Uncertainty, Financial Frictions, and Irreversible Investment
Uncertainty, Financial Frictions, and Irreversible
Investment
Simon Gilchrist1
Jae W. Sim2
1 Boston
Egon Zakrajšek2
University and NBER
2 Federal
Reserve Board
International Monetary Fund
May 2013
D ISCLAIMER: The views expressed are solely the responsibility of the authors and should not
be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System
or of anyone else associated with the Federal Reserve System.
Uncertainty, Financial Frictions, and Irreversible Investment
Introduction
E MPIRICAL O BSERVATIONS
Economic uncertainty is time-varying and countercyclical.
Campbell et al. (2001); Storesletten et al. (2004); Eisfeldt & Rampini (2006);
Bloom (2009); Bloom et al. (2011)
Credit spreads on corporate bonds are countercyclical.
Gertler & Lown (1999); Gilchrist, Yankov & Zakrajšek (2009)
Credit spreads predict economic activity.
Philippon (2009); Gilchrist & Zakrajšek (2012); Faust et al. (2012); Bleaney et al. (2012)
Uncertainty, Financial Frictions, and Irreversible Investment
Introduction
M OTIVATION
Existing literature:
◮
Investment-uncertainty nexus motivated by irreversibility.
Bernanke (1983); Abel & Eberly (1994,1996); Caballero & Bertola (1994);
Caballero & Pindyck (1996); Bloom (2009); Bloom et al. (2011)
We examine the interaction between uncertainty and investment
in the context of imperfect financial markets and irreversibility.
We also analyze macroeconomic implications of fluctuations in
capital liquidity.
Shleifer & Vishny (1992); Eisfeldt (2004); Manso (2008)
Uncertainty, Financial Frictions, and Irreversible Investment
Introduction
U NCERTAINTY, F INANCIAL F RICTIONS & I NVESTMENT
Standard debt contract:
◮
Payoff from holding a risky bond is a concave function of the
(stochastic) project return.
Mean-preserving spread in the distribution of shocks:
◮
Perfect financial markets:
• expected defaults ↑ ⇒ credit spreads ↑ ⇒ no impact on I
◮
Imperfect financial markets:
• expected defaults ↑ ⇒ credit spreads ↑ ⇒ cost of capital ↑ ⇒ I ↓
Uncertainty, Financial Frictions, and Irreversible Investment
Introduction
O UR PAPER
Provides new empirical evidence on the link between
uncertainty, business investment, and credit spreads.
Develops a quantitative GE model that replicates key empirical
relationships in the data:
◮
◮
Embeds a costly reversible investment framework in a GE model
with frictions in both the debt and equity markets.
Generalizes previous GE frameworks.
Kiyotaki & Moore (1997); BGG (1999); Jermann & Quadrini (2009)
◮
Allows for heterogeneity across firms in the economy.
Chugh (2010); Arellano, Bai & Kehoe (2010); Kahn & Thomas (2010); Midrigan
& Xu (2010); Christiano et al. (2013)
Uncertainty, Financial Frictions, and Irreversible Investment
Introduction
K EY R ESULTS
The impact of uncertainty shocks on business investment occurs
primarily through changes in credit spreads.
Model implications in response to uncertainty shock:
◮
◮
◮
Financial frictions magnify the impact of uncertainty shocks
relative to a model with irreversible investment only.
Negative comovement between credit spreads and investment.
Positive comovement between net worth and investment.
Model also implies substantial economic fluctuations in response
to capital liquidity shocks.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
A N EW U NCERTAINTY P ROXY
There is no objective measure of uncertainty.
Informational and/or contractual frictions can generate
countercyclical dispersion of economic returns.
Eisfeldt & Rampini (2006); Jurado et al. (2013)
Use information from the stock market to infer fluctuations in
uncertainty:
◮
◮
Cross Section: 11,303 U.S. nonfinancial corporations
Time Series: July 1, 1963 to September 30, 2012
Use a standard asset pricing framework to purge our uncertainty
proxy of forecastable variation.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
T HREE -S TEP E STIMATION P ROCEDURE
Standard (linear) factor model of asset returns:
(Ritd − rtfd ) = αi + β ′i ftd + uitd
◮
Risk factors: market excess return, SMB, HML, MOM
Idiosyncratic uncertainty:
v
u
Dt
u1 X
σit = t
(ûitd − ūit )2 ;
Dt
d=1
ūit =
Dt
1 X
ûitd
Dt
d=1
Dynamic volatility model:
log σit = γi + δi t + ρ log σi,t−1 + vt + ǫit
◮
Benchmark uncertainty estimate: v̂t , t = 1, . . . , T.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
U NCERTAINTY & C REDIT S PREADS
Percent
140
Percentage points
7
Quarterly
Uncertainty (left scale)
Credit spread (right scale)
120
6
100
5
80
4
60
3
40
2
20
1
0
0
1963
1967
1971
1975
1979
1983
1987
1991
1995
1999
N OTE: Credit spread is the (nonfinancial) 10-year BBB-Treasury spread.
