Life Insurance and Suicide: Asymmetric Information Revisited

1 Introduction

Suicide is one of the most serious and vexing issues faced by all modern societies. According to the World Health Organization (WHO), an estimated 804,000 worldwide suicide deaths occurred in 2012, and one suicide-related death is reported every 40 seconds (WHO 2014). Many medical professionals consider suicide to come as a result of depression or other psychiatric disorders (Mann et al. 2005). However, as early as in 1897, the sociologist Émile Durkheim, in his seminal book Le Suicide, developed the concept of social integration to explain suicide from a sociological perspective. ^[1] Moreover, in their economic theory on suicide, Hamermesh and Soss (1974) employed an expected lifetime utility maximization framework to explain suicide as a rational decision. Nonetheless, the existing literature has largely disregarded the role of economic or financial incentives in inducing suicide.

Suicides induced by economic incentives are not rare in real life. ^[2] Governmental policies can even encourage suicide through moral hazard. For example, some states in India have seen an increase in their suicide rate, presumably due to the governmental policy of compensating bereaved families for their loss of a breadwinner who has killed himself (The Economist, June 21, 2007). Life insurance contracts also provide incentives to commit suicide, as death benefits are paid in cases of suicide after expiry of the suicide exemption period. ^[3] In fact, Toyokawa and Shirouzu (1998), Tsukitari (2001), and Amamiya (2002) stated that there was an increase in the number of suicides among life insurance policy holders immediately after expiry of the suicide exemption period. A figure from Tsukitari (2001) is reproduced as Figure 1. The figure shows a suicide index which was set to 100 for the average number of suicides in the first 12 months after activation of a life insurance contract, and jumped to about 150 in the thirteenth month – the month immediately after the expiration of the suicide exemption period. Moreover, according to a media report, a major Japanese life insurance company saw 10% of its total insurance payments go to suicide-related deaths in 2005 (Mainichi Shinbun, October 4, 2005). ^[4]

Figure 1:

Jump in the suicide index after expiration of the suicide exemption period in Japan.

In developing countries, microfinance (hereafter, MF) programs have been attracting wide attention, leading to the 2006 Nobel Peace Prize of Professor Muhammad Yunus and Grameen Bank of Bangladesh (Banerjee and Duflo, 2011). MF is defined as a variety of programs providing small-scale financial services to the poor lacking collateralizable assets, who are excluded from the formal banking sector. Theoretical developments in the 1990s revealed that the success of MF programs was driven by joint liability (group lending) loan arrangements in which adverse selection was prevented by peer selection, moral hazard was mitigated by peer monitoring, and strategic default was precluded by social sanction and ostracism (Armendáriz and Morduch 2010).

However, in March 2006 and October 2010, the Krishna District collector – i.e., the head of the district administration – of India’s Andhra Pradesh state restricted the operations of MF institutions, believing that their single-minded focus on profitability led to usurious interest rates, over-indebtedness, abusive collection practices, and alleged borrower suicides. A rationale for this incident was given as follows: “… the incentives at the micro level were geared towards pushing clients to their desperate measures….. In many other cases, a government study found that MFI agents had urged non-performing clients to commit suicide; under the loan terms, borrower’s debts were covered by insurance in case of death….” (Mader, p. 285). Focusing on a different aspect of MF programs, Chen, Choi, and Sawada (2010) also showed in their theoretical model that the joint-liability lending of MF institutions could induce the suicide of borrowers in cases in which the magnitude of the social stigma and the degree of altruism were high. This seems to be especially true in circumstances of adverse selection and moral hazard problems arising from information asymmetry.

These examples imply that some suicides are induced by adverse selection and/or moral hazard under imperfect informational conditions. In the presence of substantial adverse selection and moral hazard, life insurance participants will have a higher suicide rate than nonparticipants.

