Optimum Taxation of Life Annuities

The market for private life annuities is characterised by adverse selection, that is, contracts offer lower than fair payoffs to individuals with low life expectancy. Moreover, life expectancy and income have been found to be positively correlated. The paper shows that a linear tax on annuity payoffs, which raises more revenues from long-living individuals than from short-living, represents an appropriate instrument for redistribution, in addition to an optimally designed labour income tax. Further, we find that a nonlinear tax on annuity payoffs can be directly employed to correct the distortion of the rate of return caused by asymmetric information. These results are contrasted with theoretical findings concerning the role of a tax on capital income.Optimum taxation; life annuities; adverse selection

Optimum Commodity Taxation in Pooling Equilibria

This paper extends the standard model of optimum commodity taxation (Ramsey (1927) and Diamond-Mirrlees (1971)) to a competitive economy in which some markets are inefficient due to asymmetric information. As in most insurance markets, consumers impose varying costs on suppliers but firms cannot associate costs to customers and consequently all are charged equal prices. In a competitive pooling equilibrium, the price of each good is equal to average marginal costs weighted by equilibrium quantities. We derive modified Ramsey-Boiteux Conditions for optimum taxes in such an economy and show that they include general-equilibrium effects which reflect the initial deviations of producer prices from marginal costs, and the response of equilibrium prices to the taxes levied. It is shown that condition on the monotonicity of demand elasticities enables to sign the deviations from the standard formula. The general analysis is applied to the optimum taxation of annuities and life insurance.asymmetric information, pooling equilibrium, Ramsey-Boiteux Conditions, annuities

The Trick is to Live: Is the Estate Tax Social Security for the Rich?

Because estate tax liability usually depends on how long one lives, it implicitly provides annuity income. In the absence of annuity markets, lump-sum estate taxation may be used to achieve the first-best solution for individuals with a sufficiently strong bequest motive. Calculations of the annuity embedded in the U.S. estate tax show that people with $10 million of assets may be effectively receiving more than$100,000 a year financed at actuarially fair rates by their tax payments. According to my calibrations, the insurance effect reduces the marginal cost of funds (MCF) for the estate tax by as much as 30% and the resulting MCF is within the range of estimates for the marginal cost of funds for the income tax.

Differentiated Annuities in a Pooling Equilibrium

Regular annuities provide payment for the duration of an owner’s lifetime. Period-Certain annuities provide additional payment after death to a beneficiary provided the insured dies within a certain period after annuitization. It has been argued that the bequest option offered by the latter is dominated by life insurance which provides non-random bequests. This is correct if competitive annuity and life insurance markets have full information about individual longevities. In contrast, this paper shows that when individual longevities are private information, a competitive pooling equilibrium which offers annuities at common prices to all individuals may have positive amounts of both types of annuities in addition to life insurance. In this equilibrium, individuals self-select the types of annuities that they purchase according to their longevity prospects. The break-even price of each type of annuity reflects the average longevity of its buyers. The broad conclusion that emerges from this paper is that adverse-selection due to asymmetric information is reflected not only in the amounts of insurance purchased but, importantly, also in the choice of insurance products suitable for different individual characteristics. This conclusion is supported by recent empirical work about the UK annuity market (Finkelstein and Poterba (2004)).annuities, period-certain annuities, pooling equilibrium

Note on the Optimum Pricing of Annuities

In a perfectly competitive market for annuities with full information, the price of annuities is equal to individuals’ (discounted) survival probabilities. That is, prices are actuarially fair. In contrast, the pricing implicit in social security systems invariably allows for cross subsidization between different risk groups (males/females). We examine the utilitarian approach to the optimum pricing of annuities and show how the solution depends on the joint distribution of survival probailities and incomes in the population.

Estate Taxation

In this paper we examine the properties of the optimal linearestate tax in the presence of a complete set of tax instrumentsavailable to the social planner. We allow for both types of bequestmotives, namely altruistic and accidental. We examine the casefor estate taxation which seems to be the strongest (but notimpeccable) with accidental bequests. In general, the estate tax ishighly sensitive to the relative importance of the two bequestmotives.

Optimum and Risk-Class Pricing of Annuities

When information on longevity (survival functions) is unknown early in life, individuals have an interest to insure themselves against future ’risk-class’ classification. Accordingly, the First-Best typically involves transfers across states of nature. Competitive equilibrium cannot provide such transfers if insurance firms are unable to precommit their customers. On the other hand, public insurance plans that do not distinguish between ’risk-class’ realizations are also inefficient. It is impossible, a-priori, to rank these alternatives from a welfare point of view.

Longevity and Aggregate Savings

For the last fifty years, countries in Asia and elsewhere have witnessed a surge in aggregate savings per capita. Some empirical studies attribute this trend to the increases in life longevity of the populations of these countries. It has been argued that the rise in savings is short-run, eventually to be dissipated by the dissaving of the elderly, whose proportion in the population rises along with longevity. This paper examines whether these conclusions are supported by economic theory. A model of life-cycle decisions with uncertain survival is used to derive individuals' consumption and chosen retirement age response to changes in longevity from which changes in individual savings are derived. Conditions on the age-profile of improvements in survival probabilities are shown to be necessary in order to predict the direction of this response. Population theory (e.g. Coale, 1952) is used to derive the steady-state population age density function, enabling the aggregation of individual response functions and a comparative steady-state analysis. Under certain conditions, increased longevity is shown to increase aggregate savings per capita. These conclusions pertain to an economy with a competitive annuity market. The absence of such market compels individuals to leave unintended bequests, whose size depends on the (random) age of death. While an increase in longevity raises individual savings for given endowments, it is shown that the effect on expected steady-state aggregate savings, taking into account the endogenous ergodic distribution of endowments, cannot be determined a-priori.longevity, annuities, life cycle savings, retirement age, steady-state, aggregate savings

Endogenous differential mortality, non monitored effort and optimal non linear taxation

This paper studies the normative problem of redistribution among individuals who can influence their longevity through a non-monetary effort but have different taste for effort. As benchmarks, we first present the laissez-faire and the first best. In the first best, the level of effort is always lower than in the laissez-faire as the social planner takes into account the consequences of higher survival on the budget constraint. However, since we suppose that effort is private and non-monetary (like exercising), it is reasonable to think that the social planner has no control over it. Thus, we modify our framework and assume for the rest of the paper that effort is determined by the individual while the social planner only allocates consumptions. Under full information with non monitored effort, early consumption is preferred to future consumption and the high-survival individual obtains higher future consumption. Under asymmetric information, the distortion is identical for the low-survival individual while the direction of the distortion for the high-survival individual is ambiguous. We finally show how to decentralize these allocations through a perfect annuity market and (positive or negative) taxes on annuities.annuities, effort, differential mortality, non linear taxation.

Endogenous Differential Mortality, Non-Contractible Effort and Non Linear Taxation

This paper studies a problem of non linear taxation when individuals have different longevities resulting from a non-monetary effort (like exercising). We first present the laissez-faire and the first best. Like Becker and Philipson (1998), we find that the laissez-faire level of effort is too high compared with the first best, because individuals do not internalize the impact of survival on the return of their savings. We also claim that because of its non-monetary form, effort is not contractible. That is why we modify our framework and assume, for the rest of the paper, that effort is determined by the individual while the social planner only allocates consumptions. It turns out that, under full information, a tax on the return of annuitized savings is desirable for both types. This tax is higher for the low-survival individual. Under asymmetric information, the low-survival individual still faces a tax while the high-survival individual might now face a positive or negative tax on annuities. Interestingly, our results depend on the value of life.annuities, effort, differential mortality, non linear taxation, value of life