NBER WORKING PAPER SERIES LIFE INSURANCE OF THE ELDERLY: ADEQUACY AND DETERMINANTS Alan 3. Auerbach Laurence 3. Kotlikoff Working Paper No. 1737 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 October 1985 We thank Gary Burtless, Peter Diamond, Jagadeesh Gokhale, and Jerry Hausman for many useful comments and suggestions. Jagadeesh Gokhale provided excellent research assistance. Research support was provided by the Brookings Institution and the Department of Health and Human Services under Brookings project on Retirement and Aging. Copyright on this paper is held by the Brookings Institution. The research reported here is part of the NBER's research programs in Taxation and in Financial Markets and Monetary Economics and project in Pensions. Any opinions expressed are those of the authors and not those of the National Bureau of Economic Research. NBER Working Paper #1737 October 1985 Life Insurance of the Elderly: klequacy and Determinants ABSTRTCT Despite a general reduction in poverty among the aged, roughly one third of elderly nonmarried women are officially poor. Many of these women are widows. The fact that poverty rates are significantly larger for widows than for married women suggests that many households may fail to buy sufficient life insurance. This paper considers the adequacy and determinants of life insurance among the elderly. Its principal conclusions are: (1) Combined private and public life insurance is inadequate for a significant minority of elderly households; (2) Of those elderly households in which the husband's future income represents a significant fraction of total household resources, roughly half are inadequately insured; (3) Households do not significantly offset Social Security's provision of survivor insurance by reducing their private purchase of life insurance; and (4) The actual determinants of the purchase of life insurance appear to differ greatly from those predicted by economic theory. Ala J. Auerbach Laurence J. Kotlikoff Economics Departitent DeparbTnt of Economics of Pennsylvania University Boston University 3718 Locust Walk/CR Boston, W 02115 Faculty of Arts and Sciences iiladelphia, PA 19104 I. Introduction In the past several decades there has been a significant improvement in the general economic position of the elderly. In contrast to 1960, when over a third of elderly households had incomes below the poverty line, the current figure is roughly 15 percent. Despite the general reduction in poverty among the aged, the poverty rate amoung elderly nonmarried women, including widows, remains high. Today roughly one third of elderly nonmarried women are officially poor. The fact that 31 percent of elderly nonmarried women, but only 8 percent of elderly married women are in poverty suggests a significant economic risk from the dissolution of marriage through divorce or death. While divorce insurance is unavailable, life insurance is readily available. However, many households may fail to buy enough life insurance. Presumably, concern about insufficient life insurance underlies the provision of survivor and death benefits by the Social Security system. This paper examines the adequacy of the life insurance protection provided by the combination of private and public insurance. It also investigates the determinants of private life insurance purchases. There are three central questions addressed in the study: (1) How large are private life insurance holdings relative to the amounts needed to maintain prior living standards of surviving spouses? (2) Do Social Security survivor benefits significantly increase the amount of life insurance protection? (3) Is the pattern of private insurance purchases in general accord with the predictions of economic theory, particularly the proposition that Social Security survivor insurance should substitute (under assumptions specified below) dollar for dollar for private life insurance? —2— The answers to these questions are clearly very important for understanding the cause of poverty among widows, the extent of the government's intervention in the life insurance market, and the effectiveness of that intervention in increasing the sum of private plus public life insurance. The data set chosen for this study, the Retirement History Survey (RHS), is attractive because it focuses on the elderly and because it permits the observation of household economic status before and after the death of a spouse. These data are, however, deficient in several respects for the study of life insurance. First they include the face value, but not the cash value of life insurance policies. Second, while there are a variety of questions about retirement plans and expected future income, many of these questions were not answered by a considerable number of respondents. Understanding the size of expected future income, particularily labor earnings, is obviously of great importance for assessing the adequacy of life insurance holdings. Given these data problems our results should be viewed cautiously. However, in some important cases, correcting biases arising from missing data would likely strengthen our conclusions. The principal inferences we draw from this study are: (1) Combined private and