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How Bad was Lehman Shock?:How Bad was Lehman Shock?:Estimating a DSGE model with Firm and Bank Balance Sheets in a Data-Rich Environment*Balance Sheets in a Data-Rich Environment
(with H. Iiboshi, T. Matsumae, and R. Namba)
SWET ConferenceAugust 7 2011August 7, 2011
Shin-Ichi NishiyamaShin Ichi Nishiyama(Tohoku University)
1* The views expressed in this presentation are those of the presenter and does not necessarily reflect those of ESRI or Cabinet Office, Government of Japan.
Motivation of this paperMotivation of this paper
R t fi i l i i i U S hi h i it t d bRecent financial crisis in U.S. which was precipitated by so-called ‘Lehman Shock’ has exemplified that deterioration of balance sheet condition, especially that , p yof financial sector, can cause a deep and long-lasting recession.
As Alan Greenspan puts, “We are in the midst of a once-in-a century credit tsunami ” (Testimony made atonce-in-a century credit tsunami. (Testimony made at the House of Representatives, Oct. 23, 2008)
Since two years have past since Lehman Shock, time seems to be ripe in assessing the impact of the shock.
How Bad was Lehman Shock? 2
Objective of this paperObjective of this paper
I thi tif d th i t fIn this paper, we quantify and assess the impact of Lehman Shock.
We ask two questions:• How large was the magnitude of Lehman Shock?How large was the magnitude of Lehman Shock?
• How large was the effect of Lehman Shock to the geconomy?
Strategy: We identify Lehman Shock by banking sector net worth shock.
How Bad was Lehman Shock? 3
Contributions of this paperContributions of this paperWe combine two canonical financial friction models. • For corporate balance sheet, we adopt BGG (1999)• For bank balance sheet, we adopt Gertler and Kiyotaki
(2010) and Gertler and Karadi (2010)(2010) and Gertler and Karadi (2010)• We need to model two balance sheets to identify Lehman
Shock• Related work is Hirakata, Sudo, and Ueda (2010)
W d t D t Ri h th d d b B i i dWe adopt Data-Rich method proposed by Boivin and Giannoni (2006)• By utilizing multiple time series information for each y g p
observable, we can expect an improved efficiency in estimating parameters and structural shocks.
How Bad was Lehman Shock? 4
Model DescriptionModel Description
Th id i t b d t b l h t d b kThe idea is to embed corporate balance sheet and bank balance sheet to the stylized DSGE model.
Includes standard features: habit formation, sticky price, sticky wage, investment-adjustment cost, Taylor rule, y g j yetc.
Th 8 l h k TFP h k fThere are 8 structural shocks: TFP shock, preference shock, labor supply shock, investment-specific technology shock, govt. expenditure shock, monetarytechnology shock, govt. expenditure shock, monetary policy shock, entrepreneur net worth shock, and bank net worth shock
How Bad was Lehman Shock? 5
Goods and Factor Inputs Flow ChartGoods and Factor Inputs Flow ChartHousehold Government
τ
gc
Final Goods Mkt.
Y
Retailer
Labor Mkt.Y
i
y(j)y(j)
6Entrepreneur j Capital ProducerCapital Goods Mkt.
