The Value of Planned Death

The US Supreme Court ruled in 1997 that the average American as no constitutional right to a physician assisted suicide. How- ver, the court also implied that there is no constitutional bar that ould prevent a state from passing a law permitting physician

ssisted suicide. Subsequently, Oregon became the first state in he US in which physician assisted suicide is legalized. Around the orld, Switzerland has the longest history of allowing euthana-

ia (allowing both physician and non physician assisted suicide ince 1941). In 2002, Belgium and the Netherlands joined the list f European countries in which physician assisted suicide is legal. n 2008, the state of Washington in the US also passed a referen- um that legalizes physician assisted suicide. While its legal status

s unclear in most states in the US, physician assisted suicide (or uthanasia1), when considered implicitly, is a relatively common ractice in the United States. Markson (1995) points to the Amer-

can Hospital Association’s recognition that in the United States

s many as 6000 deaths per day are in some way planned by the atients, their families or physicians.

There have been a large number of published literatures that eal with the legal and ethical issues of euthanasia, particularly

∗ Corresponding author. Tel.: +1 801 863 8428. E-mail addresses: leohchan@yahoo.com, lchan@uvu.edu (L. Chan).

1 We feel that euthanasia is a broader term that includes physician assisted sui- ide and non physician assisted suicide. Any form of planned death can be seen as uthanasia. Thus, we use euthanasia, physician assisted suicide and planned death nterchangeably in this paper.

053-5357/$ – see front matter © 2010 Elsevier Inc. All rights reserved. oi:10.1016/j.socec.2010.06.007

since the Supreme Court’s ruling in 1997. Few attempts, however, have been made in the field of economics to tackle the issue of life and death analytically. The earliest attempt was Hamermesh and Soss (1974), in which they propose a model of suicide and suggest that a person will commit suicide when the expected remaining lifetime utility from living is negative. Their conjecture is tested with empirical data. Their empirical results show that the elderly, as a group, have a higher suicide rate. The suicide rate also increases as the unemployment rate goes up. These results suggest that there is a correlation between income, age, and the likelihood to commit suicide. The elderly, as a group, have lower income and are more likely to suffer medical conditions that require a large sum of money to cure or manage. Following Dixit and Pindyck (1994), the suicide model of Hamermesh and Soss is not complete because it ignores the uncertainty factor and, thus, the option value of living. Since the option value to live usually is very large, the circumstances under which suicide is rational must be far bleaker than those found by Hamermesh and Soss (1974).

What circumstances can be bleaker than a diagnosis of terminal illness? For terminally ill patients, death is not the only certainty, but so are physical pain and mental suffering. In a way, we can view life after a diagnosis of terminal illness as a period of time in which the patient’s overwhelming experience is that of futil- ity. This period can be viewed as an experience of disutility. There are also high medical costs that must be borne by the patient, the

patient’s family, or the society to prolong life. Thus, the decision to not prolong death could be beneficial to all parties involved.

On the other hand, the active decision to not prolong life beyond its natural course can have a direct economic cost. For instance, the legal preparation (e.g., obtaining and possibly enforcing the pro-

Socio-

v f c t i t

2

h a a b V a a a c t o s

v T a c a z h d

d V p s a p c i t t g

w e d W a w f

T e l p e

t a

value of Vt, the benefit of euthanasia will increase. Note that our model has some important policy implications as

well. If a given society wants to reduce the demand for euthana- sia, then more money should be spent on medical researches and

ill, even though six months is a finite time, at any given point in time, the outlook is uncertain. Most importantly, the probability of dying or living through to the

L. Chan, D. Lien / The Journal of

isions of an advance directive) and the arrangement of medical acilities required to ensure a more comfortable and dignified death an be quite expensive. Furthermore, such decisions impose emo- ional costs on both the patient and the family members. Therefore, f the potential benefits from euthanasia are greater than the costs, hen its selection can be seen as a rational choice.

