Professor Janice Eberly

We derive a closed-form solution for Tobin’s Q in a stochastic dynamic framework. We show analytically that investment is positively related to Tobin’s Q and cash flow, even in the absence of adjustment costs or financing frictions. Both Q and investment move in the same direction as expected revenue growth, so changes in expected revenue growth induce Q and investment to comove positively. Similarly, shocks to current cash flow, arising from shocks to the user cost of capital in ourmodel, cause investment and cash flow per unit of capital to comove positively. Furthermore, we show that this alternative mechanism for the relationship among investment, Q, and cash flow delivers larger cash flow effects for smaller and faster-growing firms, as observed in the data. Moreover, the empirically small correlation between investment and Tobin’s Q does not imply implausibly large adjustment costs in our model (since there are no adjustment costs). Calibrating the model generates values of Q similar to those in the data; investment is more sensitive to cash flow than it is to Q, and both responses are of empirically plausible magnitudes.

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.

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 diversification against the potential productivity and efficiency 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 efficiency and growth.

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 diversification against the potential productivity gains of investing more heavily in one sector. Moreover, investment depends on both the consumer's saving decision and on the reallocation of capital between sectors. These considerations, unique to the multi-sector model, result for example, in continuing investment in a "dwindling" sector, and negative dividend yields in a small, growing (or recovering) sector. Existing multisector equilibrium models assume either that capital is perfectly liquid and can be reallocated frictionlessly, as in Cox, Ingersoll, and Ross (1985), or that capital is completely illiquid and fixed, as with Lucas (1978) trees and the "two trees" model by Cochrane, Longstaff, and Santa Clara (2008). When capital is perfectly liquid as in the former, Tobin's q is one at all times and heterogeneity plays no role in equilibrium. When capital is completely illiquid as in the latter, asset prices vary but investment is zero at all times.

Which investment model best fits firm-level data? To answer this question we estimate alternative models using Compustat data. Surprisingly, the two best-performing specifications are based on Hayashi.s (1982) model. This model’s foremost implication, that Q is a sufficient statistic for determining a firm’s investment decision, has been often rejected because cash-flow and lagged-investment effects are present in investment regressions. However, we find that these regression results are quite fragile and ineffectual for evaluating model performance. So, forget what investment regressions tell you. Models based on Hayashi (1982) provide a very good description of investment behavior at the firm level.

The cost of an irreversible investment cannot be recovered once it is installed. This restriction not only truncates negative investments, but also raises the threshold for positive investment. With uncertainty, the threshold return that justifies an irreversible investment increases with uncertainty, or more precisely, with the probability mass in the lower tail of outcomes. Irreversibility constrains the ability to redeploy capital in "bad" states, so the agent is particularly sensitive to these states when investing ex ante. This finding is analagous to valuation and exercise of financial options, and irreversible investments are valued and understood using option pricing techniques.

Inattentive agents update their information sporadically, rather than continuously, and thus respond belatedly to news. We generate optimally inattentive behavior by assuming that to observe the value of his investment portfolio the consumer must pay a cost that is proportional to the portfolio's contemporaneous value. It is optimal for the consumer to check his investment portfolio at equally spaced points in time, consuming from a riskless transactions account in the interim. The riskless transactions account that finances consumption guarantees that funds are never unwittingly exhausted. We show that the optimal interval of time between consecutive observations of the value of the portfolio is the unique positive solution to a nonlinear equation. Quantitatively, even a small observation cost (one basis point of wealth) implies a substantial (8 month) decision interval under conventional parameter values.

We develop a model in which the opportunity for a firm to upgrade its technology to the frontier (at a cost) leads to growth options in the value of the firm. Variation in the technological frontier leads to variation in firm value that is unrelated to current cash flow and investment, though variation in firm value anticipates future upgrades and investment. We simulate this model and show that in situations in which growth options are important, regressions of investment on Tobin's Q and cash flow yield small positive coefficients on Q and larger coefficients on cash flow, consistent with the empirical literature. We also show that when growth options are important, the volatility of firm value can substantially exceed the volatility of cash flow, as empirically documented by Shiller (1981) and West (1988).

