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LIQUIDITY, ESTATE LIQUIDATION, CHARITABLE MOTIVES, AND LIFE INSURANCE DEMAND BY RETIRED SINGLES.

ABSTRACT

In this article, a model of life insurance holding is formulated. It takes into account the liquidation values and liquidity of estate assets and the ability of life insurance death benefits to bypass the probate process. Tobit regressions based on the model are run using the U.S. Survey of Consumer Finances 1989 data set. The results showed net worth (fixing net liquid assets and annuity wealth) and annuity wealth (fixing net liquid assets and net worth) to be positively related to life insurance holding. Moreover, net liquid asset holding (fixing net worth and annuity wealth) and charitable motives also affect life insurance holding.

INTRODUCTION

The U.S. Survey of Consumer Finances (SCF) 1989 data set shows that about 47 percent of the singles age 65 or older have life insurance coverage with an average life insurance holding of $10,959 and a standard deviation of $69,480. The average term value of life insurance holdings is $23,268. [1] The figures for the single and the married white males in the sample are $101,925 and $150,971, respectively. The average for the subjects with net worth below $1 million equals $4,231 for term value and $9,059 for life insurance holders. Although the last figures are significantly smaller than those of the entire sample, these figures are certainly not negligible. Therefore, the presence of life insurance in retired singles' portfolios deserves an explanation.

Economists have proposed several reasons for holding life insurance. Yaari (1965) recognizes that life insurance is a financial instrument for allocating resources under lifetime uncertainty. Campbell (1980) suggests that life insurance can be used to insure against the loss of family income upon a wage earner's death. Bernheim (1991) argues that life insurance is used to counteract the forced savings in annuity wealth due to excessive social security taxes. The usefulness of these explanations for the case of retired singles is doubtful. First, a retired individual does not need to insure against any future wage loss due to early death. Second, no one in this age group in the SCF data set has children under 18; it is unlikely that the subjects have immediate needs for supporting their children or have particularly strong altruistic bequest motives.

One conjecture is that since bequest motives might be weak for this age group, life insurance is held mainly for paying immediate costs of death, such as funeral expenses. [2] However, an average net liquid conventional asset holding (excluding stocks) of $81,660 by a holder in this age group should allow an average subject to pay his or her costs of death. Therefore, extra cash from life insurance death benefits seems unnecessary unless the holder plans to bequeath. [3] Perhaps nonaltruistic bequest motives towards children (see, e.g., Cox, 1987, and Bernheim et al., 1985) remain strong when altruistic bequest motives weaken as the children become financially independent. Another possibility is that the bequest motives towards others such as charities and relatives remain strong as a single person ages. The latter explanation is quite plausible, as Barthold and Plotnick (1984) find that charitable bequests and bequests towards children and spouses may be substitutes for each other.

Two problems remain even if a retired single has bequest motives. First, the presence of bequest motives does not guarantee that the individual gives bequests instead of inter vivo transfers. Second, even when the individual decides to give bequests, he or she may choose liquid or nonliquid assets other than life insurance death benefits as a bequest medium because of the actuarial unfairness of life insurance as a result of imperfect competition, high commissions to agents, and adverse selection.

Berhnheim et al. (1985) provide a plausible answer to the first problem. They develop a model of strategic bequests in which a testator influences the decisions of the beneficiaries by holding wealth in bequeathable forms and by conditioning the division of bequests on the beneficiaries' actions. To provide an answer to the second problem, it suffices to look at several functions of life insurance stressed by life insurance textbooks (e.g., Mehr, 1977, and Black and Skipper, 1994) but often ignored by economists. [4] (i) Nonliquid conventional assets might shrink in value during the probate process as estate properties become less profitable or valuable because of the loss of managerial skills. Moreover, although estate properties are appealing to the estate owner, they might have little value to the beneficiaries. Life insurance death benefits and liquid conventional assets do not lose value for these reasons. (ii) Life insurance death benefits are distributed to particular designated beneficiaries and bypas s the long and tedious probate process. The absence of the cost of waiting means that life insurance death benefits have a higher value than liquid conventional assets. (iii) Similar to liquid conventional assets, life insurance death benefits may serve as immediate cash for paying debts and other death costs and hence speed the probate process and enhance the value of estate assets. [5]

This article establishes a death-contingent claim model of an individual who allocates his or her resources into consumable and bequeathable wealth. The model attempts to capture the relation between the holdings of life insurance and other assets. The comparative statics of the model have several implications that can be tested using Tobit regressions on the SCF 1989 data set. First, an increase in net liquid conventional asset holding (accompanied by an equal decrease in nonliquid conventional asset holding, keeping net worth and annuity wealth constant) decreases life insurance holding. Second, an increase in annuity wealth (keeping net worth and net liquid conventional asset holding constant) increases life insurance holding, supporting Bernheim's (1991) conclusion that life insurance is used to counteract the forced savings in annuity wealth due to excessive social security taxes. Third, it is likely that an increase in net worth (due to an increase in nonliquid conventional asset holding, other things t he same) raises life insurance holding. The regression results are consistent with these implications. This article conjectures that Bernheim's conclusion that life insurance is an inferior good might be a result of the lack of an accurate estimate for the pure term component of life insurance policies and the omission of net liquid conventional asset holding in his regressions. Finally, charitable bequest motives proxied by past charitable donation have a positive effect on life insurance holding.

LITERATURE

Historically, many empirical studies (e.g., Duker, 1969, and Hammond et al., 1968) use expenditure on life insurance premiums as a proxy for the life insurance holding of an individual. This is problematic because the periodic premium payments are highly vulnerable to changes in economic situations, loading methods, and the terms in life insurance contracts. [6] With the availability of new survey data sets, such as the Retirement History Survey (RHS), economists can now use the face value of life insurance instead of the expenditure on life insurance premium as the dependent variable (see, e.g., Ferber and Lee, 1980; Fitzgerald, 1987; and Bernheim, 1991).

