"Suicide: An Economic Approach" Becker & Posner 2004:
No fully reliable statistics give the numbers of miserable persons during any year or other time period, but various indirect measures indicate that it is substantial. Surveys suggest that in the US there are 20.5 millions users of crack and other heavy drugs, some 15.9 millions of individuals are classified as heavy drinkers (more than 5 drinks per day), the number of seriously depressed persons is estimated at 9.9 millions, crimes of violence amount to more than 7.26 per 100,000 population, almost half of all first marriages end in divorce, with many divorce proceedings being quite bitter. In happiness surveys, about 10% percent of persons report themselves as not happy.
...Suicide is the eighth leading cause of death in the US, and the third among teenagers. The combined number of deaths from drug use, heavy drinking, murder by a relative or a gang member, and car accidents when drinking are many times as frequent as suicides.
The modern approach to suicide stresses its immorality on the one hand and its connection to mental illness on the other hand. But the Greeks and Romans, as well as Asian cultures – especially the Japanese and Indian – considered suicide to be a rational response to illness, disgrace, and other pain and suffering. Both Hume and Schopenhauer in brief essays looked upon suicide as a perfectly reasonable response to bad circumstances. In an essay not published until his death (for fear of offending the Church), Hume stated,
> "That suicide may often be consistent with interest and with our duty to ourselves, no one can question, who allows, that age, sickness, or misfortune may render life a burden, and make it worse than annihilation. I believe that no man ever threw away life, while it was worth having. For such is our natural horror of death... (Essays on Suicide and the Immorality of the Soul, by the late David Hume, page 588)."
Schopenhauer added,
> "It will generally be found that, as soon as the terrors of life reach the point at which they outweigh the terrors of death, a man will put an end to his life. But the terrors of death offer considerable resistance . . ." (Parerga and Paralipomena, Vol. 2, page 156).
Our purposive choice approach to the behavior of unhappy people assumes they maximize their utility in a forward-looking fashion, taking account of the uncertainty of future events, and the consequences of their actions. Rather than imposing a tight fitting strait jacket on the analysis, the view that even very unhappy individuals compare the benefits and costs of different actions before deciding on the best, or least worst, steps provides a flexible and fruitful framework. We incorporate some of the insights of sociologists, psychiatrists, and philosophers about the factors that determine suicides and other actions of miserable persons.
Depressed persons are quite miserable. They often have trouble getting pleasure out of lives that would not be considered especially difficulty by others. Patients in mental hospitals do have particularly high suicide rates, especially those with depressive disorders (see Dublin [1963, p. 171]). And many other suicides might be judged to be by mentally disturbed individuals. This inability to get pleasure out of circumstances that most people would not find oppressive may define a mental disorder. Although depressed individuals are quite unhappy much of the time, this does not mean that their suicides are not maximizing responses to their circumstances. They may become willing to end their misery and face the terrors of death. Still, suicide seems to offer a strong challenge to explanations based on maximizing behavior.
Yet there is obviously much more to suicide than mental disturbance or an inability to enjoy life. Suicide rates respond to illness, economic circumstances – such as bankruptcy and unemployment – divorce, widowhood, family responsibilities, disgrace, disappointment, fear of punishment, aging, and other variables that affect the utility from living. A utility-maximizing approach to suicide does rather well in explaining these and other regularities in suicide rates.
For some miserable individuals the best policy is to do nothing desperate and wait for the situation to get better. Section 4 considers the effects of the rate of discount on the future, the degree of uncertainty about future events, and other variables on this “option” value of waiting.
Hamermesh and Soss (1974) is a pioneering study three decades ago that uses a utility maximizing approach to suicide. This paper is based on, and extends, several other papers, including two that were written more than a decade ago (Becker, 1991 in references, and Becker and Kilburn, 1993), as well as the more recent, Becker and Posner. Cutler, Glaeser and Norberg (2001) published an important paper that in several dimensions takes a similar approach to ours, although their main purpose is to explain the rise in youth suicide rates in the United States. As in this paper, they also assume that suicide is contemplated when utility drops below a fixed level (0) that utility is maximized sequentially over time, and that there is an option value from delaying suicide if times may get better.
There are however, also important differences. Cutler, Glaeser and Norberg do not draw out the risk-taking implications of this approach to suicide, including how attempted- suicides fit into a risk approach. They do not fully extract the implications of the option value of remaining alive, do not rely on the special form of preferences with habits and social interactions that seems consistent with the evidence on suicide and other behavior, have a different interpretation of the ratio of suicide attempts to “successes”, and do not discuss suicide bombers and the cost of suicide
Even if suicide will occur at some age because lifetime utility is negative, it could occur either later or earlier depending on the time sequence of utilities. If utilities are negative initially and perhaps positive later on – perhaps because of a major reversal of fortune at an early age – suicide would occur earlier. Conversely, if utilities decline monotonically with age from positive values initially – say because of declining health – suicide would occur when utilities first became negative. Thus Hamermesh and Soss (1974) are mistaken in their claim that rational behavior under certainty generally implies a rising propensity to commit suicide with age (also see Cutler, Glaeser, and Norberg (2001) for a correct analysis).
