Uncertainty, Financial Frictions, and Irreversible Investment
Uncertainty, Financial Frictions, and IrreversibleInvestment
Simon Gilchrist1 Jae W. Sim2 Egon Zakrajsek2
1Boston University and NBER
2Federal Reserve Board
International Monetary FundMay 2013
DISCLAIMER: 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
EMPIRICAL OBSERVATIONS
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 & Zakrajsek (2009)
Credit spreads predict economic activity.Philippon (2009); Gilchrist & Zakrajsek (2012); Faust et al. (2012); Bleaney et al. (2012)
Uncertainty, Financial Frictions, and Irreversible Investment
Introduction
MOTIVATION
Existing literature:◮ Investment-uncertainty nexus motivated byirreversibility.
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 investmentin the context ofimperfect financial marketsandirreversibility.
We also analyze macroeconomic implications of fluctuations incapital liquidity.Shleifer & Vishny (1992); Eisfeldt (2004); Manso (2008)
Uncertainty, Financial Frictions, and Irreversible Investment
Introduction
UNCERTAINTY, FINANCIAL FRICTIONS & I NVESTMENT
Standard debt contract:◮ Payoff from holding a risky bond is aconcavefunction of the
(stochastic) project return.
Mean-preserving spread in the distribution of shocks:◮ Perfectfinancial markets:
• expected defaults↑ ⇒ credit spreads↑ ⇒ no impact onI◮ Imperfectfinancial markets:
• expected defaults↑ ⇒ credit spreads↑ ⇒ cost of capital↑ ⇒ I ↓
Uncertainty, Financial Frictions, and Irreversible Investment
Introduction
OUR PAPER
Provides new empirical evidence on the link betweenuncertainty, business investment, and credit spreads.Develops a quantitative GE model that replicates key empiricalrelationships in the data:
◮ Embeds a costly reversible investment framework in a GE modelwith 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
KEY RESULTS
The impact of uncertainty shocks on business investment occursprimarily through changes in credit spreads.Model implications in response to uncertainty shock:
◮ Financial frictions magnify the impact of uncertainty shocksrelative to a model with irreversible investment only.
◮ Negativecomovement between credit spreads and investment.◮ Positivecomovement between net worth and investment.
Model also implies substantial economic fluctuations in responseto capital liquidity shocks.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
A NEW UNCERTAINTY PROXY
There is no objective measure of uncertainty.
Informational and/or contractual frictions can generatecountercyclical dispersion of economic returns.Eisfeldt & Rampini (2006); Jurado et al. (2013)
Use information from the stock market to infer fluctuations inuncertainty:
◮ 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 uncertaintyproxy of forecastable variation.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
THREE-STEP ESTIMATION PROCEDURE
Standard (linear) factor model of asset returns:
(Ritd − rftd) = αi + β′
iftd + uitd
◮ Risk factors: market excess return, SMB, HML, MOM
Idiosyncratic uncertainty:
σit =
√
√
√
√
1Dt
Dt∑
d=1
(uitd − uit)2; uit =1Dt
Dt∑
d=1
uitd
Dynamic volatility model:
logσit = γi + δit + ρ logσi,t−1 + vt + ǫit
◮ Benchmark uncertainty estimate: vt, t = 1, . . . ,T.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
UNCERTAINTY & CREDIT SPREADS
0
20
40
60
80
100
120
140
1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007 20110
1
2
3
4
5
6
7Percent Percentage points
Uncertainty (left scale)Credit spread (right scale)
Quarterly
NOTE: Credit spread is the (nonfinancial) 10-year BBB-Treasury spread.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
SVAR ANALYSIS
8-variable VAR(4) system:◮ it = log of real business fixed investment◮ cD
t = log of real PCE on durable goods◮ cN
t = log of real PCE on nondurable goods & services◮ yt = log of real GDP◮ pt = log of the GDP price deflator◮ vt = 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 invt◮ Financial: orthogonalized innovations inst
Identification Scheme I: (it, cDt , c
Nt , yt, pt, vt, st,mt)
Identification Scheme II: (it, cDt , c
Nt , yt, pt, st, vt,mt)
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
IMPLICATIONS OF AN UNCERTAINTY SHOCKIdentification scheme I
0 2 4 6 8 10 12-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
Business fixed investment
0 2 4 6 8 10 12-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
Business fixed investment
Quarters after shock 0 2 4 6 8 10 12
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5Percent
PCE - durables
0 2 4 6 8 10 12-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5Percent
PCE - durables
Quarters after shock 0 2 4 6 8 10 12
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3Percent
PCE - nondurables & services
0 2 4 6 8 10 12-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3Percent
PCE - nondurables & services
Quarters after shock
0 2 4 6 8 10 12-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4Percent