2003
2007
2011
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
SVAR A NALYSIS
8-variable VAR(4) system:
◮
◮
◮
◮
◮
◮
◮
◮
it = log of real business fixed investment
cDt = log of real PCE on durable goods
cNt = log of real PCE on nondurable goods & services
yt = log of real GDP
pt = log of the GDP price deflator
v̂t = economic uncertainty
st = 10-year BBB-Treasury corporate bond spread
mt = effective (nominal) federal funds rate
Implications of two types of shocks:
◮
◮
Uncertainty: orthogonalized innovations in v̂t
Financial: orthogonalized innovations in st
Identification Scheme I: (it , cDt , cNt , yt , pt , v̂t , st , mt )
Identification Scheme II: (it , cDt , cNt , yt , pt , st , v̂t , mt )
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
I MPLICATIONS OF AN U NCERTAINTY S HOCK
Identification scheme I
Business fixed investment
PCE - durables
PCE - nondurables & services
Percent
0
2
4
6
8
10
Percent
1.5
0.3
0.5
1.0
0.2
0.0
0.5
-0.5
0.0
0.0
-1.0
-0.5
-0.1
-1.5
-1.0
-0.2
-2.0
-1.5
-0.3
-2.5
-2.0
12
0
2
Quarters after shock
4
6
8
10
12
-0.4
-0.6
-0.8
10
12
8
10
12
Credit spread
-0.2
8
6
Percentage points
0.5
12
10
8
6
4
2
0
-2
0.0
6
4
Percentage points
0.2
4
2
Quarters after shock
0.4
Quarters after shock
-0.4
0
Uncertainty
Percent
2
0.1
Quarters after shock
GDP
0
Percent
1.0
0
2
4
6
8
10
12
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
0
Quarters after shock
N OTE: The shaded bands represent the 95-percent confidence intervals.
2
4
6
8
Quarters after shock
10
12
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
I MPLICATIONS OF A F INANCIAL S HOCK
Identification scheme I
Business fixed investment
PCE - durables
PCE - nondurables & services
Percent
0
2
4
6
8
10
Percent
1.5
0.3
0.5
1.0
0.2
0.0
0.5
-0.5
0.0
0.0
-1.0
-0.5
-0.1
-1.5
-1.0
-0.2
-2.0
-1.5
-0.3
-2.5
-2.0
12
0
2
Quarters after shock
4
6
8
10
12
-0.4
-0.6
-0.8
10
12
8
10
12
Credit spread
-0.2
8
6
Percentage points
0.5
12
10
8
6
4
2
0
-2
0.0
6
4
Percentage points
0.2
4
2
Quarters after shock
0.4
Quarters after shock
-0.4
0
Uncertainty
Percent
2
0.1
Quarters after shock
GDP
0
Percent
1.0
0
2
4
6
8
10
12
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
0
Quarters after shock
N OTE: The shaded bands represent the 95-percent confidence intervals.
2
4
6
8
Quarters after shock
10
12
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
I MPLICATIONS OF AN U NCERTAINTY S HOCK
Identification scheme II
Business fixed investment
PCE - durables
PCE - nondurables & services
Percent
Percent
1.0
0.3
0.5
0.5
0.2
0.0
6
8
10
-2.0
-1.5
-2.5
-2.0
12
0
2
Quarters after shock
4
6
8
10
12
-0.4
-0.6
-0.8
10
12
8
10
12
Credit spread
-0.2
8
6
Percentage points
0.5
12
10
8
6
4
2
0
-2
0.0
6
4
Percentage points
0.2
4
-0.4
2
Quarters after shock
0.4
Quarters after shock
-0.3
0
Uncertainty
Percent
2
-0.2
Quarters after shock
GDP
0
-0.1
-1.0
-1.5
4
0.0
-0.5
-1.0
2
0.1
0.0
-0.5
0
Percent
1.0
0
2
4
6
8
10
12
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
0
Quarters after shock
N OTE: The shaded bands represent the 95-percent confidence intervals.