This conclusion is even more problematic after incorporating heterogeneity among people. Those people with the worst prospects tend to commit suicide earlier, while those with better ones survive to older ages and may never want to commit suicide. As is usual in such situations, like divorce, heterogeneity implies a declining relation of suicide to age: at later ages, only the happiest people would be surviving.
Only a small fraction of any cohort commits suicide; about 0.01% of the US population committed suicide in year 2001. This implies that those with utilities less than zero are located in the extreme left-hand tail – several standard deviations from the mean – in the distribution of utilities among people of the same age, etc. Therefore, even a modest shift in the mean utility – with the variability held constant – would have a very large effect on the fraction of persons whose utilities fall below zero since the extreme tails of most distributions are very sensitive to changes in the mean. For example, even a 10 percent difference in the mean I.Q. of two groups implies enormous differences in the fraction of “geniuses” and “retards”.
We believe that this sensitivity of the tails helps explains (along with mean reversion in utilities) why suicides have been quite responsive to moderate business cycle changes in economic circumstances (see Hamermesh and Soss (1974). This does not necessarily imply utility is so sensitive to changes in income, but that even moderate changes in income push relatively many more people below the suicide threshold (although the data on happiness do suggest rather large responses in happiness to unemployment). This also explains why the suicide rate for young people doubled in the United States from the late 1950s to the present: the decline in the emotional and other circumstances of children due in part to the deterioration in family stability had an especially large effect on the small fraction of young people thrown below the suicide threshold (Cutler, Glaeser, and Norberg, 2001, give a fuller analysis of the effects of changes in family structure and other variables on suicide rates of youths when there is social interactions).
Unhappy people often take risky actions that appear to be acts of desperation and even irrationality. An unhappy ghetto teen-ager may join a gang that significantly raises the chance that he will end up in jail or murdered. A person rejected by a spouse or lover may on the “rebound” quickly get involved in another relationship that is likely also to be unsuccessful: “marry in haste, repent at leisure”. A businessman who goes bankrupt may commit suicide even though he remains wealthy by most persons standards. These and other examples suggest that misery often leads to actions that may be bad risks from an actuarial viewpoint. Our analysis of suicide can explain why this is so without assuming that these are irrational impulsive actions induced by desperation. They are induced by desperation, but they appear to be consistent with maximization of utility with uncertainty about consequences.
... Suppose a person has an income I_0 < I_d . If he had to remain with I_0 , he would rationally commit suicide if the cost of doing so is negligible since u ( I_0 ) < 0 . However, he might end up wanting to live if he can buy a lottery. For since he would commit suicide for all I < I_d , suicide truncates the effective utility to u ( I ) = 0 for all I < I_d . Such truncation makes the utility function convex over part of the income range starting at the origin. Convexity in the utility function creates an incentive to gamble.
There is an important difference between gambles that are attractive to suicidal persons and those attractive to persons above the suicidal cut-off. The former prefer gambles with a chance of a large gain, whereas the latter prefer those with a (small) chance of a large loss. This behavioral difference may help determine whether gamblers fall in the suicidal category.
In our judgment, economists have overstated the general importance of risk aversion because of their concentration on the behavior of the middle and upper classes who own financial instruments, take out fire and other insurance on their homes, have health insurance, and engage in other behavior that reflects some aversion to risk. But none of this evidence helps to explain the behavior of the significant numbers of those at the bottom, or reasonable close to the bottom, who do not own houses, stocks, or bonds, and have little or no auto or health insurance. Nor does it explain the behavior of persons who are miserable, or close to being miserable, perhaps because they experienced sizable declines in their circumstances, even though by absolute standards their circumstances are still quite good.
The main implication of our approach to the analysis of suicide is that persons at the bottom end of the utility distribution are likely to be risk preferrers rather than risk averse. They are willing to take risks, even with bad terms, that might pull them out of their dire or bad circumstances. Such risk-taking behavior takes many different forms.
Psychiatrists have claimed that many accidental and other deaths are due to a “death instinct” that leads to “carelessness, foolhardiness, neglect of self, imprudence, resignation to death, mismanagement of alcohol or drugs, disregards of live-saving medical regimes, brink of death patterns, etc.” (Shneidman [1968, page 387]; see also the collection of articles in Farberow [1980]).
Our analysis also concludes that many deaths result from a weak desire to live, but we do not presuppose any “death instinct”. Quite the opposite: according to our analysis, miserable people turn drugs, gangs, drinking, overeating, risky jobs, etc. in a sometimes desperate effort to find a way out of their circumstances. They are willing to take these risks to their lives because they would be worse off if they did not.
