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Credit Shocks in an Economywith Heterogeneous Firms and
Defaultby Aubhik Khan, Tatsuro Senga and Julia K. Thomas
Discussed by Urban Jermann
Contribution
I Present GE model with heterogenous firms and default
I Similar objectives as Gomes and Schmid (2010),Arellano, Bai and Kehoe (2012)
I Solve & calibrate the model, and study TFP and creditshocks
I Credit shocks have persistent effects on N, I and GDP
I Slow recovery
I Fluctuations in entry and exit are important
Contribution
I Present GE model with heterogenous firms and defaultI Similar objectives as Gomes and Schmid (2010),Arellano, Bai and Kehoe (2012)
I Solve & calibrate the model, and study TFP and creditshocks
I Credit shocks have persistent effects on N, I and GDP
I Slow recovery
I Fluctuations in entry and exit are important
Contribution
I Present GE model with heterogenous firms and defaultI Similar objectives as Gomes and Schmid (2010),Arellano, Bai and Kehoe (2012)
I Solve & calibrate the model, and study TFP and creditshocks
I Credit shocks have persistent effects on N, I and GDP
I Slow recovery
I Fluctuations in entry and exit are important
Contribution
I Present GE model with heterogenous firms and defaultI Similar objectives as Gomes and Schmid (2010),Arellano, Bai and Kehoe (2012)
I Solve & calibrate the model, and study TFP and creditshocks
I Credit shocks have persistent effects on N, I and GDP
I Slow recovery
I Fluctuations in entry and exit are important
Contribution
I Present GE model with heterogenous firms and defaultI Similar objectives as Gomes and Schmid (2010),Arellano, Bai and Kehoe (2012)
I Solve & calibrate the model, and study TFP and creditshocks
I Credit shocks have persistent effects on N, I and GDPI Slow recovery
I Fluctuations in entry and exit are important
Contribution
I Present GE model with heterogenous firms and defaultI Similar objectives as Gomes and Schmid (2010),Arellano, Bai and Kehoe (2012)
I Solve & calibrate the model, and study TFP and creditshocks
I Credit shocks have persistent effects on N, I and GDPI Slow recovery
I Fluctuations in entry and exit are important
ModelI Firms’production function
yi = zεikai n
νi , α+ ν < 1
z aggregate TFP
εi firm specific TFP
I
k ′i = (1− δ) ki + iiI Fixed cost
ξ0I Labor choice
π (k, ε; s, µ) = maxnzεkanν −ω (s, µ) n
= (1− ν) y (k, ε; s, µ)
ModelI Firms’production function
yi = zεikai n
νi , α+ ν < 1
z aggregate TFP
εi firm specific TFP
I
k ′i = (1− δ) ki + ii
I Fixed costξ0
I Labor choice
π (k, ε; s, µ) = maxnzεkanν −ω (s, µ) n