GDP
0 2 4 6 8 10 12-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4Percent
GDP
Quarters after shock 0 2 4 6 8 10 12
-2
0 2 4
6 81012
Percentage points
Uncertainty
0 2 4 6 8 10 12
-2
0 2 4
6 81012
Percentage points
Uncertainty
Quarters after shock 0 2 4 6 8 10 12
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5Percentage points
Credit spread
0 2 4 6 8 10 12-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5Percentage points
Credit spread
Quarters after shock
NOTE: The shaded bands represent the 95-percent confidence intervals.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
IMPLICATIONS OF A FINANCIAL SHOCKIdentification scheme I
0 2 4 6 8 10 12-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
Business fixed investment
0 2 4 6 8 10 12-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
Business fixed investment
Quarters after shock 0 2 4 6 8 10 12
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5Percent
PCE - durables
0 2 4 6 8 10 12-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5Percent
PCE - durables
Quarters after shock 0 2 4 6 8 10 12
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3Percent
PCE - nondurables & services
0 2 4 6 8 10 12-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3Percent
PCE - nondurables & services
Quarters after shock
0 2 4 6 8 10 12-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4Percent
GDP
0 2 4 6 8 10 12-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4Percent
GDP
Quarters after shock 0 2 4 6 8 10 12
-2
0 2 4
6 81012
Percentage points
Uncertainty
0 2 4 6 8 10 12
-2
0 2 4
6 81012
Percentage points
Uncertainty
Quarters after shock 0 2 4 6 8 10 12
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5Percentage points
Credit spread
0 2 4 6 8 10 12-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5Percentage points
Credit spread
Quarters after shock
NOTE: The shaded bands represent the 95-percent confidence intervals.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
IMPLICATIONS OF AN UNCERTAINTY SHOCKIdentification scheme II
0 2 4 6 8 10 12-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
Business fixed investment
0 2 4 6 8 10 12-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
Business fixed investment
Quarters after shock 0 2 4 6 8 10 12
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
PCE - durables
0 2 4 6 8 10 12-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
PCE - durables
Quarters after shock 0 2 4 6 8 10 12
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3Percent
PCE - nondurables & services
0 2 4 6 8 10 12-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3Percent
PCE - nondurables & services
Quarters after shock
0 2 4 6 8 10 12-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4Percent
GDP
0 2 4 6 8 10 12-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4Percent
GDP
Quarters after shock 0 2 4 6 8 10 12
-2
0 2 4
6 81012
Percentage points
Uncertainty
0 2 4 6 8 10 12
-2
0 2 4
6 81012
Percentage points
Uncertainty
Quarters after shock 0 2 4 6 8 10 12
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5Percentage points
Credit spread
0 2 4 6 8 10 12-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5Percentage points
Credit spread
Quarters after shock
NOTE: The shaded bands represent the 95-percent confidence intervals.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Macro-Level Evidence
IMPLICATIONS OF A FINANCIAL SHOCKIdentification scheme II
0 2 4 6 8 10 12-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
Business fixed investment
0 2 4 6 8 10 12-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
Business fixed investment
Quarters after shock 0 2 4 6 8 10 12
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
PCE - durables
0 2 4 6 8 10 12-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0Percent
PCE - durables
Quarters after shock 0 2 4 6 8 10 12
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3Percent
PCE - nondurables & services
0 2 4 6 8 10 12-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3Percent
PCE - nondurables & services
Quarters after shock
0 2 4 6 8 10 12-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4Percent
GDP
0 2 4 6 8 10 12-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4Percent
GDP
Quarters after shock 0 2 4 6 8 10 12
-2
0 2 4
6 81012
Percentage points
Uncertainty
0 2 4 6 8 10 12
-2
0 2 4
6 81012
Percentage points
Uncertainty
Quarters after shock 0 2 4 6 8 10 12
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5Percentage points
Credit spread
0 2 4 6 8 10 12-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5Percentage points
Credit spread
Quarters after shock
NOTE: The shaded bands represent the 95-percent confidence intervals.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
FIRM-LEVEL PANEL ANALYSIS
Examine the link between uncertainty, credit spreads, andbusiness investment using afirm-level panel dataset.
