Northwestern
University
Janice C. Eberly
John L. and Helen Kellogg
Distinguished Professor of Finance
Northwestern University
Current Working Papers:
·
Capital Reallocation and Growth
Joint
with Neng Wang, January 2009, current version January 2009
Version
with uncertainty, “Reallocating and pricing illiquid capital,” from the AEA
meetings, January 2009,
Introductiont: Heterogeneity is ubiquitous in firm-level
and sectoral data. Equilibrium models,
however, typically assume a representative firm, as in Andrew B. Abel and
Olivier J. Blanchard (1983). The
representative firm paradigm leaves no role for the distribution of capital. We model capital reallocation in a general
equilibrium model with two sectors.
Capital adjustment costs capture illiquidity in our model, similar to
Hirofumi Uzawa's (1969) capital installation technology. We follow Fumio
Hayashi (1982) in assuming that the production technology is linearly
homogeneous, which allows us to focus on the sectoral distribution of capital,
separately from the level of total capital.
The two sectors may have different levels of productivity, and we show
that the distribution of capital between the two sectors is the single state
variable governing investment, growth, and valuation in the economy.
We analytically characterize prices and
quantities including investment, growth, the interest rate, and the price of
capital (Tobin's q) at both aggregate and sectoral levels, along with the
effects of sectoral heterogeneity and reallocation in the economy. Without adjustment costs, capital is
immediately reallocated to the more productive sector. With adjustment costs, the central planner
optimally trades off growth against the cost of reallocating capital. Hence, reallocation to the high productivity
sector is not immediate, and reallocation itself expends resources. When the more productive sector is initially
small, investment exceeds output in the high productivity sector, so output
from the less productive sector finances growth in the more productive
sector. Nonetheless, investment and
growth optimally continue in the initially larger, low productivity sector. This occurs because, while the sector is
relatively less productive, its output can be re-invested in the other, more
productive, sector. This is more
efficient than directly un-installing capital from the less productive sector
and re-installing in the more productive sector because of adjustment
costs. The capital stock in the less
productive sector dwindles over time as its growth rate shrinks, and eventually
the economy specializes in the more productive technology. As the economy moves toward specialization,
the growth rate is non-monotonic. At
first, the aggregate growth rate falls, because more resources are expended on
reallocation, but eventually the growth rate rises as the economy specializes
in the high productivity sector. The
interest rate follows this same non-monotonic pattern, first falling and then
rising along with the aggregate growth rate because the equilibrium interest
rate must rise with the growth rate of aggregate consumption to clear the
market.
·
Optimal Inattention to the Stock Market with Information Costs and
Transactions Costs
Joint
with Andrew B. Abel and Stavros Panageas, May 2007, NBER working paper #15010, current
version May 2009
Abstract: 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.
·
Investment and Value: A Neoclassical Benchmark
Joint
with Sergio Rebelo and Nicolas Vincent, July 2006. NBER working paper #13866, [PDF file
for current version, March 2009]
Abstract:. Do investment models fit firm-level data?
- which model fits best? To answer this question we estimate alternative models
using Compustat data. We find that both a version of the Hayashi (1982) and a
model with decreasing returns to scale in production fit firm-level data very
well. Our estimates suggest that there is substantial measurement error in Q.
This measurement error implies that the investment-cash-flow regressions that
have received so much attention are ineffectual to discriminate among
alternative models. In fact, the models that we estimate generate empirically
plausible cash-flow and lagged-investment effects even though they were not
designed to produce them.
·
Investment, Valuation, and Growth Options
Joint with Andrew Abel, June 2003. [PDF file for current version, October 2005]
Abstract: 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).
·
Q for the Long Run
Joint with Andrew Abel, February 2002. [PDF
file for current version, July 2002]
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.
·
How Q and Cash Flow Affect Investment without Frictions: An Analytic
Explanation
Joint with Andrew Abel, November 2008. [PDF file for current version]
Abstract: 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. In the
spirit of Brainard and Tobin (1968),
shocks to firm growth move Q and investment together since both increase with
positive shocks to revenue growth. Similarly, shocks to current cash flow,
arising from shocks to the user cost of capital in our model, 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), but simply reflects a
common response to changes in the firm’s revenue growth.
·
Investment and q With Fixed Costs: An Empirical Analysis
Joint with Andrew Abel, revised 2002. [PDF
file for current version]
Abstract: 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.
Published Research Papers:
·
Irreversible Investment
The New Palgrave
Dictionary of Economics, Second Edition,
Eds. Steven Durlauf and Lawrence Blume, 2008
Stable URL here
Abstract: 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.
·
Optimal Inattention to the Stock Market
Joint
with Andrew B. Abel and Stavros Panageas, American Economic Review Papers
and Proceedings, May 2007
[working
paper version, as forthcoming]
Abstract: 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.
·
The Effects of Irreversibility and
Uncertainty on Capital Accumulation
Journal of
Monetary Economics 44:3, December 1999, pp. 339-377, with Andrew B. Abel
Abstract:
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
·
The Mix and Scale of
Factors with Irreversibility and Fixed Costs of Investment
Carnegie-Rochester Conference Series on Public
Policy 48,
October 1998, pp. 101-135, with Andrew B. Abel.
Abstract:
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.
Journal of
Economic Dynamics and Control 21, August 1997, pp. 831-852, with Andrew B. Abel.
Abstract:
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.
·
Multi-factor Dynamic Investment
Under Uncertainty
Journal of
Economic Theory 75(2), August 1997, pp. 345-387, with Jan van Mieghem.
Abstract: 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.
·
International Evidence on Investment and
Fundamentals
Abstract: 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.
· Options, the Value of Capital, and
Investment
Quarterly Journal of Economics 111(3), August 1996, pp.
753-777, with Andrew B. Abel, Avinash K. Dixit, and Robert S. Pindyck.
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.
·
Optimal Investment with
Costly Reversibility
The Review of Economic Studies, Vol. 63, No. 4. (Oct.,
1996), pp. 581-593, with Andrew B. Abel.
Abstract:
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.
·
Unified Model of Investment Under Uncertainty
The American Economic Review, Vol. 84, No. 5. (Dec.,
1994), pp. 1369-1384, with Andrew B. Abel.
Reprinted in Kevin
D. Hoover, Ed., The Economic
Legacy of Robert Lucas, Jr., Edward
Elgar Publishing, U.S. publication
October 1999.
[Full text
available on JSTOR]
Abstract:
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)
·
Adjustment of Consumers' Durables Stocks: Evidence from Automobile
Purchases
The Journal of Political
Economy,
Vol. 102, No. 3. (Jun., 1994), pp. 403-436.
[Full text
available on JSTOR]
Abstract:
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.
Published
Comments & Popular Publications:
· “Once you have a job offer –
what next?” AEA Committee on the Status of Women (CSWEP) Newsletter, Fall 2007.
[full text PDF]
· Time-varying Risk Premia and the Cost of Capital:
An Alternative Implication of the Q Theory of Investment, Comment, Carnegie-Rochester
Conference Series on Public Policy 2001.
· The Stock Market and
Investment in the New Economy: Some Tangible Facts and Intangible Fictions,
Comments,
Brookings Papers on Economic Activity 2000:1, pp. 109-114. [Editors' Summary of the
Volume][full
text PDF]
· On Irreversibility and
Aggregate Investment: Comment, 1993 Macroeconomics Annual, National Bureau
of Economic Research, pp. 303-312.
Finance Department
| Kellogg | Northwestern University
