Comment on “Credit risk and the macroeconomy:
Evidence from an estimated DSGE model”
by Simon Gilchrist, Alberto Ortiz, Egon Zakrajšek
Tomoyuki Nakajima
Institute of Economic Research
Kyoto University

Bank of Japan, May 27, 2009

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/20091 / 15

Introduction

Main question

How important are credit market shocks to account for businesscycles?
Develop a DSGE model with financial market frictions and estimate itusing a new index of corporate credit spread.

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/20092 / 15Introduction

Previous result by GYZ (2009)

Construct a new index of corporate credit spread for the 1990-2008
period.
Their credit spread index outperforms standard default-risk indicators
in terms of the predictive power for economic activity.
Their FAVAR results suggest that shocks to the corporate credit
market accounts for more than 30% of the forecast error variance ineconomic activity at 2-4 year horizon.

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/20093 / 15

Introduction

What is done in this paper

Extend the corporate credit spread index of GYZ to a longer period:
1973-2008.
Show that its predictive power for economic activity outperforms
some commonly used financial indicators.
Conduct Baysian ML estimation of a DSGE model with financial
market frictions using their data on the corporate credit spread.

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/20094 / 15

Comments

Comments

Very interesting data and very important project.
Financial market data has a lot of information which could be used toadvance our understanding on macroeconomic fluctuations.

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/2009

5 / 15

Comments

Comments

Is this a good model to explain the corporate credit spread?
Generally, asset prices are difficult to explain.
In particular, fluctuations in risk premium are difficult to account for.
Maybe this model, with habit persistence and adjustment cost ofcapital, can account for the corporate credit spread, but ...

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/20096 / 15

Comments

Comments
Even if the original model is capable of explaining the risk premium,its linear approximation is not.
An exogenous “risk-premium shock” may have to be added togenerate risk premium in a linearized model.
Indeed, such shocks are assumed in this paper as:k− (rt − Et πt+1 ) = · · · + fd
Et rt+1t(24)Adding such exogenous shocks may cause a bias in estimation.

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/20097 / 15

Comments

ExampleExampleConsider a version of Jermann (1998):
max E0

∞
X
t=0βt

1−σ1
ct − bct−11−σsubject toα
ct + it = yt = exp(zt )kt−1
it
kt−1
kt = (1 − δkt−1 ) + it − H
kt−1

zt = ρz zt−1 + t
where
H(x) ≡Tomoyuki Nakajima (Kyoto University)ξ(x − δ)22δ
Comment on Gilchrist et al

5/27/20098 / 15

Comments

ExampleExampleBenchmark parameter values:
α = 0.36,
ξ = 5,

β = 0.99,

ρz = 0.9,

δ = 0.025,

σ = 5,

b = 0.8,

std() = 0.007.

Equity premium generated by the model (annualized rates):
E[rf ,t ] = 0.0267
E[rk,t ] = 0.0727
E[rpt ] = 0.0460Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/20099 / 15

Comments

ExampleExperiment

The model is simulated for 1200 periods.
Conduct Baysian ML estimation of a linearized version of the modelusing the following data generated by the original model:
1

output;2

output and equity premium.

A sizable bias when the equity premium is used in the estimation.

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/200910 / 15

Comments

ExampleEstimation 1

Use data {yt } to estimate the linearized version of the model.
Take α = 0.36, β = 0.99, and δ = 0.025 as given.
Estimate σ, b, ξ, ρz , and std() with priors:σ ∼ G (5, 0.1),b ∼ B(0.8, 0.03),

ρz ∼ B(0.9, 0.03),

Tomoyuki Nakajima (Kyoto University)ξ ∼ G (5, 0.1),std() ∼ IG (0.007, inf)

Comment on Gilchrist et al

5/27/200911 / 15

Comments

ExampleEstimation 1

Estimation result given data on {yt }:σbξρzstd()prior mean

5.00

0.800

5.00

0.900

0.007

post. mean

4.99

0.800

5.00

0.877

0.007

Tomoyuki Nakajima (Kyoto University)Comment on Gilchrist et al

5/27/200912 / 15

Comments

ExampleEstimation 2
Use simulated data {yt , rpt }.
Augment the linearized model with a risk-premium shock, at :rpt = · · · + at
at = (1 − ρa )ā + ρa zt−1 + νt
Estimate σ, b, ξ, ρz , and std(), ā, ρa , std(ν) with priors:σ ∼ G (5, 0.1),b ∼ B(0.8, 0.03),

ρz ∼ B(0.9, 0.03),ā ∼ N(0, 0.03),
Tomoyuki Nakajima (Kyoto University)ξ ∼ G (5, 0.1),std() ∼ IG (0.007, inf),ρa ∼ N(0, 0.03),
Comment on Gilchrist et alstd(ν) ∼ IG (0.001, inf)
5/27/200913 / 15

CommentsExample

Estimation 2
Estimation result given data on {yt , rpt }:σbξρzstd()prior mean

5.00

0.800

5.00

0.900

0.007

post. mean

4.81

0.94

4.40

0.975

0.0074ā

ρastd(ν)

prior mean

0.00

0.00

0.001

post. mean

0.007

0.19

0.064

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/200914 / 15

Conclusion

Conclusion

The authors have constructed a very interesting index of corporate
credit spread, which could be used to better understandmacroeconomic fluctuations.
One concern about the authors’ approach is that using a linearized
model augmented with risk premium shocks to account for asset
prices may yield a biased result.

Tomoyuki Nakajima (Kyoto University)

Comment on Gilchrist et al

5/27/200915 / 15