Mind the Gap – Assessing the Size and Determinants of the Life Insurance Gap

Preparing for the monetary loss associated with premature death of the breadwinner has become more relevant during the COVID-19 pandemic. However, very little is known about how much of the financial vulnerabili - ties are covered by the life insurance holdings in differ - ent population groups. We employ unique individual-level life insurance data of the Finnish population to study the voluntary life insur-ances, the components of financial loss following from a death of a breadwinner, and the gap in death cover (life insurance gap) calculated as the difference of the two. We find that only about 10% of Finns have a voluntary life insurance, and that they are concentrated on married people, people of working age and with higher income. The largest insurance gaps are among young individuals, men, high income and highly educated people. We also find that the insurance behavior is poorly ex - plained by the net losses following from a death.


Introduction
Preparing for the monetary loss associated with premature death of the breadwinner has become more relevant during the COVID-19 pandemic.The increased mortality risk has caused many individuals to consider the adequacy of their life insurance.However, assessing the needed life insurance protection is not easy.Households are protected against financial losses due to the death of a family breadwinner by both social insurance and voluntary life insurance policies.The insurance coverage needed to maintain the previous standard of living depends, among other things, on the age and income of the breadwinner, the net wealth of the family, as well as on the number of children living in the household and their ages.For example, in the case of the death of a young breadwinner, the lost future income is often greater than in the case of an older breadwinner.
This paper employs unique individual-level data to study the voluntary life insurances of Finns, the amount of financial loss following from a death of a breadwinner, and the gap in death cover (life insurance gap) calculated as the difference of the two.The life insurance gap indicates how much insurance is needed, in addition to any current policies, to maintain the standard of living of the widow and children at the level preceding the breadwinner's death.Earlier study by Bernheim et al. (2003) uses the same type of individual data to study the matching of insurance needs and insurance coverage in the United States.Compared to their use of the HRS survey data, we can also analyse the insurance gap in younger households.
A previous life insurance gap study in Finland (Kari et al. 2007) showed that the average insurance gap in Finland is large.On the other hand, it is known from studies concerning other countries that life insurance purchases and the compensation amounts often do not coincide with the insurance need at the micro level.In this study, we use unique individual and family-level data with information on the family's and the insured person's net income, the protection provided by social security for the widow and children, and the family's voluntary life insurances.For net wealth, we use age-specific averages from aggregate statistics.A key objective is to examine whether there are differences between population groups in the life insurance gap and both the take-up and the amount of life insurance, for example, by age, gender or family size.The study employs individual-level life insurance data1 , which were combined with background information covering the insured and the entire population of Finland2 .The period analysed is 2018-2020.
The high quality of our data allows us to measure the life insurance gap including several margins that together determine the size of the gap.We also show the contribution of each of the margins to the gap, which enables to consider also possible different measures, depending on which of the losses following from a breadwinner's death are sought to be covered with the insurance.While the narrowest metric measures how large percentage of the Finns has a voluntary term life insurance, the broadest one tries to account for not only changes in household income and consumption, but also other factors related to the amount of the insurance gap, such as social insurance compensations and net wealth.Our study thus deepens the knowledge about the components of the insurance gap, albeit the more broadly the gap is defined, the more difficult it becomes to measure.
Our results reveal some clear differences by population groups in the frequency of taking out insurance, in the amount of insurance, in the losses following from a death, and in insurance gap formed through these losses and the insurances that provide protection against them.Based on our results, voluntary term life insurances cover on average only a fraction of the losses following from a death.Also, the need for life insurance poorly explains the size of life insurance in the data.
The structure of the paper is as follows.The follow-up section briefly reviews the central results in the economic literature related to the insurance market3 .Section 3 describes the Finnish life insurance market and the death cover provided by the social security system.Section 4 describes the life insurances, the losses following from a death of a person and the life insurance gap.Section 5 studies econometrically the relationship between the persons' characteristics and the life insurance gap.Section 6 draws the conclusions.

Life insurance in research literature
This section reviews briefly the relevant literature on life insurance markets and the few key studies that have previously analysed the life insurance gap.We start with the factors that explain the demand for the insurances -a topic that has got a lot of attention.One way to classify the studies is to start with the studies that use the life-cycle model as the framework explaining the behaviour, the empirical work that challenges some of the predictions of this framework, and the alternative frameworks that use behavioural economics and imperfect information as a starting point.We also discuss the implications of asymmetric information related to the individual's mortality probability on the supply and prices of life insurances.

