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Dissecting Saving DynamicsMeasuring Credit, Wealth and Precautionary Effects
Christopher Carroll1 Jiri Slacalek2 Martin Sommer3
1Johns Hopkins University and [email protected]
2European Central [email protected]
3International Monetary [email protected]
Presentation at Goethe-Universitat Frankfurt, May 2012
US Personal Saving Rate (s), 1966–2011
1970 1975 1980 1985 1990 1995 2000 2005 20100
2
4
6
8
10
12
14
Perc
ent o
f Dis
posa
ble
Inco
me
Literature
I “Wealth Effects”I Modigliani, Klein, MPS model, ...
I st = −0.05mt + other stuff
I “Precautionary”I Carroll (1992)
I Saving rate rises in recessionsI ∆ logCt+1 strongly related to Et(ut+1 − ut)
I “Credit Availability”I Secular Trend:
I Parker (2000), Dynan and Kohn (2007), Muellbauer (manypapers)
I Cyclical Dynamics:I Guerrieri and Lorenzoni (2011), Eggertsson and Krugman
(2011), Hall (2011)
Great Recession 2007–2009
I s rises by ∼4–5 pp
I Bigger & more persistent increase than any postwar recessionI But all three indicators also move a lot:
I Credit conditions tightenI Unemployment Expectations riseI Wealth falls
Personal Saving Rate 2007– ↑
−4−2
02
4D
evia
tion
from
Sta
rt−of
−Rec
essi
on V
alue
in %
0 2 4 6 8 10 12 14 16 18 20Quarters after Start of Recession
Historical Range Historical Mean 2007−2011
Household Wealth 2007– ↓ by 150% of Income
−150
−100
−50
050
100
Dev
iatio
n fro
m S
tart−
of−R
eces
sion
Val
ue
0 2 4 6 8 10 12 14 16 18 20Quarters after Start of Recession
Historical Range Historical Mean 2007−2009 Recession
Sustained Expectations of Rising Unemp RiskThomson Reuters/University of Michigan Et(ut+4 − ut)
1970 1975 1980 1985 1990 1995 2000 2005 2010
30
40
50
60
70
80
90
100
110
120
130
Tighter HH Credit Supply (Based on Muellbauer)
1970 1975 1980 1985 1990 1995 2000 2005 20100
0.2
0.4
0.6
0.8
1
Our Contributions
I TheoryI Simple model with transparent role for all 3 channelsI Qualitative implications of the model
I “Overshooting” ⇒ possible role for fiscal policy
I EvidenceI Quantify importance of the 3 channelsI Two estimated models of s
I Reduced-form—OLSI Structural—Nonlinear least squares
Why Do We Care?
I Quantify role of credit, wealth and uncertainty
I Useful for in-sample and out-of-sample analysis
I Strength of recovery/dynamics of GDP
Theory a la Carroll and Toche (2009)
I CRRA utility, labor supply `, agg wage W, emp status ξ:
v(mmmt) = maxccct
u(ccct) + βEt
[v(mmmt+1)
]s.t.
mmmt+1 = (mmmt − ccct)R + `t+1Wt+1ξt+1
I ξt+1 ∈ {ξu, ξe} where ξu < ξe
I ` and W grow at constant rateI Tractability: unemployment shocks are permanent
I If ξt = ξu then ξt+1 = ξu
I Target wealth m exists and is stable:I Consumption chosen so that mt → m
Target Wealth m
Closed-form solution for target wealth depends on unemploymentrisk f and generosity of unemployment insurance ξu:
m = f ( f(+), ξu
(−), preferences, . . . )
Consumption After a Wealth Shock
Dmt+1e = 0 �
cHmL�
ct � � ct+1
Wealth Shock
� Target
cHmL�
mÇ
mt
m
cÇ
c
Overshooting and Fiscal Policy
DSGE models:
I Frictions, frictions everywhere; but missing hereI If ∆c imposes ‘external’ costs
I Sticky prices/wagesI Capital (or Investment) adjustment costsI Other reasons for ‘pecuniary externalities’
I ⇒ ‘stimulus’ payments, fiscal policy may reduce cost of cycle
I Justification for ‘automatic stabilizers’?