2
4
6
8
Quarters after shock
10
12
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
I MPLICATIONS OF A F INANCIAL S HOCK
Identification scheme II
Business fixed investment
PCE - durables
PCE - nondurables & services
Percent
Percent
1.0
0.3
0.5
0.5
0.2
0.0
6
8
10
-2.0
-1.5
-2.5
-2.0
12
0
2
Quarters after shock
4
6
8
10
12
-0.4
-0.6
-0.8
10
12
8
10
12
Credit spread
-0.2
8
6
Percentage points
0.5
12
10
8
6
4
2
0
-2
0.0
6
4
Percentage points
0.2
4
-0.4
2
Quarters after shock
0.4
Quarters after shock
-0.3
0
Uncertainty
Percent
2
-0.2
Quarters after shock
GDP
0
-0.1
-1.0
-1.5
4
0.0
-0.5
-1.0
2
0.1
0.0
-0.5
0
Percent
1.0
0
2
4
6
8
10
12
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
0
Quarters after shock
N OTE: The shaded bands represent the 95-percent confidence intervals.
2
4
6
8
Quarters after shock
10
12
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
F IRM -L EVEL PANEL A NALYSIS
Examine the link between uncertainty, credit spreads, and
business investment using a firm-level panel dataset.
CRSP/Compustat panel of U.S. nonfinancial firms matched with
prices of outstanding corporate bonds traded in the secondary
market.
Lehman/Warga & Merrill Lynch issue-level data:
◮
◮
◮
◮
◮
Sample period: Jan1973–Sep2012 (month-end)
1,164 U.S. nonfinancial issuers
6,725 senior unsecured, fixed-coupon issues
385,062 bond/month observations
Information: price, issue date, maturity, coupon, issue size, etc.
SummaryStatistics
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
U NCERTAINTY & C REDIT S PREADS
Credit-spread regression:
log sit [k] = β1 log σit + β2 REit + β3 [Π/A]it
+ β4 log[D/E]i,t−1 + θ ′ Xit [k] + ǫit [k]
◮
◮
◮
◮
◮
sit [k] = credit spread on bond k (issued by firm i)
[D/E]it = debt-to-equity ratio
REit = realized return on equity
[Π/A]it = OIBDA-to-assets ratio
Xit [k] = bond-specific control variables
(par value, coupon, duration, age, callable indicator)
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
U NCERTAINTY & C REDIT S PREADS
Explanatory Variable
log σit
REit
[Π/A]it
log[D/E]i,t−1
Adjusted R2
p-value: credit rating effects
p-value: industry effects
p-value: time effects
(1)
(2)
(3)
(4)
0.730
(0.041)
-0.095
(0.026)
-4.100
(0.698)
0.212
(0.024)
0.474
-
0.459
(0.046)
-0.112
(0.025)
-1.835
(0.502)
0.056
(0.013)
0.641
0.000
-
0.484
(0.049)
-0.109
(0.024)
-1.500
(0.475)
0.049
(0.013)
0.648
0.000
0.000
-
0.216
(0.021)
-0.053
(0.009)
-1.318
(0.385)
0.078
(0.011)
0.797
0.000
0.000
0.000
N OTE: Robust standard errors in parentheses.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
U NCERTAINTY, C REDIT S PREADS & I NVESTMENT
Investment regression:
log[I/K]it = β1 log σit + β2 log sit + θ log Zit + ηi + λt + ǫit
Investment fundamentals (Z):
◮
◮
◮
◮
[Y/K]it = sales-to-capital ratio
[Π/K]it = operating-income-to-capital ratio
Qit = Tobin’s Q
[I/K]i,t−1 = lagged investment rate
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
U NCERTAINTY, C REDIT S PREADS & I NVESTMENT
Static specification
Explanatory Variable
(1)
(2)
(3)
(4)
(5)
(6)
-0.169
(0.036)
-
-0.081
(0.034)
-
-0.157
(0.034)
-
-
-
0.022
(0.033)
-0.172
(0.021)
-
-0.062
(0.034)
-0.152
(0.021)
-
log[Π/K]it
0.558
(0.046)
-
-
-
-
1.075
(0.088)
-
-
log Qi,t−1
1.166
(0.086)
-
-0.036
(0.035)
-0.206
(0.021)
0.535
(0.045)
-
0.325
0.307
0.349
0.323
log σit
log sit
log[Y/K]it
R2 (within)
N OTE: Robust standard errors in parentheses.