. Euthanasia as an option

Consider a patient who just learned from his physician that he as terminal illness. Assume that he can only choose between two lternatives (options): euthanasia or continue the usual or more ggressive treatments in hope of extending life. Denote Vt as the enefit of euthanasia at the time when terminal illness is diagnosed. t includes the cost of continued treatments avoided and the pain nd suffering associated with the terminal illness that can also be voided with euthanasia. To obtain Vt, a patient must pay Mt, an mount we interpret as an upfront cost consisting of: the medical ost for pain management and other related medical services to he end of life, possible legal costs, and the mental burdens placed n the patient and related family members that stem from making uch a decision (Markson, 1995).

Melinek (1974), Jones-Lee (1989), and Viscusi (1993, 2004) pro- ide foundations upon which to evaluate the economic value of life. heir methods are helpful in constructing numerical values for Vt nd Mt. These two variables are, of course, time varying. A patient an start with no pain at all and live until the last day of life without ny pain. For this patient the benefit from euthanasia is, obviously, ero. On the other hand, the patient may start with no pain and, as ealth deteriorates, increased pains start to have an effect on the ecision process.

Note that Vt aggregates the cost avoided from the day the patient iscovered he has terminal illness to his death. Thus, as t increases, t decreases. From a project valuation perspective, we can view ain and suffering as negative cash flows. The benefit of euthana- ia is to avoid the realization of the negative cash flows. We can ssume that the patient can confidently estimate the amount of ains (negative cash flows) he/she will suffer until death given the urrent technologies and medical treatments. On the other hand, mprovements in medical technologies and medicines may lead o treatments that could possible result in a cure of the illness, hus making euthanasia less attractive. Lets assume Vt follows a eometric Brownian motion of the form,

dV

V = ˛vdt + �vdzv, (1)

here ˛v ≤ 0 is the rate of decline for the potential benefits from uthanasia as the patient ponders the decision, �v is the standard eviation for the percentage change in Vt, and zv is a standard iener process. Here, the patient knows the value of euthanasia

t the time of the diagnosis. If he postpones the decision, the value ill be different. For similar reasons, we also assume the cost, Mt,

ollows another geometric Brownian motion,

dM

M = ˛mdt + �mdzm (2)

he cost for the medical service will change over time, so does the

motional cost for the patient and relatives. While the prospect of osing a family member may be unbearable at first, seeing how the atient suffers may change the family members’ attitude towards uthanasia. Therefore, the sign of ˛m tends to be negative as well.2

2 An anonymous referee pointed out that a typical terminally ill patient, with he knowledge of his/her active and malignant disease cannot be cured, has, on verage, 6 months to live with uncertainty. Thus, in the mind of the a terminally

Economics 39 (2010) 692–695 693

A similar problem involving the value of waiting to invest can be found in McDonald and Siegel (1986). They suggest the solution that involves finding a number Ct*, for every time t, such that if Vt/Mt ≥ Ct*, then, as applied to our problem, euthanasia is optimal. The problem for the patient and the family members is to find a boundary value to maximize the value

E0[(Vt − Mt)e−�t],

where E0 denotes the expectation at the time of diagnosis and � denotes a subjective discount rate. Let the present value of euthana- sia be X, McDonald and Siegel (1986) show that

X = (C∗ − 1)M0 (

V0/M0 C∗

)ε , (3)

where

ε = √(

˛v−˛m �2

− 1 2

)2 + 2(� − ˛m)

�2 +

( 1 2

− ˛v − ˛m �2

) , (4)

C* = ε/(ε − 1), �2 = �2v + �2m − 2�vm�v�m, and �vm is the instanta- neous correlation between the rates of increases in V and M. Since ˛v < 0 ≤ �, therefore ε > 1 holds and the solution is well defined.

Note that ε is decreasing in ˛v and increasing in ˛m. Since X is decreasing in ε, the value of euthanasia is increasing in ˛v and decreasing in ˛m. The economic interpretation of these two con- ditions is as follow. Since ˛v is negative, an increase in value of ˛v implies that the benefit from euthanasia (Vt) is decreasing at a slower rate. Therefore, the value of euthanasia is high. An increase in ˛m, on the other hand, implies the cost of euthanasia goes down at a slower rate. From a purely emotional standpoint, if family mem- bers are having hard time letting the patient go, then it means there would be an increasing ˛m. In that case, our formulation of the rationale for selecting euthanasia is diminished, as we would expect.