Credit Easing/Financial Innovation & Deregulation
� Orig Target� D mt+1
e = 0� Orig cHmL
New cHmL �
-h 0.m
c
m is close to linear in credit conditions
Data & Sources
I Quarterly 1966Q2–2011Q1
I Saving rate: BEA NIPAI Net worth: Flow of Funds Accounts, Fed
I (Model m corresponds to 1 + ratio of Net worth to disposableincome)
I Credit conditions: “Credit Easing Accumulated,” CEAI Senior Loan Officer Opinion Survey (SLOOS), FedI Banks’ willingness to provide consumer installment loans
I Unemployment risk: using Thomson Reuters/UMichiganunemployment expectations
Net Worth (Ratio to Quarterly Disp Income)
44.
55
5.5
66.
5
1970 1975 1980 1985 1990 1995 2000 2005 2010
Credit Easing Accumulated (CEA) (a la Muellbauer)Accumulated responses, weighted with debt–income ratio, to:“Please indicate your bank’s willingness to make consumer installment loansnow as opposed to three months ago.”
1970 1975 1980 1985 1990 1995 2000 2005 20100
0.2
0.4
0.6
0.8
1
ft Implied by Michigan U ExpectationsI Regress: ∆4ut+4 = α0 + α1UExptI U risk: ft = ut + ∆4ut+4
I ∆4ut+4 ≡ ut+4 − ut , ∆4ut+4 ≡ fitted valuesI ft tracks but precedes actual U
UExp: “How about people out of work during the coming 12 months—do you think
that there will be more unemployment than now, about the same, or less?”
24
68
10
1970 1975 1980 1985 1990 1995 2000 2005 2010
Reduced-Form Regressions
st = γ0 +γmmt +γCEACEAt +γEuEtut+4 +γt t +γuC (Etut+4×CEAt)+εt
Model Time Wealth CEA Un Risk All 3 Baseline Interact
γ0 11.95∗∗∗ 25.20∗∗∗ 9.32∗∗∗ 8.24∗∗∗ 14.90∗∗∗ 15.23∗∗∗ 15.55∗∗∗
(0.61) (1.73) (0.57) (0.42) (2.56) (2.16) (2.56)γm −2.61∗∗∗ −1.12∗∗∗ −1.18∗∗∗ −1.37∗∗∗
(0.32) (0.42) (0.35) (0.46)γCEA −14.14∗∗∗ −5.47∗∗∗ −6.12∗∗∗ −4.60∗∗∗
(1.74) (1.94) (0.57) (1.72)γEu 0.67∗∗∗ 0.32∗∗∗ 0.29∗∗∗ 0.38∗∗∗
(0.05) (0.12) (0.08) (0.11)γt −0.04∗∗∗ −0.03∗∗∗ 0.04∗∗∗ −0.05∗∗∗ −0.00 0.00
(0.00) (0.00) (0.01) (0.00) (0.01) (0.01)γuC −0.32∗∗
(0.16)
R2 0.70 0.85 0.82 0.88 0.89 0.90 0.90F stat p val 0.00 0.00 0.00 0.00 0.00 0.00 0.00DW stat 0.30 0.69 0.50 0.86 0.94 0.93 0.98
Model Baseline Uncert st−1 Debt Full Controls Post-80 IV
γm −1.18∗∗∗ −1.21∗∗∗−0.31 −0.80∗∗ −1.30∗∗∗ −1.50 −2.02∗∗∗
(0.35) (0.36) (0.22) (0.36) (0.31) (1.25) (0.49)γCEA −6.12∗∗∗ −5.97∗∗∗−2.87∗∗∗−5.40∗∗∗ −6.24∗∗∗ −5.00∗∗ −5.85∗∗∗
(0.57) (0.65) (0.53) (0.73) (0.63) (2.00) (1.17)γEu 0.29∗∗∗ 0.28∗∗∗ 0.14∗∗∗ 0.34∗∗∗ 0.12 0.30∗∗ 0.08