0.715
(0.040)
0.297
0.645
(0.041)
0.310
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
U NCERTAINTY, C REDIT S PREADS & I NVESTMENT
Dynamic specification
Explanatory Variable
(1)
(2)
(3)
(4)
(5)
(6)
-0.272
(0.062)
-
-0.179
(0.059)
-
-0.199
(0.060)
-
0.576
(0.023)
-
0.538
(0.029)
-
-0.078
(0.054)
-0.068
(0.031)
0.567
(0.023)
-
-0.106
(0.057)
-0.080
(0.032)
0.535
(0.023)
-
log[Π/K]it
0.568
(0.028)
0.446
(0.056)
-
-
-
0.908
(0.135)
-
-
log Qi,t−1
0.918
(0.144)
-
-0.123
(0.057)
-0.101
(0.031)
0.565
(0.027)
0.452
(0.053)
-
log σit
log sit
log[I/K]i,t−1
log[Y/K]it
N OTE: Robust standard errors in parentheses.
0.548
(0.045)
-
0.507
(0.042)
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Summary
S UMMARY OF E MPIRICAL E VIDENCE
Three stylized facts:
◮
◮
◮
Fluctuations in uncertainty can have a large effect on aggregate
investment.
The impact of uncertainty on business investment occurs largely
through changes in credit spreads.
Financial shocks have a strong effect on aggregate investment,
irrespective of the level of uncertainty.
Implications: Financial frictions are an important part of the
transmission mechanism through which fluctuations in
uncertainty are propagated to the real economy.
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
AGENTS & T ECHNOLOGICAL E NVIRONMENT
Representative household: consumes, works, and saves by
investing in stocks and corporate bonds.
Heterogeneous firms: use DRS technology to produce
final-good output and accumulate capital.
◮
◮
◮
Production subject to persistent aggregate and idiosyncratic
technology shocks.
Volatility of idiosyncratic technology shocks is time varying.
Nonconvex capital adjustment costs:
• fixed costs
• costly reversibility ⇒ purchase price of capital > sale price of
capital
◮
Liquidation value of capital follows a stochastic process ⇒
capital liquidity shocks.
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
R EPRESENTATIVE H OUSEHOLD
The household earns a competitive real market wage w by
working h hours and saves by purchasing bonds and equity
shares of firms in the economy.
Household preferences:
u(c, h) =
c1−θ − 1
h1+ϑ
−ζ
;
1−θ
1+ϑ
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
P RODUCTION T ECHNOLOGY
Decreasing returns-to-scale and fixed costs of production:
y = (az)(1−α)χ (kα h1−α )χ − Fo k
◮
◮
◮
◮
a = aggregate technology shock
z = idiosyncratic technology shock
χ = degree of DRS in production
Fo = fixed operation costs
Profits are linear in a and z:
n
o
π(a, z, w, k) = max (az)(1−α)χ (kα h1−α )χ − Fo k − wh
h
= azψ(w)kγ − Fo k
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
T ECHNOLOGY S HOCKS
Aggregate technology shock:
log a′ = ρa log a + log ǫ′a ;
ǫ′a ∼ N(−0.5ωa2 , ωa2 )
Idiosyncratic technology shock: N-state Markov chain process
with time-varying volatility
log σz′ = (1 − ρσ ) log σ̃z + ρσ log σz + ǫ′σ ;
◮
◮
ǫ′σ ∼ N(−0.5ωσ2 , ωσ2 )
Fluctuations in σz do not affect the conditional expectation of z′ .
An increase in σz represent a mean-preserving spread of z′ .
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
C APITAL ACCUMULATION
Nonconvex capital adjustment:
p(k′ , k) = Fk k × 1[k′ 6= (1 − δ)k]
◮
◮
◮
◮
+ p+ × 1[k′ ≥ (1 − δ)k]
+ p− × 1[k′ ≤ (1 − δ)k] k′ − (1 − δ)k
Fk = fixed investment adjustment costs
p+ = purchase price of capital
p− = liquidation price of capital
p− /p+ < 1 ⇒ capital specificity
Liquidation price of capital p− :
log p−′ = (1 − ρp− ) log p̃− + ρp− log p− + ǫ′p−
◮
log ǫ′p− ∼ N(−0.5ωκ2 , ωκ2 ) = capital liquidity shock
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
F INANCIAL D ISTORTIONS
Moral hazard and limited liability in credit markets.