There has been a growing body of literature on asymmetric information in the life insurance market. ^[5] Using Life Insurance Marketing Research Association (LIMRA) data, Beliveau (1984) found a positive relationship between the life insurance premium rate and the amount of coverage purchased, which he regarded as evidence for adverse selection. However, using three data sets including LIMRA data, Cawley and Philipson (1999) showed that the unit prices did not rise with the coverage, which is inconsistent with the theory of life insurance under asymmetric informational conditions. Polborn, Hoy, and Sadanand (2006) showed that while the regulation preventing insurers’ access to individuals’ genetic test results created adverse selection in the life insurance market, it also ameliorated the premium risks in a context in which relatively few people have genes related to high risks. Gatzert, Hoermann, and Schmeiser (2009) pointed out the possibility of adverse behavior from an insured, that is, an insured with impaired health and reduced life expectancy who chooses the secondary market alternative and remains in the pool of insureds. ^[6] They showed that after controlling for other risks, the people who died within a 12-year window were likely to have bought life insurance. This positive correlation between the insured’s private information and the likelihood of a life insurance purchase suggests the existence of asymmetric information in the U.S. life insurance industry.

However, almost no economic research has directly explored this potential link between suicide and life insurance (Villeneuve 2000). ^[7] One exception was the 2006 study by Tseng, which employed the mortality data submitted by large U.S. insurance companies to the Society of Actuaries. The results revealed that the suicide rate of the insured quadrupled following expiry of the suicide exemption period. However, Tseng (2006) presented contradictory data: the suicide rate of the general population was two to three times higher than that of the insured population.

In this paper, we investigate the causal relationship between the life insurance demand and the suicide rate, based on the asymmetric information theory. The primary difficulty in establishing causality between life insurance and suicide is the potential endogeneity associated with the use of the life insurance variable to explain the suicide rate. Controlling for observable socioeconomic factors, the demand for life insurance augments with the increase in unobservable factors such as the risk type, i.e., the tendency to commit suicide, the degree of risk aversion, and the degree of altruism. These unobservable factors may also affect suicide decisions, thereby causing an endogeneity problem. The novelty of our analysis lies in the use of cross-country variations for the lengths of the suicide exemption periods of life insurance policies and of the foreign market shares in the life insurance industries as instruments for identifying the life insurance demand. The cross-country variations in the suicide exemption periods generate a situation of quasi-natural experiments in which representative agents are faced with different incentive schemes for exogenous reasons (Chiappori 2000). Furthermore, the level of foreign market shares may reflect trade barriers in the market or the degree of competitiveness among domestic insurance companies. Hence, both the length of the exemption period and the foreign market share in the life insurance market are correlated with the life insurance demand. On the other hand, these two variables are not correlated directly with suicide: the lengths of the exemption periods are mostly constant, and suicide decisions would not be affected by the nationality of the policy writers.

Using data for OECD countries from 1980 to 2002, our first-stage IV regression employs the lengths of the exemption periods and the foreign market shares as instruments, and the results show a negative relationship between the length of the exemption period and the life insurance demand. Our second-stage, semiparametric regressions, reveal that there exists a positive causality from the life insurance demand to the suicide rate. The negative relationship in the first-stage regression suggests the existence of adverse selection, and the positive relationship in the second-stage regression is consistent with the existence of adverse selection and/or moral hazard. We believe that these findings contribute to the existing literature by confirming the existence of asymmetric information in the life insurance market, which is the largest private insurance market.

The remainder of this paper is organized as follows. Section 2 presents the empirical model, and Section 3 describes the data used in this study. Section 4 provides the results of the empirical analysis, and Section 5 offers some concluding remarks and implications for further studies.

2 Empirical model

At least two types of asymmetric information problems are involved in the nexus between life insurance and suicide: moral hazard and adverse selection. First, the adverse selection problem is defined as a situation in which life insurance contracts induce the participation of people with a higher probability of death than those with a lower probability of death. Second, the moral hazard problem is defined as a situation in which some of the insured who had no intention of committing suicide before purchasing the insurance commit suicide after subscribing to a life insurance policy, while they would not have chosen to do so had they not been insured. ^[8] In either case, there exists a positive correlation between the life insurance purchase and the probability of committing suicide.