(0.08) (0.09) (0.05) (0.07) (0.09) (0.14) (0.13)γσ 0.26
(0.47)γs 0.57∗∗∗
(0.07)γd −1.91
(1.16)γr 0.13∗∗∗
(0.04)γGS −0.12
(0.08)γCS −0.31∗∗
(0.14)γ0post80 −1.48
(7.90)γmpost80 0.56
(1.29)γCEApost80 −2.35
(2.13)
Reduced-Form Regressions—Summary
The three factors explain saving well:
1. Credit conditions
2. Wealth
3. Unemployment risk
Structural Estimation—Nonlinear Least Squares
Minimize distance between model-implied stheort and actual smeas
t :
Θ = arg minT∑t=1
(smeast −stheor
t
(Θ;mt−m
(m(CEAt),f(Etut+4)
)))2
,
where
I Θ = {β, θm, θCEA, θf, θu}I mt = θm + θCEACEAt
I ft = θf + θuEtut+4
I β: discount factor
Structural Estimation—Asymptotics
Delta Method
T 1/2(Θ−Θ)→d N (0,D−1ED ′−1),
where
I D = E∂qt(Θ)∂Θ′
I E = var(qt(Θ)
)I Scores qt(Θ) =
(smeast − stheor
t (Θ))∂stheor
t (Θ)∂Θ′
Structural Estimates
stheort = stheor
t
(Θ;mt − m(mt ,ft)
),
mt = θm + θCEACEAt ,ft = θf + θuEtut+4.
Parameter Description Value
Calibrated Parametersr Interest Rate 0.04/4∆W Wage Growth 0.01/4ρ Relative Risk Aversion 2
Estimated Parameters Θ = {β, θm, θCEA, θf, θu}β Discount Rate 1− 0.0064∗∗∗
(0.0018)θm Scaling of mt 0.0072
(0.0206)θCEA Scaling of mt 5.2215∗∗∗
(0.1396)θf Scaling of ft 5.3758×10−5
(8.4334×10−5)θu Scaling of ft 0.0363
(0.1227)
R2 0.821DW stat 0.950
Estimated Extent of Credit Constraints mt (Frac of DI)
1970 1975 1980 1985 1990 1995 2000 2005 20100
1
2
3
4
5
6
Estimated Permanent Unemployment Risk ft
1970 1975 1980 1985 1990 1995 2000 2005 20106.5
7
7.5
8
8.5
9
9.5x 10
−5
Fit of the Structural Model
1970 1975 1980 1985 1990 1995 2000 2005 20100
2
4
6
8
10
12Actual PSRFitted PSR
Decomposition of Fitted PSRFix ft and CEAt at their sample means, back out the implied st
1970 1975 1980 1985 1990 1995 2000 2005 20100
2
4
6
8
10
12
Fitted PSRFitted PSR excl. UncertaintyFitted PSR excl. Uncertainty and CEA
Fit: Structural Model vs Reduced-Form
24
68
1012
1970 1975 1980 1985 1990 1995 2000 2005 2010
Actual Reduced−Form Structural
Reduced-Form Regressions on Model Data
stheort = γ0+γmmt+γCEACEAt+γEuEtut+4+γt t+γuC (Etut+4×CEAt)+εt
Model Time Wealth CEA Un Risk All 3 Baseline Interact
γ0 11.96∗∗∗ 21.44∗∗∗ 9.35∗∗∗ 8.42∗∗∗ 12.24∗∗∗ 12.51∗∗∗ 12.49∗∗∗
(0.50) (1.11) (0.41) (0.16) (0.60) (0.53) (0.55)γm −2.33∗∗∗ −0.79∗∗∗ −0.85∗∗∗ −0.94∗∗∗
