Andrew B. Abel

Risk premia and term premia in general equilibrium

The equity premium consists of a term premium reflecting the longer maturity of equity relative to short-term bills, and a risk premium reflecting the stochastic nature of equity payoffs and the deterministic nature of payoffs on reckless bills. This paper analyzes term premia and the risk premia in a general equilibrium model with catching up with the Joneses preferences and a novel formulation of leverage. Closed-form solutions for moments of asset returns are derived. First-order approximations illustrate the effects of parameters and provide an algorithm to match the means and variances of the riskless rate and the rate of return on equity.

Options, the Value of Capital, and Investment

Capital investment decisions must recognize the limitations on the firms ability to later sell or expand capacity. This paper shows how opportunities for future expansion or contraction can be valued as options, how their valuation relates to the q theory of investment, and their effect on the incentive to invest. Generally, the option to expand reduces the incentive to invest, while the option to disinvest raises it. We show how these options determine the effect of uncertainty on investment, how they are changed by shifts of the distribution of future profitability, and how the q-theory and option pricing approaches are related.

Optimal Investment with Costly Reversibility

Investment is characterized by costly reversibility when a firm can purchase capital at a given price and sell capital at a lower price. We solve for the optimal investment of a firm that faces costly reversibility under uncertainty and we extend the Jorgensonian concept of the user cost of capital to this case. We define and calculate cU and cL as the user costs of capital associated with the purchase and sale of capital, respectively. Optimality requires the firm to purchase and sell capital as needed to keep the marginal revenue product of capital in the closed interval [cL, cU). This prescription encompasses the case of irreversible investment as well as the standard neoclassical case of costlessly reversible investment.

Dynamic effects of permanent and temporary tax policies in a q model of investment

Abstract This paper incorporates the tax policy analysis of Hall and Jorgenson into a dynamic optimizing model with adjustment costs to develop a q model of investment. This framework is particularly useful for analyzing the dynamic effects on investment of permanent and temporary changes in tax policy. It is shown that, contrary to the conventional intertemporal substitution argument, a temporary investment tax credit need not be nore expansionary than a permanent investment tax credit. The role of depreciation allowances in determining the dynamic response of investment to temporary changes in the tax rate is also investigated.

Will Bequests Attenuate the Predicted Meltdown in Stock Prices When Baby Boomers Retire

Jim Poterba finds that consumers do not spend all of their assets during retirement, and he projects that the demand for assets will remain high when the baby boomers retire. Based on his forecast of continued high demand for capital, Poterba rejects the asset market meltdown hypothesis, which predicts a fall in stock prices when the baby boomers retire. I develop a rational expectations general equilibrium model with a bequest motive and an aggegate supply curve for capital. In this model, a baby boom generates an increase in stock prices, and stock prices are rationally anticipated to fall when the baby boomers retire, even though, as emphasized by Poterba, consumers do not spend all of their assets during retirement. This finding contradicts Poterbas conclusion that continued high demand for assets by retired baby boomers will prevent a fall in the price of capital.

Capital Accumulation and Uncertain Lifetimes with Adverse Selection

This paper examines the implications of adverse selection in the private annuity market for the pricing of private annuities and the consequent effects on constrption and bequest behavior. With privately known heterogeneous mortality probabilities, adverse selection causes the rate of return on private annuities to be less than the actuarially fair rate based on population average mortality. However, a fully funded social security system with compulsory participation can offer an implied rate of return equal to the actuarially fair rate based on population average mortality. Thus, since social security offers a higher rate of return than private annuities, consumers cannot completely offset the effects of social security by transacting in the private annuity market. Using an overlapping generations model with uncertain lifetimes, we demonstrate that the introduction of actuarially fair social security reduces the steady state rate of return on annuities and raises the steady state levels of average bequests and average consumption of the young. The steady state national capital stock rises or falls according to the strength of the bequest motive.

An exact solution for the investment and value of a firm facing uncertainty, adjustment costs, and irreversibility

This paper derives closed-form solutions for the investment and market value, under uncertainty, of competitive firms with constant returns to scale production and convex costs of adjustment. Solutions are derived for the case of irreversible investment as well as for reversible investment. Optimal investment is a non-decreasing function of q, the shadow value of capital. The conditions of optimality imply that q cannot contain a bubble; thus, optimal investment depends only on fundamentals. However, the value of the firm may contain a bubble that does not affect investment behavior. Relative to the case of reversible investment, the introduction of irreversibility does not affect q, but it reduces the fundamental market value of the firm.

The effects of irreversibility and uncertainty on capital accumulation

When investment decisions cannot be reversed and returns to capital are uncertain, the firm faces a higher user cost of capital than if it could reverse its decisions. This higher user cost tends to reduce the firms capital stock. Opposing this effect is the irreversibility constraint itself: when the constraint binds, the firm would like to sell capital but cannot. This effect tends to increase the firms capital stock. We show that a firm with irreversible investment may have a higher or a lower expected capital stock, even in the long run, compared to an otherwise identical firm with reversible investment. Furthermore, an increase in uncertainty can either increase or decrease the expected long-run capital stock under irreversibility relative to that under reversibility. However, changes in the expected growth rate of demand, the interest rate, the capital share in output, and the price elasticity of demand all have unambiguous effects.

A Stochastic Model of Investment, Marginal q and the Market Value of the Firm

This paper presents closed-form solutions for the investment and valuation of a competitive firm with a Cobb-Douglas production function and a constant elasticity adjustment cost function in the presence of stochastic prices for output and inputs. The value of the firm is a linear function of the capital stock. The optimal rate of investmentis an increasing function of the slope of the value function with respect to the capital stock (marginal q). A mean preserving spread of the distribution of future price increases investment. An increase in the scale of the random component of a price can increase, decrease or not affect the rate of investment depending on the sign of the covariance of this price with a weighted average of all prices.

Specification of the Joy of Giving: Insights from Altruism

This paper analyzes the joy of giving bequest motive in which the utility obtained from leaving a bequest depends only on the size of the bequest. It exploits the fact that this formulation can be interpreted as a reduced form of an altruistic bequest motive to derive a relation between the value of the altruism parameter and the value of the joy of giving parameter. Using previous discussions of an a priori range of plausible values for the altruism parameter we then derive plausible restrictions on the joy of giving parameter. We demonstrate that this parameter may well be orders of magnitude larger than assumed in the existing literature.