THE United States estate tax raises little revenue. In 2000, it is projected to generate approximately $30 billion.(1) Nevertheless, the tax engenders many complaints. Particularly vocal are the owners of family businesses, who bemoan the fact that estate taxes prevent them from passing their enterprises onto their children. Thus, for example, Daisy Crowder, the owner of a small construction company with her husband, pointed out that they had "plowed the earnings from their business for years into equipment, building, land, and other assets to help expand." As a result, they had little cash or other liquid wealth, and she was fearful that her four children "would be forced to sell some or all of the business to pay the [estate tax] bill when she and her husband died" (Stevenson, 1997). A case that recently made headlines concerned John Senstacke, the owner of the nation's largest chain of African-American newspapers. Senstacke and his children all wanted to keep the business in the family. But, when Mr. Senstacke died, his estate's tax liability was $4 million. The estate did not have enough cash to pay the bill, and the children feared that parts of the chain would have to be sold off to pay the taxes (Christian, 1998). More generally, a Wall Street Journal editorial lamented, "You and your heirs [build your] business together. But when you depart this earth, those heirs often find they have to dissolve your legacy, just to pay the tax bill on it."(2)
The discussion sometimes becomes quite emotional. The president of the National Federation of Independent Business argued that, because of the estate tax, people who "are dealing with the death of a loved one [also] have the IRS coming in and trying to rip what's left out of the heart of the family" (Stevenson, 1997). Surveys of small businesses suggest that these concerns are widespread. For example, a survey by Travis Research Associates (1995) noted that 65% of the interviewed family-business owners indicated that the federal estate tax would make survival of the family business significantly more difficult or impossible.
As one considers both the overheated rhetoric and the survey results, a natural question is what role, if any, life insurance plays in this situation. Might a business owner who is concerned that estate taxes will force liquidation of his business simply purchase enough life insurance to pay the taxes? A survey conducted by Arthur Andersen (1997) indicated that more than two-thirds of family business owners expected life insurance to be the primary source of funds to cover estate taxes. But the Andersen sample included only firms with annual sales in excess of a million dollars, and what is true for such large enterprises may not be true for smaller ones: "smaller businesses don't generate the surpluses necessary to be socked away in life insurance policies" (Jenkins, 1997). Even if a business owner purchases insurance, it may not be enough to cover the estate tax. After all, the market value of a business is often difficult to estimate, leading to problems in predicting estate tax liability (Bosland, 1963). (Of course, such uncertainty could equally well induce business owners to purchase excessive life insurance.) Indeed, even individuals with illiquid assets other than a business might want to use life insurance to help meet their estate tax liability.
To what extent do people use life insurance to provide the wherewithal to meet estate tax liabilities? We know of no econometric research aimed at answering this question.(3) The purpose of this paper is to examine whether and how people use life insurance to deal with the estate tax. We focus particularly on business owners because of the aforementioned concerns that the illiquid nature of their assets makes the estate tax particularly harmful to them.
In section II, we sketch the analytic underpinnings of our analysis. In section III, we discuss the data and present some preliminary evidence. Section IV motivates the econometric specification and reports our results. We find that, other things being the same, business owners purchase more life insurance than do other individuals. However, on the margin, their insurance purchases are less responsive to estate tax considerations, and they are less likely to have the wherewithal to meet estate tax liabilities with only liquid assets plus insurance. The final section provides a summary and conclusions.
II. Analytic Preliminaries
Our focus is on the incentives to employ life insurance as a means to meet the cash-flow requirements of the estate tax. To fix ideas, suppose that the business owner has a total wealth of W, consisting of B in business assets and L of liquid assets (W = B + L). The individual obtains utility both from passing along her wealth (including business assets) in the event of death and consuming her wealth during life. If [Pi] is the probability of death, the goal is to maximize expected utility:
(1) (1 - [Pi])U([W.sub.1]) + [Pi]V([W.sub.d])
where U([W.sub.1]) is the utility of wealth to be enjoyed if the individual lives, and V([W.sub.d]) is the utility of wealth transferred in the event of death. The V([multiplied by]) function depends, inter alia, on the individual's wealth relative to his heir's wealth and the degree of altruism. We assume that both U([multiplied by]) and V([multiplied by]) display diminishing marginal utility, implying that the individual is averse to fluctuations in wealth. As shown below, this is important for motivating a demand for life insurance. Although, the setting in equation (1) is static, one should note that both the U([multiplied by]) and V([multiplied by]) functions would be expected to depend on the individual's stage of the lifecycle.
