Sticky Leverage. João Gomes, Urban Jermann & Lukas Schmid Wharton School and UCLA/Duke. September 28, 2013

Transcription

1 Sticky Leverage João Gomes, Urban Jermann & Lukas Schmid Wharton School and UCLA/Duke September 28, 213

2 Introduction Models of monetary non-neutrality have traditionally emphasized the importance of sticky prices and/or wages This seems perhaps overdone We focus on an alternative channel for monetary non-neutrality Nominal debt that is both long-term and defaultable This is both large and quite costly to adjust (at least the principal) This creates two problems for firms Default risk Debt overhang

3 Preview of Findings Debt deflation is a quantitatively powerful propagation mechanism Sticky or persistent leverage is the key Conventional Taylor rules can stabilize output in response to shocks

4 Related Literature Debt deflation: De Fiore, Teles, and Tristani (211), Kang and Pflueger (212), Christiano, Motto and Rostagno (29), Bhamra, Fisher and Kuehn (211) Debt overhang: Occhino and Pescatori (212), Moyen (27), Hennessy (24), Chen and Manso (21) Default, general equilibrium: Gomes and Schmid (213), Gourio (212), Miao and Wang (21) No quantitative business cycle analysis with defaultable nominal, long-term debt

5 Model Continuum of firms of measure one, firm j produces y j t = A t (k j t ) α ( ) 1 α nt j with aggregate productivity ln A t = ρ ln A t 1 + σε t, and ) ( ) k j t+1 (1 = δ + it j kt j g it j kt j Define ) α ( 1 α R t kt j max A t (k j nt j t nt) j wt nt j After-tax operational profits, with idiosyncratic IID shock zt j ( ) (1 τ) R t kt j zt j kt j

6 Debt Nominal debt outstanding requires payment (c + λ) bj t µ t where b t B t /P t 1, c coupon, λ amort., µ t inflation rate After issuing s j t p j t market value of debt b j t+1 = (1 λ) bj t µ t + sj t p j t

7 Equity Value and Default Value to equity holders/owners ) E (k t, j bt, j zt j, µ t = max where ) V (k t, j bt, j µ t Firms default when = max b j t+1,kj t+1 [, (1 τ) ( ) R t zt j kt j ((1 τ) c + λ) bj ( ) ] t + V k j µ t, bt, j µ t t { p j t ( ) b j t+1 (1 λ) bj t It j + τδkt j + µ t )} E t M t,t+1 E (k t, j bt, j zt j, µ t (1 τ) ( R t k j t z j t k j t ) + V t (k j t, b j t, µ t ) < ((1 τ) c + λ) bj t µ t

8 Debt Pricing b j t+1 pj t = E t M t,t+1 z j z j, t+1 Φ(z j t+1 ) [c + λ] bj t+1 µ t+1 + (R (1 τ) t+1 k j t+1 zj t+1 kj t+1 ( ) +V k j t+1, bj t+1, µ t+1 ξk t+1 + (1 λ) pj t+1 bj t+1 µ t+1 ) dφ (z t+1 )

9 Households and Equilibrium Consumer/Investor preferences max E {C,N} β t [(1 θ) ln C t + θ ln (3 N t )] t= Aggregate resource constraint Inflation Process Y t [1 Φ (z )] ξ r ξk t = C t + I t ln µ t = (1 ρ µ ) ln µ + ρ µ ln µ t 1 + ε µ t

10 Characterization v (ω, µ) = max ω,i g (i) EM z z ( p [ ) i + τδ+ ω g (i) (1 λ) ω µ (1 τ) (R z ) ((1 τ) c + λ) ω µ + v (ω, µ ) ] dφ (z ) with ω b/k, v V /k State of economy: (ω, K, µ, A)

11 Optimal Leverage FOC for ω pg (i) + p ( ω ω g (i) (1 λ) ω ) µ = g (i) EM Φ ( z ) 1 µ [ (1 τ) c + λ + (1 λ) p ]

12 Sticky Leverage One-period debt, λ = 1 Proposition: p + p ω ω = EM Φ ( z ) [((1 τ) c + 1) 1µ ] Assume µ i.i.d., ξ r =, and no shocks for a long time so that µ t 1 = µ, ω t = ω Then, shock on µ t has no effect on ω t+1 = ω