Issuance costs in equity markets.
Implications:
◮
◮
Full set of capital structure choices (i.e., debt vs. equity vs.
internal funds)
Strategic default and debt renegotiation (i.e., Chapter 11
bankruptcy)
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
N ET W ORTH
Realized net worth next period equals the sum of net profits and
the market value of undepreciated capital less the face value of
debt:
n′ = a′ z′ ψ(w(s′ ))k′γ − Fo k′ + p−′ (1 − δ)k′ − b′ .
◮
The value of capital follows a stochastic process and entails a
discount in the amount of 1 − p−′ /p+ .
Net liquid asset position:
x′ (σz ) ≡ a′ z′ (σz )ψ(w′ )k′γ − Fo k′ − b′ = n′ (σz ) − p−′ (1 − δ)k′
Value of the firm: v = vi (k, x; s)
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
E NDOGENOUS D EFAULT
Limited liability: lower bound on net worth n̄
Default level of idiosyncratic technology, conditional on the next
period’s aggregate state s′ and individual state (k′ , b′ ):
zD (k′ , b′ ; s′ ) ≡
n̄ + b′ + Fk k′ − p−′ (1 − δ)k′
a′ ψ(w′ )k′γ
Set of default states:
D = j | j ∈ {1, . . . , N} and z′j (σz ) ≤ zD (k′ , b′ ; s′ )
Firm defaults if and only if z′j (σz ) ∈ D
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
D EBT R ENEGOTIATION
With limited liability, renegotiated debt equals the amount
consistent with the lower bound of the net worth n̄:
bR ≤ b̄(k′ , z′ (σz ); s′ ) ≡ a′ zD (σz )ψ(w′ )k′γ − Fo k′ + p−′ (1 − δ)k′
No bargaining power for firm implies the maximum recovery in
equilibrium:
bR = b̄(k′ , z′ (σz ); s′ )
◮
Subject to bankruptcy costs: ξ(1 − δ)k′ ;
0<ξ<1
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
B OND F INANCING
Recovery rate in the case of default:
R(k′ , b′ , z′ (σz ); s′ ) =
b̄(k′ , z′ (σz ), s′ )
k′
− ξ(1 − δ) ′
′
b
b
Bond price:
qi (k′ , b′ ; s′ ) = E




m(s, s′ ) 1 +
X
j∈D
pi,j
 

R(k′ , b′ , z′j (σz ); s′ ) − 1  s

Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
E QUITY F INANCING
Letting e represent equity issuance, then dividends satisfy:
d ≡ azi ψ(w)kγ − Fo k − p(k′ , k) − b + qi (k′ , b′ ; s′ )b′ + e
Frictions in equity market:
◮
Dividend constraint:
d ≥ d̄ ≥ 0
◮
Equity dilution costs:
ϕ̄(e) ≡ e + ϕ max{e, 0};
0<ϕ<1
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Recursive Problem
F IRM VALUE M AXIMIZATION P ROBLEM
Discrete choice problem:
where
−
vi (k, x; s) = max v+
i (k, x; s), vi (k, x; s) ,
+
vi (k, x; s) = min
φ,λ+
max
d+ ,e+ ,k+ ,b+

+ ηE m(s, s′ )
vi (k, x; s) = min
−
φ,λ−
N
X
max
+ ηE m(s, s′ )
d+ + φ(d+ − d) − ϕ̄(e+ ) + λ+ [k+ − (1 − δ)k]
pi,j max vj (k+ , x+ (σz ); s′ ), vj (k+ , xR+ (σz ); s′ )
j=1
d− ,e− ,k− ,b−

(

s
(
N
X
j=1
d− + φ(d− − d) − ϕ̄(e− ) − λ− [k− − (1 − δ)k]
pi,j max vj (k− , x− (σz ); s′ ), vj (k− , xR− (σz ); s′ )

s
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
O PTIMAL C APITAL S TRUCTURE
FOC: equity issuance:
1 + φ = 1 + ϕ × 1[e > 0]
FOC: debt issuance:
qi (k′ , b′ ; s) + qi,b (k′ , b′ ; s)b′
=
=

ηE m(s, s′ )

ηE m(s, s′ )
X
pi,j