CRSP/Compustat panel of U.S. nonfinancial firms matched withprices of outstanding corporate bonds traded in the secondarymarket.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
UNCERTAINTY & CREDIT SPREADS
Credit-spread regression:
logsit[k] = β1 logσit + β2REit + β3[Π/A]it
+ β4 log[D/E]i,t−1 + θ′Xit[k] + ǫit[k]
◮ sit[k] = credit spread on bondk (issued by firmi)◮ [D/E]it = debt-to-equity ratio◮ RE
it = 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
UNCERTAINTY & CREDIT SPREADS
Explanatory Variable (1) (2) (3) (4)
logσit 0.730 0.459 0.484 0.216(0.041) (0.046) (0.049) (0.021)
REit -0.095 -0.112 -0.109 -0.053
(0.026) (0.025) (0.024) (0.009)[Π/A]it -4.100 -1.835 -1.500 -1.318
(0.698) (0.502) (0.475) (0.385)log[D/E]i,t−1 0.212 0.056 0.049 0.078
(0.024) (0.013) (0.013) (0.011)AdjustedR2 0.474 0.641 0.648 0.797p-value: credit rating effects - 0.000 0.000 0.000p-value: industry effects - - 0.000 0.000p-value: time effects - - - 0.000
NOTE: Robust standard errors in parentheses.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
UNCERTAINTY, CREDIT SPREADS& I NVESTMENT
Investment regression:
log[I/K]it = β1 logσit + β2 logsit + θ logZit + 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
UNCERTAINTY, CREDIT SPREADS& I NVESTMENTStatic specification
Explanatory Variable (1) (2) (3) (4) (5) (6)
logσit -0.169 -0.081 -0.157 -0.036 0.022 -0.062(0.036) (0.034) (0.034) (0.035) (0.033) (0.034)
logsit - - - -0.206 -0.172 -0.152(0.021) (0.021) (0.021)
log[Y/K]it 0.558 - - 0.535 - -(0.046) (0.045)
log[Π/K]it - 1.166 - - 1.075 -(0.086) (0.088)
logQi,t−1 - - 0.715 - - 0.645(0.040) (0.041)
R2 (within) 0.325 0.307 0.297 0.349 0.323 0.310
NOTE: Robust standard errors in parentheses.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Micro-Level Evidence
UNCERTAINTY, CREDIT SPREADS& I NVESTMENTDynamic specification
Explanatory Variable (1) (2) (3) (4) (5) (6)
logσit -0.272 -0.179 -0.199 -0.123 -0.078 -0.106(0.062) (0.059) (0.060) (0.057) (0.054) (0.057)
logsit - - - -0.101 -0.068 -0.080(0.031) (0.031) (0.032)
log[I/K]i,t−1 0.568 0.576 0.538 0.565 0.567 0.535(0.028) (0.023) (0.029) (0.027) (0.023) (0.023)
log[Y/K]it 0.446 - - 0.452 - -(0.056) (0.053)
log[Π/K]it - 0.918 - - 0.908 -(0.144) (0.135)
logQi,t−1 - - 0.548 - - 0.507(0.045) (0.042)
NOTE: Robust standard errors in parentheses.
Uncertainty, Financial Frictions, and Irreversible Investment
Empirics
Summary
SUMMARY OF EMPIRICAL EVIDENCE
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 thetransmission mechanism through which fluctuations inuncertainty are propagated to the real economy.
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
AGENTS& T ECHNOLOGICAL ENVIRONMENT
Representative household: consumes, works, and saves byinvesting in stocks and corporate bonds.Heterogeneous firms: use DRS technology to producefinal-good output and accumulate capital.
◮ Production subject to persistentaggregateandidiosyncratictechnology shocks.
◮ Volatility of idiosyncratic technology shocks istime 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 liquidityshocks.
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
REPRESENTATIVEHOUSEHOLD
The household earns a competitive real market wagew byworking h hours and saves by purchasing bonds and equityshares of firms in the economy.
