Adverse Selection, Uncertainty Shocks andBusiness Cycles
Daisuke Ikeda
Bank of JapanThe 13th Macroeconomics Conference
November 27, 2011

The views expressed in this presentation are solely theresponsibility of the author and should not be interpreted asreflecting views of the Bank of Japan.

What Caused the Great Recession?
What Drives Business Cycles?

The great recession and shocks:.1.

Financial shocks• Gilchrist and Zakrasjek (2010), Hall (2010).

.2.

Shocks to marginal efficiency of investment (MEI)• Justiniano, et al (2010).

... exogenous, unknown mechanisms.
Uncertainty and business cycles• Bloom (2009) and Bloom, et al (2010).

A Question

What microfoundations are behind financial and MEI shocks?

“Uncertainty shocks which change the degree ofasymmetric information in financial markets”

What I do: Main results• Build a dynamic model with adverse selection in financialmarkets.
• Unobserved riskiness: Stiglitz and Weiss (1981).
• Variable scale of investment.

• Uncertainty shocks emerge as financial shocks if adverse

selection in the demand side of capital.
• Uncertainty shocks emerge as MEI shocks if adverse

selection in the supply side of investment.
• Quantitative analysis in a real business cycle framework.

Road Map

.1.

Partial equilibrium model.2.

General equilibrium model.
• Basic framework: Real business cycle model.
• Model I: Adverse selection in demand side.
• Model II: Adverse selection in supply side.

.3.

Quantitative analysis• Impulse responses.
• Amplification mechanisms.

.4.

Related Literature.5.

Conclusion

Partial Equilibrium ModelOne Time Financing Problem• Many risk-neutral entrepreneurs and intermediaries.
• Competitive intermediaries in lending. The cost of funds R f .
• Entrepreneur has net worth Nn .
• Entrepreneur uses net worth and borrowing fromintermediaries, and invests in project.

One Time Financing Problem, cont’d• Project succeeds with probability p and yields expected return

Re > R f .
• Probability, p ∼ i.i.d.F(p), is private information.
• Fraction 1 − ϕ of entrepreneur’s return is pledgeable tointermediaries.
• Entrepreneur is protected by limited liability.

Timing of Events

0. Nature assigns p ∼ F(p) i.i.d. among entrepreneurs.
1. An intermediary provides a schedule of contracts specifying
loans and payment, {Bn (p), Xn (p)} p .
2. An intermediary chooses to leave or stay in the market.
3. Entrepreneurs choose an intermediary and a pair{Bn (p), Xn (p)}.
4. The outcome, success or failure, is realized, and the profits
are realized.

Macro Implication of Equilibrium Contract

Only two equations summarize the aggregate relationship:
1. Aggregate loan:[](1 − ϕ)Re /R f
B=F(p∗ )N
1 − (1 − ϕ)Re /R f[]
(1 − ϕ)Re /R f
<N
1 − (1 − ϕ)Re /R f
2. Intermediary zero profit condition: determine p∗ given Re /R f .

Dynamic General Equilibrium ModelBasic Framework: Real Business Cycle Model• A household as many family members: workers and entrepreneurs.
(Gertler and Karadi, 2010)• Preferences and budget constraint:

∞
∑

L1+1/ν  ,E0βt log(Ct ) − ψ t
1 + 1/ν
t=0
Ct + Bt = Rt Bt−1 + wt Lt + Θt .
• Counter-cyclical markup in wages:
λw,t = λw( Y )−ωtY,λw > 1,

• Technologies:
Yt = (ut Kt )α Lt1−α ,Kt+1 = (1 − δ)Kt + I¯t ,ω > 0.

Two Dynamic Models and Uncertainty Shocks• Investment:
K − (1 − δ)Kt = I¯t .
| t+1 {z} |{z}SupplyDemand• Uncertainty shocks and distribution of riskiness of project:
Ft (p) =qp − p exp(υt )1 − p exp(υt ),0 < p < 1.

