The economics of suicide, revisited.

• Author: Marcotte, Dave E.

1. Introduction

   Economists have contributed important insights into the motivations underlying suicidal behavior. In particular, economists have formalized the notion that utility maximization plays a role in shaping suicidal behavior and have found empirical evidence suggesting that suicide rates respond to economic factors in ways predicted by economic theory. At the very least, economists have established that suicide is not an act arising purely from social isolation or mental illness. Rather, even for this most drastic of behavioral choices, at some level individuals respond to the same types of incentives that govern other aspects of their economic and social lives.

   The economics of suicide, however, remains very understudied. In this paper, I attempt to advance economic understanding of suicidal behavior in two ways. First, I focus on suicide attempts rather than on completed suicides. Completed suicides have been the focus of all previous economic work on the subject, although only a small fraction of suicide attempts are successful. One advantage of the current focus is that it broadens economic analysis to a much wider scope of behavior.

   Second, I carry out the first examination of the economic determinants of suicidal behavior using individual-level data. In doing so, I employ information from a national probability sample of Americans aged 18-54 in 1991-1992. The focus of previous research on completed suicides is largely the consequence of data limitations. Since information about suicidal behavior for individuals is hard to come by, researchers have exclusively focused on the economic correlates of aggregate suicide rates. This approach is somewhat unsatisfying, since underlying the economic conceptualization of suicidal behavior are microlevel utility maximization decisions. Focusing on individuals' behavior can provide more direct tests of economic models of suicidal behavior.

2. Background

   Suicide is the eighth leading cause of death in the United States, with 30,535 deaths being ruled suicides in 1997, for a rate of 1.14 suicides per 10,000 people (CDC 1999). Petronis et al. (1990) estimate the rate of suicide attempts to be 22 per 10,000 each year in the United States. The difference in these reported annual incidence rates suggests that suicide attempts occur about 20 times as often as completed suicides. The CDC (2001) estimate that every day, 17 suicide attempts occur for each completed suicide. Moscicki et al. (1988) estimate that 2.9% of the U.S. population have attempted suicide.

   For obvious reasons, suicidal behavior is the subject of much research in public health and psychiatry. Much suicidal behavior is due to psychiatric illness, for which an individual's reasoning and behavior is not tractable within the context of economic theory, which requires rationality. However, economic analysis can still illuminate suicidal behavior. (1)

   The social scientific view of suicide has been dominated by the work of the sociologist Emile Durkheim. Durkheim (1951) proposed two dimensions along which suicide could be categorized. The first dimension pertained to integration into social groups and institutions, and the second was defined by imbalance between means and needs. In an important respect, this sounds like an economic conceptualization, and although Durkheim meant something broader, he believed that deficits between economic means and needs precipitated suicide.

   These concepts have dominated sociological work on suicide and have variously been incorporated or extended. For example, demographers have noted the importance of cohort size in shaping prospects, including suicide propensity, throughout the life course. Demographers have suggested that persons born in large cohorts are more likely to be frustrated in their attempts to obtain means to satisfy their needs. (2)

   Clearly, these theories imply an economic component to the motives behind suicidal behavior and fit well in the framework of relative supply and demand shifts. Recognizing the importance of economic motivations, economists have developed models of suicidal behavior. Most notably, Hamermesh and Soss (1974) formalized a model of the utility maximization decision faced by those contemplating suicide. Hamermesh and Soss's paper and subsequent work by economists developed the notion that suicide occurs when the discounted stream of expected utility over a person's lifetime is sufficiently low, perhaps negative. (3) Within this framework, suicide rates are expected to rise as lifetime income falls. Suicide rates are also predicted to increase with age under certain conditions.

   Hamermesh and Soss (1974) examined empirical data and found evidence in support of these predictions. In general, subsequent work has supported these predictions as well. Chuang and Huang (1997) found that per capita income served as the best predictor of regional suicide rates in Taiwan. Kimenyi and Shughart (1986) also found that suicide rates fall with real income. Hamermesh (1974), however, found that the suicide rate among Blacks in the United States during the late 1960s and early 1970s was less responsive to variations in income. Yang (1992) and others have also found that suicide rates rise with the unemployment rate.