Household preferences:
u(c, h) =c1−θ − 1
1− θ− ζ
h1+ϑ
1+ ϑ;
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
PRODUCTION TECHNOLOGY
Decreasing returns-to-scale and fixed costs of production:
y = (az)(1−α)χ(kαh1−α)χ − Fok◮ a = aggregate technology shock◮ z = idiosyncratic technology shock◮ χ = degree of DRS in production◮ Fo = fixed operation costs
Profits are linear ina andz:
π(a, z,w, k) = maxh
{
(az)(1−α)χ(kαh1−α)χ − Fok − wh}
= azψ(w)kγ − Fok
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
TECHNOLOGY SHOCKS
Aggregate technology shock:
loga′ = ρa loga + logǫ′a; ǫ′a ∼ N(−0.5ω2a, ω
2a)
Idiosyncratic technology shock:N-state Markov chain processwith time-varyingvolatility
logσ′z = (1−ρσ) log σz +ρσ logσz + ǫ′σ; ǫ′σ ∼ N(−0.5ω2
σ, ω2σ)
◮ Fluctuations inσz do not affect the conditional expectation ofz′.◮ An increase inσz represent amean-preserving spreadof z′.
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Economic Evironment
CAPITAL ACCUMULATION
Nonconvex capital adjustment:
p(k′, k) = Fkk × 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+ = purchaseprice of capital◮ p− = liquidationprice of capital◮ p−/p+ < 1 ⇒ capital specificity
Liquidation price of capitalp−:
logp−′ = (1− ρp−) log p− + ρp− logp− + ǫ′p−
◮ logǫ′p− ∼ N(−0.5ω2κ, ω
2κ) = capital liquidityshock
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
FINANCIAL DISTORTIONS
Moral hazard and limited liability in credit markets.
Issuance costs in equity markets.Implications:
◮ Full set of capital structure choices (i.e., debt vs. equityvs.internal funds)
◮ Strategic default and debt renegotiation (i.e., Chapter 11bankruptcy)
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
NET WORTH
Realized net worth next period equals the sum of net profits andthe market value of undepreciated capital less the face value ofdebt:
n′ = a′z′ψ(w(s′))k′γ − Fok′ + p−′(1− δ)k′ − b′.
◮ The value of capital follows a stochastic process and entails adiscount in the amount of 1− p−′/p+.
Net liquid asset position:
x′(σz) ≡ a′z′(σz)ψ(w′)k′γ − Fok′ − 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
ENDOGENOUSDEFAULT
Limited liability: lower bound on net worthn
Default level of idiosyncratic technology, conditional on the nextperiod’s aggregate states′ and individual state (k′, b′):
zD(k′, b′; s′) ≡n + b′ + Fkk′ − p−′(1− δ)k′
a′ψ(w′)k′γ
Set of default states:
D ={
j | j ∈ {1, . . . ,N} andz′j(σz) ≤ zD(k′, b′; s′)}
Firm defaults if and only ifz′j(σz) ∈ D
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
DEBT RENEGOTIATION
With limited liability, renegotiated debt equals the amountconsistent with the lower bound of the net worthn:
bR ≤ b(k′, z′(σz); s′) ≡ a′zD(σz)ψ(w′)k′γ − Fok′ + p−′(1− δ)k′
No bargaining power for firm implies the maximum recovery inequilibrium:
bR = b(k′, z′(σz); s′)
◮ Subject tobankruptcy costs: ξ(1− δ)k′; 0< ξ < 1
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
BOND FINANCING
Recovery rate in the case of default:
R(k′, b′, z′(σz); s′) =b(k′, z′(σz), s′)
b′− ξ(1− δ)
k′
b′
Bond price:
qi(k′, b′; s′) = E
m(s, s′)
1+∑
j∈D
pi,j[
R(k′, b′, z′j(σz); s′)− 1]
∣
∣
∣s
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Financial Markets
EQUITY FINANCING
Letting e represent equity issuance, then dividends satisfy:
d ≡ aziψ(w)kγ − Fok − p(k′, k)− b + qi(k
′, b′; s′)b′ + e
Frictions in equity market:◮ Dividend constraint:
d ≥ d ≥ 0