...This analysis implies that individuals with low levels of utility would be more likely to smoke, drink heavily, use drugs, become criminals, and engage in other dangerous activities. A study by the National Center for Health Statistics shows that 40 million adult Americans who were often either depressed, lonely, restless, bored, or upset during the previous two week period are far more likely to smoke, drink heavily, or do both (see NCHS, 1993, November 4).
If the gambles of miserable people fail, and they become drug addicts, alcoholics, obese, or spend much of their time in jail, they would be worse off than they were before they desperately turned to these activities. They may then be attracted by suicide, even if they were not suicidal before they these gambles. Suicide rates are unusually high for alcoholics (see Covan [xxxx]; Plot, et al. [xxxx]; Maris [1981]; Rushing [1968]; and Farberow [xxxx]). Male drug users are 20 times more likely than non users to commit suicide (see Lipsedge, 1996), and men who smoke a pack of cigarette per day are about 4 times more likely than non smokers to commit suicide (see Miller and Rimm, 2000). This analysis also explains why people who take risky jobs, engage in stunts, drive fast, use drugs, etc. often appear to attach little value to their lives. If I 0 < I w , a person would be willing to engage in an actuarially unfair activity that may involve death; by unfair is meant from equation (3.4) that pI w < I 0 . He could still be raising his expected utility considerably above what it would be if he didn’t gamble u ( I 0 ) . This does not even imply that he places no value on living without the risk - u ( I 0 ) could be greater than 0. But the gamble may raise his utility even if it increases the probability that he dies, and even if the gamble is unfair from an actuarial standard.
Nor does the signaling approach seem as good an explanation of why women and teenagers have very high ratios of attempts to suicides. Do sympathizers have less information about the true state of women than of men? The opposite seems to be the case since machoism prevents many men from speaking about their feelings, while most women have no such inhibitions. A more reasonable story is that it is easier for women to elicit sympathy than men- the g(p) is higher and possibly steeper for women- because men are supposed to be “strong” and more immune to psychological distress. Of course, the proximate reason for why women “succeed” less often is that they choose methods - such as poison and pills – that are less likely to succeed than those chosen by men – guns and other violent methods. But why do women choose these methods? As suggested above, one compelling explanation is that women can get sympathy more easily than men, although women may be less familiar with more lethal methods (see section 6). Note that women not only have a much lower propensity to commit suicide, but also they are far less likely to die from drug overdoses, alcoholism, homicides, and other self-inflicted causes. The same story may explain the high ratio of teenagers attempts to suicides This analysis suggests two separate variables: the ratio of suicide attempts to successes, and the rate of suicide. Both women and teen-agers have much higher attempt ratios than adult men, but women have a low actual suicide rate while teenagers in recent years have a reasonably high rate (see Cutler, Glaeser, and Norber, 2001). The signaling story has trouble explaining the growth in teen age suicide rates, but not one based on deterioration in their utility levels due to the increase in divorce rates and related factors (see Cutler, Glaeser, and Norborg, 2001)
With perfect certainty, a person could continue living for a while with the expectation that he would commit suicide at a particular point in the future. Future decisions become much murkier when utility streams are highly uncertain. Yet uncertainty adds an additional major advantage to postponing suicide; namely, the chance that the situation will improve enough to change one’s mind about suicide - perhaps an illness was wrongly diagnosed or becomes treatable by new methods, or a would-be-suicider discovers a way to rebuild a lost fortune. If the situation worsens rather than improves, suicide can always be used at that time to truncate the magnitude of any fall in utility (although, see section 6 for some qualifications due to the cost of suicide).
Maximizing individuals recognize that there will be no second chance if they are killed or permanently injured from actions that might reduce or eliminate their present unhappiness. As a result, even very unhappy persons might decide to postpone drastic actions in the hope that their situations will get better in the future. They can always take these actions later if their misery continues or worsens. The opportunity to postpone to the future provides unhappy persons with an “option value” from waiting.
The value of the option from waiting depends on several variables with a clear economic interpretation (see Dixit,1992, for a good exposition of option price theory; he also briefly mentions an application of the theory to the analysis of suicides; also see Cutler, Glaeser, and Norberg, 2001). The value of waiting is smaller, the greater is the discount rate on future utilities since the discounted value of future benefits is then smaller relative to the present cost of being miserable. Even with the same degree of unhappiness, this implies more desperate actions, including suicide attempts, among poorer, less educated, and younger persons since they tend to discount the future more (see Becker and Mulligan, 1997).