Factors influencing the demand for life insurance
The basic life-cycle model claims that forward-looking families smoothen their lifetime consumption with labour supply and saving.Insurances increase welfare of the risk averse individuals and help to make the optimal lifetime plans.Chambers et al. (2011) builds an overlapping generations model to study the family consumption smoothing through life insurance.The model is calibrated to US data, and it includes households that face not only mortality risk but also the risk of loss of wage income.The main result of the model simulations is that consumption smoothing of a couple requires life insurance policies that are approximately twice as large compared to the actual levels shown by insurance statistics.In addition, insurances should be taken out earlier in the life-cycle.The simulations also show that the income differences of a couple are more important for men's greater demand for life insurance than the differences in life expectancy between the spouses.Wang (2019) builds a corresponding stochastic partial-equilibrium, life-cycle model with lifetime and earned income risk with a considerably more detailed family structure.The model predicts that increased risk aversion, more children, higher incomes, and lower margins of insurance companies will increase the demand for life insurance.Also, the correlation of the couple's wage income shocks influences the take-out.Hambel et al. (2016) aims to explain the late purchases by introducing long-term contracts and health risk in the model.In a young household, the loss of income following from the death of a breadwinner would be large, but the health shock would lower the income and reduce the optimal size of the policy.There are, however, costs in reducing the sum insured or surrendering the policy, and new insurance will be more expensive due to the increased probability of death.Therefore, life insurance is less attractive to the young than to older people, whose income risk is lower and who have a shorter policy period of validity.
Results of statistical studies show some inconsistencies with the predictions of welfare-maximizing life-cycle models.Theoretical models predict that the demand for term life insurance will decrease as wealth increases.This is because there are fixed costs associated with insurance, which can be avoided by precautionary saving.However, when Gropper and Kuhnen (2021) studied the coverage of term life insurance policies with US register data, they found that their ownership is strongly positively correlated with wealth.Li et al. (2007) studied the demand for life insurance statistically using panel data on OECD countries.According to the results, a country's higher level of education, higher disposable income and number of children are associated with larger average life insurance premiums paid per capita.The result is justified in the study by two factors: A person with a higher income is better able to afford the premiums and there is greater loss of income when the insured person dies.The same need for protection also explains the effect of the number of children increasing insurance premiums.The impact of education on demand can come through several channels.It improves knowledge about insurance needs and insurances and is also connected to foresight and higher incomes.
According to the study, a general decrease in the probabilities of death at working age reduces the need for life insurance, as does the coverage of social security.The competitiveness of the insurance market and the general sophistication of the financial market also increase average insurance premiums according to the study.On the other hand, higher expected inflation and higher real interest rates reduce the demand for insurance4 .A more recent, non-peer-reviewed study of OECD countries (Tynjälä 2019) supports these results regarding the effects of income, life expectancy and interest rates.In addition, it is observed that larger income differences increase the premium income of life insurance in a country.
Risk aversion should increase the demand for life insurances5 .However, Luciano et al. (2016a) shows that women in Italy have fewer insurance policies even when the effects of other factors are controlled.Nam and Sherman (2018) studied single-adult households in the United States and finds that increased risk aversion reduces the demand for term life insurances, but increases cash value life insurance policies.According to the researcher's interpretation, it is difficult to find a rational explanation for the choices, because the income risk is greatest in a single-adult family.Eling et al. (2021) studied the connection between the willingness of people over the age of 50 to take financial risk and long-term insurance in 14 European countries.This study also found a positive link between the desire to take risks and the take up of life insurances.It was stronger for cash value life insurance policies than for term life insurances.According to a study by Hedengren and Stratmann (2016), people with either a high subjective risk of premature death or premature death observed in registers have fewer life insurance policies in the United States.
The surprising results mentioned above have increased the interest in studying alternative6 behaviour patterns as explanations for insurance demand.One of the premises of prospect theory is that losses reduce welfare more than gains of the same amount.People are ready to pay a lot and give up uncertain large gains in order to avoid the realisation of losses.From this point of view, life insurance is interpreted as a risky investment, the return of which is measured by whether the compensations received are as large as the premiums paid.Applied to life insurance, the behaviour leads to people having too low life insurance protection at working age and excessive coverage at retirement age (Gottlieb 2012).
According to that theory, underinsurance at a young age is explained by the fact that the compensation from death is unlikely and risky, but the loss in the form of a paid premium is certain.As person gets older, he/she gradually comes to a situation where he/she have been paying insurance premiums for a long time without receiving compensation.To avoid the realisation of the accumulated "loss" from the paid premiums, the sum insured is increased even when the premium is already high.
Another exception to rational behaviour is the inconsistency related to time.It is often modelled using a hyperbolic discount rate that decreases over time.In practice, this means that people value current consumption highly relative to near-term future consumption, but at the same time think that they will be less impatient in the future7 .Zhang et al. (2021) models decision-making in which individuals who are aware of their inconsistent behaviour save a lot, in which case life insurance is not needed to protect inheritances.Individuals unaware of the inconsistency purchase life insurance policies.In Koo's and Lin's (2021) model, hyperbolic discounters own fewer life insurance policies than time-consistent individuals, regardless of preference awareness.Coe et al. (2016) used surveys to investigate the existence of limitations of thinking related to people's choices that explain insufficient life insurance take-up.According to the results, insurance coverage is generally considered necessary, but people do not want to spend a lot of energy on the purchase decision or its subsequent reevaluation (status quo bias).They are usually not able to calculate the amount of death cover needed, and for almost half of the respondents, the need is determined by how much is left over after expenses deemed essential.Those who tried to calculate the need often used as a rule of thumb that the compensations can be used to pay off the mortgage in the event of death (mental accounting).The extent of the insurance need can also be underestimated because the compensation is received as a lump sum, even though the loss of income is long-term (money illusion).Some respondents determined the insurance amount through the monthly premium by keeping to an easily understandable point of comparison, such as the amount of a coffee shop bill, as the upper limit of the premium (anchoring).
Deviating from rational behaviour can also be due to potential policyholders being unable to make informed purchase decisions due to missing information.An example of this is mortality expectations.Kutlu-Koc and Kalwij (2017) found that people have better knowledge of individual probabilities of death than can be inferred from health-related information.On the other hand, the same study shows that especially women, on average, underestimate the length of their lifespans.One possible explanation may be that individuals predict their mortality using the observed life spans of the current old population.As long as mortality decreases in a trend-like manner, life expectancy calculated on the basis of annual mortality significantly underestimates the expected lifespan of the birth cohort (Myrskylä 2010).People's financial literacy has also often been linked to insurance take-up.Luciano et al. (2016b) and Lin et al. (2017) show that better financial literacy increases life insurance ownership.