public life insurance is inadequate for a significant minority of elderly households. (2) Almost one half of households at risk (those for whom a significant portion of household resources take the form of earnings and benefits that cease with the death of the husband or wife) are inadequately insured. (3) Empirical estimation of the demand for life insurance produces many results that are greatly at odds with theorectical predictions. —3- (4) Households do not appear to significantly offset Social Security's provision of survivor insurance by reducing their private purchase of life insurance. There are four remaining sections in the paper. The next presents general descriptive information about the extent and adequacy of life insurance. Adequacy of life insurance is assessed in terms of the ability of surviving spouses to maintain their previous living standards. Comparisons of previous with current living standards are made for households in which a spouse dies between 1969 and 1971. In addition, for all married households in 1969 similar comparisons are made for hypothetical surviving spouses. After presenting these comparisons of pre- and post-death living standards of actual and potential surviving spouses we discuss six potential biases -in these comparisons. In our view, these six biases, on net, lead us to understate the inadequacy of life insurance holdings. The third section examines optimal choice of life insurance holdings within a simple two period model. The substitutability of private and public insurance is considered as well as the proper valuation of future income streams under the assumption of incomplete life insurance and annuity markets. The model illustrates the interdependent choices of life insurance of husbands and wives. As stressed in this section, the insurance demand of one spouse depends on whether the other spouse has positive or zero life insurance. The model assumes that private annuities are unavailable. As pointed out by Yaari (1965), purchasing private annuities is effectively equivalent to having negative holdings of life insurance. Negative holdings of life insurance are ruled out because annuities appear available on the private market only at -4-. extremely unfair rates (Friedman and Warshawsky 1985). None of the households in our RHS sample reported holdings of private annuities. The theoretical model of section III motivates the econometric specification of a two indicator switching regressions model, which is presented in section IV. Section V discusses the empirical findings and uses the results to evaluate Social Security's impact on the purchase of private insurance. The final section summarizes the paper's findings and suggests ideas for additional research. II. The Adequacy of Life Insurance A. Conceptual Framework This section considers the adequacy of life insurance by comparing living standards before and after either the actual or hypothetical death of a spouse. The definition of living standard is obviously arbitrary. By living standard we mean the sustained level of consumption of goods and services that can be afforded, based on the household's current assets and current and future income. Calculating affordable consumption annuities both prior to and after the death of a spouse requires information on the net worth, future labor earnings, private pensions, and Social Security benefits available to the couple when both spouses are alive as well as to actual or hypothetical surviving spouses. Life insurance obviously raises the resources available to surviving spouses, and its purchase can protect surviving spouses from a reduction in their affordable standards of living. The size of consumption streams that can be financed from a given amount of resources depends on actuarial factors, such as the interest rate, the extent —5— to which annuities are implicitly, if not explicitly available, and household economies to scale in joint consumption. "Economies to scale" refers to the "two can live cheaper than one' proposition. Obviously many goods, such as heating, lighting, and other housing services, are jointly consumed by married couples. Other goods, such as food and clothing, do not have this public goods feature. To see the importance of the economies of scale issue, consider at one extreme that all goods consumed by couples are local public goods like heating. In this case, for surviving spouses to maintain prior affordable living standards, they need to be able to purchase the same commodities when single that they and their spouse would have purchased when married. To do so obviously requires the same economic resources. By full insurance of the survival—contingent income stream of each spouse, the living standard of the surviving spouse will be fully insured. While fully insuring the survival contingent income stream is required to maintain living standards of survivors when all household consumption is joint, this is not true in the absence of significant economies to scale. Consider the case of no joint consumption by married couples. In this setting the surviving spouse will suffer a drop in affordable living standard only if the uninsured decedent's survival-contingent income stream would