Janice C. Eberly

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.

Adjustment of Consumers' Durables Stocks: Evidence from Automobile Purchases

This paper tests an optimal (S, s) rule in household durable purchases and examines directly the resulting aggregate expenditure dynamics. The observed decision rule responds to income uncertainty and growth as predicted by an (S, s) model resulting from transactions costs. Tests against liquidity constraints find that about half the households purchase according to an optimal (S, s) rule. Aggregating the (S, s) rule over households produces a cross-section distribution of durables holdings. The empirical distribution is similar to that predicted theoretically, as is its response to aggregate shocks. Furthermore, simulations of aggregate expenditure based on the household distribution exhibit dynamics consistent with those observed in the 1980s.

International evidence on investment and fundamentals

Abstract If a firms costs of installing capital are not quadratic, then its optimal investment is not a linear function of fundamentals, such as the returns and costs of capital. This study specifies a model in which a firm may face fixed, linear, and convex costs of investing, and estimates the resulting investment function using firm-level data from 11 countries. The evidence suggests important nonlinearities, consistent with the presence of fixed or other non-quadratic costs, in the relationship between investment and fundamentals for most countries. These findings are statistically signficant at the level of the firm, and economically significant when aggregated by country.

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.

Optimal inattention to the stock market with information costs and transactions costs

Recurrent intervals of inattention to the stock market are optimal if consumers incur a utility cost to observe asset values. When consumers observe the value of their wealth, they decide whether to transfer funds between a transactions account from which consumption must be financed and an investment portfolio of equity and riskless bonds. Transfers of funds are subject to a transactions cost that reduces wealth and consists of two components: one is proportional to the amount of assets transferred, and the other is a fixed resource cost. Because it is costly to transfer funds, the consumer may choose not to transfer any funds on a particular observation date. In general, the optimal adjustment rule—including the size and direction of transfers, and the time of the next observation—is state-dependent. Surprisingly, unless the fixed resource cost of transferring funds is large, the consumer’s optimal behavior eventually evolves to a situation with a purely time-dependent rule with a constant interval of time between observations. This interval of time can be substantial even for tiny observation costs. When this situation is attained, the standard consumption Euler equation holds between observation dates if the consumer is sufficiently risk averse.

The Mix and Scale of Factors with Irreversibility and Fixed Costs of Investment

When factors of production can be adjusted costlessly, the mix of factors can be considered separately from their scale. We examine factor choice and utilization when investment is irreversible and subject to a fixed cost, so that the capital stock is a quasi-fixed factor that is adjusted infrequently and by discrete amounts. We derive and analyze analytic approximations for optimal investment behavior, and show how the quasi-fixity of capital eliminates the dichotomy between factor mix and scale. We show that the quasi-fixity of capital can give rise to labor hoarding, even when labor is a purely flexible factor.

Efficient Credit Policies in a Housing Debt Crisis

Consumption, income, and home prices fell simultaneously during the financial crisis, compounding recessionary conditions with liquidity constraints and mortgage distress. We develop a framework to guide government policy in response to crises in cases when government may intervene to support distressed mortgages. Our results emphasize three aspects of efficient mortgage modifications. First, when households are constrained in their borrowing, government resources should support household liquidity up-front. This implies modifying loans to reduce payments during the crisis rather than reducing payments over the life of the mortgage contract, such as via debt reduction. Second, while governments will not find it efficient to directly write down the debt of borrowers, in many cases it will be in the best interest of lenders to do so, because reducing debt is an effective way to reduce strategic default. Moreover, the lenders who bear the credit default risk have a direct incentive to partially write down debt and avoid a full loan loss due to default. Finally, a well-designed mortgage contract should take these considerations into account, reducing payments during recessions and reducing debt when home prices fall. We propose an automatic stabilizer mortgage contract which does both by converting mortgages into lower-rate adjustable-rate mortgages when interest rates fall during a downturn—reducing payments and lowering the present value of borrowers’ debt.

Reallocating and Pricing Illiquid Capital: Two Productive Trees

We develop a two sector general equilibrium model with capital accumulation and convex adjustment costs. We use the model to study capital asset pricing and reallocation, as well as optimal consumption and investment decisions. With two sectors, the consumer balances diversication against the potential productivity and eciency gains of investing more heavily in one sector. The general framework nests and extends standard equilibrium macro-asset pricing models. We show conditions under which aggregates are immune to the distribution of capital and in contrast, when the distribution becomes crucial for both sectoral and aggregate values. Applications of the framework highlight the importance of heterogeneity and capital liquidity - the ability to reallocate capital - for economic growth and asset pricing. Misallocated capital creates risk and reduces utility, but correcting it through capital reallocation reduces eciency and growth.