◮ Equity dilution costs:
ϕ(e) ≡ e + ϕmax{e,0}; 0< ϕ < 1
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Recursive Problem
FIRM VALUE MAXIMIZATION PROBLEMDiscrete choice problem:
vi(k, x; s) = max{
v+
i (k, x; s), v−
i (k, x; s)}
,
where
v+
i (k, x; s) = minφ,λ+
maxd+,e+,k+,b+
{
d+ + φ(d+ − d)− ϕ(e+) + λ+[k+ − (1− δ)k]
+ ηE
m(s, s′)N∑
j=1
pi,j max{
vj(k+, x+(σz); s′), vj(k
+, xR+(σz); s′)}
∣
∣
∣s
v−
i (k, x; s) = minφ,λ−
maxd−,e−,k−,b−
{
d− + φ(d− − d)− ϕ(e−)− λ−[k− − (1− δ)k]
+ ηE
m(s, s′)N∑
j=1
pi,j max{
vj(k−, x−(σz); s′), vj(k
−, xR−(σz); s′)}
∣
∣
∣s
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
OPTIMAL CAPITAL STRUCTURE
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′)∑
j∈Dc
pi,j
(
1+ φ′
1+ φ
)
∣
∣
∣s
= ηE
m(s, s′)∑
j∈Dc
pi,j
(
1+ ϕ× 1(e′ > 0)1+ ϕ× 1(e > 0)
)
∣
∣
∣s
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
OPTIMAL CAPACITY CHOICECapital expansion problem
Q+
i (k, x; s) = ηE
[
m(s, s′)N∑
j=1
pi,j
(
1+ φ′j1+ φi
)
×[
πj,k(k+; s′) + (1− δ)Q′
j(k+, x′(σz); s′)
]
∣
∣
∣s
]
+ qi,k(k+, b+; s)b+
− ηE
m(s, s′)∑
j∈D
pi,j
(
1+ φ′j1+ φi
)
[
πj,k(k+; s′) + (1− δ)p−′
]
∣
∣
∣s
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
OPTIMAL CAPACITY CHOICECapital contraction problem
Q−
i (k, x; s) = ηE
[
m(s, s′)N∑
j=1
pi,j
(
1+ φ′j1+ φi
)
×[
πj,k(k−; s′) + (1− δ)Q′
j(k−, x′(σz); s′)
]
∣
∣
∣s
]
+ qi,k(k−, b−; s)b−
− ηE
m(s, s′)∑
j∈D
pi,j
(
1+ φ′j1+ φi
)
[
πj,k(k−; s′) + (1− δ)p−′
]
∣
∣
∣s
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
TOBIN’ S Q
Tobin’s Q:
Qi(k, x; s) = min
{
p+,max
{
p−, p+ −λ+
i (k, x; s)1+ φi(k, x; s)
}}
= min
{
p+,max
{
p−, p− +λ−
i (k, x; s)1+ φi(k, x; s)
}}
◮ With partial irreversibility,Q is still monotonic and nonincreasingin k, but truncated from above byp+ and below byp−.
◮ With fixed investment adjustment costs,Q is no longermonotonic.
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Optimality Conditions
OPTIMAL INVESTMENT POLICY
Generalized(S, s) policy:
k′i(k, x; s) = min{
k−
i (k, x; s),max{k+
i (k, x; s), (1− δ)k}}
(S, s) capital targets:k−
i (k, x; s), k+
i (k, x; s) are functions of thefirm’s overall financial condition(k, x).
Ss-Policy-1 Ss-Policy-2
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Closing the Model
HOUSEHOLDS
Household maximization problem:
W(s) = maxb′,s′,c,h
{
u(c, h) + βE[W(s′)| s]}
subject to a budget constraint,
c +∫
(
qb′ + pSs′)
µ(dz, dk, dx) = wh +
∫
[
Rb + (d + pS)s]
µ(dz, dk, dx)
+
∫
Fokµ(dz, dk, dx).
where
Rb ≡[
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 EFFICIENCY CONDITIONS
Consistency between firm and household problems.
Ex-dividend value of equity:
pS(k, x, z; s) = E
[
βu′(c′, h′)u(c, h)
[
d′ − ϕ(e′) + p′S(k′, x′, z′; s′)
]
∣
∣
∣z, s
]
Price of bond:
q(k′, b′, z; s) =
E
[
βu′(c′, h′)u(c, h)
[
1+ 1[z′ ∈ D′(k′, b′; s′)]× [R′(k′, b′, z′; s′)− 1]]
∣
∣
∣z, s
]
Uncertainty, Financial Frictions, and Irreversible Investment
Model
Aggregation
MARKET CLEARING
Market-clearing conditions:
Stock market: s′ = s = 1
Labor market: hs(s) =∫
hd(z, k; s)µ(dz, dk, dx)
Goods market: c(s) =∫
y(z, k, h; s)µ(dz, dk, dx)
−
∫
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
LAW OF MOTION FORµ
µ is the join distribution ofz ∈ Z, k ∈ K, andx ∈ X:
µ′(Z,K,X, s′) =∫
1[zj ∈ Z]× 1[k′i ∈ K]× 1[x′j(k′i ,min{b′i , b
R}, s) ∈ X]
× pi,jµ(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 ofµ to forecastequilibrium prices.