One problem of the RHS data set, however, is that it does not distinguish between term and whole life insurance. The face value of whole life insurance, which contains a savings component (cash value), tends to overstate the life-protecting term value of an insurance contract. To tackle this problem, Bernheim (1991) estimates the total term value of all life insurance policies and uses this estimate as the dependent variable in his regressions. Unfortunately, it is not clear whether his estimation of the term component is indeed precise.

The choice of explanatory variables is even more complicated. Table 1 shows that the effects of different explanatory variables on life insurance holding vary wildly amongst studies that employ different data sets, independent variables, and econometrics techniques. Most studies include demographic and personal characteristics in the regressions. [7] Hammond et al. (1968) suggest that the effect of age depends on which income group is considered. Ferber and Lee (1980) conclude that age has a negative effect on purchase decision, which might depend on the number of years of marriage. Bernheim (1991) suggests that the effect of marital status depends on whether the individual is widowed or has never married. Ferber and Lee (1980) suggest that the effect of number of children depends on the type of insurance policies concerned (such as individual versus group and whole versus term). Although the results on the effect of education are mixed, many studies suggest that professional, self-employed, and managerial pe ople have relatively more life insurance holdings. Finally, Ferber and Lee (1980) suggest that the effect of a spouse's work status depends on whether the dependent variable is purchase decision or face value of life insurance.

For the studies that look at the effects of wealth on life insurance holding, family income, net worth, and social security benefits (social security wealth) are often used as measures of wealth and annuity wealth. The results on the wealth variables are again mixed. Anderson and Nevin (1975) suggest that the effect of family income depends on which income group is under consideration. Although most studies conclude that net worth has a positive effect on life insurance holdings, Bernheim (1991) finds that the term component of all life insurance polices held by an individual is an inferior good. Finally, the results on the effect of social security benefits vary with studies (see, e.g., Bernheim, 1991, and Fitzgerald, 1987).

So far, almost none of the studies have investigated the role ot life insurance as a liquid financial asset upon an insured's death. An exception is the study by Ferber and Lee (1980). They have the following conclusions: (i) debts rather than assets are the primary determinants of term life insurance holding, (ii) households with husbands who manage the family's financial matters are more likely to own life insurance, and (iii) the husband's and the wife's priority for savings and the number of credit cards might affect life insurance demand. Unfortunately, the absence of a theoretical model and the use of simple econometrics techniques (such as linear probability and ordinary least squares regressions) have made their findings inconclusive.

THEORETICAL MODEL

The model is a death-contingent claim model similar to those of Campbell (1980) and Fitzgerald (1987). Consider an individual with a single-period horizon. At the beginning of the period, he or she faces a probability of death p. The individual's endowed net worth is given by the following identity: [8]

W [equivalent] N + L + A - D, (1)

where N, L, A, and D denote nonliquid conventional asset holding, liquid conventional asset holding, annuity wealth, and total debt, respectively. In the presence of insurance markets, the individual can allocate his or her endowed net worth into consumable or bequeathable form by buying life insurance.

Consumable wealth is the wealth contingent on the individual's survival given by: N + L + A - D - [pi]I [equivalent] W - [pi]I, (2)

where [pi] is the premium rate and I is the term value of life insurance. Throughout the analysis, it is assumed for simplicity that the effect of adverse selection is absent or insignificant. [9] In the presence of adverse selection, the potential private information held by the insured implies that the insurance company might underestimate the probability of death of the insured. When the underestimation is sufficiently large, the cost of insurance is negligible or even negative (i.e., [pi] [less than] p), encouraging the individual to hold more life insurance. This is possible particularly for life insurance products that are renewed for many years so that the insurance company may be selected against over time. Now, the utility from consumable wealth conditional on survival is given by

U(W - [bi]I). (3)

Here, U is assumed to satisfy standard assumptions, namely, U' [greater than] 0, [lim.sub.x[rightarrow]0] U'(x) = [infinity], and U" [less than] 0 where U' and U" are the first and second derivatives of U.

Bequeathable wealth is the liquidated value of assets in bequeathable form upon the individual's death given by:

l[[delta]N + (L - D),(L - D)] + I, (4)

where l is the estate liquidation value function of conventional assets (in the first argument) and 0 [less than] [delta] [less than] 1 is the liquidation factor of nonliquid conventional assets due to immediate liquidation and lack of management skill as discussed in the introduction. The formulation in (4) assumes that life insurance death benefits are distributed directly to designated beneficiaries to bypass the probate process instead of used for providing additional estate liquidity. [10] Denote [l.sub.i] and [l.sub.ij] as the first and second derivatives of l with respect to the [i.sup.th] argument and the [i.sup.th] and arguments, respectively. Here, 0 [less than] [l.sub.1] [less than] 1 captures the fact that the long and tedious probate process results in time cost of waiting before estate assets can be distributed. Debt is subtracted from liquid conventional asset holding because debt reduces net worth and has to be settled (using liquid conventional assets first) before any part of the estate is di stributed. The effective liquidity represented by net-of-debt liquid conventional assets, L - D, can be distributed or used for paying administrative and other expenses to speed the probate process and reduce the shrinkage in the value of estate assets. Therefore, [l.sub.2] [greater than] 0 and [l.sub.12][greater than] 0. It seems reasonable to assume that [l.sub.12] [less than] 0; that is, the marginal effect of liquidity diminishes. The individual's utility from bequeathable wealth is given by: [11]

B{l[[delta]N + (L - D),(L - D)] + I} [equivalent] B{I[[delta](W - A) + (1 - [delta])(L - D),(L - D)] + I}. (5)

This identity is due to (1). B is assumed to exhibit positive and diminishing marginal utility of bequeathable wealth; that is B'[greater than] 0 and B" [less than] 0 where B' and B" are the first and second derivatives of B.