Supply of life insurances and the life insurance market
The central problem of the life insurance market is that the policyholder knows their own life expectancy better than the insurance company.In the insurance market, this should be reflected in those with a higher risk of premature death having larger insurance policies.In that case, the logical reaction of the insurance companies would be to increase the price of the insurance as the sum insured increases.At the same time, however, it should be possible to prevent the taking out of several smaller insurance policies for the same person.Cawley and Philipson (1999) showed that these predictions of theoretical asymmetric information market models do not hold in the US life insurance market.The sums insured of high-risk individuals are smaller, the prices of insurances decrease as the sums insured increase, and it is possible to take out several life insurance policies.
A study by He (2009) examines potential new policyholders and finds a positive correlation between purchasing insurance and subsequent death when the person's risk classification is taken into account.This points specifically to the person having more detailed information about their own condition than the insurance provider.He (2011), in turn, observes adverse selection in that lower-risk individuals surrender their insurance more often than higher-risk individuals.
On the other hand, in a study by Hedengren and Stratmann (2016), an individual's higher risk of premature death reduces the likelihood of purchasing term life insurance in the United States.The authors point to the possibility of positive selection; risk averse individuals both take out insurances and reduce the possibility of harm by their behaviour.It is also possible to direct demand with price discrimination that emphasises risks to create a positive correlation between low risk and owning insurance.According to the results, in the group life insurance market, where the possibilities for price discrimination are low, the correlation contrary to expectations is no longer observed.From this it can be concluded that price discrimination directs low-risk people to buy life insurances more than positive selection.
In addition to pricing, insurance companies can react to asymmetric information by refusing to sell insurances.Hendren (2013) shows that individuals have such subjective information about their own risks that cannot be elicited from demographic or health data.Insurance companies take this into account when making their pricing and refusal decisions based on public information.No market emerges for insuring the most high-risk individuals, because the premiums would become unsustainably high for the policyholder in such a situation.In this way, asymmetric information prevents large groups from entering the long-term care, disability and life insurance market in the US.
Policyholders' knowledge of the insurance market affects prices.Brown and Goolsbee (2002) examine online market premiums observing that the Internet enables easier price comparison and thus reduces search costs.This is found to have intensified competition between insurance companies and lowered prices.Based on their results, insurance prices fell by 8-15% in the 1990s as a result of the Internet.

Need for life insurances and the life insurance gap
A family's need for life insurances and its relationship with the existing death cover is complicated to assess.Different insurance companies use different methods and online calculators have been developed to help the customers.
Research-based estimates of the gap are represented by Bernheim et al. (1999), which assesses the adequacy of death cover for US couples approaching retirement age.The starting point is a description of the current circumstances using a large family-level sample data.The need is assessed with a financial planning tool based on the life-cycle model (ESPlanner) and the goal is to smooth life-cycle consumption8 .According to the results, the gap affects women in particular: for more than half, their standard of living would drop when a spouse dies, and 15 percent would see a drop of at least 40 percent.The insurance gap is particularly large for families with only one member who is working.Bernheim et al. (2003) used the same method to study the matching of insurance needs and insurance coverage in the United States.The average sum insured of all insured persons exceeded the insurance need.In addition, more than half of spouses had a larger sum insured than would have been needed to maintain the standard of living after the spouse's death.On the other hand, the study discerned groups with a particularly large insurance gap; low-income people, couples with large income differences, young households, and non-whites.Just over 14 percent of women would have been left below the poverty line if they were widowed with the death cover of the time of the study.Raising it to the recommended level would have reduced falling below the poverty line by a third.The insurance gap decreased systematically with age.
Harris and Yelowitz (2018) studied the importance of life insurances in reducing the risk of poverty following from the death of a spouse.The study focused on couples in which the spouse died near the end of their working career (between the ages of 55 and 68).The widow's standard of living was monitored for three years after that.According to the data, the majority of insurance compensations were paid to middle-or high-income earners, and the insurance compensations were mostly small (median around $25,000).According to the results, one-time compensations had on average only a minor effect on the risk of poverty.On the other hand, compensation amounts below $10,000 had a significant effect, which illustrates the smallness of the death cover compensation amounts for low-income people, but also their importance to them.
Based on the results of these studies, life insurance coverage in the United States is adequate on average, but there are significant problems in the allocation.Harris and Yelowitz (2018) interpret some of the country's life insurance policies to be more often part of life-cycle financial planning than about protecting the widow from the loss of income following from the death of a spouse.Naylor et al. (2011) conducted a similar detailed assessment of the life insurance gap of different families in New Zealand, where life insurance coverage is significantly lower than in the United States.The assessment was based on a life-cycle model and extensive statistical data.According to this study as well, the correlation between owning life insurances and the insurance need was weak.In more than half of the families, the death of the higher income spouse would cause a reduction of more than 40 percent in the present value of the family's combined consumption.Kari et al. (2007) assessed the adequacy of Finns' death cover.The life insurance coverage gap was calculated for three household types and four age groups.The goal of cover was set at the standard of living that the family members had before the death of a breadwinner.According to the results, the average gross insurance gap (of a typical household) calculated using income, net wealth and social security was around €140,000 in 2006.When voluntary insurances were taken into account, the average of which was around €12,000 per household, the remaining net average gap was €126,000 per household.
Additional information about the need for supplementary insurances can also be obtained by looking at the widow's income before and after the death of a spouse.Rantala (2013) studied the livelihood of widowed people in Finland in 2005.The majority of them were retired women.Only 12 percent were between the ages of 18 and 55.In two-thirds of cases, the change in family situation was from a two-person household to a one-person household.After being widowed, the total income of the household dropped on average by approximately 30-40 percent.The decrease was greater for working widows when measured in euros, but relatively greater for pensioners.When taking into account the reduction in the size of the household and the consequent reduction in the scale benefits of living together, the livelihood of retired widows decreases by about a tenth, but the livelihood of a working widow remains almost unchanged, except for the drop in the year of death.In the case of widows of working age, this is explained not only by the survivors' pension, but also by the increase in the widow's average earned income.The metric used does not take into account the impact of net wealth.
3 Death cover in Finland