Financial Flow ChartFinancial Flow Chart
D it Bankers EntrepreneursDepositor Bankers Entrepreneurs
b b_Fb E
b_E
Q*K
b_E
n_F
n_EAgency Cost
(Moral Hazard/Costly Enforcement)
Agency Cost
(Costly state verification)
Model DescriptionModel Description
Representative Household’s Problem
⎤⎡
1)(
1)(E
0i
111
t∑∞
=
++
+
−−++
+⎥⎥⎦
⎤
⎢⎢⎣
⎡
+−
−−
LitL
itcititc
iti
Lc
lhccσ
χσ
χβσσ
0i ⎥⎦⎢⎣
R FEdi{ { { { { {
-bRb
bankersfromer net transf
Ft
urentreprenefromer net transf
Et
dividend
divt
incomelabor t1-t
t
1-t
depositt
nconsumptio
Ξ+Ξ+Ξ++=+ tt wc τπ
p
Model Description: Entrepreneur’s ProblemModel Description: Entrepreneur s Problem
EFaces stochastic survival rate, γEt+1
Each entering entrepreneur receives ‘start-up’ transfer from the household. Total ‘start-up’ transfer is ξE nE
t
For exiting 1- γEt+1 entrepreneurs, they transfer their
existing net worth back to household.e s g e o bac o ouse o d
So, the net transfer that household receive is (1- γE
t+1- ξE) nEt
Model Description: Entrepreneur’s ProblemModel Description: Entrepreneur s Problem
ααω −1)()()()( jljkAjjyProduction Function: {ω=
ShockTFP
Shockticidiosyncra
)()()()( jljkAjjy ttttt 321
Balance sheet equation is given by
)()()(1 jnjbjkq Et
Ettt +=+ )()()(
Net WorthLiabilityAsset
1 32132143421jnjbjkq tttt +
Income statement equation is given by
)( jRE
{ 44344214434421
43421capital of valueresale
tb i
11
costlabor revenue
)()1()()()()()( jkqjbjRlwjyjpjn ttEt
t
tttt
mct
Et δ
π−+−−= −
−
How Bad was Lehman Shock? 11
costborrowing
Model Description: Entrepreneur’s ProblemModel Description: Entrepreneur s Problem
Capital demand equation is given by
111 )1()()()(⎥⎤
⎢⎡ −+
⎥⎤
⎢⎡ +++ tt
mct
Et qjmpkjpEjRE δ
444444 3444444 2143421investmentcapitalofreturn marginalexpected
111
corporate expected
1
)()()()(⎥⎦
⎢⎣
=⎥⎦
⎢⎣
+++
+ t
tttt
t
tt q
qjpjpEjEπ
Debt contract between entrepreneur and banker
pgprate borrowing real
pp
• Exist information asymmetry: costly state verification
1 )()( ⎟⎞
⎜⎛ + jkqj tt )()( jRRE
EtF
{43421ratioleverage
1
premiumfinance external
)()()( ⎟⎟⎠
⎜⎜⎝
= +
jnjqsjs E
t
ttt )(
)()(
ratelendingadjusted-risk
1 jsjmRE
t
tFtt =+ 43421
How Bad was Lehman Shock? 12
ratioleverage ratelending
Model Description: Entrepreneur’s ProblemModel Description: Entrepreneur s Problem
A tiAggregation• Thanks to constant-return-to-scale production technology and
risk-neutrality of entrepreneur, marginal cost, MPL, MPK, and y p gleverage ratio are the same across entrepreneurs.
A t t th t itiAggregate net worth transition
1111 ][ Et
EEt
Et
ttk
tEt
Et nbRkqrn ξγ +−= ++++ 321
32143421
household from transferup-start
repaymentdebt
1capital from
return gross realized
1111 ][ ttt
ttttt q ξπ
γ+
++++
Notice that stochastic survival rate act like an aggregate net worth shock in corporate sector
13
Model Description: Banker’s ProblemModel Description: Banker s Problem
FFaces stochastic survival rate, γFt+1
Each entering banker receives ‘start-up’ transfer from the household. Total ‘start-up’ transfer is ξF nF
t
For exiting 1- γFt+1 bankers, they transfer their existing
net worth back to the household.e o bac o e ouse o d
So, the net transfer that household receive is (1- γF
t+1- ξF) nFt
Model Description: Banker’s ProblemModel Description: Banker s Problem
Balance sheet equation is given by
)()()( mnmbmb Ft
Ft
Et +=
321321321
net worthsbanker'
liabilitysbanker'
assetsbanker'
)()()( ttt
• Notice that banker’s asset becomes entrepreneur’s liability
Income statement equation is given byIncome statement equation is given by
)( RmR FEF
F
4342144 344 21 11
11 )()()()( mbRmbmRmn F
tt
tEt
t
tFt
++
++ −=
ππ
15
22repaymentdebt lending fromreturn gross