According to Bernheim (1991), I should be the term value of all life insurance policies. The face value of a whole life insurance policy equals the cash value plus the term value. The cash surrender value can be borrowed against for consumption purposes (through policy loans) like any liquid conventional assets. Therefore, the cash value should be included as part of liquid conventional asset holding. Moreover, even though whole life insurance holding is not totally flexible because the cancellation of the policy often involves high transaction costs due to back loading, the policy loan provision actually allows a whole-life holder to adjust the death benefits of the policy. [12]

Following Hurd (1989) and Bernheim (1991), A is assumed to be exogenously given. First, social security and private pension annuity wealth is accumulated before an individual retires. Second, private life annuities are usually thought of as retirement instruments that are seldom bought after retirement. Finally, private annuity markets are often inactive due to the actuarial unfairness of private annuities, possibly as a result of imperfect competition or adverse selection. [13]

Another simplifying assumption is that L and D are exogenous. [14] This assumption is reasonable because many people do not realize their needs for an estate plan nor do they have sufficient life insurance coverage until they are approached by life insurance salespersons. A salesperson normally asks the potential client to write down his or her asset and liability items and any immediate needs for cash. [15] Under this procedure, it seems natural for the insured to purchase life insurance as if he or she is given the existing portfolio of conventional assets. Furthermore, since liquid conventional assets are held for transaction, precautionary, and speculative purposes and the insurance premium is only a small fraction of total transactions, the insured is unlikely to change his or her existing asset portfolio or spending and payment pattern drastically as a result of the insurance purchase.

The individual chooses life insurance holding to maximize his or her expected utility

EU = pB{l[[delta](W - A) + (1 - [delta])(L - D),(L - D)] + I} + (1 - p)U(W - [pi]I) (6)

subject to I [greater than or equal to]0. The first-order condition for an optimum is given by

pB' - (1 - p)[pi]U' [less than or equal to] 0. (7)

When I has an interior solution, (7) holds as an equality and gives

I = I(W,A,L - D,...). (8)

The assumptions on U, B, and I guarantee that the second-order condition for a maximum is satisfied.

Differentiating the L.H.S. of (7) with respect to A, W, and L - D yields

[[partial].sup.2]EU / [partial]W[partial]I = p[delta][l.sub.1]B" - [pi](1 - p)U" [greater than][less than] 0?; (9)

[[partial].sup.2]EU / [partial]A[partial]I = -p[delta][l.sub.1]B" [greater than] 0; (10)

[[partial].sup.2]EU / [partial](L - D)[partial]I = p[(1 - [delta])[l.sub.1] + [l.sub.2]B" [less than] 0. (11)

Equations (9) through (11) imply the following comparative statics results: [16]

First, (11) and the second-order condition imply that [partial]I / [partial](L - D) [less than] 0. When W and A are kept constant, an increase in net liquid conventional asset holding (accompanied by an equal decrease in nonliquid conventional asset holding) raises bequeathable wealth and estate liquidity and hence lowers the marginal utility of bequeathable wealth. To strike a balance, the individual will raise the marginal utility of bequeathable wealth by holding less life insurance.

Second, (10) and the second-order condition imply that [partial]I / [partial]A [greater than] 0. When W and L - D are kept constant, an increase in annuity wealth reduces nonliquid conventional asset holding and hence increases the marginal utility of bequeathable wealth. To strike a balance, the individual will reduce the marginal utility of bequeathable wealth by holding more life insurance.

Finally, (9) implies that the sign of [partial]I / [partial]W is ambiguous. When L - D and A are constant, an increase in net worth (due to an increase in nonliquid conventional asset holding) not only reduces the marginal utility of consumption and tends to increase life insurance holding, but also reduces the marginal utility of bequeathable wealth and tends to decrease life insurance holding. However, the marginal utility of bequeathable wealth is likely to be much smaller than the marginal utility of consumption and is bounded below by zero. Therefore, B" is likely to be smaller than U" in absolute terms. Moreover [pi] [greater than or equal to] p, whenever life insurance is fair or unfavorable, whereas 1 - p should be close to one at any given time. These together with [l.sub.1] [less than] 1 and [delta] [less than] 1 imply that it is likely that [[partial].sup.2]EU / [partial]W[partial]I [greater than] 0 and hence [partial]I / [partial]W [greater than] 0. In other words, the term component of life insurance is likely to be a normal good contradicting Bernheim's (1991) conclusion.

DATA

The data set used is the U.S. Survey of Consumer Finances (SCF) 1989 sponsored by the Federal Reserve Board. [17] It is a multiple-imputed data set containing information on the different assets held by 3,143 subject households as well as their attitudes towards risks and credit, their employment history and pension rights, and their demographic and family characteristics. [18]

The final sample used for regression analysis consists of 275 subjects. This sub-sample is selected so that the following difficulties are circumvented. (i) Only those households with single household heads are picked, where "single" means separated, divorced, widowed, or never married. One reason for choosing single individuals is that the SCF 1989 data set does not contain any information on survivor benefits that serve as some sort of life insurance protection for the surviving spouses. Ignoring survivor benefits understates the value of life insurance holdings by married couples. (ii) Only subjects age 65 or older (in 1988) are selected. They are assumed to be retired so that we do not need to calculate the present value of their future expected salaries by making arbitrary assumptions on the growth rate of their future wage income streams. (iii) Subjects with zero or negative net conventional asset holding (representing less than 5 percent of the sample) are eliminated. The reason is that the life insura nce holding behavior of these subjects might not be representative because their conventional asset holdings are at a corner while the censoring effect is insignificant. (iv) Any subject whose imputed social security and pension wealth figures have the highest imputed values larger than the lowest values (among the five imputed data sets) by three times or more are dropped. This improves the reliability of the data. [19]

A summary of the relevant variables is given in Table 2. The means and standard deviations of the variables of interest are calculated using the method suggested by Rubin (1987). The definitions and computation of some crucial variables, namely, total term value of life insurance holdings (VLI), social security and pension annuity wealth (SSW), liquid conventional asset holdings (LASSET), total debt (DEBT), and net liquid conventional asset holdings (NL) are discussed below.

VLI

Ferber and Lee (1980) use both the values of term and whole life insurance policies as the dependent variables in their regressions and find that term life and whole life insurance policies are affected by quite different variables. However, according to the model in this paper (see also Bernheim, 1991), what is important is the total value of the term component of all life insurance policies denoted by VLI.