Social insurance compensations in Finland
When a breadwinner dies in Finland, the social security system provides survivors' pensions for the widow and orphans under certain conditions.There are several statutory schemes that may pay survivors' pensions: the earnings-related pension scheme, the national pension scheme and accident insurances.In addition, a large majority of the employees are insured by group life insurance taken out by employers on the basis of collective agreements.The main rules for the entitlements and paid amounts are as follows.
In the earnings-related pension scheme, the entitlement for widow's pensions is clear, if the survivor has under-aged children with the deceased, but otherwise there are several conditions related to age of the widow, the age of the spouses, when they married, and the period of time lived together.While for widow's born before 1975 the pension is for a lifetime, for widows born in 1975 and later it is paid for 10 years at the most, but at least until the youngest child turns 18.Also, a common-law spouse is entitled to the surviving spouse's pension, when the couple has common under-aged children.The children have entitlement to orphans' pensions until they turn 20.
The basis of the survivors' pension is in this pension scheme the deceased person's earnings-related pension, or if not retired, computational disability pension.In addition, the widow's pension, or a computational disability pension, if the widow is not retired, influence the paid amount.The widow and the orphans share the survivor's pension so that the number of under-aged children affects both the widow's and the individual orphan's pensions.The pensions are taxable, and the wage income of the widow influences the income tax rate applied.If the survivors' pensions are based on statutory accident insurance, they will lower the pensions paid from the earnings-related pension scheme.
In the national pension scheme, survivors' pensions are paid to survivors permanently living in Finland, but since the pensions are small and income tested, there are less than 5000 widows that draw these pensions and the average monthly pension is less than 200 euros.The group life insurance pays an age-dependent lump sum to the widow and a fixed sum to the orphans.
The complicated rules for the entitlements and the paid amounts, the progressive and wage-dependent taxation of survivors' pensions and the interaction of the pensions with other means-tested social security exacerbates greatly the evaluation of the net compensation paid after the breadwinner dies.

The life insurance market in Finland
There are many products developed for different purposes available in the Finnish life insurance market.Their classification and content of concepts varies somewhat depending on the source.Insurances where the insured risk is the death of a person are usually called term life insurance policies.However, coverage in case of disability or illness can also be attached to these policies, as is typical for so-called extensive loan protection insurance that is often attached to a mortgage.Companies also take out voluntary life insurances for their personnel, which may include other insurance coverage.Term life insurances do not usually involve saving.
The insurance premium for term life insurances can increase with age, which makes it possible to keep the compensation unchanged.Correspondingly, the insurance premium can be fixed if the insurance compensation decreases with age.The insurance compensations are paid on a one-time basis after the death of the insured person.
Compensations from private life insurances do not reduce the widow's or orphan's pensions provided by social security, but they are subject to inheritance tax for next of kin and estates10 , and capital income tax for other beneficiaries.An exception from liability to taxation is the part of loan protection insurance compensation that goes directly to the repayment of a mortgage.
Term life insurance policies are sometimes purchased as joint cover insurances, which are cheaper in terms of premiums, where the compensation is paid to the widow of the spouse who dies first and the insurance terminates after that.Joint cover can also consist of two life insurance policies, in which case the beneficiaries are the children after the death of both parents.Many trade unions and organisations have signed agreements with insurance companies for self-funded group insurances offered to members.Their price is typically significantly cheaper than in policies sold individually due to savings in marketing and administrative costs and a reduction in adverse selection.In addition, companies can take out voluntary life insurances for their employees.Almost all employees are insured with the employer's group life insurance linked to collective agreements, the compensation of which is, however, quite small.Endowment insurances are fixed-term savings policies where the capital is in principle transferred to the insurance company upon the death of the insured person during the insurance period.In practice, however, life insurance is attached to the policies, whereby the saved amount is transferred to the beneficiaries named in the policy in the event of death.The insured person can influence the investment portfolio and change it without having to pay tax on the profitable investments before withdrawing the savings.Endowment insurance policies are mainly marketed as savings and investment items.In voluntary pension insurance policies, the assets are usually protected in a similar way by life insurance in case of premature death.
Life insurances are thus taken out not only to directly compensate for the loss of income following from the death of a family breadwinner, but also to secure the repayment of a mortgage and to ensure the return of the amount saved in the endowment insurance and pension insurance upon the death of the saver.The sale of new voluntary individual pension insurances has practically stopped due to the changes related to their taxation and withdrawal age and changes in the taxation of competing products, but there are still many old policies left.
Table 1 below depicts the annual premium income of life insurance companies from different products.Individual risk insurances include term life insurance policies and loan protection insurance.Their share of premium income is small compared to endowment insurances.Life insurance companies also have voluntary pension insurances and capital redemption policies in their product range.In 2019, the premium income of endowment insurances and capital redemption policies grew exceptionally large, because these investment policies were liquidated in anticipation of the tightening of taxation, and new ones were taken out to replace them.

The life insurance gap in Finland
The life insurance gap arises as the difference between the loss following from a death and the cover against it provided by the insurances.In this section, we examine the determinants of life insurance gap of Finnish persons and the average size of the gap using individual-level data.We begin the examinations by describing the data in Section 4.1.Thereafter, we examine the life insurance take-up and the sums insured of Finnish persons in Section 4.2.Section 4.3 focuses on the amounts of losses following from a death.In section 4.4 we study the contribution of social security on the life insurance gap.Section 4.5 examines the insurance gap, which indicates how much the sums insured should be changed to maintain the standard of living of the widow and children of the remaining household at the level preceding the breadwinner's death.

Data
The data employed in the study consists of information from life insurance companies' customer registers for the years 2018-2020, which has been combined with Statistics Finland's FOLK register data at individual level. 11From the information in the FOLK data, the study employs both basic personal information on persons living permanently in Finland and information related to their households.
Of the products of life insurance companies, the analysis includes the voluntary term life insurance (also known as pure life insurance) policies taken out by households.12Insurances taken out to protect the savings amounts of endowment insurances and pension insurances have been excluded from the insurance gap calculations, because they are interpreted more as part of investment activities.
Regarding the sums insured in 2020 the individual risk insurances cover slightly more than half (€36.1 billion) of the total amount of the sums insured in the data (€67.3 billion). 13In the calculations below, we focus on individual life insurances.
From Statistics Finland's information, we employ information from the FOLK basic data module on a person's age, gender, marital status, income and education.From the FOLK family module, in turn, we employ information on the size and location (place of residence) of a household.