13 Sticky Leverage Long-term debt, λ < 1 Proposition pg (i) + p ( ω ω g (i) (1 λ) ω ) µ = g (i) EM Φ ( z ) 1 [ ((1 τ) c + λ) p µ (1 λ) ] Assume µ i.i.d., ξ r =, and no shocks for a long time so that µ t 1 = µ, ω t = ω A negative shock on µ t increases ω t+1 > ω. Sticky leverage: high ω/µ high ω

14 Optimal Investment and Debt Overhang FOC for i z 1 pω = EM z (1 τ) (R z ) ((1 τ) c + λ) ω µ +v (ω, µ ) dφ ( z ) Proposition: Assume µ i.i.d., ξ r =, and no shocks for a long time so that µ t 1 = µ, ω t = ω, R t+1 > R Then, shock on µ t has no effect on R (and i) iff ω t+1 = ω However if ω t+1 > ω then R t+1 > R

15 Calibration Parameter Description Value β Subjective Discount Factor.99 γ Risk Aversion 1 θ Elasticity of Labor.63 α Capital Share.36 δ Depreciation Rate.25

16 Calibration Parameter Description Value β Subjective Discount Factor.99 γ Risk Aversion 1 θ Elasticity of Labor.63 α Capital Share.36 δ Depreciation Rate.25 λ Debt Amortization Rate.6 τ Tax Wedge.4 η 1 Distribution Parameter.6617 ξ Default Loss.38 ξ r Fraction of Resource Cost 1

17 Idiosyncratic Shocks Use general quadratic approximation to p.d.f.: φ(z) = η 1 + η 2 z + η 3 z 2 Symmetry z = z = 1, and E (z) = One free parameter η 1

18 Shocks VAR process for inflation and productivity [ ] [ ] [ at ρa ρ = a,µ at 1 µ t ρ a,µ ρ µ µ t 1 ] + [ ε a t ε µ t ] Estimated values Γ = [ ] σ a =.74, σ µ =.45, ρ µa =.19 AR(1) version: ρ a =.97, σ a =.7 ρ µ =.85, σ µ =.4 ρ a,µ = ρ a,µ = ρ µa =

19 Inflation shock x 1-3 μ Y I 5 x 1-3 c 2 x 1-3 r x 1-3 N 2 x 1-3 defr.15 p ω

20 Key Moments Data Model Model AR(1) VAR(1) First Moments Investment/Output, I /Y Leverage, ω Default Rate, 1 Φ(z ).42%.42%.42% Credit Spread.39%.39%.39% Second Moments σ Y 1.7% 1.6% 1.7% σ I /σ Y σ C /σ Y σ N /σ Y σ ω 1.7% 1.5% 1.7%

21 Variance decomposition, AR(1) Y Inv Cons Hrs Lev Default Benchmark, ω =.42 TFP shock a Inflation shock µ Low Leverage, ω =.32 TFP shock a Inflation shock µ High Leverage, ω =.52 TFP shock a Inflation shock µ

22 Variance decomposition, AR(1) Y Inv Cons Hrs Lev Default Benchmark, λ =.6 TFP shock a Inflation shock µ Long maturity, λ =.3 TFP shock a Inflation shock µ One period debt, λ = 1 TFP shock a Inflation shock µ

23 Monetary policy rule Taylor rule with interest rate smoothing ˆr f t = ρ R ˆr f t 1 + (1 ρ R ) {ν m ˆµ t + ν y ŷ t } + ζ t Calibration ˆr f t =.6 ˆr f t {1.5 ˆµ t +.5 ŷ t } + ζ t

24 Monetary policy shock 4 x 1-3 ζ 2 x 1-3 μ Y I 5 x 1-3 c 2 x 1-3 rf Policy rule -5 Exogenous inflation x 1-3 N 2 x 1-3 defr.15 p ω

25 Productivity shock 8 x 1-3 a x 1-3 μ.15 Y Policy rule Exogenous inflation I 8 x 1-3 c 1 x 1-3 rf x 1-3 N x 1-3 defr x 1-3 p ω

26 Wealth/capital shock 3 δ 15 x 1-3 μ.1 Y I c Policy rule Exogenous inflation x 1-3 rf N 1 x 1-3 defr.3 p ω

27 Conclusion Model with nominal long-term debt produces strong inflation non-neutrality without sticky prices Key mechanisms: sticky leverage and debt overhang Taylor rule implies a significant increase in inflation in response to both low productivity and wealth shocks