Abstract: Traditional Q theory relates a firm's investment to its value of Q at all frequencies; weekly or even daily fluctuations in Q should be just as informative for investment decisions as quarterly or annual data. We develop a model in which investment is more responsive to Q at long horizons than at short horizons; instantaneous investment is responsive to contemporaneous cash flow. These effects arise because a firm's value depends on both its existing capital and its available technologies, even if they are not yet installed. In contrast, the firm's current investment depends only on the currently installed technology. Thus, the value of the firm, and hence Tobin's Q, are "too forward-looking" relative to the investment decision. Cash flow, on the other hand, reflects only current technology and demand. The excessively forward-looking information in Tobin's Q, while extraneous to high-frequency investment decisions, does predict future adoptions of the frontier technology. In this way, it is a better predictor of long-run investment than of short-run investment. Short-run investment is better predicted by the firm's cash flow.

Optimal investment depends both on expected returns and the costs of acquiring and installing capital. Empirical work using q-theory has emphasized the measurement of expected returns using Tobin's q, while more recent theoretical work focuses on investment costs, particularly fixed costs and irreversibility. This paper uses panel data to estimate a model of optimal investment and disinvestment using q to measure expected returns and allowing for a general "augmented adjustment cost function" -- incorporating fixed, linear, and convex adjustment costs. The results indicate both statistically and economically important nonlinearities, potentially arising from fixed costs, in the relationship between investment/disinvestment and its determinants. Our model suggests that investment and disinvestments should not be netted out empirically, and we find that disinvestment is non-negligible and behaves differently than positive investments. The nonlinearities we find imply that the cross-sectional distribution of q affects aggregate investment, so that the nonlinear model predicts annual aggregate investment substantially more successfully than does the linear model, particularly during large cyclical fluctuations.

Irreversibility and uncertainty increase the user cost of capital which tends to reduce the capital stock. Working in the opposite direction is a hangover effect, which arises because irreversibility prevents the firm from selling capital even when the marginal revenue product of capital is low. Neither the user cost effect nor the hangover effect dominates globally, so that irreversibility may increase or decrease capital accumulation. Furthermore, an increase in uncertainty can either increase or decrease the long-run capital stock under irreversibility relative to that under reversibility. Other effects that we consider, however, have unambiguous effects on long-run capital accumulation.

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. In addition, the quasi-fixity of capital has important implications for the dynamics of employment by the firm. We show that labor hoarding can arise, even though labor is modeled as a purely flexible factor.

This paper derives closed-form solutions for the investment and value of a competitive firm with a constant-returns-to-scale production function 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. Relative to the case of reversible investment, the introduction of irreversibility does not affect q, but it reduces the fundamental value of the firm.

We characterize a firm's optimal factor adjustment when any number of factors face "kinked" linear adjustment costs so that all factor accumulation is costly to reverse. We first consider a general non-stationary case with a concave operating profit function, unrestricted form of uncertainty and a horizon of arbitrary length. We show that the optimal investment strategy follows a control limit policy at each point in time. The state space of the firm's problem is partitioned into various domains, including a continuation region where no adjustment should optimally be made to factor levels. We then consider two specific model classes and exploit their special structure to derive expressions for their continuation regions.

If a firm's 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.

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 cost 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.

Abstract: Capital investment decisions must recognize the limitations on the firm's 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.

This paper extends the theory of investment under uncertainty to incorporate fixed costs of investment, a wedge between the purchase price and sale price of capital, and potential irreversibility of investment. In this extended framework, investment is a nondecreasing function of q, the shadow price of installed capital. The optimal rate of investment is in one of three regimes (positive, zero, or negative gross investment), depending on the value of q relative to two critical values. In general however, the shadow price q is not directly observable, so we present two examples relating q to observable variables. (JEL E22)

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.