(0.25) (0.12) (0.10) (0.11)γCEA −13.82∗∗∗ −5.85∗∗∗ −6.49∗∗∗ −5.33∗∗∗
(1.12) (0.59) (0.14) (0.47)γEu 0.63∗∗∗ 0.33∗∗∗ 0.30∗∗∗ 0.37∗∗∗
(0.02) (0.04) (0.02) (0.03)γt −0.04∗∗∗ −0.03∗∗∗ 0.04∗∗∗ −0.05∗∗∗ −0.00 0.00
(0.00) (0.00) (0.01) (0.00) (0.00) (0.00)γuC −0.19∗∗∗
(0.04)
R2 0.80 0.93 0.93 0.98 0.99 0.99 0.99F stat p val 0.00 0.00 0.00 0.00 0.00 0.00 0.00DW stat 0.05 0.22 0.09 0.39 0.72 0.71 0.99
Reduced-Form Regressions on Actual Data
smeast = γ0+γmmt+γCEACEAt+γEuEtut+4+γt t+γuC (Etut+4×CEAt)+εt
Model Time Wealth CEA Un Risk All 3 Baseline Interact
γ0 11.95∗∗∗ 25.20∗∗∗ 9.32∗∗∗ 8.24∗∗∗ 14.90∗∗∗ 15.23∗∗∗ 15.55∗∗∗
(0.61) (1.73) (0.57) (0.42) (2.56) (2.16) (2.56)γm −2.61∗∗∗ −1.12∗∗∗ −1.18∗∗∗ −1.37∗∗∗
(0.32) (0.42) (0.35) (0.46)γCEA −14.14∗∗∗ −5.47∗∗∗ −6.12∗∗∗ −4.60∗∗∗
(1.74) (1.94) (0.57) (1.72)γEu 0.67∗∗∗ 0.32∗∗∗ 0.29∗∗∗ 0.38∗∗∗
(0.05) (0.12) (0.08) (0.11)γt −0.04∗∗∗ −0.03∗∗∗ 0.04∗∗∗ −0.05∗∗∗ −0.00 0.00
(0.00) (0.00) (0.01) (0.00) (0.01) (0.01)γuC −0.32∗∗
(0.16)
R2 0.70 0.85 0.82 0.88 0.89 0.90 0.90F stat p val 0.00 0.00 0.00 0.00 0.00 0.00 0.00DW stat 0.30 0.69 0.50 0.86 0.94 0.93 0.98
Structural Estimation—Summary
I Model fits well. . .
I . . . almost as well as reduced form(Mincer–Zarnowitz puts weight 0.45 on structural model)
I Substantial role for time-varying precautionary saving
I CEA matters for low frequency,wealth for business-cycle frequency
PSR Forecasts—In Sample
Great Recession 2007–2010
Variable Reduced-Form Model Structural Model Actual ∆st
γm ×∆mt −1.18×−1.39 = 1.64 −0.97×−1.39 = 1.34γCEA ×∆CEAt −6.12×−0.11 = 0.64 −6.38×−0.11 = 0.67γEu ×∆Etut+4 0.29× 4.33 = 1.24 0.32× 4.33 = 1.39
Explained ∆st 3.53 3.40 2.93
PSR Forecasts—Out of Sample
2012–2015
0
2
4
6
8
0
2
4
6
8
2005 2007 2009 2011 2013 2015
Baseline Scenario
Upside Risk Scenario
Downside Risk Scenario
Fitted values of model
(percent of disposable personal income)
Scenarios based on SPF and our judgement
Conclusions
I All three effects present
I Easier borrowing largely explains secular decline sI Order of importance in Great Recession:
1. Wealth shock2. Labor income risk3. Credit tightening
I PSR to remain elevated
References
Carroll, Christopher D. (1992): “The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence,”Brookings Papers on Economic Activity, 1992(2), 61–156,http://econ.jhu.edu/people/ccarroll/BufferStockBPEA.pdf.