The presence of the estate tax raises the possibility that the individual will not be able to pass along the entire business as part of [W.sub.d]. Specifically, if the tax liability, T, exceeds liquid assets, then the estate is forced to liquidate the business or sell off part of it to meet the tax liability.(4) However, by their nature, the business assets are illiquid and have greater value in place than upon liquidation, requiring the sacrifice of more than a dollar of business value in order to obtain each dollar for the tax collector.(5) Alternatively, the individual could purchase life insurance, I, at a price, p, to meet the estate tax. The motivation for purchasing life insurance rather than just saving more is the same as the motivation for buying any insurance: the presence of uncertainty may make it a cheaper way to meet the objective. This depends, in part, on the price of life insurance. Previous research has indicated that the load factors for life insurance are substantial (Fischer, 1973).
In any case, by purchasing insurance, the individual reduces liquid wealth:
(2) L = L - pI.
(3) [W.sub.l] = B + L - pI.
Although the purchase of insurance decreases [W.sub.l], it reduces cash-flow constraints associated with the estate tax. Specifically,
(4) [W.sub.d] = B + L + I - T - [Psi][T - (L + I)]
where [Psi] is a positive constant that reflects the penalty for liquidating business assets.(6) In practice, the determinants of [Psi] are quite complex. For example, certain provisions of the law allow estate tax payments on some businesses to be stretched out over a number of years. This would tend to reduce (but not eliminate) liquidation penalties.(7) Further, it may be easier to borrow against certain types of business assets than others. Finally, the opportunity cost of liquidation may depend on the heirs' willingness actually to run the operation.
For simplicity, assume that the estate tax is levied at a proportional rate [Tau] on a base that equals the sum of business assets (B), liquid assets (L), and insurance (I)
(5) T = [Tau][B + L + I],
(6) [W.sub.d] = B(1 - (1 + [Psi])[Tau])
+ [L+(1 - p)I](1 + [Psi])(1 - [Tau]).
The solution to the problem of optimal purchase of insurance is
(7) (1 - [Pi])U'([W.sub.l])p [is greater than or equal to] [Pi]V'([W.sub.d)(1 + [Psi]) X (1 - [Tau])(1 - p).
Expression (7) holds with equality when the individual chooses to buy insurance, and holds with inequality when the price of insurance is too high relative to its benefits. Thus, as suggested above, if life insurance is sufficiently unfair, the individual will not purchase it.
Assuming now for simplicity that insurance is priced on an actuarially fair basis (p = [Pi]) we can reduce the condition for an interior maximum to(8)
(8) U' ([W.sub.l]) = V' ([W.sub.d])(1 + [Psi])(1 - [Tau]).
Intuitively, the left side of equation (8) is the utility lost by giving up a dollar to obtain insurance. This dollar of life insurance generates two benefits, which appear on the right side. The first is simply the transfer of $1 to the beneficiary; the second is the value of relaxing the cash-flow constraint.
In the empirical analysis to follow, we focus on the extent to which insurance is used to fill the gap between tax liability and liquid assets, conditional upon the individual's net wealth, health status, the structure of the estate tax, and so forth. In the terms of the simple framework we have developed, we seek to estimate how the individual's insurance decision changes when the gap, G(= T - L), changes for fixed values of W, [Pi], and [Tau]. To interpret such a conceptual experiment within our framework, notice that a $1 reduction in liquid assets, (L), that is offset by a $1 increase in business assets, (B), leaves the individual's net wealth and estate tax liability, (T), unchanged, although it generates a $1 increase in the gap between tax liability and liquid assets plus insurance. Thus, our interest is in
(9) [differential]I/[differential]G [equivalent] [differential]I/[differential]B - [differential]I/[differential]L (1 + [Psi])(1 - [Tau])V"([W.sub.d])[(1 + [Psi])(1 - [Tau]) - (1 - (1 + [Psi])[Tau])]/U"([W.sub.l])p + [(1 + [Psi]).sup.2] V"([W.sub.d])(1 - p)
Expression (9) is unambiguously positive under our assumption that [Psi] [is greater than] 0 (provided that there is not a corner solution).(9) Importantly, this result implies only that we expect individuals to purchase more insurance as the gap increases, not that they should necessarily buy enough insurance to fill the gap.
Our discussion has focused on the illiquid nature of business assets, but the same considerations apply to other illiquid assets, such as housing. Thus, although one might expect concerns about illiquidity and estate taxes to be most pronounced for owners of small businesses, they may be present more generally. Indeed, to the extent that various provisions in the law allow deferral of the estate taxes on some small businesses, we might actually expect liquidity issues to …