Model Description: Banker’s ProblemModel Description: Banker s Problem
Banker’s objective function is given by
)1()( FFFiF nEmV∞
∑= γγβ44444 344444 21
businessbankingofluepresent vanet
10
1 ,11)1()( iti
ittttt nEmV ++=
++++∑ −= γγβ
Moral hazard / costly enforcement problem
businessbanking of luepresent vanet
• Banker has a technology to divert fraction λ of his asset• Incentive constraint for a banker to remain in business becomes
EF
43421n valuereservatio
)()( mbmV Et
Ft λ≥
16bankerby retained
n valuereservatio
Model Description: Banker’s ProblemModel Description: Banker s Problem
Imposing this constraint, Gertler and Kiyotaki (2010) shows the NPV of banking business to be
Al th h b k l ti t b t i d b
)()()( mnmbmV Ftt
Ett
Ft ην +=
Also, they show bank leverage ratio to be constrained by
tEt mb ηφ≤)(
t
ttF
t
t
mn νληφ−
≡≤321
ratioleveragebank
)()(
Notice the similarity with Basel Regulation
ratioleveragebank
How Bad was Lehman Shock? 17
Model Description: Banker’s ProblemModel Description: Banker s Problem
AggregationAggregation• Gertler and Kiyotaki (2010) shows that νt, ηt, and φt to be equal
across bankers which makes the aggregation very simple.• Also given that E RF (m) is equal across m we can obtain the• Also given that EtRF
t(m) is equal across m, we can obtain the following aggregate transition of banking sector net worth.
Aggregate net worth transition of banking sector1
11 ][ Ft
FFt
tEt
FtF
tFt nbRbRn ξγ +−= +
321321321
household from transferup-start
repaymentdebtgross aggregate
1
lendingfromreturngross aggregate
111 ][ tt
tt
ttt nbbn ξ
ππγ +
++++
Notice that stochastic survival rate act like an aggregate net worth shock in banking sector.
repaymentdebt lendingfromreturn
net worth shock in banking sector.How Bad was Lehman Shock? 18
Model Description: Recap of Interest RatesModel Description: Recap of Interest Rates
There are two types of interest rate spreads in this model• External finance premium• Profit margin of bank lending rate
FE RRR { { ttEt RRR
tl dib kofmargin profit
ifinance external
>>ratelendingbank premium
Stemming from agency problem between entrepreneur and banker:
Stemming from agency problem between banker and depositor:
M l h d / tl f t
How Bad was Lehman Shock?19
Costly state verification Moral hazard / costly enforcement
Data Rich EstimationData-Rich Estimation
f G ( )The idea of Boivin and Giannoni’s (2006) Data-Rich method is to extract a common factor from multiple time series data and to match that with each observable variable in the model.match that with each observable variable in the model.• One-to-one matching (standard Bayesian estimation)• One-to-many matching (Data-Rich estimation)
A merit of this approach is that we can expect improved efficiency in estimating parameters and structural shocksefficiency in estimating parameters and structural shocks.
Why Data-Rich estimation in this paper?Why Data Rich estimation in this paper?• Since our focus is to obtain a reliable estimate of the impact of
Lehman Shock, Data-Rich estimation is vital.
How Bad was Lehman Shock? 20
Data Rich EstimationData-Rich Estimation
DSGE model in state-space form…
{ { { { {eq.)n transitiostate (optimal
)()(− Γ+Φ=
JNNNt1tt uss
{ { {
{ { { {equation)nt (measureme
)1()()1()()1( ×××××
+=JJNNNNN
ttt esΛx
The idea is to increase the dimension of X (i e larger
{ { { {)1()1()()1( ×××× MNNMM
The idea is to increase the dimension of Xt (i.e., larger M) by supplying multiple time series, while keeping the dimension of Φ, Γ, st, and ut constant. ⇒ Can expect efficiency gain in estimating structural parameters, smoothing states and structural shocks.