Uncertainty, Financial Frictions, and Irreversible Investment
Calibration
MODEL CALIBRATION
Idiosyncratic productivity process:
logYit = θ logKi,t−1 + ηi + λst + uit
uit = ρzui,t−1 + ǫit
◮ α = 0.3 andθ = 0.65⇒ DRS parameterχ = 0.85
Idiosyncratic uncertainty process:
log
[√
π
2|ǫit|
]
= γi ++σt + ζit
◮ Estimate:σt = µ+ ρσσt−1 + et◮ Calibration:σ = 0.15;ρσ = 0.90;ωσ = 0.04
Uncertainty, Financial Frictions, and Irreversible Investment
Calibration
UNCERTAINTY BASED ON PROFITABILITY SHOCKS
10
20
30
40
50
60
1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 20100
1
2
3
4
5
6
7Percent Percentage points
Uncertainty (left scale)Credit spread (right scale)
Quarterly
Uncertainty, Financial Frictions, and Irreversible Investment
Calibration
CALIBRATION (CONT.)
Resale price of capital:p− = 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
IMPACT OF AN AGGREGATETECHNOLOGY SHOCK
0 20 40
−0.2
0
0.2
0.4
0.6
0.8
1
Output, pct.
0 20 40
−0.2
0
0.2
0.4
0.6
0.8
Consumption, pct.
0 20 40
−2
0
2
4
6
8
10
12Investment, pct.
0 20 40−0.2
0
0.2
0.4
0.6Hours worked, pct.
0 20 40−10
−5
0
5
10
15
20
25Risk−free rate, bps.
0 20 40−0.1
0
0.1
0.2
0.3Debt/Capital, pps.
0 20 40−20
0
20
40
60
80
100Credit spreads, bps.
0 20 40
−0.2
0
0.2
0.4
0.6
0.8
1
Inactive firms, pps.
NOTE: Model w/ financial frictions.Model w/o financial frictions.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
CONDITIONAL BUSINESSCYCLE MOMENTSAggregate technology shocks only
Relative Volatility
Model Specification STD(I) STD(C) STD(H) STD(Y)
With financial frictions 2.60 0.95 0.12 2.47Without financial frictions 2.90 0.98 0.12 2.32Memo: Data 2.79 0.43 0.60 1.12
Comovements
Model Specification Corr(I, Y) Corr(C, Y) Corr(H, Y) Corr(C, I)
With financial frictions 0.63 0.99 0.46 0.54Without financial frictions 0.53 0.99 0.22 0.53Memo: Data 0.63 0.56 0.65 0.43
NOTE: 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
IMPACT OF AN UNCERTAINTY SHOCK
0 20 40−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1Output, pct.
0 20 40−0.2
−0.1
0
0.1
0.2
0.3Consumption, pct.
0 20 40
−10
−5
0
Investment, pct.
0 20 40−0.8
−0.6
−0.4
−0.2
0
0.2Hours worked, pct.
0 20 40−25
−20
−15
−10
−5
0
5Risk−free rate, bps.
0 20 40−0.4
−0.3
−0.2
−0.1
0
0.1Debt/Capital, pps.
0 20 40
0
50
100
150
200Credit spreads, bps.
0 20 40−1
0
1
2
3
4Inactive firms, pps.
NOTE: Model w/ financial frictions.Model w/o financial frictions.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
CONDITIONAL BUSINESSCYCLE MOMENTSUncertainty shocks only
Relative Volatility
Model Specification STD(I) STD(C) STD(H) STD(Y)
With financial frictions 13.5 0.63 0.88 0.23Without financial frictions 14.6 0.63 0.71 0.10Memo: Data 2.79 0.43 0.60 1.12
Comovements
Model Specification Corr(I, Y) Corr(C, Y) Corr(H, Y) Corr(C, I)
With financial frictions 0.65 0.49 0.78 -0.33Without financial frictions 0.76 0.71 0.78 0.10Memo: Data 0.63 0.56 0.65 0.43
NOTE: 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
IMPACT OF A CAPITAL L IQUIDITY SHOCK
0 20 40
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
Output, pct.