SSW

Social security and private pension annuity wealth (SSW) is the sum of social security wealth and private pension annuity wealth [20] It represents the total annuity wealth of an individual. Social security wealth is the present value of the social security retirement, disability, and other welfare benefits adjusted for survival probabilities. It is calculated based on the assumption that all subjects age 65 or older were retired in 1988 and that the maximum attainable age equals 105:

(Benefits in 1988). [[[sigma].sup.105-t].sub.i=1][(1+r).sup.-i](1-[p.sub.i]).

Here, t is the age of the subject in 1988; r is the real interest rate; 1 - [p.sub.i] is the probability of survival at age t + i conditional on the individual's survival at age t. The (1 - [p.sub.i]) term accounts for the fact that an individual is entitled to receive benefits only if he or she is alive in year t + i. The value of [p.sub.i] is calculated using the life table of 1988 compiled by the Census Bureau.

For the subjects with pension plans whose face values are not reported, pension wealth is calculated as follows:

(Expected Future Annual Benefits). [(1+r).sup.-(s-t)][[[sigma].sup.105-s].sub.i=1][(1+r).sup.-i](1-[p.su b.i].

Notice that (1 - [p.sub.i]) is now the objective probability of survival at age i + s conditioned on the individual's survival at age t in 1988, where s is the age at which the subject is first eligible to receive pension benefits.

Two values of SSW are calculated based on the assumptions of r = 3% and r = 0%, respectively. Notice that Bernheim (1991) includes social security benefits but not private annuity wealth in his regressions. This tends to understate the total annuity wealth of a subject.

LASSET, DEBT, and NL

Liquid conventional asset holding (LASSET) refers to the holding of conventional assets that do not incur, or incur little, capital loss upon imnaediate liquidation. Unlike cash and bonds, corporate stocks may be subject to substantial capital loss upon immediate liquidation and may not be totally liquid. Taking this fact into consideration, two values of liquid conventional asset holdings are calculated. LASSET(1) includes the holdings of savings and checking accounts, government and corporate bonds, other money market instruments, and the cash value of whole life policy. LASSET(2) equals LASSET(1) plus corporate stock holdings.

Total debt (DEBT) is the sum of mortgages on real estate and vehicles, personal loans, loans from credit lines, loans from the individual's own business, and other debt. The value of net liquid conventional assets (NL) equals liquid conventional asset holding minus total debt. Two values, namely, NL(1) and NL(2) are calculated corresponding to LASSET(1) and LASSET(2), respectively.

WORTH

Net worth (WORTH) equals total conventional asset holding plus SSW minus DEBT. Conventional assets include savings and checking accounts, government and corporate bonds, money market investments, corporate stocks, real estate properties, vehicles, private businesses, trusts, loans to individuals and businesses, cash value of whole life insurance, and other assets.

EMPIRICAL MODEL AND ESTIMATION

In the sub-sample of the SCF 1989 data set, 30.9 percent of the subjects hold term life insurance, 27.8 percent hold whole life insurance, and 47.3 percent hold either (11.7 percent of them holding both). The high percentage of subjects holding no life insurance suggests that a Tobit model should be used. The average face values of term and whole life insurance are $4,103 and $8,399, respectively. Their sum is larger than the average term component of total life insurance holdings ($10,959) because the latter excludes the cash value of whole life insurance. Further calculation shows that the average term life insurance holdings is $13,278; the average face value of whole life policy holdings is $30,212; and the average term value of all life insurance holders is $23,268.

The following Tobit model is based on the one described in the section titled "Theoretical Model." [21] Denoting the observed life insurance holding of individual i by [VLI.sub.i], we have

[VLI.sub.i] = [[VLI.sup.*].sub.i] if [[VLI.sup.*].sub.i] [greater than] 0, and 0 otherwise, (12)

where [[VLI.sup.*].sub.i] is the latent life insurance holding by individual i. When life insurance holding has an interior solution, optimal life insurance holding is given by (8). Linearizing (8) and adding an error term [[epsilon].sub.i] gives

[[VLI.sup.*].sub.i] = [b.sub.0] + [b.sub.1][WORTH.sub.i] + [b.sub.2][SSW.sub.i] + [b.sub.3] [NL.sub.i] + [x.sub.i][b.sub.4] + [[epsilon].sub.i], (13)

where [NL.sub.i], [WORTH.sub.i], and [SSW.sub.i] are the net liquid conventional asset holding, net worth, social security and private pension wealth, respectively. Here, [x.sub.i] is a row vector of personal characteristics. Possible candidates in the SCF data set are age (AGE), presence of children (CHILD), sex (MALE), number of years of education (EDU), and past charitable donation (DONATE). These variables, except DONATE, are often included in the literature as can be seen in Table 1.

According to McDonald and Moffitt (1980), the coefficients estimated by Tobit regressions do not represent the marginal effects of the corresponding independent variables on the dependent variable. [22] Particularly, if we want to know the marginal effects of the independent variables for those subjects who are above the limit (i.e., with VLI [greater than] 0), we need to first compute the probability of being above the limit (fraction of mean total response due to response above limit). The marginal effects of independent variables for those subjects who are above the limit equal the corresponding estimated coefficients multiplied by the fraction of mean total response due to response above limit (see McDonald and Moffitt, 1980, eqn. 7). [23] The fractions of mean total response due to response above limit for different Tobit regressions are reported in Table 3 under "Estimated Probabilities."

HYPOTHESES AND EXPECTED RESULTS

Modigliani (1988) proposes that life-cycle precautionary savings constitutes a major part of total savings and represents a significant portion of bequests. However, previous sections of this article showed that many retired singles in the SCF data set have non-trivial life insurance holdings. Funeral expenses and other death costs may account for some but not all life insurance holdings because only a small fraction of life insurance death benefits are paid to estates (see footnote 5). Therefore, bequest motives (charitable or non-charitable) may be important determinants for bequeathable wealth and life insurance holdings.