To explore the existence of asymmetric information, we postulate a model of suicide as a function of the amount of life insurance purchased. If the suicide and life insurance purchase are positively correlated, the findings will be consistent with the hypothesis of life insurance-induced adverse selection and/or moral hazard. In order to analyze the model empirically, we employ the following semiparametric regression model of suicide as a nonparametric function of the life insurance demand D:

where i and t represent the countries and years, respectively. ^[9] The dependent variable log S_it is the natural log of the suicide rate; X_it is a set of attributes including socioeconomic variables such as the real GDP per capita, growth rate of the real GDP per capita, Gini coefficient, female labor participation rate, birth rate, divorce rate, and per capita alcohol consumption; and the life insurance demand D_it is captured by the life insurance density, defined as the per capita gross life insurance premium sold by both domestic and foreign-controlled companies. The final term, u_it, is an error term.

The econometric concern of eq. [1] is that the life insurance variable D_it is likely to be correlated with the error term u_it due to unobserved factors affecting both suicide and the demand for life insurance. Such factors may include the risk type, the degree of risk aversion, and the extent of altruism. This type of private information about the insured which is not revealed to insurers may lead to adverse selection: people with a higher (suicidal) risk are more likely to purchase life insurance than those with a lower risk.

Therefore, there can be a correlation between the error term and the insurance variable, such that E(u|log D, X)≠0. This will generate a bias in the estimation of the nonparametric function f(･) in eq. [1]. In order to resolve this endogeneity problem, we impose two refinements on eq. [1]. First, we decompose the error term in eq. [1] as follows: u_it=α_i+β_t+δ_iT+ε_it. This decomposition controls for the omitted variable bias arising from unobserved country-specific and time-specific fixed effects through the addition of α_i and β_t respectively. ^[10] Further, the decomposition controls for unobserved country-specific but time-varying effects by allowing for a country-specific coefficient δ_i in the linear time trend T:

Second, we introduce an IV regression equation for the life insurance density using the length of the exemption period and the foreign market shares as instruments, in order to mitigate the endogeneity bias arising from the simultaneity problem as in eq. [3]. ^[11] For the relationship between the life insurance density and the length of the exemption period, we can hypothesize that a shorter exemption period may increase the life insurance demand by attracting riskier types, which is consistent with the existence of adverse selection in the life insurance market. For example, in the extreme case where life insurance policies deny death benefits in suicide cases – i.e., the length of the exemption period is infinite –, individuals who are seriously contemplating suicide in near future would not purchase such life insurance policies.

On the other hand, the foreign market share variable has been considered as one of the determinants for the life insurance demand in Li et al. (2007) and Ma and Pope (2008). ^[12] The foreign market share may reflect trade barriers in the market or the degree of competitiveness among domestic insurance companies. Regarding the former, a low level of foreign participation in a domestic market suggests strong regulations and/or low levels of insurance demands. On the other hand, in the latter case, a low level of foreign participation may be due to severe domestic competition and could hence be associated with high levels of insurance demands. Therefore, the direction of the overall effect is an empirical question. ^[13] If the latter channel is important, a low foreign market share (due to domestic competition) will coincide with a low price level, theoretically leading to more density D_t. Indeed, the foreign market share has a negative coefficient in the density regression.

In terms of econometric framework, we apply the augmented regression technique of Holly and Sargan (1982) to the IV regression equation for the life insurance density:

where Z is the set of determinants of the life insurance density. This includes the length of the life insurance exemption period variable and the foreign market shares in the life insurance industries as identifying instruments, as well as a lagged log for the life insurance density and the socioeconomic variables X from eq. [1]. Based on the previous discussion, if the estimated coefficients for the length of the exemption period variable show negative signs in eq. [2], we can interpret them as being consistent with the presence of adverse selection in the life insurance market.