Carroll, Christopher D., and Patrick Toche (2009): “A Tractable Model of Buffer Stock Saving,” NBERWorking Paper Number 15265, http://econ.jhu.edu/people/ccarroll/papers/ctDiscrete.
Dynan, Karen E., and Donald L. Kohn (2007): “The Rise in US Household Indebtedness: Causes andConsequences,” in The Structure and Resilience of the Financial System, ed. by Christopher Kent, and JeremyLawson, pp. 84–113. Reserve Bank of Australia.
Eggertsson, Gauti B., and Paul Krugman (2011): “Debt, Deleveraging, and the Liquidity Trap: AFisher-Minsky-Koo Approach,” Manuscript, NBER Summer Institute.
Guerrieri, Veronica, and Guido Lorenzoni (2011): “Credit Crises, Precautionary Savings and the LiquidityTrap,” Manuscript, MIT Department of Economics.
Hall, Robert E. (2011): “The Long Slump,” AEA Presidential Address, ASSA Meetings, Denver.
Parker, Jonathan A. (2000): “Spendthrift in America? On Two Decades of Decline in the U.S. Saving Rate,”in NBER Macroeconomics Annual 1999, ed. by Ben S. Bernanke, and Julio J. Rotemberg, vol. 14, pp.317–387. NBER.
Alternative Measures of Credit Availability
.6.7
.8.9
1A
biad
et a
l. In
dex
of F
inan
cial
Lib
eral
izat
ion
0.5
11.
5C
EA
/Deb
t−In
com
e R
atio
1970 1975 1980 1985 1990 1995 2000 2005 2010
Assumptions/Scenarios for Out-of-Sample Forecasts
Sources: Haver Analytics and authors' estimates.
400
450
500
550
600
650
700
400
450
500
550
600
650
700
2005 2007 2009 2011 2013 2015
Baseline scenario
Upside risk scenario
Downside risk scenario
(percent of disposable personal income)
4
6
8
10
12
4
6
8
10
12
2005 2007 2009 2011 2013 2015
Baseline scenario
Upside risk scenario
Downside riskscenarioUnemploymentexpectations
(percent of labor force)
0.7
0.8
0.9
1.0
1.1
1.2
1.3
0.7
0.8
0.9
1.0
1.1
1.2
1.3
2005 2007 2009 2011 2013 2015
Baseline scenario
Upside risk scenario
Downside risk scenario
0
2
4
6
8
0
2
4
6
8
2005 2007 2009 2011 2013 2015
Baseline Scenario
Upside Risk ScenarioDownside Risk Scenario
Fitted values of model
(percent of disposable personal income)
Household net wealth Unemployment rate
Credit conditions Household saving rate
Assumptions/Scenarios for Out-of-Sample Forecasts
Sources: Haver Analytics and authors' estimates.
400
450
500
550
600
650
700
400
450
500
550
600
650
700
2005 2007 2009 2011 2013 2015
Baseline scenario
Upside risk scenario
Downside risk scenario
(percent of disposable personal income)
4
6
8
10
12
4
6
8
10
12
2005 2007 2009 2011 2013 2015
Baseline scenario
Upside risk scenario
Downside riskscenarioUnemploymentexpectations
(percent of labor force)
0.7
0.8
0.9
1.0
1.1
1.2
1.3
0.7
0.8
0.9
1.0
1.1
1.2
1.3
2005 2007 2009 2011 2013 2015
Baseline scenario
Upside risk scenario
Downside risk scenario
0
2
4
6
8
0
2
4
6
8
2005 2007 2009 2011 2013 2015
Baseline Scenario
Upside Risk ScenarioDownside Risk Scenario
Fitted values of model
(percent of disposable personal income)
Household net wealth Unemployment rate
Credit conditions Household saving rate