How Bad was Lehman Shock? 21
Data Rich Estimation: Measurement EqData-Rich Estimation: Measurement Eq.Case A set-up: (Standard Bayesian estimation)
tt es +⋅⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
OMM
L
L
M
1001
#1 datainflation #1 dataoutput
Case B set-up: (Data-Rich estimation)
⎥⎦⎢⎣⎥⎦⎢⎣ OMMM
⎤⎡⎤⎡
⎥⎥⎥⎤
⎢⎢⎢⎡
⎥⎥⎥⎤
⎢⎢⎢⎡
MMMM
L
L
M
00001
#2 dataoutput #1dataoutput
2yλ
tt es +⋅⎥⎥⎥⎥⎥
⎢⎢⎢⎢⎢
=⎥⎥⎥⎥⎥
⎢⎢⎢⎢⎢
L
L
MMMMM
01000
#1 datainflation n# dataoutput y ynλ
⎥⎥⎥⎥⎥
⎢⎢⎢⎢⎢
⎥⎥⎥⎥⎥
⎢⎢⎢⎢⎢
MMMM
L
M
00#2 datainflation 2πλ
22⎥⎥
⎦⎢⎢
⎣⎥⎥
⎦⎢⎢
⎣ MMMM
L
M
00n#datainflation nππ λ
Data SetData SetSample Period: 1985Q2 to 2010Q2
Case A Data Set (11 data series)• 1. real GDP, 2. personal consumption expenditure, 3. business fixed
G finvestment, 4. GDP deflator, 5. real wage, 6. hours worked, 7. Fed Funds rate, 8. Moody’s Baa corporate bond index, 9. business leverage ratio, 10. commercial bank leverage ratio, 11. charge-off rates (all financial institution)rates (all financial institution)
Case B Data Set (21 data series)• In addition to Case A data set• In addition to Case A data set…• 12. Personal consumption expenditure (non-durable), 13. Private
domestic investment, 14. Price deflator (PCE), 15. Core CPI (ex. food and energy), 16. Civilian labor force, 17. Employees (total non-gy) p y (farm), 18. Core capital leverage ratio, 19. Domestically chartered commercial banks leverage ratio, 20. Charge-off rate (all loans and leases), 21. Charge-off rate (all loans)
How Bad was Lehman Shock? 23
Estimation Results: Smoothed Observables
Actual DataSmoothed (Case A)
How Bad was Lehman Shock? 26
Smoothed (Case B)
Estimation Results: Estimated Shocks
Est. Shock (Case A)Est. Shock (Case B)
How Bad was Lehman Shock? 28
Estimation Results: Bank Net Worth Shock
Est. Shock (Case A)Est. Shock (Case B)
How Bad was Lehman Shock? 30
Historical Decomposition: Output (Case A)p p ( )
4
6
‐2
0
2
‐6
‐4
‐12
‐10
‐8
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TFP Shock Preference Shock
Entrepreneur Net Worth Shock Banking Sector Net Worth Shock
Government Spending Shock Investment Specific Technology ShockGovernment Spending Shock Investment Specific Technology Shock
Labor Supply Shock Monetary Policy Shock
Output Smoothed (Output)
How Bad was Lehman Shock? 31
Historical Decomposition: Output (Case B)p p ( )
4
6
‐2
0
2
‐6
‐4
‐12
‐10
‐8
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TFP Shock Preference Shock
Entrepreneur Net Worth Shock Banking Sector Net Worth Shock
Government Spending Shock Investment Specific Technology ShockGovernment Spending Shock Investment Specific Technology Shock
Labor Supply Shock Monetary Policy Shock
Output Smoothed (Output)
How Bad was Lehman Shock? 32
Historical Decomposition: Investment (Case A)p ( )
20
30
‐10
0
10
‐30
‐20
‐60
‐50
‐40
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TFP Shock Preference Shock
Entrepreneur Net Worth Shock Banking Sector Net Worth Shock
Government Spending Shock Investment Specific Technology ShockGovernment Spending Shock Investment Specific Technology Shock
Labor Supply Shock Monetary Policy Shock
Investment Smoothed (Investment)
How Bad was Lehman Shock? 33
Historical Decomposition: Investment (Case B)p ( )
20
30
‐10
0
10
‐30
‐20
‐60
‐50
‐40
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TFP Shock Preference Shock