Following Holly and Sargan (1982), Blundell, Duncan, and Pendakur (1998), and Gong, van Soest, and Zhang (2005), we assume that E(η|Z, X)=0 and E(ε|log D, Z, X, M)=ρη, where M includes the country-specific and time-specific fixed effects and the country-specific linear time trend. The first conditional mean assumption implies that the length of the exemption period and the foreign market share in the life insurance industry are uncorrelated with the error term η in eq. [3]; the error term η includes unobserved factors such as the risk type, the degree of risk aversion, and the extent of altruism. The second conditional mean assumption provides the structure of the way in which ε and η are related.

One may have doubts about the validity of the first conditional mean assumption with respect to the length of the suicide exemption period variable. This is because the life insurance industry would presumably adopt a long exclusion period in any country in which the suicide rate is high. Nonetheless, after examining the data, we can dismiss this concern. First, within the sample period, despite the variations in the suicide rates, the length of the exemption period is the same within each OECD country, being determined either by insurance laws or industrial norms. The only exception is the United States, where the length of the suicide exemption period differs across the states (see Table 1 for details). Hence, the length of the exemption period can be considered to be exogenous. ^[14] Second, even in Belgium, Finland, Greece, and Japan, where the lengths of the exemption periods were modified, the changes were made with significant lags and can therefore be considered as predetermined. ^[15],[16] As to the validity of the first conditional mean assumption with respect to the foreign market share variable, since both foreign and domestic life insurance companies operating in the same market have the same length of exemption period, suicide decisions should not be affected by the nationality of the insurer. Hence, both the length of the exemption period and the foreign market share in the life insurance market are correlated with the life insurance demand, but not directly with the suicide rate. ^[17]

Finally, the semiparametric regression model in eq. [2] can be rewritten as follows:

where v_it is a mean-zero error term, i.e., E(v|log D, Z, X, M)=0, with a variance of σ_v². ^[18] We estimate eq. [4] by a two-step procedure using the fitted value of η from the residual of eq. [3]. As to the nonparametric estimation technique, we use Lokshin’s (2006) algorithm, which is based on the differencing method for the estimation of the partial linear models introduced by Yatchew (1997). ^[19] In sum, if the estimated nonparametric part in eq. [4] shows that f′(･)>0, we can interpret the derivative as being consistent with the presence of adverse selection and/or moral hazard in the life insurance market.

3 Data

Our data set includes all OECD countries for the period 1980–2002. The raw number of suicides and the population were obtained from the WHO Mortality Database. An age-standardized suicide rate per 100,000 inhabitants was calculated by using the world standard population figures published by the WHO. ^[20] By using this adjustment, the differences in the age structure across countries and time could be controlled for. In other words, this eliminated the need to include the ratio of specific age groups in the analysis (Neumayer 2003).

The life insurance density, defined as the per capita gross life insurance premium sold by both domestic and foreign-controlled companies, was obtained from the Swiss Re Sigma Database. The foreign market share in the life insurance industries, defined as the ratio of the gross premium of foreign-controlled undertakings and branches and agencies of foreign undertakings to the total gross premiums, was obtained from the OECD (2008) Insurance Statistical Yearbook.

A considerable amount of time and effort was devoted to the collection of information for the key identifying instrument, the length of the suicide exemption period, through our own survey of life insurance associations and/or companies in each OECD country. We also asked if there were related laws, regulations, and/or industrial norms governing the exemption period. Some countries had regulations. Others did not, so that the insurance companies were free to choose, but they tended to follow the industrial norms on the specific length. ^[21] These data were gathered for the first time for this study. The dummy variables representing the length of the suicide exemption period were constructed as follows: the one-year exemption dummy variable took one if the exemption period was one year, and 0 otherwise; the two-year exemption dummy variable took one if the exemption period was two years, and 0 otherwise; the three-year exemption dummy variable took one if the exemption period was three years, and 0 otherwise; and the infinite exemption period dummy variable took one if there was no payment for suicide-related deaths, and 0 otherwise. The number of observations for the zero-year exemption period was taken as the default variable for the exemption period dummy variables. ^[22] The United States, the Netherlands, and the United Kingdom were excluded because the length of the exemption period differed across states in the United States, and precise information on the length of the suicide exemption period was not available for the Netherlands and the United Kingdom.