have financed more than his or her own stream of consumption; i.e., fully insuring the surviving spouse requires buying insurance equal to the difference between the value of the decedent's future income stream and the value of his or her future consumption. If this difference is negative, i.e., the value of the future income stream the decedent would have earned is less than the potential future value of his or her —6- the surviving spouse's living standard will be greater than it consumption, would have been had his or her spouse not died. Since we do not know the precise extent of economies to scale, we present economies to scale and our adequacy of life insurance calculations assuming no then discuss the likely bias arising from ignoring scale economies. "Living could be standard" is measured in the calculations as the level annuity that financed with available resources. Prior to the actual or hypothetical death of a spouse, we calculate the combined resources of the couple and compute the level annuity, 4m' that could be purchased for each spouse under the assumption that that each spouse receives an equal annuity. Next we determine the annuity could be afforded by the surviving spouse, A. The ratio of the second annuity to the first annuity (As/Am) is our measure of the adequacy of insurance. Ratios below .75 are described as "inadequate." More formally, let PVRm be the present value of resources of the couple the when they are both alive, and let PVR5 be the present value of resources of surviving spouse. We calculate As/Am: where Am: the annuity of the surviving after the spouse when married and A5, the annuity of the surviving spouse partner's death, are determined by: + D)A (im) PVRm = (Dh (is) PVR5 = D5A5, s = h,w are discount factors for the husband and wife; 0h equals the In (1) Dh and until his death; D is present value of $1 received annually by the husband represents the discount factor for the surviving correspondingly defined. —7- spouse, where s = h or w. As discussed by Yaari (1965), Kotlikoff and Spivak (1981), and Bernheim (1986) and as indicated in the next section, in the presence of life span uncertainty, the proper valuation of future income streams depends critically on the nature of explicit and implicit insurance arrangements. At one extreme one could assume a perfect market in annuities and life insurance in which insurance prenria are actuarially fair. In this case PVRm and PVRS would correspond to the present expected values of resources of married couples and surviving spouses, where the expectation is taken over survival probabilities. Similarily, Dh. D, and would be the expected value discount factors. Even if there were no public market in annuities, Kotlikoff and Spivak (1981) indicate that risk sharing amoung family members (e.g., parents and children) can closely approximate perfect annuity insurance even when the number of family members is as few as four. While families are not as effective in hedging the loss of future income streams (i.e., providing life insurance) as they are in hedging the duration of future consumption streams (i.e., providing annuity insurance), the combination of life insurance that is close to actuarially fair plus family annuity insurance arrangements may approximate the situation of perfect life and annuity insurance. In this case, using actuarially fair discounting in forming PVRm PVR5, Dh, and would be roughly appropriate. If public insurance markets are far from perfect such that market insurance is effectively unavailable and if family arrangements do not arise, then simple discounting by only the interest rate is appropriate (assuming no constraints on borrowing and lending). Between the case of perfect insurance and zero —8- ,nsurance are a range of partial insurance environments in which future streams are priced (discounted) using survival probabilities to some extent depending on the availability and pricing of particular insurance policies. The next section examines such cases. Since assessing the precise degree to which the insurance market is complete is difficult, if not impossible, we examine the As/Am ratios assuming, at one extreme, perfect insurance, and, at the other extreme, no insurance. In our view the assumption of perfect insurance is a closer approximation to the reality experienced by the RHS sample than the assumption of zero insurance. This assessment is based on the fact that 65 percent of our 1969 RHS sample of elderly couples report positive life insurance for both spouses and for another 22 percent of couples the life insurance of at least one spouse is positive. At least some of this life insurance surely represents term insurance, and, as demonstrated by Yaari (1965), buying additional life insurance is equivalent to selling an annuity. Hence, for at least those couples in which both spouses have term life insurance, one can argue that annuities were available at the margin; had these couples purchased less term insurance they would have had more annuities. In addition, the ability of parents implicitly to insure longevity risk with their children leads us to view the perfect insurance benchmark as more appropriate than the zero insurance benchmark.