pi,j
j∈D c
X
j∈D c
′
1+φ
1+φ

s
′
1 + ϕ × 1(e > 0)
1 + ϕ × 1(e > 0)

s
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
O PTIMAL C APACITY C HOICE
Capital expansion problem
"
Qi (k, x; s) = ηE m(s, s′ )
+
N
X
pi,j
j=1
′
× πj,k (k ; s ) + (1 −
+
1 + φ′j
1 + φi
δ)Q′j (k+ , x′ (σz ); s′ )
s
#
+ qi,k (k+ , b+ ; s)b+


′
X
1
+
φ
j
πj,k (k+ ; s′ ) + (1 − δ)p−′ s
− ηE m(s, s′ )
pi,j
1 + φi
j∈D
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
O PTIMAL C APACITY C HOICE
Capital contraction problem
"
Qi (k, x; s) = ηE m(s, s′ )
−
N
X
pi,j
j=1
′
× πj,k (k ; s ) + (1 −
−
1 + φ′j
1 + φi
δ)Q′j (k− , x′ (σz ); s′ )
s
#
+ qi,k (k− , b− ; s)b−


′
X
1
+
φ
j
πj,k (k− ; s′ ) + (1 − δ)p−′ s
− ηE m(s, s′ )
pi,j
1 + φi
j∈D
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
T OBIN ’ S Q
Tobin’s Q:
λ+
+
−
+
i (k, x; s)
Qi (k, x; s) = min p , max p , p −
1 + φi (k, x; s)
λ−
i (k, x; s)
= min p+ , max p− , p− +
1 + φi (k, x; s)
◮
◮
With partial irreversibility, Q is still monotonic and nonincreasing
in k, but truncated from above by p+ and below by p− .
With fixed investment adjustment costs, Q is no longer
monotonic.
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
O PTIMAL I NVESTMENT P OLICY
Generalized (S, s) policy:
ki′ (k, x; s) = min ki− (k, x; s), max{ki+ (k, x; s), (1 − δ)k}
(S, s) capital targets: ki− (k, x; s), ki+ (k, x; s) are functions of the
firm’s overall financial condition (k, x).
Ss-Policy-1
Ss-Policy-2
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Closing the Model
H OUSEHOLDS
Household maximization problem:
W(s) = ′max
u(c, h) + βE[W(s′ )| s]
′
b ,s ,c,h
subject to a budget constraint,
Z
Z
b
′
′
c+
qb + pS s µ(dz, dk, dx) = wh +
R̃ + (d + p̃S )s µ(dz, dk, dx)
Z
+ Fo kµ(dz, dk, dx).
where
R̃b ≡ 1 + 1(z ∈ D(k, b, z)) × [R(k, b, z(σz )) − 1] b
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Closing the Model
DYNAMIC E FFICIENCY C ONDITIONS
Consistency between firm and household problems.
Ex-dividend value of equity:
′ ′ ′
u (c , h ) ′
′
′ ′ ′ ′ ′
d − ϕ̄(e ) + pS (k , x , z ; s ) z, s
pS (k, x, z; s) = E β
u(c, h)
Price of bond:
q(k′ , b′ , z; s) =
′ ′ ′
u (c , h ) ′
′ ′ ′ ′
′ ′ ′ ′ ′
E β
1 + 1[z ∈ D (k , b ; s )] × [R (k , b , z ; s ) − 1] z, s
u(c, h)
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Aggregation
M ARKET C LEARING
Market-clearing conditions:
Stock market:
Labor market:
Goods market:
s′ = s =Z1
hs (s) = hd (z, k; s)µ(dz, dk, dx)
Z
c(s) = y(z, k, h; s)µ(dz, dk, dx)
Z
− p(k′ (k, x, z; s), k)µ(dz, dk, dx)
Bond market clears by Warlas’ law.
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Aggregation
L AW OF M OTION FOR µ
µ is the join distribution of z ∈ Z, k ∈ K, and x ∈ X:
µ′ (Z, K, X, s′ ) =
Z
1[zj ∈ Z] × 1[ki′ ∈ K] × 1[xj′ (ki′ , min{b′i , bR }, s) ∈ X]
× pi,j µ(dz, dk, dx, s)G(s, ds′ )
Solution method for GE models with heterogeneous agents:
Krusell & Smith (1998)
◮
Agents use only a finite number of momments of µ to forecast
equilibrium prices.
