Miles S. Kimball

Background Risk, Prudence, and the Demand for Insurance

This paper addresses the question of whether uninsurable background risk will lead people to buy more insurance against other risks that are insurable. The conditions of decreasing absolute risk aversion and decreasing absolute prudence on the utility function and either statistical independence or a general condition indicating a positive relationship between the background risk and the other risk are shown to be enough to guarantee that background risk will increase the optimal amount of insurance against the other risk. In particular, background risk raises the optimal coinsurance rate and reduces the optimal level of the deductible (for any given coinsurance rate).

Making sense of two-sided altruism

Abstract Recursive dependence of altruistic utility on the utility of both children and parents is analyzed. Given reasonable restrictions on the extent of altruism, it is shown that in the static steady state of a simple overlapping generations model there will be some interval around the Golden Rule in which the economy responds to marginal changes just as would a Diamond economy. Dynamic inefficiency cannot be ruled out even in the presence of two-sided altruism. When per-capita income and consumption are growing at a constant rate, the gift motive can insure dynamic efficiency for some parameter values.

Taxation of Labor Income and the Demand for Risky Assets

The effect of uninsured labor income risk on the joint saving/portfolio composition decision is analyzed using new techniques from the theory of multiple risk-bearing. Applying this analysis, the effect of labor income taxes on the demand for risky securities is considered. It is well known that when private insurance markets are incomplete, the insurance afforded by labor income taxes can reduce overall saving. This paper establishes that - given plausible restrictions on preferences - the insurance afforded by labor income taxes increases the demand for risky securities, even when labor income is statistically independent of the returns to risky securities.

The effect of demand uncertainty on a precommitted monopoly price

Under plausible conditions on the shape of a monopolist’s or a monopolistic competitor’s cost function, multiplicative demand uncertainty is shown to raise the firm’s optimal precommitted price. It is argued that this effect can be substantial.

The Decline of Drudgery and the Paradox of Hard Work

We develop a theory that focuses on the general equilibrium and long-run macroeconomic consequences of trends in job utility. Given secular increases in job utility, work hours per capita can remain approximately constant over time even if the income effect of higher wages on labor supply exceeds the substitution effect. In addition, secular improvements in job utility can be substantial relative to welfare gains from ordinary technological progress. These two implications are connected by an equation flowing from optimal hours choices: improvements in job utility that have a significant effect on labor supply tend to have large welfare effects.

Negative Interest Rate Policy as Conventional Monetary Policy

As long as all interest rates move in tandem – including the rate of return on paper currency – economic theory suggests no important difference between interest rate changes in the positive region and interest rate changes in the negative region. Indeed, in standard models, only the real interest rate and spreads between real interest rates matter. Thus, in most respects, negative interest rate policy is conventional. It is only (a) what needs to be done with paper currency, (b) difficulties in understanding negative rates or (c) institutional features interacting with negative rates that make negative interest rate policy unconventional.

Portfolio Rebalancing in General Equilibrium

Standard portfolio advice is that agents should hold a constant share of risky assets. All agents cannot, however, follow this advice because supply and demand of risky assets must be equal. To study equilibrium rebalancing, the paper develops an overlapping generations model in which agents differ both in age and risk tolerance. Equilibrium rebalancing is driven by a leverage effect that affects levered and unlevered agents in opposite directions, an aggregate risk tolerance effect which depends on the distribution of wealth, and an intertemporal hedging effect. Optimal equilibrium portfolio rebalancing departs significantly from the standard advice.

Social Security, Retirement and Wealth: Theory and Implications

The effect of Social Security rules on the age people choose to retire can be critical in evaluating proposed changes to those rules. This research derives a theory of retirement that views retirement as a special type of labor supply decision. This decision is driven by wealth and substitution effects on labor supply, interacting with a fixed cost of working that makes low hours of work unattractive. The theory is tractable analytically, and therefore well-suited for analyzing proposals that affect Social Security. This research examines how retirement age varies with generosity of Social Security benefits. A ten-percent reduction in the value of benefits would lead individuals to postpone retirement by between one-tenth and one-half a year. Individuals who are relatively buffered from the change—because they are wealthier or because they are younger and therefore can more easily increase saving to offset the cut in benefits— will have smaller changes in their retirement ages. Authors’ Acknowledgements This work was supported by a grant from the Social Security Administration through the Michigan Retirement Research Center (Grant #10-P-98358-5). The opinions and conclusions are solely those of the authors and should not be considered as representing the opinions or policy of the Social Security Administration or any agency of the Federal Government. The authors gratefully acknowledge this support.

Toward a Systematic Approach to the Economic Effects of Risk: Characterizing Utility Functions: Toward a Systematic Approach

The Diffidence Theorem, together with complementary tools, can aid in illuminating a broad set of questions about how to mathematically characterize the set of utility functions with specified economic properties. This paper establishes the technique and illustrates its application to many questions, old and new. For example, among many other older and other technically more difficult results, it is shown that (1) several implications of globally greater risk aversion depend on distinct mathematical properties when the initial wealth level is known, (2) whether opening up a new asset market increases or decreases saving depends on whether the reciprocal of marginal utility is concave or convex, and (3) whether opening up a new asset market raises or lowers risk aversion towards small independent risks depends on whether absolute risk aversion is convex or concave.

The importance of precautionary motives in explaining individual and aggregate saving* A comment

Glenn Hubbard, Jonathan Skinner, and Stephen Zeldes take up the difficult but important task of doing a realistic life-cycle model of saving that incorporates the effects of uncertainty and of uncertainty in interaction with social insurance. They have a maintained assumption that private income insurance is not available and that health insurance is incomplete. This puts the model in more or less the same “world” as the models of Barsky, Mankiw, and Zeldes (1986), Zeldes (1989), and Kimball (1990). The assumption of incomplete income or medical insurance seems on solid ground to me.’ There are four things going on in this model: the effects of (1) lifespan risk, (2) medical expense risk, (3) 1 a b or income risk, and (4) means-tested social insurance. Let me address each in turn. Lifespan risk. From Hubbard, Skinner, and Zeldes’ tables, it is apparent that lifespan risk is not doing very much, given the particular parameters they choose. An illustrative calculation suggests why they are getting so little action from lifespan risk. In Blanchard’s (1985) overlapping generations model with a constant death rate S, when the real interest rate is constant at r, the (marginal and)