Dissecting Saving Dynamics - Deutsche Bundesbank · Dissecting Saving Dynamics Measuring Credit, Wealth and Precautionary E ects Christopher Carroll1 Jirka Slacalek2 Martin Sommer3

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

















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), . . .



















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+


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


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.

http://econ.jhu.edu/people/ccarroll/BufferStockBPEA.pdf

http://econ.jhu.edu/people/ccarroll/papers/cstwMPC

http://econ.jhu.edu/people/ccarroll/papers/ctDiscrete

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.

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


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



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


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




4

6

8

10

12

4

6

8

10

12

2005 2007 2009 2011 2013 2015

Baseline 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



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


Household net wealth Unemployment rate

Credit conditions Household saving rate

Actual and Target Wealth

1970 1975 1980 1985 1990 1995 2000 2005 2010

16

18

20

22

24

26

Actual WealthTarget Wealth

Documents

Dissecting Saving Dynamics - Deutsche Bundesbank · Dissecting Saving Dynamics Measuring Credit, Wealth and Precautionary E ects Christopher Carroll1 Jirka Slacalek2 Martin Sommer3