The take-up and the sums insured
In this subsection, we examine the share of people in the data that have acquired voluntary term life insurance (hereafter also life insurance).We also look at how the coverages of life insurance differs between population groups.The data shows that during the analysis period of years 2018-2020, on average 8.02% of people had a term life insurance.There is not much difference between the years. 15We first study how a person's background factors (age, gender, marital status, income, education) and household factors (size of household, place of residence) relate to life insurance.The first column of Table 3 shows that take-out of life insurances is largely concentrated in the working age population and that young people and pensioners have fewer policies.It also shows that men have slightly more often life insurances than women, although no major difference between the sexes is observed in terms of life insurance take-up.Among marital statuses, taking out insurances is most common among married people, next most common among divorced people, and least common among unmarried people and widows.Life insurance take-up is found to be very different with respect to income.People with higher incomes (have higher than average taxable income in government income taxation) have life insurance more than twice as often as people with lower incomes: among people above the average, 12.6% have life insurance, while only 5.2% of people below the average have it.Some differences are also observed according to education.Especially those with a low level of education (unknown or upper secondary level of education) have fewer life insurance policies than others.According to the size of household, life insurance is most common in households of 3-5 people.The place of residence in turn does not seem to make a significant difference in life insurance between those living in an urban area and those living in a rural area.
Next, we consider the amount of life insurances in the data.The second column of Table 3 shows the sums insured with respect to the same characteristics as above for those people who have life insurance.The table shows that the largest life insurances are also among working age, married people with higher education.Contrary to the take-up the average magnitudes of the life insurances of those who have one are the largest for the largest households.The third column of Table 3 shows the corresponding numbers for all the observations, including people who do not have a life insurance.The results show highly similar pattern compared to the take-up results.
In summary, the take-up of life insurance is the largest among people of working age, people with higher incomes and married people, as well as those who live in households of 3-5 people.Of all the observations 8% has a life insurance.The largest average magnitudes of life insurances, conditional on having one, are among working age people, married individuals and large households.On average the amount of life insurance is €5,868 in the data.For those who have a life insurance, it is on average €73,150.For those persons having income, other members in their household, all family members identified and at most two breadwinners in the household, the average life insurance is €11,847 (see also the right column of Table 4).

Losses following from a death
While the take-out of voluntary life insurances and sums insured, one component that limits the insurance gap, was examined above, this section describes another component of the insurance gap, the financial losses following from a death.The financial losses arise as a sum from several different margins: while the overall incomes of the household decrease after the death of a breadwinner, also the amount of consumption decreases, and the possible savings are reallocated within the household.In addition, social security and progressive taxation limit the net losses.All these margins affect the standard of living of the surviving family members.Next, we describe the construction of each of these margins separately.After considering the lost after-tax income following from a death (Section 4.3.1),we focus on the reduced consumption (Section 4.3.2), on wealth reallocation within a household (Section 4.3.3)and finally on the changes in social security benefits (Section 4.4).We start by estimating how much the after-tax income of a household is reduced due to the death of a breadwinner.

Lost after-tax expected income
The lost future income following from a death depends on several factors, in particular, on the income profile of the remaining life-cycle, the taxation of income and the discount rate.Regarding the income profile, we account for in the calculations that income depends, in addition to age, strongly on level of education.We make use of the wage profiles reported in previous research and they are depicted in Figure A1 in the Appendix. 16With regard to tax rates, we use the 2020 tax rates depicted in Figure A2 in the Appendix.
Of the 16,576,444 observations in the data, 10,452,560 (63.1%) concern persons aged 20-69.17Of these, lost discounted after-tax income arises for 6,658,426 (63.7%).For them the average discounted after-tax income is €424,697 and the distribution is illustrated in Figure A3. 18The figure shows, for example, that losses of less than €100,000 account for a little more than 15% of the observations, i.e., about one million.For those persons having income, other members in their household, all family members identified and at most two breadwinners in the household, the average discounted loss of income is €447,270 (see also Table 4).

Change in household consumption
In addition to the losses of income, a person's death reduces the overall consumption of the remaining household.For approximating the consumption change following from a death of a breadwinner we employ an equivalence scale, often used in the assessment of household consumption, which aims to account for that households of different sizes and structures have different amounts of consumption.For instance, the consumption of a large family with children is different from that of a one-person household.In a larger household, the consumption share of each member is smaller, in addition to which the contents of these consumption baskets can differ considerably.
In our chosen (Oxford) scale19 , the first adult in the household is assigned a weight of 1, the other adults a weight of 0.7 and the children each a weight of 0.5.Adding up the weights of everyone living in the household results in a measure describing the household's consumption.For example, in a household of two adults and one child, the measure is given the value 2.2 (=1+0.7+0.5).In our calculations, the change in consumption is based on the change in this measure, when accounting for the departure of a deceased person from the household.For example, the measure of a household consisting of two adults changes from 1.7 to 1.0 as a result of the death of one member of the household, i.e. consumption is considered to decrease by 41% (= (1.7-1.0)/1.7) in this case.We limit the analysis to cases where one member of the household dies.
Figure A4 illustrates the relative changes in consumption in case one member of the household dies.The largest share of relative changes in the figure is at -0.41, which corresponds to the change in the consumption of a two-adult household when one person dies.The value -1 corresponds to the death of the only person in a one-person household, while 0.66 (=(1.5-0.5)/1.5)corresponds to a situation where the adult dies in a household of one adult and one child.The average reduction in household consumption in the figure is 48%.
Regarding the amount of the change in consumption, the future discounted income of the household is initially added up and 90% of it is assumed to be consumed (marginal propensity to consume 0.9).Following a death, on the other hand, only a part of the household's discounted future income is consumed compared to what would have been without the death (on average 0.9 * 0.52 = 0.9 * (1-0.48)).Calculated in this way, household consumption is reduced by €106,148 on average.The distribution of reductions in consumption is given in monetary terms in Figure A5.For those persons having income, other members in their household, all family members identified and at most two breadwinners in the household, the average consumption reduction is €270,994 (see Table 4).