...this implication is not consistent with the observation mentioned shortly that some people commit suicide only after being miserable and depressed for a while. To explain these and other observations, it is useful to bring in the option value from uncertainty about the future utility stream. An important implication of option theory for our purposes is that a person might not commit suicide even if current utility is negative, and even if the discounted value of expected utilities is negative over all segments of life from the present into the future. The reason for postponing is that events may not turn out to be as bleak as they look at present. In particular, a forward looking person definitely would not commit suicide at t if u (t ) = 0 , and if expected utility over all future segments were negative. For there is no loss in utility from waiting until t+1, and the next year may bring sufficiently good news which eliminates the desire to commit suicide. If bad news comes instead, he could commit suicide at t+1 and be no worse off than if he ended his life at t.
But then the option value of delaying implies that he might want to continue living at t even if u (t ) < 0 , and even if all expected utility sequences were also negative. The possibility of getting good news during t, and of truncating the consequences of bad news, could make him willing to endure another unpleasant year or more. How low utility during t could be before it “pays” to commit suicide depends on the nature and extent of variability in future outcomes. The greater the variability, the greater the advantage of continuing to live even if the present and future appear rather grim.
Option value theory has an even stronger implication. Suicide attempts and other drastic steps may be conditional simply on not getting good “news”. A person who waits to see what the future brings may take drastic actions when the future does not significantly improvement his circumstances. A person may not attempt suicide on the onset of a serious depression, but may do so if it does not lift after a while. Only the hope that the future will get better enables many depressed persons to cope with their misery, often for years.
Virginia Woolf, for example, committed suicide only after several prior bouts of serious depression. A person who becomes unemployed may not do anything drastic right away because he expects to find another job, but he may turn to heavy drinking and other drastic steps if he remains unemployed for a lengthy period. One study found that while all unemployed men had higher than average suicide rates, the rates were far higher for the long term unemployed (see Hawton and Catalan, 1987). This analysis also implies that teenagers who join very violent gangs, or persons who stop “fighting” serious and painful illnesses, have given up expecting any significant natural improvement in their circumstances.
...This implication [sudden shifts] is confirmed by the evidence on what circumstances lead to greater propensities to commit suicide. Thus, suicide is much greater for unemployed workers, for the recently divorced and those rejected by long term partners, for persons recently jailed, for persons who retire, for those who contract an incurable disease, and for persons who suffer large losses in their wealth. For example, 13% of jail suicides occur within the first 3 hours of confinement, 33% within first 24 hours, 89% within first 3 months, and only 4% occur after 5 months1. All these persons have experienced significant declines in their incomes, or in their esteem relative to their past esteem.
Table 1 present data on the distribution of reported degree of happiness by ages of men and women, and for whites and blacks. Women are somewhat happier than men. But these happiness data do not offer support for the much greater rate of suicide attempts among women, and their much lower suicide rate.
What stands out is that young black males - and to a lesser extent young black females - report being much less happy than young whites. This obviously would not explain the lower suicide rate of young blacks than young whites, but the data do shed light on the much greater propensity of young blacks than young whites to engage in crime, heavily use crack, smoke, and take other life-endangering risks.
The emphasis on mean reversion in utility and the option value of waiting for good news indicates that there may be considerable gain from not committing suicide during various periods of negative utility. For favorable events may occur, and utility would increase as one becomes accustomed to reduced circumstances. This emphasis on the advantages of waiting raises the question of whether a significant fraction of suicides are “impulsive”
...We believe that some suicides are impulsive in any reasonable meaning of that word, but we do not believe that impulsiveness is the dominant cause of suicide. To be sure, one explanation of why heavy smokers, heavy drinkers, and heavy users of other drugs are more likely to commit suicide is myopic individuals become heavy users of harmfully addictive drugs.
However an alternative explanation that is an application of rational behavior is that persons with low utility, and hence potential suiciders, are likely to turn to smoking, drinking heavily, and other risky activities.
We do not provide any decisive tests about the importance of impulsive suicides, but differences in suicide rates among various demographic and other groups are not likely to be explained mainly by differences in their impulsive propensities. For it is hard to argue that older men are more impulsive than middle-aged or young men, or that whites are more impulsive than blacks, or that men are so much more impulsive than women, or that doctors are more impulsive than others with similar education, or that the propensity to impulsiveness rises after divorce or unemployment.
...Indeed, we believe that the fear of death and other “costs” of suicide are probably more important in reducing the number of suicides than impulsiveness is in increasing their number. Teen-agers may be good candidates for impulsive behavior, but they had low suicide rates in most nations prior to 25 years ago. Our theory implies that young persons had low suicide rates because they have high option values of waiting for better times. Cutler, Glaeser, and Norberg (2001) explain the sharp growth in suicides rates among American teenagers during the post 25 years mainly by the deterioration of families, and by a social multiplier that produces a large increase in teen suicides from relatively small initial causes. Moreover, impulsiveness does not help explain why both women and teenagers have high ratios of suicide attempts to “successes”.
