Dissecting Saving Dynamics
Measuring Credit, Wealth and Precautionary Effects
Christopher Carroll1 Jirka Slacalek2 Martin Sommer3
1Johns Hopkins University and NBER
2European Central Bank
3International Monetary Fund
Deutsche Bundesbank DSGE / Macro Workshop
The views expressed are mineand do not necessarily reflect those of the ECB.
Modelling household heterogeneity
Two (complementary) approaches
1. Simple spender–saver two agent NK models, TANKBilbiie (2008), Debortoli and Galı (2017), . . .
2. Complex heterogeneous agent NK model, HANKKrueger, Mitman, and Perri (2016), . . .
This paper: ‘Middle ground’
I Simple, partial equilibrium model of personal saving rate . . .
I . . . modelling effects of precautionary saving (uncertainty), . . .
I . . . estimated on US aggregate time series
Modelling household heterogeneity
Two (complementary) approaches
1. Simple spender–saver two agent NK models, TANKBilbiie (2008), Debortoli and Galı (2017), . . .
2. Complex heterogeneous agent NK model, HANKKrueger, Mitman, and Perri (2016), . . .
This paper: ‘Middle ground’
I Simple, partial equilibrium model of personal saving rate . . .
I . . . modelling effects of precautionary saving (uncertainty), . . .
I . . . estimated on US aggregate time series
Modelling household heterogeneity
Two (complementary) approaches
1. Simple spender–saver two agent NK models, TANKBilbiie (2008), Debortoli and Galı (2017), . . .
2. Complex heterogeneous agent NK model, HANKKrueger, Mitman, and Perri (2016), . . .
This paper: ‘Middle ground’
I Simple, partial equilibrium model of personal saving rate . . .
I . . . modelling effects of precautionary saving (uncertainty), . . .
I . . . estimated on US aggregate time series
US personal saving rate (s), 1966–2015
1970 1975 1980 1985 1990 1995 2000 2005 2010 20150
5
10
15
Perc
ent
Literature on drivers of personal saving s
1. “Wealth Effects”
I Modigliani, Klein, MPS model, . . .I st = −0.05mt + other stuff
2. “Precautionary”: Unemployment risk
I Carroll (1992), . . .I Saving rate rises in recessionsI ∆ logCt+1 strongly related to Et(ut+1 − ut)
3. “Credit Availability”
I Secular Trend: Parker (2000), Muellbauer (many papers)
I Cyclical Dynamics: Guerrieri and Lorenzoni (2017), Eggertsson and Krugman (2012), . . .
I Great Recession: Justiniano, Primiceri, and Tambalotti (2019), Huo and Rıos-Rull (2016), . . .
Literature on drivers of personal saving s
1. “Wealth Effects”
I Modigliani, Klein, MPS model, . . .I st = −0.05mt + other stuff
2. “Precautionary”: Unemployment risk
I Carroll (1992), . . .I Saving rate rises in recessionsI ∆ logCt+1 strongly related to Et(ut+1 − ut)
3. “Credit Availability”
I Secular Trend: Parker (2000), Muellbauer (many papers)
I Cyclical Dynamics: Guerrieri and Lorenzoni (2017), Eggertsson and Krugman (2012), . . .
I Great Recession: Justiniano, Primiceri, and Tambalotti (2019), Huo and Rıos-Rull (2016), . . .
Literature on drivers of personal saving s
1. “Wealth Effects”
I Modigliani, Klein, MPS model, . . .I st = −0.05mt + other stuff
2. “Precautionary”: Unemployment risk
I Carroll (1992), . . .I Saving rate rises in recessionsI ∆ logCt+1 strongly related to Et(ut+1 − ut)
3. “Credit Availability”
I Secular Trend: Parker (2000), Muellbauer (many papers)
I Cyclical Dynamics: Guerrieri and Lorenzoni (2017), Eggertsson and Krugman (2012), . . .
I Great Recession: Justiniano, Primiceri, and Tambalotti (2019), Huo and Rıos-Rull (2016), . . .