= (1− ν) y (k, ε; s, µ)
ModelI Firms’production function
yi = zεikai n
νi , α+ ν < 1
z aggregate TFP
εi firm specific TFP
I
k ′i = (1− δ) ki + iiI Fixed cost
ξ0
I Labor choice
π (k, ε; s, µ) = maxnzεkanν −ω (s, µ) n
= (1− ν) y (k, ε; s, µ)
ModelI Firms’production function
yi = zεikai n
νi , α+ ν < 1
z aggregate TFP
εi firm specific TFP
I
k ′i = (1− δ) ki + iiI Fixed cost
ξ0I Labor choice
π (k, ε; s, µ) = maxnzεkanν −ω (s, µ) n
= (1− ν) y (k, ε; s, µ)
FinancingI One-period defaultable debt
due : bisold : q
(k ′i , b
′i , εi ; s, µ
)b′i
I Financial fixed cost
χθ (s) ξ1 (ε) , withχθ (s) = 1, if θ ∈ crisisχθ (s) = 0, if θ /∈ crisis
I Cash on hand
x (.) = (1− ν) y (.) + (1− δ) k − b− ξ0 − χθ (s) ξ1 (ε)
I DividendsD = x − k ′ + q (.) b′
I Nonnegative dividends, no external equity
D ≥ 0
FinancingI One-period defaultable debt
due : bisold : q
(k ′i , b
′i , εi ; s, µ
)b′i
I Financial fixed cost
χθ (s) ξ1 (ε) , withχθ (s) = 1, if θ ∈ crisisχθ (s) = 0, if θ /∈ crisis
I Cash on hand
x (.) = (1− ν) y (.) + (1− δ) k − b− ξ0 − χθ (s) ξ1 (ε)
I DividendsD = x − k ′ + q (.) b′
I Nonnegative dividends, no external equity
D ≥ 0
FinancingI One-period defaultable debt
due : bisold : q
(k ′i , b
′i , εi ; s, µ
)b′i
I Financial fixed cost
χθ (s) ξ1 (ε) , withχθ (s) = 1, if θ ∈ crisisχθ (s) = 0, if θ /∈ crisis
I Cash on hand
x (.) = (1− ν) y (.) + (1− δ) k − b− ξ0 − χθ (s) ξ1 (ε)
I DividendsD = x − k ′ + q (.) b′
I Nonnegative dividends, no external equity
D ≥ 0
FinancingI One-period defaultable debt
due : bisold : q
(k ′i , b
′i , εi ; s, µ
)b′i
I Financial fixed cost
χθ (s) ξ1 (ε) , withχθ (s) = 1, if θ ∈ crisisχθ (s) = 0, if θ /∈ crisis
I Cash on hand
x (.) = (1− ν) y (.) + (1− δ) k − b− ξ0 − χθ (s) ξ1 (ε)
I DividendsD = x − k ′ + q (.) b′
I Nonnegative dividends, no external equity
D ≥ 0
FinancingI One-period defaultable debt
due : bisold : q
(k ′i , b
′i , εi ; s, µ
)b′i
I Financial fixed cost
χθ (s) ξ1 (ε) , withχθ (s) = 1, if θ ∈ crisisχθ (s) = 0, if θ /∈ crisis
I Cash on hand
x (.) = (1− ν) y (.) + (1− δ) k − b− ξ0 − χθ (s) ξ1 (ε)
I DividendsD = x − k ′ + q (.) b′
I Nonnegative dividends, no external equity
D ≥ 0
Default
I Firms with negative equity default
V 1 (x, ε; sl , µ) = πdx + (1− πd )V2 (x, ε; sl , µ) < 0
I with
V 2 (.) = maxk ′,b′
[x − k ′ + q (.) b′+
∑Nsm=1 πslmdm (sl , µ)∑ πε
ijV0 (.′)
]s.t.
x − k ′ + q (.) b′ ≥ 0
Default
I Firms with negative equity default
V 1 (x, ε; sl , µ) = πdx + (1− πd )V2 (x, ε; sl , µ) < 0
I with
V 2 (.) = maxk ′,b′
[x − k ′ + q (.) b′+
∑Nsm=1 πslmdm (sl , µ)∑ πε
ijV0 (.′)
]s.t.