With regard to the socioeconomic variables, the economic variable – the real GDP per capita – was obtained from the Penn World Table 6.2 and the growth rate was calculated based on the real GDP per capita. The unemployment rate was obtained from OECD health data. As a proxy for income inequality, Gini coefficients based on different definitions were acquired from the United Nations University’s World Income Inequality Database (WIID), and the average of the available Gini coefficients for each country in each year was used as a single index. The birth rate, measured by the ratio of live births to the total population, was taken from the WHO Mortality Database. The divorce rate, measured by the ratio of the number of divorces to the total population, was obtained from the United Nations Common Database.

The female labor force participation rate, measured as a percentage of the female population aged 15–64, was acquired from the World Development Indicators of the World Bank. Finally, with respect to alcohol consumption, the sales data of pure alcohol, per individual over 15 years of age, measured in liters, were taken from OECD health data. Table 2 lists the definitions of the socioeconomic variables and their sources.

4 Results of the empirical analysis

As discussed in Section 2, since we imposed two refinements in order to deal with the endogeneity problem, we conducted the estimations in the following order: first, eq. [1] was estimated without considering the omitted variables and the simultaneity problems (the baseline specification); second, only the simultaneity problem in eq. [1] was addressed by using the IV technique through eq. [3] (the IV specification); third, only the omitted variable problem in eq. [1] was addressed by including the time- and country-specific fixed effects as well as the country-specific time trend (the FE specification); finally, we estimated eq. [4], in which both the omitted variable problem and the simultaneity problem were accounted for (the FE-IV specification). For the following discussion, the nonparametric estimation results are presented in Figure 2(A)–2(D), and the estimation results of the parametric part are provided in Table 3. Since the main focus is on the relationship between the suicide rate and the life insurance density, we commence our discussion with the nonparametric estimation results.

Figure 2(A) and 2(B) present the nonparametric estimation results of the baseline and IV specifications, respectively. These two figures show a slightly U-shaped relationship between the suicide rate and the life insurance density and are quite similar. This either implies that there is no endogeneity problem or that the IV method alone fails to appropriately address the endogeneity problem. Indeed, the estimate for the coefficient of η in Table 3 is not significant. However, this may be an artifact from not addressing the omitted variable bias, although the positive part of the U-shaped relationship is consistent with the existence of adverse selection and/or moral hazard in the life insurance markets.

Figure 2:

Nonparametric plots of relationship between suicide rate and life insurance density.

Figure 2(C) and 2(D) present the nonparametric estimation results of the FE and FE-IV specifications, respectively. Taking into account the fixed effects, the results in these two figures are significantly different from the previous ones. Figure 2(C) and 2(D) present a positive relationship between the suicide rate and the life insurance density, except at their right-end tails, where the life insurance density is high. ^[23] This positive relationship is consistent with the existence of adverse selection and/or moral hazard in the life insurance markets. The steeper slope in Figure 2(C) suggests a more substantial asymmetric information problem. However, the estimate for the coefficient of η in the FE-IV specification (the fourth column in Table 3) is significantly positive. This positive correlation implies that the FE specification overestimates the nonparametric part without taking into account the simultaneity pertaining to life insurance density and suicide. Since the results presented in Figure 2(D) and in the fourth column of Table 3 take into account both refinements, we hold them to be the most accurate.