Contribution of household net wealth
The wealth of a household reduces the need for life insurance because it supports maintaining the level of consumption, or, more precisely, the consumption possibilities, after the death of a breadwinner.Wealth typically increases with age and as life conditions change.Students and those who have just started their working career have little wealth.One's own dwelling is often purchased almost entirely by loan, in which case net wealth is still low and it is mainly increased through loan repayments.A dwelling is the main form of wealth for all but those with the very highest incomes.Families with children have a larger portion of their wealth tied up in a dwelling than those without children.
In a situation where a breadwinner dies at the time when the family with children needs a large dwelling and a sizeable mortgage, the utility from life insurance is great.The insurance is also quite cheap because the probabilities of death are low for young adults.The situation justifies a loan protection insurance type of life insurance, the compensations from which can be used to pay off the mortgage.Elimination of the need to save for loan installments significantly increases a family's disposable income for consumption, and insurance thus acts as a liquidity safeguard.On the other hand, when the children move out in due course, the widow will be left with considerable housing wealth.
Finnish middle and high income households typically save throughout their life-cycle, which is why net wealth is on average at its highest and the life insurance gap at its lowest towards the end of the life-cycle.The medians of assets, liabilities and net wealth of different households according to the age of the reference person are shown in Figure A6 in the Appendix.
We employ the net wealths20 (in Figure A6) together with the changes in consumption (in Figure A4) to estimate how much of the household's net wealth is transferred from the deceased person to the consumption possibilities of the surviving members.This part of net-wealth would have been available to the deceased person in the absence of death.We use age group averages in our estimates, and the age of the household's reference person is considered as the age of the oldest member of the household.Using average values ignores information related to the distribution of net wealth, including particularly high net wealth as well as low and, for young households, more often negative net wealth.
The distribution of unconsumed net wealth is illustrated in Figure A7.The figure shows that slightly more than 15% of the observations have no unconsumed net wealth, which relates to these households not having accumulated any net wealth.On average, the net wealth left unconsumed due a person's death is €48,004.
For those persons having income, other members in their household, all family members identified and at most two breadwinners in the household, the average contribution of net wealth is €43,560 (see Table 4).

Social security responses to a death (Survivors' pensions)
Survivors' pensions are granted in accordance with both laws concerning employee pensions and the National Pensions Act.In pensions according to both, family cover consists of widow's pension and orphan's pension (for example, the legal provisions under the Employees Pensions Act are TyEL: Sections 54-62 and 84-91, and for the National Pensions Act KEL: Sections 26-50).Based on data from 2018, survivors' pensions granted based on laws concerning employee pensions amounted to €1,713 million and survivors' pensions based on national pension to €27 million (HE 66/2021 vp). 21The share of national pensions is therefore 1.5% of all survivors' pensions.For this reason, in the calculations, we focus on accounting survivors' pensions to the extent that they are formed through the employee pension system.
In the calculations related to survivors' pensions, we use several types of information, which together determine the amounts of survivors' pensions.The basis for survivors' pensions in the calculations is the person's income information. 22With regard to the household, we employ information on the number of adults and children, whether the spouses have children together, and the age of the youngest person, which determine, among other things, the division between widow's pension and orphan's pension and, in part, the length of the widow's pension.With regard to the spouse, information about their age, year of birth, gender and income is used, which in part determines, among other things, the right to a widow's pension, the duration of the widow's pension (lifetime vs. 10 years, except if the widow has a child under the age of 18 after 10 years) and the amount of the deduction from the full widow's pension. 23With regard to children, their age is taken into account, which determines the duration of the orphan's pension.The calculations also account for the compensation in the amount of the widow's pension included in the orphan's pension when there is no widow.For spouses born in or before 1974, the duration of the widow's pension is defined by means of the age and gender dependent life expectancies shown in Figure A8 in the Appendix.The expectancy is higher for women.
Figure A9 shows the discounted survivors' pensions following from a death of a person.The left graph of the figure shows that for the most of observations survivors' pensions are zero, because of having too large income or living in a single person household.The right graph (no zeros included) shows that the higher the survivors' pension the fewer observations we have.The tail of the distribution goes close to zero at €400,000.
For those persons having income, other members in their household, all family members identified and at most two breadwinners in the household, the average survivors' pension is €55,676 (see Table 4).

