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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.


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)


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)


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 ↓


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)


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.


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.


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.


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.


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)


Empirics


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


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


-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


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


-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


-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


Credit spread


NOTE: The shaded bands represent the 95-percent confidence intervals.


Empirics


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


0 2 4 6 8 10 12-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0Percent



-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


-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3Percent


0 2 4 6 8 10 12-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3Percent



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


-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


-0.2

-0.1

0.0

0.1

0.2

0.3

0.4


Credit spread

0 2 4 6 8 10 12-0.2

-0.1

0.0

0.1

0.2

0.3

0.4


Credit spread




Empirics


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


0 2 4 6 8 10 12-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0Percent



-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


-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3Percent


0 2 4 6 8 10 12-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3Percent



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


-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


-0.2

-0.1

0.0

0.1

0.2

0.3

0.4


Credit spread

0 2 4 6 8 10 12-0.2

-0.1

0.0

0.1

0.2

0.3

0.4


Credit spread




Empirics


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


0 2 4 6 8 10 12-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0Percent



-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


-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3Percent


0 2 4 6 8 10 12-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3Percent



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


-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


-0.2

-0.1

0.0

0.1

0.2

0.3

0.4


Credit spread

0 2 4 6 8 10 12-0.2

-0.1

0.0

0.1

0.2

0.3

0.4


Credit spread




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


Empirics



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)


Empirics



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.


Empirics


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


Empirics


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



Empirics


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)



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.


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.


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;


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


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′.


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


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)


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)


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


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


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


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


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


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


Model


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


Model


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


Model


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.


Model


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


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


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

]


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.


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.


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


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


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


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.


Model Simulations


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)


NOTE: All variables are expressed in deviations from their respective steady-state values.


Model Simulations


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 20 40−25

−20

−15

−10

−5

0


0 20 40−0.4

−0.3

−0.2

−0.1

0


0 20 40

0

50

100

150


0 20 40−1

0

1

2

3

4Inactive firms, pps.



Model Simulations


CONDITIONAL BUSINESSCYCLE MOMENTSUncertainty shocks only

Relative Volatility



Comovements


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



Model Simulations


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 20 40−80

−60

−40

−20

0


0 20 40−2.5

−2

−1.5

−1

−0.5

0


0 20 40−20

0

20

40

60

80


0 20 40−0.5

0

0.5

1

1.5

2

2.5Inactive firms, pps.



Model Simulations


CONDITIONAL BUSINESSCYCLE MOMENTSCapital Liquidity shocks only

Relative Volatility



Comovements





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



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.


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


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


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


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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