0 20 40−0.4
−0.2
0
0.2
0.4Consumption, pct.
0 20 40−20
−15
−10
−5
0
5Investment, pct.
0 20 40−1
−0.5
0
0.5Hours worked, pct.
0 20 40−80
−60
−40
−20
0
20Risk−free rate, bps.
0 20 40−2.5
−2
−1.5
−1
−0.5
0
0.5Debt/Capital, pps.
0 20 40−20
0
20
40
60
80
100Credit spreads, bps.
0 20 40−0.5
0
0.5
1
1.5
2
2.5Inactive firms, pps.
NOTE: Model w/ financial frictions.Model w/o financial frictions.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
IRFs and Business Cycle Moments
CONDITIONAL BUSINESSCYCLE MOMENTSCapital Liquidity shocks only
Relative Volatility
Model Specification STD(I) STD(C) STD(H) STD(Y)
With financial frictions 6.71 0.60 0.55 1.11Without financial frictions 14.3 0.63 0.69 0.09Memo: Data 2.79 0.42 0.60 1.12
Comovements
Model Specification Corr(I, Y) Corr(C, Y) Corr(H, Y) Corr(C, I)
With financial frictions 0.61 0.88 0.86 0.16Without financial frictions 0.78 0.73 0.78 0.14Memo: Data 0.63 0.56 0.65 0.43
NOTE: All variables are expressed in deviations from their respective steady-state values.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
Properties of Credit Spreads
CYCLICAL PROPERTIES OFCREDIT SPREADS
Conditional on the Type of Shock
Selected Correlations Technology Uncertainty Liquidity Data
Corr(S, Y) 0.927 -0.811 -0.938 -0.457Corr(S, I) 0.626 -0.515 -0.577 -0.531Corr(S,C) 0.916 -0.368 -0.816 -0.498Corr(S,NW) -0.813 0.802 -0.703 -0.297Corr(STD(S), Y) 0.933 -0.832 -0.950 -0.245
CreditSpreads
NOTE: All variables are expressed in deviations from their respective steady-state values.
Uncertainty, Financial Frictions, and Irreversible Investment
Model Simulations
Conclusion
CONCLUDING REMARKS
Financial market frictions have an important effect on theinvestment-uncertainty nexus.
The presence of financial market frictions significantly amplifiesthe response of investment and output to both uncertainty andliquidity shocks.
An important extension of our framework would involveendogenizing the price of capital.
Uncertainty, Financial Frictions, and Irreversible Investment
Appendix
SUMMARY STATISTICSSelected bond characteristics
Bond Characteristic Mean StdDev Min Median Max
# of bonds per firm/month 2.99 3.69 1.00 2.00 76.0Mkt. value of issue (millions, $2005) 339.9 338.9 1.22 249.2 5,628Maturity at issue (years) 12.8 9.2 1.0 10.0 50.0Term to maturity (years) 11.1 8.5 1.0 8.0 30.0Duration (years) 6.49 3.28 0.91 6.03 18.0Credit rating (S&P) - - D BBB1 AAACoupon rate (pct.) 7.06 2.14 0.60 6.88 17.5Nominal effective yield (pct.) 7.23 2.98 0.22 6.92 30.0Credit spread (bps.) 202 223 5 128 2,000
Back
Uncertainty, Financial Frictions, and Irreversible Investment
Appendix
(S, s) INVESTMENT POLICY FUNCTIONPartial irreversibility only
02
46
8
−10
−5
0
51
2
3
4
5
k(t), capitalx(t), net liquid assets
k(t+
1)
Back
Uncertainty, Financial Frictions, and Irreversible Investment
Appendix
(S, s) INVESTMENT POLICY FUNCTIONPartial irreversibility and fixed adjustment costs
02
46
8
−10
−5
0
51
2
3
4
5
6
k(t), capitalx(t), net liquid assets
k(t+
1)
Back
Uncertainty, Financial Frictions, and Irreversible Investment
Appendix
CORPORATEBOND CREDIT SPREADS
1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 0
2
4
6
8
10Percentage points
MedianInterquartile range
Monthly
1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 0
2
4
6
8
10Percentage points
Monthly
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