+Scott Siskind
No fully reliable statistics give the numbers of miserable persons during any year or other time period, but various indirect measures indicate that it is substantial. Surveys suggest that in the US there are 20.5 millions users of crack and other heavy drugs, some 15.9 millions of individuals are classified as heavy drinkers (more than 5 drinks per day), the number of seriously depressed persons is estimated at 9.9 millions, crimes of violence amount to more than 7.26 per 100,000 population, almost half of all first marriages end in divorce, with many divorce proceedings being quite bitter. In happiness surveys, about 10% percent of persons report themselves as not happy.
...Suicide is the eighth leading cause of death in the US, and the third among teenagers. The combined number of deaths from drug use, heavy drinking, murder by a relative or a gang member, and car accidents when drinking are many times as frequent as suicides.
The modern approach to suicide stresses its immorality on the one hand and its connection to mental illness on the other hand. But the Greeks and Romans, as well as Asian cultures – especially the Japanese and Indian – considered suicide to be a rational response to illness, disgrace, and other pain and suffering. Both Hume and Schopenhauer in brief essays looked upon suicide as a perfectly reasonable response to bad circumstances. In an essay not published until his death (for fear of offending the Church), Hume stated,
> "That suicide may often be consistent with interest and with our duty to ourselves, no one can question, who allows, that age, sickness, or misfortune may render life a burden, and make it worse than annihilation. I believe that no man ever threw away life, while it was worth having. For such is our natural horror of death... (Essays on Suicide and the Immorality of the Soul, by the late David Hume, page 588)."
Schopenhauer added,
> "It will generally be found that, as soon as the terrors of life reach the point at which they outweigh the terrors of death, a man will put an end to his life. But the terrors of death offer considerable resistance . . ." (Parerga and Paralipomena, Vol. 2, page 156).
Our purposive choice approach to the behavior of unhappy people assumes they maximize their utility in a forward-looking fashion, taking account of the uncertainty of future events, and the consequences of their actions. Rather than imposing a tight fitting strait jacket on the analysis, the view that even very unhappy individuals compare the benefits and costs of different actions before deciding on the best, or least worst, steps provides a flexible and fruitful framework. We incorporate some of the insights of sociologists, psychiatrists, and philosophers about the factors that determine suicides and other actions of miserable persons.
Depressed persons are quite miserable. They often have trouble getting pleasure out of lives that would not be considered especially difficulty by others. Patients in mental hospitals do have particularly high suicide rates, especially those with depressive disorders (see Dublin [1963, p. 171]). And many other suicides might be judged to be by mentally disturbed individuals. This inability to get pleasure out of circumstances that most people would not find oppressive may define a mental disorder. Although depressed individuals are quite unhappy much of the time, this does not mean that their suicides are not maximizing responses to their circumstances. They may become willing to end their misery and face the terrors of death. Still, suicide seems to offer a strong challenge to explanations based on maximizing behavior.
Yet there is obviously much more to suicide than mental disturbance or an inability to enjoy life. Suicide rates respond to illness, economic circumstances – such as bankruptcy and unemployment – divorce, widowhood, family responsibilities, disgrace, disappointment, fear of punishment, aging, and other variables that affect the utility from living. A utility-maximizing approach to suicide does rather well in explaining these and other regularities in suicide rates.
For some miserable individuals the best policy is to do nothing desperate and wait for the situation to get better. Section 4 considers the effects of the rate of discount on the future, the degree of uncertainty about future events, and other variables on this “option” value of waiting.
Hamermesh and Soss (1974) is a pioneering study three decades ago that uses a utility maximizing approach to suicide. This paper is based on, and extends, several other papers, including two that were written more than a decade ago (Becker, 1991 in references, and Becker and Kilburn, 1993), as well as the more recent, Becker and Posner. Cutler, Glaeser and Norberg (2001) published an important paper that in several dimensions takes a similar approach to ours, although their main purpose is to explain the rise in youth suicide rates in the United States. As in this paper, they also assume that suicide is contemplated when utility drops below a fixed level (0) that utility is maximized sequentially over time, and that there is an option value from delaying suicide if times may get better.
There are however, also important differences. Cutler, Glaeser and Norberg do not draw out the risk-taking implications of this approach to suicide, including how attempted- suicides fit into a risk approach. They do not fully extract the implications of the option value of remaining alive, do not rely on the special form of preferences with habits and social interactions that seems consistent with the evidence on suicide and other behavior, have a different interpretation of the ratio of suicide attempts to “successes”, and do not discuss suicide bombers and the cost of suicide
Even if suicide will occur at some age because lifetime utility is negative, it could occur either later or earlier depending on the time sequence of utilities. If utilities are negative initially and perhaps positive later on – perhaps because of a major reversal of fortune at an early age – suicide would occur earlier. Conversely, if utilities decline monotonically with age from positive values initially – say because of declining health – suicide would occur when utilities first became negative. Thus Hamermesh and Soss (1974) are mistaken in their claim that rational behavior under certainty generally implies a rising propensity to commit suicide with age (also see Cutler, Glaeser, and Norberg (2001) for a correct analysis).
