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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