Entrepreneur Net Worth Shock Banking Sector Net Worth Shock
Government Spending Shock Investment Specific Technology ShockGovernment Spending Shock Investment Specific Technology Shock
Labor Supply Shock Monetary Policy Shock
Investment Smoothed (Investment)
How Bad was Lehman Shock? 34
Historical Decomposition: Corporate Borrowing Rate (Case A)
3
4
2
3
0
1
‐2
‐1
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TFP Shock Preference Shock
Entrepreneur Net Worth Shock Banking Sector Net Worth Shock
Government Spending Shock Investment Specific Technology ShockGovernment Spending Shock Investment Specific Technology Shock
Labor Supply Shock Monetary Policy Shock
Corporate Borrowing Rate Smoothed (Corporate Borrowing Rate)
How Bad was Lehman Shock? 35
Historical Decomposition: Corporate Borrowing Rate (Case B)
3
4
2
3
0
1
‐2
‐1
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TFP Shock Preference Shock
Entrepreneur Net Worth Shock Banking Sector Net Worth Shock
Government Spending Shock Investment Specific Technology ShockGovernment Spending Shock Investment Specific Technology Shock
Labor Supply Shock Monetary Policy Shock
Corporate Borrowing Rate Smoothed (Corporate Borrowing Rate)
How Bad was Lehman Shock? 36
Historical Decomposition: Bank Leverage (Case A)p g ( )15
5
10
0
‐10
‐5
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TFP Shock Preference Shock
Entrepreneur Net Worth Shock Banking Sector Net Worth Shock
Government Spending Shock Investment Specific Technology ShockGovernment Spending Shock Investment Specific Technology Shock
Labor Supply Shock Monetary Policy Shock
Bank Leverage Smoothed (Bank Leverage)
How Bad was Lehman Shock? 37
Historical Decomposition: Bank Leverage (Case B)p g ( )15
5
10
0
‐10
‐5
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TFP Shock Preference Shock
Entrepreneur Net Worth Shock Banking Sector Net Worth Shock
Government Spending Shock Investment Specific Technology ShockGovernment Spending Shock Investment Specific Technology Shock
Labor Supply Shock Monetary Policy Shock
Bank Leverage Smoothed (Bank Leverage)
How Bad was Lehman Shock? 38
Historical Contribution of Bank Net Worth Shock
output
investinvest.
corp. borr. rate
profit margin
bank lev.
39
hist. cont. bank nw shock (Case A)
Historical Contribution of Bank Net Worth Shock
output
investinvest.
corp. borr. rate
profit margin
bank lev.
How Bad was Lehman Shock? 40
hist. cont. bank nw shock (Case A) hist. cont. bank nw shock (Case B)
Conclusion: Contributions of this paperConclusion: Contributions of this paper
Theoretical Contribution:• Combined two canonical financial friction
models and embedded to the stylized DSGE model.
E i i l C t ib tiEmpirical Contribution:• Adopted Data-Rich estimation method in
estimating bank net worth shock.
How Bad was Lehman Shock? 41
Conclusion: So How Bad was Lehman Shock?Conclusion: So How Bad was Lehman Shock?How large was the magnitude of Lehman Shock?• Largest bank net worth shock at least in past 25 years.
Much larger than those during S&L crisis.
How large was its impact to the economy?• Quite large. Lehman Shock may have suppressed
investment by nearly 10%.
Is it over?Is it over?• The shock seems to have been successfully countered by
TARP and aggressive credit easing that the recessionary effect directly caused by Lehman Shock seems to be over.
How Bad was Lehman Shock? 42