x − k ′ + q (.) b′ ≥ 0
Debt pricing
I q (k ′, b′, εi ; sl , µ) b′ =
Ns
∑m=1
πslmdm (.)∑ πεij
[χ(x ′jm, εj ; sm, µ
′)b′+
(1− χ (.))min {b′, ρ (θ) (1− δ) k}
]
Frictions in the model
I Default cost
I Nonnegative dividends / no equity injectionI Financial (crisis) fixed cost χθ (s) ξ1 (ε)
I Exit & entry
Frictions in the model
I Default costI Nonnegative dividends / no equity injection
I Financial (crisis) fixed cost χθ (s) ξ1 (ε)
I Exit & entry
Frictions in the model
I Default costI Nonnegative dividends / no equity injectionI Financial (crisis) fixed cost χθ (s) ξ1 (ε)
I Exit & entry
Frictions in the model
I Default costI Nonnegative dividends / no equity injectionI Financial (crisis) fixed cost χθ (s) ξ1 (ε)
I Exit & entry
Many moving parts
I Credit shock = Recovery shock + Fixed cost shock
I Default vs Entry&ExitI Capital distribution at entry
I Pareto distribution with lower bound k0 and curvatureparameter κ0
I Firm specific "Disaster Shocks"
I 10% probability of ε = 0
Many moving parts
I Credit shock = Recovery shock + Fixed cost shockI Default vs Entry&Exit
I Capital distribution at entry
I Pareto distribution with lower bound k0 and curvatureparameter κ0
I Firm specific "Disaster Shocks"
I 10% probability of ε = 0
Many moving parts
I Credit shock = Recovery shock + Fixed cost shockI Default vs Entry&ExitI Capital distribution at entry
I Pareto distribution with lower bound k0 and curvatureparameter κ0
I Firm specific "Disaster Shocks"
I 10% probability of ε = 0
Many moving parts
I Credit shock = Recovery shock + Fixed cost shockI Default vs Entry&ExitI Capital distribution at entry
I Pareto distribution with lower bound k0 and curvatureparameter κ0
I Firm specific "Disaster Shocks"
I 10% probability of ε = 0
Many moving parts
I Credit shock = Recovery shock + Fixed cost shockI Default vs Entry&ExitI Capital distribution at entry
I Pareto distribution with lower bound k0 and curvatureparameter κ0
I Firm specific "Disaster Shocks"
I 10% probability of ε = 0
Many moving parts
I Credit shock = Recovery shock + Fixed cost shockI Default vs Entry&ExitI Capital distribution at entry
I Pareto distribution with lower bound k0 and curvatureparameter κ0
I Firm specific "Disaster Shocks"I 10% probability of ε = 0
Simplified partial equilibrium model
I
V (x) =
= maxk ′,b′
x − k ′ + q (k ′, b′) b′
+βE max
Aε′k ′
a1−ν + (1− δ) k ′
−b− ξ0 − χθ
(θ′)
ξ1 (ε′)
, 0
I Assumek ′ = q
(b′)b′ + x
Simplified partial equilibrium model
I
V (x) =
= maxk ′,b′
x − k ′ + q (k ′, b′) b′
+βE max
Aε′k ′
a1−ν + (1− δ) k ′
−b− ξ0 − χθ
(θ′)
ξ1 (ε′)
, 0
I Assume
k ′ = q(b′)b′ + x
Simplified partial equilibrium model ll
I
maxB ′
βE∫ ε̄′
ε∗′(B ′)
ε′[
A (B ′ + x)a1−ν
+ (1− δ) (B ′ + x)
]−B ′Rc (B ′)− ξ0 − χθ
(θ′)
ξε′
dΦ(ε′)
IB ′
β= E
{Φ(ε∗′)BRc
}+E
{∫ ε∗′(B ′)
εmin
[ρ (θ) (1− δ) ε′
(B ′ + x
),BRc
]dΦ
(ε′)}
Simplified partial equilibrium model ll
I
maxB ′
βE∫ ε̄′
ε∗′(B ′)
ε′[
A (B ′ + x)a1−ν
+ (1− δ) (B ′ + x)
]−B ′Rc (B ′)− ξ0 − χθ
(θ′)
ξε′
dΦ(ε′)
IB ′
β= E
{Φ(ε∗′)BRc
}+E
{∫ ε∗′(B ′)
εmin
[ρ (θ) (1− δ) ε′
(B ′ + x
),BRc
]dΦ
(ε′)}
Conclusion
I Progress: GE with default and heterogenous firms
I I would like
I tighter calibration and more clarityI more explicit empirical evaluation
Conclusion
I Progress: GE with default and heterogenous firmsI I would like
I tighter calibration and more clarityI more explicit empirical evaluation
Conclusion
I Progress: GE with default and heterogenous firmsI I would like
I tighter calibration and more clarity
I more explicit empirical evaluation
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