   Without exception, previous work on the economics of suicide has relied on aggregate data derived from vital statistics on the number of completed suicides. Researchers have then exploited variation across space and/or time in aggregate suicide rates and aggregate income or the age or gender composition of the population to identify the effects of economic factors on suicidal behavior.

   Reliance on such data for testing hypotheses derived from economic theories of suicidal behavior is less than ideal. Such data do not permit direct observation of the behavior that economic models attempt to explain. Rather, these data provide information on one consequence of such behavior: death by suicide. Since the vast majority of suicide attempts do not result in death, these data provide no information about the bulk of the behavior economic models attempt to explain. Furthermore, in the absence of data on suicide attempts, previous researchers have been unable to consider a more complete range of motivations behind suicidal behavior. In particular, individuals may well recognize that suicide attempts are not always (or even often) fatal. This information may play a role in their decisions. (4)

   In this paper, I attempt to develop a more complete assessment of suicidal behavior that focuses at once on the behavior of individuals and on suicide attempts, rather than on deaths resulting from suicide attempts. In doing so, I attempt to extend the utility maximization framework to account for the fact that individuals engage in suicide attempts, some of which result in death, some of which do not.

3. Model

   As a first approach to understanding suicidal behavior, consider the model first laid out by Hamermesh and Soss (1974). Here, individuals decide to commit suicide if they determine that the expected stream of lifetime utility falls below some threshold. Let Z(a, I) represent the discounted present value of an individual's expected lifetime utility at age a. Then,

   Z(a, I) = [[integral].sup.d.sub.a] [e.sup.-r(m-a)]U[C(m, I) - K(m)]P(m) dm, (1)

   where U[*] and C(*) represent utility and consumption functions, m is age, I is income that could be devoted to consumption, K describes the costs of maintaining oneself alive in each year, d is the maximum life expectancy, P(m) is the probability of living to age m given living to age a, and r is the discount rate. An individual kills himself or herself when the discounted stream of utility falls below some critical threshold. (5)

   This basic model underlies all empirical work on the economics of suicide to date. First, the model predicts that suicide propensity falls with income, since [partial]Z/[partial]I > 0. This is the principal hypothesis tested in all previous economic work on suicide. The model does not generate a clear prediction about how the propensity to kill oneself changes as the age of contemplation increases, although empirically, suicide rates increase with age.

   By modeling the valuation of the discounted stream of the benefits and costs of living, this framework captures the essential element of an individual's decision calculus as that individual contemplates suicide. However, this formulation omits important aspects of suicidal behavior. First, it is not the case that individuals choose between life and death. Instead, the decision faced is between whether or not to attempt suicide. Second, suicide attempts may affect future utility, through either consumption or maintenance costs, if they are survived. Below, I extend the basic model to accommodate these aspects of suicidal behavior in turn.

   The basic model can be easily expanded to take into account that suicide attempts do not result in death with certainty. Most directly, engaging in a life-threatening suicide attempt affects the probability of survival. Introducing suicide as a choice variable that influences the discounted stream of lifetime utility by limiting survival probability, we obtain

   Z(a, I, s) = [[integral].sup.d.sub.a] [e.sup.-r(m-a)]U[C(m, I) - K(m)]P(m, s) dm, (2)

   where the probability of surviving additional years is now affected by whether or not suicide is attempted, and s is a binary variable (1 if an attempt is made; 0 otherwise). (6) When it is recognized that a suicide attempt does not result in certain death, the individual's decision is guided by a comparison of two different states, one in which suicide is not attempted, and one in which it is. The individual assesses his or her expected utility in the absence of a suicide attempt as

   Z(a, I \ s = 0) = [[integral].sup.d.sub.a] [e.sup.-r(m-a)] U[C(m, I) - K(m)]P(m \ s = 0) dm, (3)

   and this individual assesses his or her expected utility if a suicide...