This conclusion is even more problematic after incorporating heterogeneity among people. Those people with the worst prospects tend to commit suicide earlier, while those with better ones survive to older ages and may never want to commit suicide. As is usual in such situations, like divorce, heterogeneity implies a declining relation of suicide to age: at later ages, only the happiest people would be surviving.
Only a small fraction of any cohort commits suicide; about 0.01% of the US population committed suicide in year 2001. This implies that those with utilities less than zero are located in the extreme left-hand tail – several standard deviations from the mean – in the distribution of utilities among people of the same age, etc. Therefore, even a modest shift in the mean utility – with the variability held constant – would have a very large effect on the fraction of persons whose utilities fall below zero since the extreme tails of most distributions are very sensitive to changes in the mean. For example, even a 10 percent difference in the mean I.Q. of two groups implies enormous differences in the fraction of “geniuses” and “retards”.
We believe that this sensitivity of the tails helps explains (along with mean reversion in utilities) why suicides have been quite responsive to moderate business cycle changes in economic circumstances (see Hamermesh and Soss (1974). This does not necessarily imply utility is so sensitive to changes in income, but that even moderate changes in income push relatively many more people below the suicide threshold (although the data on happiness do suggest rather large responses in happiness to unemployment). This also explains why the suicide rate for young people doubled in the United States from the late 1950s to the present: the decline in the emotional and other circumstances of children due in part to the deterioration in family stability had an especially large effect on the small fraction of young people thrown below the suicide threshold (Cutler, Glaeser, and Norberg, 2001, give a fuller analysis of the effects of changes in family structure and other variables on suicide rates of youths when there is social interactions).
Unhappy people often take risky actions that appear to be acts of desperation and even irrationality. An unhappy ghetto teen-ager may join a gang that significantly raises the chance that he will end up in jail or murdered. A person rejected by a spouse or lover may on the “rebound” quickly get involved in another relationship that is likely also to be unsuccessful: “marry in haste, repent at leisure”. A businessman who goes bankrupt may commit suicide even though he remains wealthy by most persons standards. These and other examples suggest that misery often leads to actions that may be bad risks from an actuarial viewpoint. Our analysis of suicide can explain why this is so without assuming that these are irrational impulsive actions induced by desperation. They are induced by desperation, but they appear to be consistent with maximization of utility with uncertainty about consequences.
... Suppose a person has an income I_0 < I_d . If he had to remain with I_0 , he would rationally commit suicide if the cost of doing so is negligible since u ( I_0 ) < 0 . However, he might end up wanting to live if he can buy a lottery. For since he would commit suicide for all I < I_d , suicide truncates the effective utility to u ( I ) = 0 for all I < I_d . Such truncation makes the utility function convex over part of the income range starting at the origin. Convexity in the utility function creates an incentive to gamble.
There is an important difference between gambles that are attractive to suicidal persons and those attractive to persons above the suicidal cut-off. The former prefer gambles with a chance of a large gain, whereas the latter prefer those with a (small) chance of a large loss. This behavioral difference may help determine whether gamblers fall in the suicidal category.
In our judgment, economists have overstated the general importance of risk aversion because of their concentration on the behavior of the middle and upper classes who own financial instruments, take out fire and other insurance on their homes, have health insurance, and engage in other behavior that reflects some aversion to risk. But none of this evidence helps to explain the behavior of the significant numbers of those at the bottom, or reasonable close to the bottom, who do not own houses, stocks, or bonds, and have little or no auto or health insurance. Nor does it explain the behavior of persons who are miserable, or close to being miserable, perhaps because they experienced sizable declines in their circumstances, even though by absolute standards their circumstances are still quite good.
The main implication of our approach to the analysis of suicide is that persons at the bottom end of the utility distribution are likely to be risk preferrers rather than risk averse. They are willing to take risks, even with bad terms, that might pull them out of their dire or bad circumstances. Such risk-taking behavior takes many different forms.
Psychiatrists have claimed that many accidental and other deaths are due to a “death instinct” that leads to “carelessness, foolhardiness, neglect of self, imprudence, resignation to death, mismanagement of alcohol or drugs, disregards of live-saving medical regimes, brink of death patterns, etc.” (Shneidman [1968, page 387]; see also the collection of articles in Farberow [1980]).
Our analysis also concludes that many deaths result from a weak desire to live, but we do not presuppose any “death instinct”. Quite the opposite: according to our analysis, miserable people turn drugs, gangs, drinking, overeating, risky jobs, etc. in a sometimes desperate effort to find a way out of their circumstances. They are willing to take these risks to their lives because they would be worse off if they did not.
