0455

-0.0286

-0.1490

-0.0909

Age Edu BMI Smoking Alcohol Worry

-0.1307

-0.0845

Family history

-0.0355

-0.0177

Avg. number of programs

-0.3439

-0.2367

Predicted outcome: Never test Never test Once a year Once a year Predicted probability: 0.6436 0.6436 0.3555 0.3555 N. of observations: 2502 2502 957 957 Note: marginal effects represent absolute change in the predicted probability of outcome given an increase of regressor by 1 (for continuous variables) or a change of regressor from 0 to 1 (for binary variables). Columns 2 and 4 show marginal effects when a regressor changes by one standard deviation. Marginal effects are estimated given the mean values of regressors.

Table 22. Marginal effects: self-tests for cancer.

66

Predicted probability of participation in testing Index of Self-test for cancer Ln(loss aversion) Blood pressure test Sugar level test Lung disease test rejected lottery (women) 1 1.1 0.624 0.410 0.2 0.335 2 0 0.644 0.427 0.215 0.354 3 -1.21 0.666 0.446 0.232 0.376 4 -1.85 0.678 0.455 0.241 0.388 5 -2.33 0.686 0.463 0.248 0.397 6 -2.74 0.693 0.470 0.255 0.405 7 -3.15 0.700 0.476 0.261 0.412 8 -3.56 0.708 0.482 0.267 0.420 9 -4.04 0.716 0.490 0.274 0.429 10 -4.68 0.726 0.500 0.284 0.441 11 -5.89 0.746 0.519 0.304 0.465 All “yes” Average change: 0.0122 0.0109 0.0103 0.0130 Note: Table shows predicted probability of participation in testing given each value of loss aversion and mean values of all other variables. Results for cancer screening are not provided since loss aversion is not significant for participation decision.

Table 23. Predicted probabilities of participation in testing.

67

Sample: Dependent variable:

Log loss aversion

Blood pressure testing: influence of risk Excludes loss aversion group 12 Decision to test (binary) -0.023 -0.023 (0.031)

(0.031)

Loss aversion x dummy(average risk)

-0.052

-0.053

(0.059)

(0.059)

Loss aversion x dummy(high risk)

-0.069

-0.068

(0.062)

(0.062)

Dummy (low risk)

-0.094

-0.081

(0.099)

(0.099)

Dummy (average risk)

-0.076

-0.073

(0.114)

(0.113)

-0.093

-0.126*

Gender Age Edu

(0.075)

(0.073)

0.018***

0.014***

(0.005)

(0.004)

0.053 (0.038)

Paid job

0.111 (0.094)

Long-stand. disease

0.063 (0.088)

BMI

0.022*** (0.010)

(0.010)

Smoking

-0.133**

-0.145**

(0.064)

(0.063)

Alcohol

-0.025*

-0.029*

(0.017)

(0.017)

Fam. physician

0.105***

0.111***

(0.022)

(0.021)

Med. specialist

0.021**

0.010 (0.024)

Worry

0.277***

Family history

0.285***

(0.066)

(0.065)

0.130*

0.136*

(0.074)

(0.073)

Regression type: probit probit N. of observations: 1440 1440 LR-test (prob.>chi^2): 0.000 0.000 Pseudo R-squared: 0.066 0.063 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; robust standard errors in parentheses. Loss aversion group 12 contains individuals who accepted all lotteries (loss neutral).

Table 24. Effect across different risk groups: high blood pressure/hypertension. 68

Sample: Dependent variable:

Log loss aversion

Sugar level tests: influence of risk Excludes loss aversion group 12 Decision to test (binary) -0.044* -0.045* (0.024)

(0.023)

Log loss aversion x dummy(average risk)

0.047

0.005

(0.046)

(0.046)

Log loss aversion x dummy(high risk)

-0.018

-0.019

(0.046)

(0.046)

0.030

0.031

(0.074)

(0.074)

Dummy (low risk) Dummy (average risk) Gender Age Edu

0.008

0.006

(0.087)

(0.087)

-0.136***

-0.140***

(0.057)

(0.056)

0.0192***

0.019***

(0.003)

(0.003)

-0.025 (0.029)

Paid job

0.055 (0.072)

Long-stand. disease

0.061 (0.061)

BMI Smoking Alcohol

0.007

0.007

(0.006)

(0.006)

-0.138***

-0.125***

(0.053)

(0.052)

-0.011 (0.013)

Fam. physician Med. specialist

0.048***

0.051***

(0.013)

(0.012)

0.005 (0.012)

Worry Family history

0.589***

0.589***

(0.063)

(0.063)

0.075

0.078

(0.064)

(0.064)

Regression type: probit probit N. of observations: 2354 2354 LR-test (prob.>chi^2): 0.000 0.000 Pseudo R-squared: 0.071 0.070 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; robust standard errors in parentheses. Loss aversion group 12 contains individuals who accepted all lotteries (loss neutral).

Table 25. Effect across different risk groups: high blood sugar level/diabetes. 69

Sample: Dependent variable:

Log loss aversion

Lung disease testing: influence of risk Excludes loss aversion group 12 Decision to test (binary) -0.054** -0.053** (0.026)

(0.026)

Log loss aversion x dummy(average risk)

0.027

0.027

(0.050)

(0.050)

Log loss aversion x dummy(high risk)

-0.026

-0.028

(0.051)

(0.051)

Dummy (low risk)

0.048

0.049

(0.082)

(0.082)

Dummy (average risk)

-0.063

-0.062

(0.096)

(0.096)

Gender Age Edu BMI

0.102*

0.094

(0.061)

(0.061)

0.016***

0.016***

(0.003)

(0.003)

-0.067**

-0.071**

(0.031)

(0.030)

0.007 (0.006)

Smoking

0.100*

0.097*

(0.061)

(0.061)

Alcohol

-0.005

Worry

0.250***

0.250***

(0.071)

(0.071)

(0.013)

Family history Flu frequency

0.098

0.097

(0.078)

(0.078)

0.128***

0.128***

(0.026)

(0.026)

Flu shots

0.052***

0.053***

(0.015)

(0.015)

Immunity

-0.188**

-0.186**

(0.089)

(0.089)

Regression type: probit probit N. of observations: 2384 2384 LR-test (prob.>chi^2): 0.000 0.000 Pseudo R-squared: 0.066 0.065 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; robust standard errors in parentheses. Loss aversion group 12 contains individuals who accepted all lotteries (loss neutral).