Uncertainty, Financial Frictions, and Irreversible Investment
Calibration
M ODEL C ALIBRATION
Idiosyncratic productivity process:
log Yit = θ log Ki,t−1 + ηi + λst + uit
uit = ρz ui,t−1 + ǫit
◮
α = 0.3 and θ̂ = 0.65 ⇒ DRS parameter χ = 0.85
Idiosyncratic uncertainty process:
r
π
log
|ǫ̂it | = γi + +σt + ζit
2
◮
◮
Estimate: σ̂t = µ + ρσ σ̂t−1 + et
Calibration: σ̃ = 0.15; ρσ = 0.90; ωσ = 0.04
Uncertainty, Financial Frictions, and Irreversible Investment
Calibration
U NCERTAINTY BASED ON P ROFITABILITY S HOCKS
Percent
60
Percentage points
7
Quarterly
Uncertainty (left scale)
Credit spread (right scale)
50
6
5
40
4
3
30
2
20
1
10
0
1977
1980
1983
1986
1989
1992
1995
1998
2001
2004
2007
2010
Uncertainty, Financial Frictions, and Irreversible Investment
Calibration
C ALIBRATION ( CONT.)
Resale price of capital: p̃− = 0.5; ρp− = 0.98; ωκ = 0.015
Purchase price of capital: p+ = 1
Bankruptcy costs: ξ = 0.10
Equity flotation cost: ϕ = 0.12
Survival probability: η = 0.946
Quasi-fixed operating cost: Fo = 0.05
Fixed costs of capital adjustment: Fk = 0.01
Depreciation rate: δ = 0.045
Time discount factor: β = 0.989
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
I MPACT OF AN AGGREGATE T ECHNOLOGY S HOCK
Output, pct.
Consumption, pct.
Investment, pct.
Hours worked, pct.
12
0.8
1
10
0.8
0.6
8
0.6
0.4
6
0.4
0.4
0.2
4
0.2
0.2
2
0
0
0
20
40
−2
0
Risk−free rate, bps.
25
0
0
−0.2
−0.2
20
40
0
Debt/Capital, pps.
20
40
0.1
0
0.6
0.4
20
0.2
0
0
−5
0
20
40
Inactive firms, pps.
40
0
−0.1
40
0.8
60
5
20
1
80
10
0
100
0.2
15
−0.2
Credit spreads, bps.
0.3
20
−10
0.6
0
20
40
−20
−0.2
0
20
N OTE: Model w/ financial frictions. Model w/o financial frictions.
40
0
20
40
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
C ONDITIONAL B USINESS C YCLE M OMENTS
Aggregate technology shocks only
Relative Volatility
Model Specification
With financial frictions
Without financial frictions
Memo: Data
STD(I)
STD(C)
STD(H)
STD(Y)
2.60
2.90
2.79
0.95
0.98
0.43
0.12
0.12
0.60
2.47
2.32
1.12
Comovements
Model Specification
With financial frictions
Without financial frictions
Memo: Data
Corr(I, Y)
Corr(C, Y)
Corr(H, Y)
Corr(C, I)
0.63
0.53
0.63
0.99
0.99
0.56
0.46
0.22
0.65
0.54
0.53
0.43
N OTE: All variables are expressed in deviations from their respective steady-state values.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
I MPACT OF AN U NCERTAINTY S HOCK
Output, pct.
Consumption, pct.
0.1
0.3
0
0.2
−0.1
Investment, pct.
0
0
0.1
−0.2
−0.2
−5
0
−0.3
−0.1
−0.4
−0.5
Hours worked, pct.
0.2
0
20
40
−0.2
−0.4
−0.6
−10
0
Risk−free rate, bps.
20
40
0
Debt/Capital, pps.
20
40
−0.8
Credit spreads, bps.
20
40
Inactive firms, pps.
5
0.1
200
4
0
0
150
3
−0.1
100
2
−0.2
50
1
−20
−0.3
0
−25
−0.4
−5
0
−10
−15
0
20
40
0
20
40
0
0
20
N OTE: Model w/ financial frictions. Model w/o financial frictions.
40
−1
0
20
40
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
C ONDITIONAL B USINESS C YCLE M OMENTS
Uncertainty shocks only
Relative Volatility
Model Specification
With financial frictions
Without financial frictions
Memo: Data
STD(I)
STD(C)
STD(H)
STD(Y)
13.5
14.6
2.79
0.63
0.63
0.43
0.88
0.71
0.60
0.23
0.10
1.12
Comovements
Model Specification
With financial frictions
Without financial frictions
Memo: Data
Corr(I, Y)
Corr(C, Y)
Corr(H, Y)
Corr(C, I)
0.65
0.76
0.63
0.49
0.71
0.56
0.78
0.78
0.65
-0.33
0.10
0.43
N OTE: All variables are expressed in deviations from their respective steady-state values.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
I MPACT OF A C APITAL L IQUIDITY S HOCK
Output, pct.