...This analysis implies that individuals with low levels of utility would be more likely to smoke, drink heavily, use drugs, become criminals, and engage in other dangerous activities. A study by the National Center for Health Statistics shows that 40 million adult Americans who were often either depressed, lonely, restless, bored, or upset during the previous two week period are far more likely to smoke, drink heavily, or do both (see NCHS, 1993, November 4).
If the gambles of miserable people fail, and they become drug addicts, alcoholics, obese, or spend much of their time in jail, they would be worse off than they were before they desperately turned to these activities. They may then be attracted by suicide, even if they were not suicidal before they these gambles. Suicide rates are unusually high for alcoholics (see Covan [xxxx]; Plot, et al. [xxxx]; Maris [1981]; Rushing [1968]; and Farberow [xxxx]). Male drug users are 20 times more likely than non users to commit suicide (see Lipsedge, 1996), and men who smoke a pack of cigarette per day are about 4 times more likely than non smokers to commit suicide (see Miller and Rimm, 2000). This analysis also explains why people who take risky jobs, engage in stunts, drive fast, use drugs, etc. often appear to attach little value to their lives. If I 0 < I w , a person would be willing to engage in an actuarially unfair activity that may involve death; by unfair is meant from equation (3.4) that pI w < I 0 . He could still be raising his expected utility considerably above what it would be if he didn’t gamble u ( I 0 ) . This does not even imply that he places no value on living without the risk - u ( I 0 ) could be greater than 0. But the gamble may raise his utility even if it increases the probability that he dies, and even if the gamble is unfair from an actuarial standard.
Nor does the signaling approach seem as good an explanation of why women and teenagers have very high ratios of attempts to suicides. Do sympathizers have less information about the true state of women than of men? The opposite seems to be the case since machoism prevents many men from speaking about their feelings, while most women have no such inhibitions. A more reasonable story is that it is easier for women to elicit sympathy than men- the g(p) is higher and possibly steeper for women- because men are supposed to be “strong” and more immune to psychological distress. Of course, the proximate reason for why women “succeed” less often is that they choose methods - such as poison and pills – that are less likely to succeed than those chosen by men – guns and other violent methods. But why do women choose these methods? As suggested above, one compelling explanation is that women can get sympathy more easily than men, although women may be less familiar with more lethal methods (see section 6). Note that women not only have a much lower propensity to commit suicide, but also they are far less likely to die from drug overdoses, alcoholism, homicides, and other self-inflicted causes. The same story may explain the high ratio of teenagers attempts to suicides This analysis suggests two separate variables: the ratio of suicide attempts to successes, and the rate of suicide. Both women and teen-agers have much higher attempt ratios than adult men, but women have a low actual suicide rate while teenagers in recent years have a reasonably high rate (see Cutler, Glaeser, and Norber, 2001). The signaling story has trouble explaining the growth in teen age suicide rates, but not one based on deterioration in their utility levels due to the increase in divorce rates and related factors (see Cutler, Glaeser, and Norborg, 2001)
With perfect certainty, a person could continue living for a while with the expectation that he would commit suicide at a particular point in the future. Future decisions become much murkier when utility streams are highly uncertain. Yet uncertainty adds an additional major advantage to postponing suicide; namely, the chance that the situation will improve enough to change one’s mind about suicide - perhaps an illness was wrongly diagnosed or becomes treatable by new methods, or a would-be-suicider discovers a way to rebuild a lost fortune. If the situation worsens rather than improves, suicide can always be used at that time to truncate the magnitude of any fall in utility (although, see section 6 for some qualifications due to the cost of suicide).
Maximizing individuals recognize that there will be no second chance if they are killed or permanently injured from actions that might reduce or eliminate their present unhappiness. As a result, even very unhappy persons might decide to postpone drastic actions in the hope that their situations will get better in the future. They can always take these actions later if their misery continues or worsens. The opportunity to postpone to the future provides unhappy persons with an “option value” from waiting.
The value of the option from waiting depends on several variables with a clear economic interpretation (see Dixit,1992, for a good exposition of option price theory; he also briefly mentions an application of the theory to the analysis of suicides; also see Cutler, Glaeser, and Norberg, 2001). The value of waiting is smaller, the greater is the discount rate on future utilities since the discounted value of future benefits is then smaller relative to the present cost of being miserable. Even with the same degree of unhappiness, this implies more desperate actions, including suicide attempts, among poorer, less educated, and younger persons since they tend to discount the future more (see Becker and Mulligan, 1997).