As discussed in the introduction, retired singles may hold life insurance because of its ability to bypass the probate process, its high liquidation value relative to other assets, or its liquidity-improving effects. On the other hand, a retired single's "excessive" life insurance holdings may be the result of superstition, forgetfulness, or the intensive sales effort of life insurance salespersons. The nuli hypothesis, therefore, states that estate liquidation and liquidity are unimportant concerns in estate planning and the determination of life insurance holdings or that an individual is unaware of their importance. This implies that life insurance holding has no signed relation with net liquid conventional asset holdings. The alternative hypothesis states that estate liquidation is an important concern and that life insurance holding is the optimal result of an individual's resource allocation between consumable and bequeathable wealth. Under the alternative hypothesis, an exogenous increase in net liquid conventional asset holding reduces life insurance holding as shown in the theoretical model.

The theoretical model has two other testable implications. First, an increase in net worth is likely to increase life insurance holding, contradicting Bernheim's (1991) conclusion that the term component of life insurance holdings is an inferior good. Second, an increase in total annuity wealth raises life insurance holding. This is consistent with Bernheim's conclusion that an increase in social security benefits increases life insurance holding.

Next, Barthold and Plotnick (1984) show that single individuals tend to make more charitable contributions than married individuals. The SCF data set contains information on past charitable donation that might reflect the subject's charitable motives. Charitable motives should affect an individual's utility on consumable and bequeathable wealth and hence life insurance holding.

Finally, the expected effects of other variables are discussed as follows: a married individual might need to insure against potential wage loss to his or her family due to premature death (see, e.g., Campbell, 1980). This suggests that MALE has a positive effect on life insurance holding because men are often the major breadwinners of their families. This also implies that AGE has a negative effect on life insurance holding since the expected human capital remaining falls as the individual ages (see, e.g., Gandolfi and Miners, 1996). It is uncertain whether AGE and MALE affect the life insurance holdings of retired singles, although men might hold more life insurance after retirement because of insurance holding inertia (see Bernheim, 1991). If holders have bequest motives towards children, particularly when they are young and dependent, then CHILD should have a positive effect on the utility of bequests and hence on life insurance holding. It is unclear whether this holds for our sample because all subjects have children older than 18 who might be fairly financially independent. Finally, a higher level of education may increase insurance mindedness, although the existing empirical findings are mixed (see, e.g., Ferber and Lee, 1980, and Auerbach and Kotlikoff, 1989).

REGRESSION RESULTS [24]

The results reported in this section are based on the assumption that the real interest rate equals 3 percent (r = 3 percent). The results based on the assumption that r = 0 percent are similar and are thus omitted. Columns (1) and (2) of Table 3 report the Tobit regression results when net liquid conventional asset holding is defined by NL(1) and NL(2), respectively. Since the results are similar, the following discussion focuses on column (1).

Holding net worth and annuity wealth constant, net liquid conventional asset holding has a negative effect on life insurance holding that is significant at the .01 level. This result supports the theoretical model and rejects the null hypothesis that estate liquidation and liquidity are not important concerns in life insurance holding decisions. By adjusting the estimated coefficient as discussed in footnote 23, a dollar increase in NL decreases VLI of life insurance holders by 2.67 cents (8.7 X .3067). Keeping net liquid conventional asset holding and annuity wealth constant, net worth has a positive effect on life insurance holding that is significant at the .01 level. This result rejects Bernheim's (1991) conclusion that the term component of all life insurance policies is an inferior good. A dollar increase in WORTH increases VLI of life insurance holders by 0.67 cents (0.022 x .3067). Keeping net worth and net liquid conventional asset holding constant, social security and pension annuity wealth has a po sitive effect on life insurance holding that is significant at the .10 level (one-tailed test). This result supports the theoretical model and is consistent with Bernheim's conclusion that life insurance serves to counteract excessive social security taxes. A dollar increase in SSW increases VLI of life insurance holders by 7.88 cents (0.2565 x .3067). Past charitable donation has a positive effect on life insurance holding that is significant at the .01 level. This implies that charitable motives have a positive effect on life insurance holding. A dollar increase in DONATE raises VLI of life insurance holders by 1.13 dollars (3.695 x .3067). Finally, AGE, MALE, and EDU have negative effects and CHILD has a positive effect on VLI. Except for MALE and EDU, these are consistent with our expectation. None, however, are significant. It is unclear whether age, sex, education, and the presence of children affect life insurance holding for this sample.

Next, columns (3) and (4) show the Tobit results when net liquid conventional assets are broken down into liquid conventional assets and debt. Liquid conventional asset holdings [LASSET(1) and LASSET(2)] have negative effects on life insurance holding that are significant at the .01 level in both regressions. DEBT has a positive coefficient in column (4), which differs from the coefficient of LASSET(2) and is significant at the .10 level. This seems to suggest that LASSET and DEBT may be treated separately in the utility of bequeathable wealth; however, this result is inconclusive as the coefficient of DEBT becomes insignificant in column (3). The inclusion of corporate stocks in liquid conventional assets makes the estimated coefficients of NL (or LASSET and DEBT) smaller by about a half. Table 1 shows that, on average, corporate stock holding is about one-third of liquid conventional asset holdings. This suggests that the effect of net liquid conventional asset holdings other than corporate stocks on life i nsurance holdings may be stronger than that of corporate stock holding.

CONCLUSION

The following discussion summarizes the empirical results and their implications.

First, demographic and personal characteristics seem to be less important than financial and wealth variables in explaining the life insurance holding of a retired single. This is not surprising, as life insurance is a financial asset. Perhaps retired individuals should be treated as a separate group in the study of life insurance demand.