Table 26. Effect across different risk groups: lung disease.

70

Sample: Dependent variable:

Log loss aversion Log loss aversion x dummy(high risk) Dummy (low risk) Age Edu

Self-tests for cancer(women): influence of risk Excludes loss aversion group 12 Excludes loss aversion group 12 Decision to test (binary) Frequency of tests (contin.) -0.069*

-0.070*

-0.020

(0.037)

(0.037)

(0.069)

(0.069)

0.067

0.068

-0.052

-0.054

(0.050)

(0.050)

(0.089)

(0.088)

-0.109

-0.110

0.114

0.118

(0.079)

(0.079)

(0.141)

(0.141)

-0.011

-0.010

0.008

0.009

(0.004)

(0.004)

(0.007)

(0.006)

-0.037

-0.019

(0.041)

BMI

-0.019

(0.069)

0.010

0.011

0.005

(0.007)

(0.007)

(0.012)

Smoking

-0.163**

-0.153**

-0.002

(0.078)

(0.077)

(0.143)

Alcohol

-0.027

-0.025

0.054*

0.061**

(0.017)

(0.017)

(0.031)

(0.030)

0.349***

0.345***

0.160

0.163

(0.070)

(0.069)

(0.118)

(0.114)

0.158**

0.160**

0.043

(0.076)

(0.076)

(0.134)

0.155*

0.158*

-0.133

(0.091)

(0.091)

(0.167)

Worry Family history Avg. number of programs Regression type: N. of observations: LR-test (prob.>chi^2): Pseudo R-squared:

probit probit OLS 1249 1249 786 0.000 0.000 0.000 0.045 0.045 0.013 Notes: sample consists of undiagnosed non-symptomatic people. Significance: * - at 10% level, ** - at 5% level, *** - at 1% level; robust standard errors in parentheses. Loss aversion group 12 contains individuals who accepted all lotteries (loss neutral).

Table 27. Effect across different risk groups: self-tests for cancer.

71

OLS 786 0.000 0.013

Variable name Edu

Gender Paid job

Source LISS core study (wave 3), Nov-Dec 2009 LISS core study (wave 3), Nov-Dec 2009 LISS core study (wave 3), Nov-Dec 2009

Long-stand. disease

LISS core study (wave 3), Nov-Dec 2009

BMI

computed

Smoking

Questionnaire, Aug 2010

Alcohol

LISS core study (wave 3), Nov-Dec 2009

Fam. physician

LISS core study (wave 3), Nov-Dec 2009

Med. specialist

LISS core study (wave 3), Nov-Dec 2009

Worry

Questionnaire, Aug 2010

Family history

Questionnaire, Aug 2010

Flu frequency

Questionnaire, Aug 2010

Flu shots

Questionnaire, Aug 2010

Immunity

Questionnaire, Aug 2010

Description (1) Basic (2) vmbo/havo/vwo (high school) (3) mbo (technical) (4) hbo/vo (university) 1 Female 0 Male 0 has no paid job 1 has paid job Do you suffer from any kind of long-standing disease, affliction or handicap, or do you suffer from the consequences of an accident? 1 Yes 0 No computed as: mass(kg)/(height(m))^2 How many cigarettes do you smoke a day? 1 I don't smoke 2 On average I smoke less than 20 cigarettes a day 3 On average I smoke more than 20 cigarettes a day Think of all the sorts of drink that exist. How often did you have a drink containing alcohol over the last 12 months? 1 almost every day 2 five or six days per week 3 three or four days per week 4 once or twice a week 5 once or twice a month 6 once every two months 7 once or twice a year 8 not at all over the last 12 months How often did you attend a family physician over the past 12 months? Number How often did you attend a medical specialist at a hospital over the past 12 months? Number How often do you worry about having a heart attack or a stroke (diabetes/chronic lung disease(except lung cancer)/a type of cancer) at some point in life? 1 Never 2 A few times each year or less 3 1-4 times a month 4 1-4 times a week 5 At least once a day Do any of your parents or siblings currently have or had high blood pressure or hypertension (high blood sugar level or diabetes/chronic lung disease or emphysema/cancer or malignant tumor)? 1 Yes 0 No How many times did you have flu in the past 5 years? (from the beginning of 2005 till now)? Number How many times did you have a flu shot in the past 5 years? Number Do you catch colds easily? 72 1 No 0 Yes

Avg number of programs

computed

computed as the average number of screening programs for which a woman was eligible for during the past 10 years according to the following formula: (n1/10)*m1+ (n2/10)*m2, where m1 and m2 is the number of programs a woman was eligible for because of belonging to different age groups; n1 and n2 is the number of years that she was eligible for m1 and m2 programs respectively. Example: a woman is 54 years old at the time of questionnaire study. This means that for the years from 50 to 54 she could participate in 2 screening programs, and for years from 44 to 50 in only one screening program. Therefore, her average number of programs is =(4/10)*2+(6/10)*1=1.4

Table 28. Description of control variables

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