In addition, a negative relationship between the suicide rate and the life insurance density is shown in the right-end tail of Figure 2(D). This may be considered to be inconsistent with the asymmetric information theory when the life insurance density is sufficiently high. One plausible interpretation may be the existence of some other relevant, unobservable variables which the estimation equations failed to account for. One such example may be wealth. On average, wealthier individuals are likely to purchase more life insurance (life insurance is a normal good). Nevertheless, the proportion of the loss coverage in the event of death is likely to decrease with an increase in wealth. ^[24] This implies that death benefits are less valuable in the case of wealthier people. Hence, the financial incentives for suicide from insurance payments are weaker or minimal, leading to a negative relationship as shown in the figure. This result is in line with that of Spindler’s study (2013), which demonstrated the presence of asymmetric information for low and medium insured sums in the German disability insurance system – i.e., a positive correlation between the risk and coverage –, but not for high insured sums.

As stated above, eq. [3] – a first-stage estimation regressing the log life insurance density on the exemption period dummies and the foreign market share – was used in the IV and FE-IV specifications in order to address the simultaneity problem. ^[25] In fact, since a short exemption period may induce the self-selection of riskier types with regard to life insurance contracts, the estimation result of eq. [3] can provide information on the existence of adverse selection. Table 4 shows the result of the first-stage estimation. We found that both the three-year and infinite exemption period dummies were significantly negative with regard to the level of life insurance density. This suggests that a longer exemption period or no life insurance payment in cases of suicide is associated with a decrease in the purchase of life insurance policies. In other words, a longer exemption period may deter riskier types from purchasing life insurance policies. As to the foreign market share, the results show a significantly negative trend, implying that a low level of foreign participation is associated with high levels of life insurance demands, possibly due to severe competition among domestic companies.

With respect to the parametric part shown in Table 3, a consistent finding is that the real GDP per capita is significantly negative. The female labor force participation rate is significant in the baseline specification; in addition, the birth, divorce, and alcohol consumption rates are significant in the baseline and IV specifications. However, all these variables except for the real GDP per capita become insignificant in the FE-IV specification. The coefficient of the Gini index in the baseline and IV specifications suggests a significantly negative relationship between the suicide rate and inequality. This puzzling finding may result from the omitted variables bias. Indeed, the coefficient becomes significantly positive after controlling for the fixed effects; nevertheless, it becomes insignificant in the FE-IV specification.

5 Concluding remarks

In this paper, we investigated the nexus between life insurance and suicide, using OECD cross-country data from 1980 to 2002. By using semiparametric IV regressions with fixed effects, this study found a negative relationship between the life insurance demand and the length of the suicide exemption period, together with a positive relationship between the suicide rate and the life insurance demand for a majority of observations. These two relationships suggest the presence of adverse selection and moral hazard in life insurance markets. There are exceptions in cases of high levels of life insurance density, which may be explained by the wealth effect.

This result challenges the current conception in the literature that life insurance markets are immune to the problems associated with asymmetric information. The novelty of our analysis lies in the use of data on cross-country variations, with the length of the suicide exemption periods and the foreign market share in the life insurance industries as the main identifying instrumental variables for the life insurance density. Nevertheless, the aggregate nature of the data used in this study does not allow for clean differentiation between adverse selection and moral hazard. In further studies, the issues of adverse selection and moral hazard should be investigated using individual-level data.

Through this study, we would like to emphasize the importance of studying suicides by employing a somewhat rational approach. If we recognize that some suicides may be rational, studies can be conducted to ascertain the different incentives behind suicide. This way, we believe that suicide-related research can gather sufficient resources, as is warranted by the seriousness of the current situation, and effective measures can thereby be developed and implemented for suicide prevention. Nevertheless, there is an important caveat to this study, particularly when deriving policy implications: not all suicides are driven by financial incentives. To stop making suicide-related death payments may eliminate the adverse selection and moral hazard problems, as discussed in this paper, but it also questions the very basic function of life insurance – that is to say, to protect beneficiaries against the sudden economic loss associated with the death of their loved ones. These issues should be investigated carefully in future studies.