Table 1 presents some numerical simulation results.3 Panel A shows that, for values of C0 = V0/M0 that are significantly smaller than 1, the value of X is close to zero. As the value of C0 exceeds 1, the value of X begins to increase at an increasing rate. This result suggests that if the benefit of euthanasia out-weights the cost, the benefit of euthanasia goes up faster. If the insurers follow the sug- gestion set forth in Fung (1993) and compensate the insured for choosing not to pursuer further medical treatments, the value of C0 will be significantly above 1.

Panel B shows that the value of the instantaneous correlation between the rates of increases in V and M, �vm, has a positive impact on the value of X. As the correlation coefficient increases, the value of X increases. Moreover, the value of X increases at an increasing rate as the value of �vm increases. A main implication of this result is that if the cost of euthanasia increases, along with an increase in

next moment is equal probability of ½, which is consistent with the random walk hypothesis. Yang (1993, 1994) applied the random walk model to study the suicide death rate. Although we adopt Brownian motions for the value of euthanasia and the cost to sustain the value, these assumptions do not necessarily lead to a random walk for the suicide rate. We concur that our assumption is a first attempt and may need to be modified in the future research.

3 For the simulation purpose, we arbitrarily choose ˛m = ˛v = −0.03. More pre- cisely, we may conduct a survey on the happiness of the terminally ill and estimate ˛v by the reduction rate in happiness. Meanwhile, we can estimate ˛m by the reduction rate of the lifetime medical expense over time.

694 L. Chan, D. Lien / The Journal of Socio-Economics 39 (2010) 692–695

Table 1 Numerical Simulations.

Panel A: How X varies with C0 C0 10 6.0 4.0 2.0 1.0 0.8 0.6 0.4 0.2 0.1 �2 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 ε 2.57 2.57 2.57 2.57 2.57 2.57 2.57 2.57 2.57 2.57 C* 1.64 1.64 1.64 1.64 1.64 1.64 1.64 1.64 1.64 1.64 X 662.56 297.66 157.72 53.25 17.98 12.68 8.08 4.28 1.45 0.49

Panel B: How X varies with �vm �vm −0.99 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 �2 0.04 0.036 0.032 0.028 0.024 0.02 0.016 0.012 0.008 0.004 ε 2.57 2.67 2.79 2.94 3.13 3.37 3.70 4.19 5 6.84

.47

.63

A 9.

s m

a t c a p t t ( i t T i ( t g

3

o w p c m t o c i p l L b P

l t u c m o a p

C* 1.64 1.6 1.56 1.51 1 X 157.72 172.69 193.9 224.03 269

ssumptions: ˛m = −0.03, ˛v = −0.03, � = 0.05, �m = 0.1, �v = 0.1, C0 = 4, �vm = −0.9

ervices devoted to the goal of reducing pain and suffering for ter- inally ill patients. Since the benefits of euthanasia are derived from avoiding pain

nd suffering associated with additional treatment and medica- ions, making life after a terminal illness diagnosis painless will ertainly reduce the potential benefits of euthanasia. The hospices nd palliative care medicine movement in recent years is aiming recisely at this goal. On the other hand, the society can also make he cost of euthanasia go up. Religious and political condemna- ions will definitely have a positive effect on the cost of euthanasia Markson, 1995). Likewise, the society can reallocate valuable med- cal (and financial) resources that are currently being spent on erminally ill patients, to help patients that are not terminally ill.4

hat is, euthanasia can be encouraged as a form of altruistic behav- or (see, for examples, Fung (1993), Callahan (1987), and Kevorkian 1991)). If family members see death as a “good” deed rather than a ragedy, their attitudes may change and the cost of euthanasia may o down.