Saving rate in Great Recession, 2007–
Deviation of saving rate from pre-recession value
-4.0
0-2
.00
0.0
02
.00
4.0
06
.00
De
via
tio
n fro
m S
tart
-of-
Re
ce
ssio
n V
alu
e in
%
0 2 4 6 8 10 12 14 16 18 20Quarters after Start of Recession
Historical Range Historical Mean 2007+
I s rises by ∼4–5 pp
I Bigger & more persistentincrease than any postwarrecession
But all three indicators also move a lot:
1. Household wealth 2007– ↓ by 100% of income
-100
-50
050
100
Dev
iatio
n fr
om S
tart
-of-
Rec
essi
on V
alue
0 2 4 6 8 10 12 14 16 18 20Quarters after Start of Recession
Historical Range Historical Mean 2007+
But all three indicators also move a lot:
2. Sustained expectations of rising unemployment 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
But all three indicators also move a lot:
3. Tighter household credit supply (based on Muellbauer)
1970 1975 1980 1985 1990 1995 2000 2005 20100
0.2
0.4
0.6
0.8
1
Our contribution
Theory
I Simple model with transparent role for all 3 channels
I Qualitative implications of the model
I “Overshooting” ⇒ possible role for fiscal policy
EvidenceI Estimated structural model of saving rate s
I Quantify importance of the 3 channels using aggregate time series
Preview of results
I Model matches actual dynamics of aggregate saving rate
I All three effects present
I Easier borrowing largely explains secular decline in s
I Unemployment risk significant, counter-cyclical
I Order of importance in Great Recession:
1. Wealth shock2. Unemployment risk3. Credit tightening
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 Unemployment risk (prob of becoming unemployed): fI Tractability: unemployment shocks are permanent [if ξt = ξu then ξt+1 = ξu]
I ` and W grow at constant rate
I Target wealth m exists and is stable:
I Consumption chosen so that mt → m
Consumption function
Δ+1e =0⟶
Δ+1e = 0 ↘
e()=Stable Arm⟶
SS ↘
e
e
Consumption after a wealth shock
Δ+1e = 0 ↘
()⟶
t ⟶⟵ t+1
Wealth Shock
↖ Target
()⟶
t
Permanent rise in unemployment risk f
Sustainable c �
� cHmL after unemployment rate increase
� Target
cHmL�
mÇ m
c
Saving rate after permanent rise in f
⟵ Overshooting
tTime
ˇt
ˇt
t
Credit easing/financial innovation & deregulation
↖ Orig Target⟵ Δ t+1
e = 0⟵ Orig ()
New () ⟶
-
Expansion of borrowing limit hm is close to linear in credit conditions
Data & sources
I Quarterly 1966Q2–2011Q4
I Saving rate: BEA NIPA
I Net worth: US Financial Accounts (Flow of Funds), Fed
I Credit conditions: “Credit Easing Accumulated,” CEA
I Senior Loan Officer Opinion Survey (SLOOS), Fed
I Question on banks’ willingness to provide consumer installment loans—Loan supply
I Unemployment risk: using Thomson Reuters/UMichigan unempl expectations
Net worth (ratio to disposable income) m
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 loans now as opposed to threemonths ago.”
1970 1975 1980 1985 1990 1995 2000 2005 20100
0.2
0.4
0.6
0.8
1
ft implied by Michigan unemployment 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
Structural estimation—Nonlinear least squares
Minimize distance between model-implied stheort and actual smeas
t :
Θ = arg min1
T
T∑t=1
(smeast − stheor
t
(Θ;mt − m(·)
))2
I Parameters: Θ ={β, θCEA, θf, θu
}; β: discount factor
I Target wealth m = m(ht ,ft)
I Depends negatively on credit supply CEA and positively on unemp risk f
I Shifter of target wealth: ht = θCEACEAt
I Unemployment risk: ft = θf + θuEtut+4
Structural estimation—Asymptotics
Delta method standard errors
T 1/2(Θ−Θ
)→d N
(0, σ2 ×
(lim
T→∞E(F′F/T )
)−1),
where the variance matrix can consistently be estimated with:
σ2 ×(F′F/T)−1
I Var of residuals σ2 = 1T
∑Tt=1
(smeast − stheor
t (Θ; zt))2
I Gradient of saving rate function F = ∇Θ′stheort
(Θ; zt
),
evaluated at optimal Θ (calculated numerically)
I Data zt ={mt ,CEAt ,Etut+4
}
Structural estimatesst = s
({mt ,CEAt ,Etut+4}; Θ
),
ht = 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, θCEA, θf, θu}β Discount Factor 1− 0.0065∗∗∗
(0.0005)θCEA Scaling of CEAt to ht 8.8943∗∗∗
(0.8403)
θf Scaling of Etut+4 to ft 1.2079×10−4∗∗∗
(0.2757× 10−4)
θu Scaling of Etut+4 to ft 2.6764×10−4∗∗∗
(0.6490× 10−4)
R2 0.906DW stat 0.780
Structural estimates: Interpretation of parameters
I Discount factor β = 1− 0.0065 or 0.974 at annual frequency [standard]
I Credit availability ht varies b/w 0 and 8.89/4 ≈ 2.2 ⇒Credit availability ↑ by 220% of DI due to fin deregulation 1966–2007 (peak)
I Unemployment risk ft
I Ranges b/w 1.25× 10−4 and 1.5× 10−4 per quarter
I ⇒ 3 % prob to become permanently unemployed per life cycle (50 years)
I ft is highly counter-cyclical
I 20 % ↑ in ft ⇒ 1 pp ↑ saving rate (regular recession)
Similar response to richer models [eg Carroll, Slacalek, Tokuoka, and White (2017)]
Actual and fitted saving rate
1970 1975 1980 1985 1990 1995 2000 2005 20100
5
10
15Actual PSRFitted PSR
Structural model vs. linear, reduced form model
Actual and Explained Change of the Saving Rate: 2006/07–2009/10