Second, the regressions show that net liquid conventional asset holding accompanied by a change in nonliquid conventional asset holding in the opposite direction (keeping net worth and annuity wealth constant) has a negative effect on life insurance holding. This result rejects the null hypothesis that individuals ignore the importance of estate liquidation and liquidity and supports the textbook view that life insurance death benefits serve as a good bequest medium. Particularly, life insurance death benefits have a higher value than conventional assets upon death as they can be distributed directly to designated beneficiaries to bypass the probate process and hence incur zero cost of waiting. However, unless additional data on funeral expenses and the status of the beneficiaries of life insurance policies and estates become available, it is impossible to know from the regression results whether life insurance death benefits actually improve upon the liquidity of estates.

Third, the regression results are consistent with Bernheim's (1991) empirical finding that social security taxes increase life insurance holding. However, they reject Bernheim's conclusion that the term component of life insurance holding is an inferior good. Bernheim's controversial result might be because of the lack of data on the term value of life insurance. Moreover, the finding that net liquid conventional asset holding reduces life insurance holding implies that Bernheim's estimation, which excludes net liquid conventional asset holding, may suffer from omission bias as net liquid conventional asset holding is often positively correlated to net worth.

Finally, for single retired individuals in the U.S., charitable motives may affect life insurance holding. The regression results show that past charitable donation has a positive effect on life insurance holding. This is not surprising, as past charitable donation indicates a subject's charitable motives that affect his or her utility of consumable and bequeathable wealth and hence life insurance holding.

Arthur Hau is an associate professor in the Department of Industrial Economics and Department of Insurance, Tamkang University, Tamsui, Taipei Hsien, Taiwan. This article is a substantially revised version of Chapter 2 of the author's Ph.D. dissertation. The author thanks Professor Edi Karni and Professor Will Carrington for their valuable comments and for their guidance throughout the author's Ph.D. program at Johns Hopkins University. The author also thanks Professor Robert Moffitt for his generous help on some important econometrics issues. Finally, the author thanks the editor for his encouragement of the revision of this paper and two anonymous referees for their valuable comments that have led to substantial improvement in the content of this paper. All errors in this paper are, of course, the author's own.

(1.) The median term value of life insurance holding is $3,000, but about 23 percent of the holders have at least $10,000 of term value of life insurance holding. The low percentage of life insurance beneficiaries being the insureds' estates (see footnote 5), however, suggests that even though life insurance holdings are not sizable for many holders, death benefits may be used for purposes other than paying funeral expenses. This should be true particularly for the wealthier individuals in this group.

(2.) The "Statistics of Income: Estate and Gift Tax Returns 1977" published by the U.S. Internal Revenue Service shows that, on average, funeral and estate administrative expenses were about 5 percent of the gross estates (liquidated value of all assets) of the deceased in 1977. Charitable bequests were 8 percent, while estate taxes (after marital and orphan deductibles and other exemptions) were 13 percent. Although the sample of estate tax returns is quite different from the sample of retired singles in the SCF data set, as only 20 percent of these tax returns are filed by single individuals more than 60 years old, these figures give some idea of the size of funeral expenses and other costs of death.

(3.) Nuckols (1982) stipulated from the Widows Study conducted by Life Underwriter Training Council and Life Insurance Agency Management Association in 1970 and 1971 that on average, medical bills, funeral expenses, outstanding bills, administrative costs, taxes, and so forth amount to about 40 percent of one year's normal pre-death income. Moreover, funeral expenses vary much less widely than income levels among the subjects. Therefore, it is unlikely that well-to-do individuals hold life insurance solely for funeral expenses. Finally, if an individual has no bequest motives, estate administrative expenses are unimportant and hence should never be paid using life insurance death benefits. (See also footnote 5.)

(4.) Some elderly individuals may hold life insurance because the true cost of life insurance purchase can be highly favorable because of the presence of private information and adverse selection. See the theoretical model section for a more detailed discussion of this issue.

(5.) Nuckols (1982) has found that life insurance death benefits of a married individual help the surviving spouse who needs immediate cash for paying various costs of death and hence speed the probate process. It is uncertain whether this holds for a single individual. Very often, the life insurance beneficiary of a single individual is a relative, a friend, or a child of the holder instead of the estate or trust. The Life Insurance Fact Book (1990, 1994) reports that only 4.5 percent and 5.7 percent of the beneficiaries of life insurance policies were either estates or trusts in 1985 and 1990, respectively. It is doubtful that the beneficiary would use the proceeds from life insurance death benefits for paying the costs of death to speed the probate process unless he or she is the sole beneficiary of the entire estate. Furthermore, even when life insurance death benefits are paid to a trust, the purpose is likely to be tax avoidance (for irrevocable trusts) or control of the heirs (for revocable trusts) ins tead of liquidity.

(6.) The loading methods (i.e., front loading or back loading) affect the value of the pure term component and cash surrender value of a whole life policy.

(7.) Unlike most studies of life insurance demand, a recent international study of life insurance holding by Browne and Kim (1993) looks at variables at the macro level instead of the micro level. Interestingly, they find that inflation and higher policy loan charges have significant negative effects on aggregate life insurance holding.

(8.) Notice that (1) is an accounting identity and not an additional restriction. The definition of net worth follows very closely the definition of "lifetime resources" in Bernheim's (1991) paper. It is, however, not clear whether Bernheim has taken into account the total debt of a subject.

(9.) The author thanks a referee for bringing up this important issue of the model.

(10) The author thanks a referee for suggesting some important ideas of how the theoretical model can be simplified. All errors are, of course, the author's own. Notice that when life insurance death benefits are paid directly to the estate, the liquidation value of estate assets after the probate process becomes I[[delta]N + (L - D) + I, (L - D) + I]. Similar to (4), this formulation assumes that the individual pays for the life insurance premium using the individual's annuity wealth. Under this formulation, the comparative statics results become ambiguous but will conform to the results based on final bequests function (4) under additional assumptions. The difference between the two sets of results is discussed further in footnote 16. However, notice that life insurance death benefits can be paid directly to designated beneficiaries to bypass the probate process and hence avoid any costs of waiting. The individual is unlikely to name the estate as the life insurance beneficiary especially when he or she has enough net liquid conventional asset holdings for paying various probate expenses. Footnote 5 supports this conjecture.