Life insurance gap
This section examines the formation of the life insurance gap from its various components described above.We focus on looking at the difference of the losses following from a death and the protection against it for persons with income and who live in households of at least two people.Table 4 compiles the average discounted losses of income, reductions in consumption, unconsumed household wealth, survivors' pensions, amounts of life insurances and the life insurance gaps formed through these figures.The table shows that the insurance gap of persons with income to lose and who do not live in one-person households is on average in the order of €65,000 to €70,000.
Table 4: Discounted losses of income, reductions in consumption, unconsumed wealth, life insurances and the life insurance gap for different groups 22 We assume that a person's pension is half of his/her income taxable in government income taxation. 23We limit the examination to persons whose households have no more than two adults, because otherwise it is not possible to deduce the spouse's information very precisely with the available data. Figure 1 illustrates how the insurance gap is formed as the difference between the losses following from a death and the protection against it, for persons with income and who live in households of at least two people, but no more than two adults (right-hand column of Table 4).The figure shows that of the loss of income following from a death (€447,270), the majority (€270,994; 60.6%) is compensated by the change in consumption and the still unconsumed wealth (€43,560).Survivors' pensions and life insurance cover some, but not all, of the remaining gap.
Table 5 illustrates the extent to which survivors' pension insurances and life insurances cover the losses following from a death.According to the table, survivors' pensions cover on average about 40% 24 and life insurances about 10% 25 of the losses following from a person's death, when changes in income, consumption and accumulated wealth on the future consumption of the surviving household are taken into account and looking at persons with income to lose and who live in households of at least two people.After survivors' pensions and life insurances, the remaining insurance gap is approximately €65,000 to €70,000.
In addition to the items mentioned above and included in the calculations, a breadwinner brings their own contribution to homework.Taking that into account would produce the broadest possible metric of the 24 With regard to survivors' pensions, we have only taken into account survivors' pensions granted through employee pension systems.These correspond to approximately 98.5% of all survivors' pensions (HE 66/2021 vp).Also taking into account survivors' pensions granted through the national pension system (which correspond to 1.5% of all survivors' pensions), their average amounts change by less than €1,000.In terms of the insurance gap, these therefore change the results only marginally.It is worth noting that survivors' pensions granted through the national pension system are more often targeted at low-income persons than others. 25We do not have information from all insurance companies and our information on term life insurances covers approximately 70% of all life insurances in Finland.Taking into account the missing approximately 30% results in an estimate of €16,924 (= 11,847/0.7)for the average life insurance, which is approximately €5,000 more than the life insurances shown in the data and corresponds to an insurance gap of €60,000 to €65,000, which is of the same magnitude as the results illustrated in Table 4. Therefore, the life insurance information missing from the data does not affect our results regarding the magnitude of the insurance gap.change in a household's total resources upon the death of a breadwinner.The value of household production describes the monetary value of goods and services produced by households for their own use.According to the data from Statistics Finland, in 2020, it was on average somewhat more than €50,000 per household.However, when conducting this study, there was no information available on the basis of which the value of domestic work could have been allocated to different households according to their characteristics.In addition, the death of a breadwinner reduces, in part, the need for domestic work, which in any case would have significantly weakened the relevance of the calculation.5 Analysis

The components of the life insurance gap
While section 4 described the losses from the death of a breadwinner, the life insurance to encounter these losses and the life insurance gap, this section studies how different individual characteristics are related to the magnitude of the life insurance gap and its components.Using a regression model allows us to study these correlations jointly, instead of studying each of them separately.Our regression model is the following: In the equation the outcome variable  � (lost income, change in consumption, net wealth contribution, survivors' pensions, life insurance or life insurance gap) is explained by the age group of a person, his/her gender, marital status, income level, education, household size and the area of residence.
Table 6 shows the regression results from our regression model for six outcome variables: the magnitude of lost incomes, the change in household consumption, the net wealth implications, the survivors' pensions, the magnitude of life insurance and the life insurance gap.The results show how the personal and family characteristics relate to these outcomes.The regressions focus on those persons who have incomes, other members in their household, all family members identified and at most two breadwinners in the household (the same than those in the right-hand size columns of Tables 4 and 5).
The first column of Table 6 shows the results for the discounted income losses following from the death of a breadwinner of the household.It shows that while all the other characteristics being the same, the losses of income following from a death are on average the highest for people aged 21-40.The result arises as young adults have more of their working careers left than older people.In terms of gender, the loss of income is greater for men than for women.Conditional on other characteristics being the same the widows seem to have slightly higher incomes to lose compared to people with other marital statuses.Regarding this result it is worth noting that the age and being a widow are highly correlated, which makes it less straightforward to interpret the regression coefficients, and the result for the widows is likely to arise due to this correlation.
For people with higher incomes, the loss of income following from a death is higher than for people with lower incomes.Regarding the education the loss of income for the highly educated (higher tertiary level or doctorate level education) is on average hundreds of thousands of euros higher than for those with the lowest level of education (unknown).Regarding the size of household, the loss of income is slightly higher in households of 3-5 people than in other households.The location of the household does not seem to have much of a bearing on the amount of the loss of income.
The second column of Table 6 focuses on how consumption following a death decreases differently according to the characteristics of a person and their household. 26The results show that the largest reductions in the consumption occur mostly among the same people that have the highest income losses: younger people, people with higher incomes and highly educated people.Column 3 of Table 6 depicts the results for the net wealth contribution to the consumption possibilities.It shows that the households of young people receive less support for the consumption possibilities from their net wealth as they have not accumulated wealth as much as the older people.Another result from this regression is that larger households do not receive as much help for the losses via net wealth than people living in two-person household.
The fourth column in the table shows that the discounted survivors' pensions are on average larger for young people with the same other characteristics.They are also larger (conditional on all the other characteristics being the same) for men, people with higher income, higher education level and for the larger households.
Table 6.Regression results for the determinants of losses following a death, the magnitude of life insurance and the life insurance gap Regarding the life insurances the fifth column of Table 6 shows that they are the largest for people aged 31-50, men, higher income people and for those living in larger households.The last column of the table shows the results for the life insurance gap arising as the difference between the losses following from a death and the life insurance designed to counteract the loss.The results show that while keeping the other characteristics constant, the life insurance gaps are the highest for young people, men, people with higher level of income and people living in very large households.
Regarding the results shown in Table 6, it is worth noting that several variables are correlated with each other.For example, income and gender, income and age, and income and level of education interact with each other.For this reason, a change in one factor may also change other factors at the same time.This complicates the straightforward interpretation of the coefficients, which examine how a change in one variable affects the outcome variable when other factors remain constant.