Model Decomposition
Variable Structural Reduced Form Actual ∆st
mt 1.3 −0.89×−1.19 = 1.1CEAt 0.6 −7.91×−0.12 = 1.0Etut+4 0.7 0.20× 4.6 = 0.9
Explained/Actual ∆st 2.6 3.0 2.6
Decomposition of fitted saving rate s
1970 1975 1980 1985 1990 1995 2000 2005 20100
2
4
6
8
10
12
14
Fitted PSRFitted PSR excl. UncertaintyFitted PSR excl. Uncertainty and CEA
I CEA essential to capturetrend in s
I m, f: business-cyclechanges in s
I Implied MPCW ≈ 0.015[Lower range of typicalestimates, 0.02–0.07]
Competitor models of saving
I Quadratic utility / linearized models: No role for effects of uncertainty
I Demographics: Aging implies increasing saving rate [counterfactual]
I Increasing inequality: Top income / wealth not related to s
Robustness: Saving rate and share of 65+ years
05
1015
Sha
re o
n To
tal,
Per
cent
1960 1970 1980 1990 2000 2010
Year
Robustness: Government, corporate, personal saving rate
-15
-10
-50
510
15P
erce
nt
1960 1970 1980 1990 2000 2010
Year
Government Corporate Personal
Robustness: Top 1 percent income and wealth share
05
1015
2025
3035
40S
hare
of T
op 1
% o
n To
tal,
Per
cent
1960 1970 1980 1990 2000 2010
Year
Income Wealth
Summary and conclusions
I Estimate simple model with precautionary saving
I Model matches actual aggregate saving rate dynamics
I All three effects present
I Easier borrowing largely explains secular decline in s
I Order of importance in Great Recession:
1. Wealth shock2. Unemployment risk3. Credit tightening
To Do: Need to combine aggregate time series w/ household heterogeneity
References
Bilbiie, Florin O. (2008): “Limited Asset Markets Participation, Monetary Policy and (Inverted) Aggregate Demand Logic,” Journal of EconomicTheory, 140(1), 162–196.
Carroll, Christopher D. (1992): “The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence,” Brookings Papers on EconomicActivity, 1992(2), 61–156, http://econ.jhu.edu/people/ccarroll/BufferStockBPEA.pdf.
Carroll, Christopher D., Jiri Slacalek, Kiichi Tokuoka, and Matthew N. White (2017): “The Distribution of Wealth and the MarginalPropensity to Consume,” Quantitative Economics, 8, 977–1020, At http://econ.jhu.edu/people/ccarroll/papers/cstwMPC.
Carroll, Christopher D., and Patrick Toche (2009): “A Tractable Model of Buffer Stock Saving,” NBER Working Paper Number 15265,http://econ.jhu.edu/people/ccarroll/papers/ctDiscrete.
Debortoli, Davide, and Jordi Galı (2017): “Monetary policy with heterogeneous agents: Insights from TANK models,” Manuscript.
Eggertsson, Gauti B., and Paul Krugman (2012): “Debt, Deleveraging, and the Liquidity Trap: A Fisher–Minsky–Koo Approach,” TheQuarterly Journal of Economics, 127(3), 1469–1513.
Guerrieri, Veronica, and Guido Lorenzoni (2017): “Credit crises, precautionary savings, and the liquidity trap,” The Quarterly Journal ofEconomics, 132(3), 1427–1467.
Huo, Zhen, and Jose-Vıctor Rıos-Rull (2016): “Financial Frictions, Asset Prices, and the Great Recession,” Staff Report 526, Federal ReserveBank of Minneapolis.
Justiniano, Alejandro, Giorgio Primiceri, and Andrea Tambalotti (2019): “Credit Supply and the Housing Boom,” Journal of PoliticalEconomy.
Krueger, Dirk, Kurt Mitman, and Fabrizio Perri (2016): “Macroeconomics and Household Heterogeneity,” Handbook of Macroeconomics, 2,843–921.
Parker, Jonathan A. (2000): “Spendthrift in America? On Two Decades of Decline in the U.S. Saving Rate,” in NBER Macroeconomics Annual1999, Volume 14, NBER Chapters, pp. 317–387. National Bureau of Economic Research, Inc.
Background Slides
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.
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EA
/Deb
t−In
com
e R
atio
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Assumptions/Scenarios for Out-of-Sample Forecasts
Sources: Haver Analytics and authors' estimates.
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Baseline scenario
Upside risk scenario
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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.
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450
500
550
600
650
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2005 2007 2009 2011 2013 2015
Baseline scenario
Upside risk scenario
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(percent of disposable personal income)
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2005 2007 2009 2011 2013 2015
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Upside risk scenario
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2005 2007 2009 2011 2013 2015
Baseline Scenario
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Fitted values of model
(percent of disposable personal income)
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Credit conditions Household saving rate
Actual and Target Wealth
1970 1975 1980 1985 1990 1995 2000 2005 2010
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Actual WealthTarget Wealth