(11.) The individual may derive utility from bequeathable wealth for various reasons (e.g., paying funeral expenses and making charitable and noncharitable bequests). Noncharitable bequests might be due to "altruistic," "exchange," or "strategic" motives. For simplicity, the exact nature of the bequest motives is not dealt with in this empirical study, as some of the motives involve complicated game theory (see, e.g., Cox 1987, and Bernheim et al., 1985).

(12.) The loan bears interest at about 5 to 6 percent in older policies and up to 8 percent in newer contracts (see Vaughan and Vaughan, 1996, p. 269). At such low interest, if a life insurance holder decides to reduce the term value of the policy, he or she only needs to borrow against the policy and never repay. If he or she dies, the loan plus interest will be deducted from the death benefits, and yet he or she does not need to cancel the entire policy. According to Carson and Hoyt (1992), insurance holders do adjust their portfolios by taking policy loans when market interest rates rise above the interest rates on policy loans. It was reported that policy loans outstanding in the U.S. at the end of 1970 equaled $14.4 billion and grew to $34.8 billion by the end of 1979.

(13.) According to Friedman and Warshawsky (1990, p. 136, fn. 2), "one large insurer, considered to be more active than average in this market, sold an average of $18.5 million of individual life annuities each year during 1980-83. By contrast, the same company's annual sales of individual life insurance averaged $18.1 billion during this period." They have also reported that between 1968 and 1983, the average yield of life annuities for 65-year-old males among the ten largest insurers in the U.S. are lower than those of the 20-year government bonds. This is true even when the average yield is adjusted for possible adverse selection. The low yield of life annuities might be a major reason for the inactivity of private annuity markets.

(14.) In a study of the demand for medical insurance, Levin (1995) also assumes that total wealth, annuity wealth, and liquid and nonliquid conventional assets are exogenously given. The author has tried to relax the exogeneity assumption by estimating using simultaneous Tobit regressions (see footnote 21 for more detail).

(15.) For a sample "personal balance sheet," see, e.g., Black and Skipper (1994, p. 400).

(16.) If life insurance death benefits are used for providing estate liquidity as discussed in footnote 10, the signs of [partial]I / [partial]A and [partial]I / [partial](L -- D) are no longer unambiguous. These signs depend crucially on the relative size of [l.sub.12] (i.e., the marginal effect of liquidity on the marginal contribution of net liquid conventional assets to the final bequests). These signs conform to those under bequests function (4) when liquidity affects l as a whole but has very little effect on [l.sub.1].

(17.) The SCF 1989 data set is particularly suited for this study for the following reasons: (i) Unlike the Retirement History Longitudinal Survey (RHLS), it distinguishes between term life and whole life policies. It also contains information about the cash values and the policy loans of whole life policies held by the subjects, so that the term component (life protection component) of whole life policies can be calculated. (ii) It purposefully over-samples wealthier households using tax data and, therefore, overcomes the familiar problem of most other data sets (such as the RHLS) that the wealthy are underrepresented because of non-response. It is generally believed that making bequests and estate planning are more important for the rich than for the poor. (iii) It has a detailed breakdown of different asset and debt items that allows the categorization of assets according to their degree of liquidity.

(18.) The SCF 1989 data set contains 3,143 households, but it has a total of 15,715 cases as a result of the multiple imputation of missing data. For each missing value, five different estimates have been imputed. Hence, for each subject household, there are five (multiple-imputed) observations. The five sets of observations are treated as five different data sets. The estimate of a particular parameter is obtained by averaging the estimates of that parameter over all five data sets. However, the additional variability on the estimated coefficient resulting from multiple imputation must be taken into account for the purpose of hypothesis testing. The method for handling multiple-imputed data sets is due to Rubin (1987) and can be obtained from the author on request.

(19.) There are 283 single and retired subjects who have positive conventional asset holdings. Picking subjects with not-too-large multiple imputation variability for the social security and pension figures has eliminated eight observations.

(20.) Unfortunately, some private pension plans are not in the form of life annuities and thus have bequeathable values. Therefore, SSW may overstate the annuity wealth of a subject. However, excluding private pension wealth in SSW does not affect the regression results.

(21.) Even given the discussion in the Theoretical Model section, it is not clear whether net liquid conventional asset holding is exogenous. One approach is to employ the exogeneity test introduced by Smith and Blundell (1986). Their test is not adopted for the following reasons: (i) It is not clear how multiple data imputation affects their test. (ii) With a small sample, the low power of their test is likely to generate ambiguous results. (iii) Their test applies only to Nelson and Olson's (1978) Tobit model. The author has attempted to drop the assumption that net liquid conventional asset holding is exogenous by running simultaneous equation Tobit regressions following the Lee-Maddala-Trost method (see Lee et al., 1980). The regression results are reasonably consistent with those reported in this paper. These results can be obtained from the author on request.

(22.) The author thanks a referee for suggesting that these estimated probabilities be included.

(23.) We first compute the value of X[pounds]] / [sigma]. Here X, is the vector of mean values of independent variables; [pounds]] is the vector of estimated coefficients; [sigma] is the estimated standard error in the Tobit regression. Due to the multiple imputation in the SCF data set, the X[pounds]] / [sigma] value is computed for each of the five imputed data sets and then averaged across the five data sets. The X[pounds]] / [sigma] values are relatively stable across the five data sets.

(24.) All single equation Tobit regression results are generated by Stata 4.0. The figures in brackets are the corresponding asymptotic standard deviations of the estimated coefficients adjusted for the additional variability introduced by multiple data imputation (see Rubin, 1987). The log likelihood values are not reported because for each regression equation, there are five log likelihood values from the regressions on the five imputed data sets.

REFERENCES

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Bernheim, B. Douglas. "How Strong Are Bequest Motives? Evidence Based on Estimates of the Demand for Life Insurance and Annuities." Journal of Political Economy, vol. 99, 1991, pp. 899-927.

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Carson, James M., and Robert E. Hoyt. "An Econometric Analysis of the Demand for Life Insurance Policy Loans." Journal of Risk and Insurance, vol. 59, 1992, pp. 239-251.