5.2
The monetary loss from a death and the demand for life insurance Next, we study how the monetary loss from a death and the life insurance demand are related.A high monetary (net) loss from a death provides higher incentives to shelter from the undesired outcome by buying more life insurance.We use a statistical model to analyze which factors correspond with the propensity to shelter from the economic risks of death with life insurance.The analysis can provide us important information regarding the overall propensity as well as the underlying factors behind the life insurance gap.
To study the issue empirically, we first employ a model that quantifies the average response of the life insurance coverage to the loss from the death: Here variable  � stands for the amount of the life insurance,  � stands for the (net) loss from the death and is constructed from four components described above for instance in Table 4: the loss of income, the consumption reduction, net wealth contribution and survivors' pensions.Variable  � stands for control variables, which include age group, gender, marital status, taxable income, degree, the size of household and the area of residence.The parameter of interest is  � , which describes how the life insurance is related to net loss from the death.
We also consider whether there are differences in the response with respect to person's characteristics.We run separate regressions, where the control variables are the same as above, but for each characteristic we exclude the corresponding characteristic from the control variables (see Table 7 below).
Table 7 shows the regression results of the two models.First, we study the overall propensity for people who have income, other members in their household, all the family members are identified and there are at most two breadwinners in the household ("All" in Table 7).We find that the propensity is low, 0.015: A €1000 higher net loss from the death is associated with merely €15 higher life insurance coverage.
However, the propensity is heterogeneous across different population groups.Regarding different age groups, we see that the largest response to net losses is among adults, between the ages of 41 to 50, even after controlling for other factors.They increase life insurance coverage by €24 euro in response to additional €1000 net loss from the death.People aged 61 to 70 have the lowest propensity among the age groups.The differences may, at least partly, reflect differences in the supply of insurances: restrictions of access and their higher prices.
Interestingly, the propensity for men (0.021) is about three times as much as that of women (0.008), even after controlling for differences in other background variables.Differences in the propensity across sexes may reflect differences in life expectancy among other things, despite the fact that Kutlu-Koc and Kalwij (2017) found that especially women, on average, underestimate the length of their lifespans.Correspondingly, however, Luciano et al. (2016a) show that women in Italy have fewer insurance policies even when the effects of other factors are controlled.
People with low income do not seem to respond to the incentive positively.This is consistent with, for example Gropper and Kuhnen (2021), who studied the coverage of term life insurance policies with US register data.They found that the ownership is strongly positively correlated with wealth.
The higher propensity is at least partly explained with education: The higher educated people respond more strongly than others (0.019 for higher tertiary level and 0.023 for doctorate level education).Regarding the household size the results reveal that the people living in very large households respond with life insurance to the loss from death more heavily than other people (0.028).Notably, Li et al. (2007) who studied the demand for life insurance statistically using panel data on OECD countries, also found that higher level of education, higher disposable income and number of children are associated with larger average life insurance premiums paid per capita at a country level.

Conclusions
Using individual-level data, we have examined the prevalence of voluntary term life insurances in different groups, the amounts of life insurances and the (net) losses following from the death of a breadwinner, as well as the difference of these losses and death cover, the insurance gap.The examinations are based on Finnish insurance companies' life insurance information and Statistics Finland's personal and household information from 2018-2020.
Based on the results, some clear differences between population groups are observed.The probabilities and amounts of life insurance vary depending on a person's characteristics.People of working age, people with higher incomes and married people, as well as those who live in households of 3-5 people, have life insurances more often than other people.Between 2018 and 2020, an average of 8% of individuals have had a life insurance in the data.For all observations in the data, the average amount of life insurance is €5,868, and for those who have a life insurance, the average is €73,150.The data covers approximately 70 percent of term life insurances in Finland.
A central monetary loss following from a death for a household is the person's lost future income.For persons who have income and who live in households of at least two people, the loss of earned income at present value is on average around €450,000 in the data.In addition to the income change, also the total consumption of the household changes, decreasing by an average of around €270,000 in the data, which compensates for the majority of the loss of income.In addition, a greater share of the wealth accumulated in the household is left for the surviving household to use.Taking this into account compensates for loss of income by around €45,000.Without survivors' pensions and life insurances, the life insurance gap would be approximately €130,000 to €140,000.
Statutory survivors' pensions compensate for the loss by around €55,000, which corresponds to about 40% of the loss.Life insurances, on the other hand, only compensate for a little over €10,000, which corresponds to less than 10%.The remaining insurance gap is on average around €65,000 to €70,000 in the data.An additional insurance of this amount would maintain the consumption possibilities of the surviving household at the current level.However, currently the amounts of life insurances are on average about one sixth of what they should be to maintain the current standard of living of a household.The amount of the insurance gap we observed is about half of the result of a previous study based on Finnish data (Kari et al. 2007). 27The difference is explained, in part, by us having individual-level data at our disposal, enabling finer and more precise examinations than before.
Clear differences are also observed in the insurance gap in relation to population groups.The life insurance gap is found to be the largest among young people, men, people with higher incomes and those with a higher level of education.However, the insurance gap is on average close to zero for people who have a term life insurance.Therefore, the insurance gap arises mainly due to those people having no voluntary term life insurance at all.We also studied how the life insurance responses to net loss from death.We found quite small response: on average a €1000 higher net loss from the death is associated with a €15 higher life insurance.However, some clear differences in the response occur: people of 41-50 years of age respond to net losses more than other people, the response of men is about three times that of women, highly educated people respond more strongly than others, and people living in very large households respond with life insurance to the loss from death more heavily than other people.This means that, for all observations, an average of 62% of the reduction in income following from a death is compensated through a reduction in consumption (54% without zeroes).

Figure 1 .
Figure 1.Formation of the insurance gap from its components

Figure A5 :
Figure A5: Distributions of reductions in consumption and lost income

Figure A8 :
Figure A8: Life expectancy of people of different ages by gender in 2021

Table 1 .
Premium income of life insurance companies from domestic direct insurance, EUR million Table 2 lists the variables used in the study.The data contains a total of 16,576,444 observations from years 2018-2020. 14

Table 2 :
Variables used in the analyses

Table 5 :
Coverages of survivors' pensions and life insurances in different groups

Table 7 .
Life insurance responses to the net loss from death