Consumption, pct.
Investment, pct.
0.4
0
Hours worked, pct.
5
0.1
0.5
0
0.2
−0.1
0
−5
−0.2
0
−10
−0.3
−0.4
−0.2
−0.5
0
20
40
−0.4
0
Risk−free rate, bps.
20
0
−20
−40
−0.5
−15
20
40
−20
0
Debt/Capital, pps.
20
40
−1
Credit spreads, bps.
0.5
100
0
80
2
−0.5
60
1.5
−1
40
1
−1.5
20
0.5
−2
0
0
−2.5
−20
−0.5
40
0
20
40
40
Inactive firms, pps.
−80
20
20
2.5
−60
0
0
0
20
N OTE: Model w/ financial frictions. Model w/o financial frictions.
40
0
20
40
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
C ONDITIONAL B USINESS C YCLE M OMENTS
Capital Liquidity shocks only
Relative Volatility
Model Specification
With financial frictions
Without financial frictions
Memo: Data
STD(I)
STD(C)
STD(H)
STD(Y)
6.71
14.3
2.79
0.60
0.63
0.42
0.55
0.69
0.60
1.11
0.09
1.12
Comovements
Model Specification
With financial frictions
Without financial frictions
Memo: Data
Corr(I, Y)
Corr(C, Y)
Corr(H, Y)
Corr(C, I)
0.61
0.78
0.63
0.88
0.73
0.56
0.86
0.78
0.65
0.16
0.14
0.43
N OTE: All variables are expressed in deviations from their respective steady-state values.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
Properties of Credit Spreads
C YCLICAL P ROPERTIES OF C REDIT S PREADS
Conditional on the Type of Shock
Selected Correlations
Corr(S, Y)
Corr(S, I)
Corr(S, C)
Corr(S, NW)
Corr(STD(S), Y)
Technology
Uncertainty
Liquidity
Data
0.927
0.626
0.916
-0.813
0.933
-0.811
-0.515
-0.368
0.802
-0.832
-0.938
-0.577
-0.816
-0.703
-0.950
-0.457
-0.531
-0.498
-0.297
-0.245
CreditSpreads
N OTE: All variables are expressed in deviations from their respective steady-state values.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
Conclusion
C ONCLUDING R EMARKS
Financial market frictions have an important effect on the
investment-uncertainty nexus.
The presence of financial market frictions significantly amplifies
the response of investment and output to both uncertainty and
liquidity shocks.
An important extension of our framework would involve
endogenizing the price of capital.
Uncertainty, Financial Frictions, and Irreversible Investment
Appendix
S UMMARY S TATISTICS
Selected bond characteristics
Bond Characteristic
Mean
StdDev
Min
Median
Max
# of bonds per firm/month
Mkt. value of issue (millions, $2005)
Maturity at issue (years)
Term to maturity (years)
Duration (years)
Credit rating (S&P)
Coupon rate (pct.)
Nominal effective yield (pct.)
Credit spread (bps.)
2.99
339.9
12.8
11.1
6.49
7.06
7.23
202
3.69
338.9
9.2
8.5
3.28
2.14
2.98
223
1.00
1.22
1.0
1.0
0.91
D
0.60
0.22
5
2.00
249.2
10.0
8.0
6.03
BBB1
6.88
6.92
128
76.0
5,628
50.0
30.0
18.0
AAA
17.5
30.0
2,000
Back
Uncertainty, Financial Frictions, and Irreversible Investment
Appendix
(S, s) I NVESTMENT P OLICY F UNCTION
Partial irreversibility only
5
k(t+1)
4
3
2
1
5
8
0
6
4
−5
2
x(t), net liquid assets
Back
−10
0
k(t), capital
Uncertainty, Financial Frictions, and Irreversible Investment
Appendix
(S, s) I NVESTMENT P OLICY F UNCTION
Partial irreversibility and fixed adjustment costs
6
k(t+1)
5
4
3
2
1
5
8
0
6
4
−5
2
x(t), net liquid assets
Back
−10
0
k(t), capital
Uncertainty, Financial Frictions, and Irreversible Investment
Appendix
C ORPORATE B OND C REDIT S PREADS
Percentage points
10
Monthly
Median
Interquartile range
8
6
4
2
0
1973
Back
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
2012