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 A Summary of Empirical in Life Insurance Demand
Independent
Variables Results Studies
Age (+) Berekson (1972)
 (-) Ferber and Lee (1980), Auerbach and
 Kotlikoff (1989), Bernheim (1991)
 (I) Duker (1969), Anderson and Nevin (1972),
 Fitzgerald (1987), Gandolfi and Miners (1996)
 (D) Hammond et al. (1968) (income group)
Marital status (-) Hammond et al. (1968), Berekson (1972)
(single) (D) Bernheim (1991) (never married or widowed)
Number of children (+) Bernheim (1991)
 (-) Auerbach and Kotlikoff (1989),
 Hammond et al. (1968)
 (I) Duker (1969), Anderson and Nevin (1972)
 (D) Berekson (1972) (premium or face
 value and sample used), Ferber and Lee
 (1980) (type of policy, years after marriage)
Education level (+) Hammond et al. (1968), Ferber and Lee (1980),
 Browne and Kim (1993)
 (-) Ducker (1969), Anderson and Nevin (1975),
 Auerbach and Kotlikoff (1989)
 (D) Gandolfi and Miners (1996) (sex)
Occupation (+) Hammond et al. (1968), Duker (1969), Ferber
(professional, and Lee (1980), Fitzgerald (1987), Auerbach
self-employed, and Kotlikoff (1989)
managerial)
Working wife (-) Ducker (1969), Goldsmith (1983)
 (D) Ferber and Lee (1980), Auerbach and
 Kotlikoff (1989)
Family income (+) Hammond et al. (1968), Ducker (1979), Ferber and
 Lee (1980), Browne and Kim (1993)
 (-) Anderson and Nevin (1975)
Homeownership (+) Ferber and Lee (1980), Anderson and Nevin (1975)
Net worth (+) Hammond et al. (1968), Duker (1969), Ferber and
(gross assets or Lee (1980), Anderson and Nevin (1975)
net assets) (I) Fitzgerald (1987), Auerbach and Kotlikoff (1989)
 (D) Bernheim (1991) (data de-contamination)
Social security (+) Bernheim (1991), Browne and Kim (1993)
benefits (I) Fitzgerald (1987)


(+) = positive relation; (-) negative relation; (I) = insignificant; (D) = depending on regression technique, data treatment, or other factors in brackets. For studies having some regression equations with insignificant results and some regression equations with significant positive results, I use (+) instead of (D). The same convention applies to (-).
 Data Summary Statistics
 Definitions Mean
AGE Subject's age 74.21
EDU Number of years of education 11.08
CHILD Dummy, 1 means the subject has children 0.778
MALE Dummy, 1 means the subject is a male 0.195
DONATE Amount of donation made in the past ($) 1,373
VLI Term component of all life insurance ($) 10,959
DEBT Total debt owed by subject ($) 5,994
SSW Social security and private pension wealth
 ($) (r = 3%) 53,991
WORTH Net worth ($) (r = 3%) 523,007
NL(1) Net liquid conventional asset holding
 (excluding stocks) ($) 81,660
NL(2) Net liquid conventional asset holding
 (including stocks) ($) 125,221
LASSET(1) Liquid conventional asset holding
 (excluding stocks) ($) 87,653
LASSET(2) Liquid conventional asset holding
 (including stocks) ($) 131,215
 Standard
 Deviation
AGE 6.64
EDU 3.79
CHILD 0.416
MALE 0.397
DONATE 6,815
VLI 69,480
DEBT 28,135
SSW
 55,751
WORTH 2,468,648
NL(1)
 539,656
NL(2)
 352,566
LASSET(1)
 353,943
LASSET(2)
 544,651
(N = 275). The standard deviation of each
variable has been adjusted upward to account
for the effect multiple data imputation (see Rubin, 1987).
 Single Equation Tobit Results VLI
Independent
 Variables (1) (2) (3)
AGE -735.8 -783.9 -744
 (716.6) (823.4) (706.7)
MALE -1994 -3279 -2839
 (9322) (10361) (9318)
CHILD 3570 7698 3093
 (9362) (10263) (9423)
DONATE 3.695 [***] 2.722 [***] 3.666 [***]
 (0.909) (0.884) (0.886)
EDU -537.6 -662 -609.3
 (1107) (1155) (1070)
NL(1) -0.0871 [***] - -
 (0.0177) - -
NL(2) - -0.044 [**] -
 - (0.014) -
LASSET(1) - - -0.0861[***]
 - - (0.0169)
LASSE(2) - - -
 - - -
DEBT - - 0.166
 - - (0.152)
SSW 0.2565& 0.304& 0.241&
 (0.155) (0.164) (0.161)
WORTH 0.022 [***] 0.0221 [***] 0.0219 [***]
 (0.0018) (0.00201) (0.00183)
Constant 19649 15681 21989
 (56768) (64368) (56869)
Estimated probabilities .3067 .3071 .3064
Independent
 Variables (4)
AGE -829.1
 (769.7)
MALE -5488
 (10387)
CHILD 5576
 (10162)
DONATE 2.794 [***]
 (0.91)
EDU -792.8
 (1097)
NL(1) -
 -
NL(2) -
 -
LASSET(1) -
 -
LASSE(2) -0.0454 [***]
 (0.0146)
DEBT 0.307 [*]
 (0.157)
SSW 0.243&
 (0.157)
WORTH 0.0271 [***]
 (0.00199)
Constant 25051
 (61395)
Estimated probabilities .3021


(N = 275) Here, & denotes "significant at the .10 level (one-tailed test)"; [*] denotes "significance at the .10 level (two-tailed test)"; [**] denotes "significance at the .5 level (two-tailed test)"; [***] denotes "significance at the 1 percent level (two-tailed test)". The bracketed figures are the asymptotic standard deviations of the estimates.
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Publication:Journal of Risk and Insurance
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Geographic Code:1USA
Date:Mar 1, 2000
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