. Medical breakthroughs and sudden death

While the prospect of something better coming up makes the ption of suicide for people who are not terminally ill irrational, ould the same be true for patients who are terminally ill? Sup- ose that there is a possibility that the diagnosis is incorrect. It ould be that the diagnosis is really not a terminal illness, or a cure ay soon be available if the patient waits. Furthermore, assume

here is also a possibility that a sudden death may occur. Strokes r complications from treatments and medications are some of the ommon causes of sudden death. We can incorporate these events nto our model by allowing Vt to take a discrete jump to zero (if the atient is not terminally ill the value of euthanasia is zero; simi-

arly, a sudden death also reduces the value of euthanasia to zero). et the probability of a wrong diagnosis or a medical breakthrough e �, then the stochastic process for Vt now follows a mixture of oisson–Wiener process of the form,

dV

V = ˛vdt + �vdzv + d�, (5)

4 As point out by Byrne and Thompson (2000), as much as 20% of an individual’s ifetime expenditures on health care are borne in the last year of life, and 40% of hose are borne in the last month. Expenditures on treatments that are ultimately nsuccessful account for $67 billion annually, or 12% of total spending on health are (1987 figure). Machlin (2009) reports that there is a 30% increases in annual edical expenditures for the elderly. Cohen and Yu (2010) reports that the top 1%

f the population accounts for 22.8% of the total health spending. The Wennberg et l. (2008) reports that 31.7% of Medicare spending went towards the chronically ill atient’s last 2 years of life.

1.42 1.37 1.31 1.25 1.17 345.1 488.23 828.78 2097.15 19159

where d� = −1 with probability �dt and d� = 0 with probability 1 − �dt. The expected benefit from euthanasia is now,

E0[(Vt − Mt)e−(�+�)t] (6)

Let X*(�) be the value of euthanasia at time t with probability of a wrong diagnosis or a medical breakthrough, then

X∗(�) < X (7)

Therefore, the value of euthanasia is strictly smaller if there is a positive probability of wrong diagnosis or medical breakthrough. However, this does not imply that the conjecture in Dixit and Pindyck (1994) is correct under this model. Euthanasia is still ratio- nal whenever Vt(�) − Mt ≥ 0, or as long as X* > 0. This conclusion is to be expected: Even if there is a possibility that the diagnosis is incor- rect, the patient is likely to contemplate euthanasia when suffering a certain amount of pains due to the illness. If the suffering from waiting is too high, the patient still should seek euthanasia. The same holds true for patients who wait for medical breakthroughs. However, the existence of uncertainties does guarantee that the value of euthanasia is strictly smaller than it would be if there were no uncertainties.

4. Conclusion and discussion

In this paper, we proposed a theoretical economic model of cal- culating the costs and benefits of euthanasia. The decision to seek euthanasia is modeled akin to the valuation of a real option. Our model concludes that euthanasia is optimal when certain condi- tions are satisfied. The discussion in this paper provides some policy implications. Different policies, ranging from the amount of money spent on medical research to social and religious attitude, could affect the demand for euthanasia.5 Though our model is motivated under the assumption of a diagnosis of terminal illness, the analy- sis, however, can be applied to all patients who are facing physical pain and/or psychological suffering from illnesses that have little or no chance of recovery. For further research, one direction would be to conduct surveys with terminally ill patients and their fami- lies and the medical professions to determine the likely boundary condition that will make euthanasia rational, and, perhaps, quanti-

fying the potential benefits. Specifically, if we have access to good estimates for the underlying parameter values, we can estimate the value of euthanasia via Eq. (3).

5 For example, more money could be spent on medical researches and services devoted to the goal of curing diseases before they become terminal. Thus, euthanasia can be eliminated from being an option to patients.

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cknowledgments

We would like to thank the editor and two anonymous refer- es for their valuable comments and suggestions. Leo Chan would ike to thank those who shared with him their experiences with heir deceased family member(s) who had suffered terminal illness. heir comments reaffirmed the need for this work. Thanks also go to ill Macauley and John Cita for their expert editorial helps and use-

ul comments. The view expressed in this paper and the remaining rrors are our own.

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