②Supply①DemandI

Model I: Adverse Selection in the Demand Side of Investment

Balance sheet:

qt Kt+1 = Nt + Bt .
Aggregate loan: (1 − ϕ)Et Rkt+1 /Rt+1  Ft (p∗t )Nt .
Bt = 
1 − (1 − ϕ)Et Rkt+1 /Rt+1
Uncertainty shocks emerge as financial shocks:()
Et R̂kt+1 − R̂t+1 = −χ1 N̂t − q̂t − K̂t+1 − χ2 υt .

Model II: Adverse Selection in the Supply Side of Investment

Balance sheet:

It = Nt + Bet .
Aggregate loan:[Bet =](1 − ϕ)qt µt
Ft (p∗t )Nt .
1 − (1 − ϕ)qt µt

Uncertainty shocks emerge as investment shocks: I¯t = µt It ,(Iˆ¯t =[(( ) ]))11 + χ3χ4q̂t + N̂t +µ̂t +υt .
χ3χ3χ3

Quantitative Analysis

Model Parameterization
Target values:
EFP ≡ Rb /R (or Rb ) = 2%(APR), leverage ≡ qK/N = 1.5,Parameters
Parameterβναδλw
ω′′a (1)/a′ (1)ϕpS ′′
ρυ , ρµDescription

Value

preference discount factor(1.03)−1/4
10.360.025

elasticity of labor supply
capital income sharedepreciation rate
markupselasticity of markups
capital utilization
Moral hazard
Lowest support of F(·)
adjustment costs
AR(1) coef of shocks

1.2250.550.992
10.75

L = 1.

Impulse Responses: Model I
Output, Y (%)

Investment, I (%)

t0Consumption, C (%)

tt

00−0.05

−0.1

−0.1

−0.5

−0.2

−0.15
−0.3
−0.4

−0.2

−1010200Hours, Lt (%)

10200Capital Utilization, ut (%)

1020

Price of capital, qt (%)
00−0.1
−0.2

−0.1

−0.02

−0.3
−0.4

−0.2

−0.04

−0.5
01020

Net worth, Nt (%)

010201020Shock, υt (%)
0100Extenral finance premium, EFPt (APR diff)−0.1−0.10.5−0.2−0.2−0.3−0.3−0.40102000102001020

Impulse Responses: Model IIOutput, Y (%)

Investment, I (%)

t0−0.2−0.4

υ shockµ shock−0.6010

t

0−0.5

−0.05

−1−0.1−1.5−0.15
−0.2

−2020

Hours, Lt (%)
0Consumption, C (%)

t010200Capital Utilization, ut (%)

1020

Price of capital, qt (%)

00.1

−0.2
−0.4

−0.05
0.05

−0.6
−0.8

−0.101020

Net worth, Nt (%)

00102001020Shocks, υt and µt (%)

External finance premium, EFPt (APR diff)01−0.1

0.2

−0.2

0.5

0−0.3
−0.20102000102001020

The Role of Counter-cyclical markup in wages:
IRF to uncertainty shock
Model I, Output, Y (%)

Model I, Consumption, C (%)

tt

00.1
0.05

−0.1

0−0.2

−0.05
ω=0
ω=1.5
ω=1.8
ω=2−0.3−0.405101520

−0.1
−0.15
−0.22505

Model II, Output, Yt (%)

10152025

Model II, Consumption, Ct (%)

00.1−0.1

0.05

−0.2

0−0.3

−0.05

−0.4

−0.1

−0.5
−0.15
−0.6
−0.2
05101520250510152025

C , |{z}L ) = MPL(|{z}L ),Markup(|{z}L ) × MRS (|{z}?

++−Literature Review• Adverse selection: partial equilibrium.
• Stiglitz and Weiss (1981).

• Adverse selection: dynamic general equilibrium.
• CF(1997), BGG (1999), Eisfeldt (2004), House (2006), Kurlat(2010), Bigio (2010).

• Uncertainty shocks and risk shocks.
• Bloom (2009) and Bloom, et al (2010).
• Christiano, Motto and Rostagno (2010), Gilchrist andZakrasjek (2010).

For Future Research.1.

The role of nominal rigidities.

.2.

The role of monetary policy.

.3.

Adverse selection in collateral value (Bigio, 2010).