1.6
Business cycle applications
• Outside finance premium: is it countercyclical?
• Investment volatility: is there amplification/propagation?
• general answer: it depends on the shocks (persistence)
• We focus on amplification
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• almost temporary shock ρ = .05
0.15
financial frictions
frictionless benchmark
0.1
IK 0.05
0
-0.05
-0.1
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
0.1
0.08
K 0.06
0.04
0.02
0
Figure 10:
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• more persistent shock ρ = .1
0.2
financial frictions
frictionless benchmark
0.1
IK 0
-0.1
-0.2
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
0.2
0.15
K 0.1
0.05
0
Figure 11:
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• persistent shock ρ = .5
1
financial frictions
frictionless benchmark
0.5
IK
0
-0.5
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
0.8
0.6
K 0.4
0.2
0
Figure 12:
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• Related empirical micro issue: do firms with tighter constraints respond
more/less to cash flow shocks?
• Fazzari, Hubbard, Petersen (1998): Yes
(see table before)
• Kaplan and Zingales:
— in theory: maybe
— in empirics: no
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• Crucial macro issue: are contracts state-contingent?
• Balance sheet
Rtkt − bt
• Investment
Rtkt − bt
kt+1 = m
qt − θβ C E [Rt+1]
• question is bt sufficiently responsive to shocks?
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1.6.1
Amplification
• In Kiyotaki-Moore no state contingent contracts
• Feed-back investment-asset prices in KM
• Recall that
Rt = AtF1 (Kt, 1) + qto
• Suppose we are in region where Rtkt − bt close to zero/bankruptcy
• with non-state contingent contracts that may happen
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• then small positive productivity shock increases kt+1 more than propor
tionally
• this increases qto-> larger increase in Kt+1 and so on
• Krishnamurthy (2003): it all depends on ability to condition on aggregate
shocks
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• Detour on models of Costly State Verification
• Caveat: CSV helps explain why non-state contingent debt is used at the
micro level, but it does not really help at the macro level
• In general aggregate shocks seem relatively easy to condition upon: why
sometimes balance sheets very exposed?
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1.6.2
A failure of diversification
• Three period version
• No adjustment costs
• Risk averse consumers E [u (c1 + c2)]
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• In period 0 no investment, no consumption, only financial contracting ex
ante
• Shock in period 1: s = H, L
• In period 1 entrepreneurs have initial endowment ω E
s ∈ {ω H , ω L}
• Consumers have endowment ωC
s in period 1 and work in period 2
• No aggregate shock
E
ωC
s + ωs = 1
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• Entrepreneurs
• In period 1: Invest k2,s
³
´
• In period 2: produce F k2,s, l2,s − wsl2,s
• Balance sheet of the entrepreneur at date 1
E
n1,s = ωE
+
z
s
s
• state contingent contracts zs are available at date 0
• question: will they hedge?
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• Consumer problem
max
s.t.
X
X
³
π su c1,s + c2,s
qszsC ≤ 0
´
C
c1,s = ωC
s + zs
c2,s = ws
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• Entrepreneur problem
max
s.t.
´
E
E
π s c1,s + c2,s
X
qszsE ≤ 0
E + zE
+
k
=
ω
cE
2,s
s
s
1,s
cE
2,s = R2,sk2,s
X
³
• θ = 0 only internal funds can be used
• Value function of entrepreneur now is simply
V
as long as R2,s ≥ 1.
³
´
³
´
E
E
E
E
ωs + zs , s = R2,s ωs + zs
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• Reduced form consumer’s problem
max
s.t.
X
³
C
π su ω C
s + zs + ws
X
qszsC ≤ 0
• Reduced form entrepreneur’s problem
max
s.t.
X
³
E
π sR2,s ωE
+
z
s
s
X
qszsE ≤ 0
´
´
• market clearing: financial market
zsC + zsE = 0
labor market
R2,s = F1 (Ks, 1) ,
E
Ks = ωE
s + zs
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Equilibrium
³
´
0
C
C
π Lu ωL + zL + wL
π LR2,L
qL
³
´ =
=
C
C
0
qH
π H R2,H
π H u ωH + zH + wH
• multiple equilibria possible
• symmetric equilibrium always exists: full diversification
KH = KL =
X
π sω E
s
• asymmetric equilibrium KH > KL (also the opposite possible!)
• pecuniary externality
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Example
π L = π H = 1/2
u (c) = c1−γ
F (k, 1) = Akα
E
ωE
L = 0, ω H = 1
C
ωC
L = 1, ω H = 0
E
z = zL
q
q = L
qH
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Two relations
u0 (1 − z + Az α)
= q
u0 (qz + A (1 − qz)α)
z α−1
= q
α−1
(1 − qz)
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4
3.5
3
q
2.5
2
1.5
1
0.5
0
0.1
0.2
0.3
z
0.4
0.5
0.6
0.7
Figure by MIT OCW.
Examples:
• US vs Japan asset price bubble
• real estate concentrated in banks -> feed back
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• stock market diffused -> no feed back
• Dollarized economies: consumers want deposits in US$ to be safe, then
banks lend in US$, then companies exposed to XR risk, wages more volatile,
consumers want deposits in US$...
• very different balance sheet effects
• “financial fragility” difficult to assess, credit chains...
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