...this implication is not consistent with the observation mentioned shortly that some people commit suicide only after being miserable and depressed for a while. To explain these and other observations, it is useful to bring in the option value from uncertainty about the future utility stream. An important implication of option theory for our purposes is that a person might not commit suicide even if current utility is negative, and even if the discounted value of expected utilities is negative over all segments of life from the present into the future. The reason for postponing is that events may not turn out to be as bleak as they look at present. In particular, a forward looking person definitely would not commit suicide at t if u (t ) = 0 , and if expected utility over all future segments were negative. For there is no loss in utility from waiting until t+1, and the next year may bring sufficiently good news which eliminates the desire to commit suicide. If bad news comes instead, he could commit suicide at t+1 and be no worse off than if he ended his life at t.
But then the option value of delaying implies that he might want to continue living at t even if u (t ) < 0 , and even if all expected utility sequences were also negative. The possibility of getting good news during t, and of truncating the consequences of bad news, could make him willing to endure another unpleasant year or more. How low utility during t could be before it “pays” to commit suicide depends on the nature and extent of variability in future outcomes. The greater the variability, the greater the advantage of continuing to live even if the present and future appear rather grim.
Option value theory has an even stronger implication. Suicide attempts and other drastic steps may be conditional simply on not getting good “news”. A person who waits to see what the future brings may take drastic actions when the future does not significantly improvement his circumstances. A person may not attempt suicide on the onset of a serious depression, but may do so if it does not lift after a while. Only the hope that the future will get better enables many depressed persons to cope with their misery, often for years.
Virginia Woolf, for example, committed suicide only after several prior bouts of serious depression. A person who becomes unemployed may not do anything drastic right away because he expects to find another job, but he may turn to heavy drinking and other drastic steps if he remains unemployed for a lengthy period. One study found that while all unemployed men had higher than average suicide rates, the rates were far higher for the long term unemployed (see Hawton and Catalan, 1987). This analysis also implies that teenagers who join very violent gangs, or persons who stop “fighting” serious and painful illnesses, have given up expecting any significant natural improvement in their circumstances.
...This implication [sudden shifts] is confirmed by the evidence on what circumstances lead to greater propensities to commit suicide. Thus, suicide is much greater for unemployed workers, for the recently divorced and those rejected by long term partners, for persons recently jailed, for persons who retire, for those who contract an incurable disease, and for persons who suffer large losses in their wealth. For example, 13% of jail suicides occur within the first 3 hours of confinement, 33% within first 24 hours, 89% within first 3 months, and only 4% occur after 5 months1. All these persons have experienced significant declines in their incomes, or in their esteem relative to their past esteem.
Table 1 present data on the distribution of reported degree of happiness by ages of men and women, and for whites and blacks. Women are somewhat happier than men. But these happiness data do not offer support for the much greater rate of suicide attempts among women, and their much lower suicide rate.
What stands out is that young black males - and to a lesser extent young black females - report being much less happy than young whites. This obviously would not explain the lower suicide rate of young blacks than young whites, but the data do shed light on the much greater propensity of young blacks than young whites to engage in crime, heavily use crack, smoke, and take other life-endangering risks.
The emphasis on mean reversion in utility and the option value of waiting for good news indicates that there may be considerable gain from not committing suicide during various periods of negative utility. For favorable events may occur, and utility would increase as one becomes accustomed to reduced circumstances. This emphasis on the advantages of waiting raises the question of whether a significant fraction of suicides are “impulsive”
...We believe that some suicides are impulsive in any reasonable meaning of that word, but we do not believe that impulsiveness is the dominant cause of suicide. To be sure, one explanation of why heavy smokers, heavy drinkers, and heavy users of other drugs are more likely to commit suicide is myopic individuals become heavy users of harmfully addictive drugs.
However an alternative explanation that is an application of rational behavior is that persons with low utility, and hence potential suiciders, are likely to turn to smoking, drinking heavily, and other risky activities.
We do not provide any decisive tests about the importance of impulsive suicides, but differences in suicide rates among various demographic and other groups are not likely to be explained mainly by differences in their impulsive propensities. For it is hard to argue that older men are more impulsive than middle-aged or young men, or that whites are more impulsive than blacks, or that men are so much more impulsive than women, or that doctors are more impulsive than others with similar education, or that the propensity to impulsiveness rises after divorce or unemployment.
...Indeed, we believe that the fear of death and other “costs” of suicide are probably more important in reducing the number of suicides than impulsiveness is in increasing their number. Teen-agers may be good candidates for impulsive behavior, but they had low suicide rates in most nations prior to 25 years ago. Our theory implies that young persons had low suicide rates because they have high option values of waiting for better times. Cutler, Glaeser, and Norberg (2001) explain the sharp growth in suicides rates among American teenagers during the post 25 years mainly by the deterioration of families, and by a social multiplier that produces a large increase in teen suicides from relatively small initial causes. Moreover, impulsiveness does not help explain why both women and teenagers have high ratios of suicide attempts to “successes”.
+Scott Siskind
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