This document summarizes a model that analyzes the interaction between public and private deleveraging in a small open economy. The model shows that larger and front-loaded fiscal consolidations entail larger output and welfare losses by postponing the end of the private deleveraging process. The model finds that deleveraging-friendly fiscal consolidations that are more gradual in nature minimize these losses.

1. When Fiscal Consolidation Meets Private Deleveraging1
Javier Andrés2, Óscar Arce3 and Carlos Thomas3
ADEMU Workshop "Fiscal Risk and Public Sector Balance Sheets",
6-7 July 2017
1The views expressed herein are those of the authors and not necessarily those of
Banco de España or the Eurosystem
2Universidad de Valencia, Banco de España
3Banco de España
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2. Outline
1 Introduction
2 Model
3 Baseline deleveraging scenario
4 Fiscal consolidation
Consolidation size
Gradualism
5 Concluding remarks
6 Appendix
2 / 32

3. Introduction
Many countries face lengthy private and public debt consolidation
processes
I amid low growth and in‡ation, and binding ZLB.
Key question: e¤ects of …scal consolidation in an environment of high
private debt cum deleveraging
This paper: develop a framework to analyze the interaction between
public and private deleveraging
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4. Framework and main questions
Model of small open economy in a monetary union with private and
public debt
Households and …rms borrow long term subject to collateral
constraints
Large negative …nancial shock triggers a slow private deleveraging
process
I Exit from deleveraging is endogenous
Analyze how the size and speed (and composition) of …scal
consolidation a¤ects the economy
I including (and especially) through its impact on private deleveraging
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5. Main result
Larger and front-loaded consolidations entail larger (relative)
output/welfare losses
I largely by postponing the end of private deleveraging
Argument in favor of deleveraging-friendly consolidations
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6. Related literature (I)
Before the crisis: extensive literature on the e¤ects of consolidations.
I Front-loaded adjustments more e¤ective and less costly
I Adjustments in public spending, rather than tax hikes, more e¤ective,
lasting and less costly.
The crisis has called these results called into question.
I Christiano et al. (2011), Woodford, 2011 and Eggertsson (2010): at
the ZLB, spending cuts depress output more than tax hikes
I Erceg and Lindé (2014): …scal multipliers depend on the incidence of
…scal shocks on the duration of ZLB.
Little work on the interaction between private debt and …scal
consolidations:
I Batini, Melina and Villa (2016) is one exception (see also: IMF Fiscal
Monitor Oct 2016)
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7. Related literature (II)
The role of economic policies in a high debt & deleveraging
environment cum ZLB:
I Andrés, Arce and Thomas (2017): "Structural reforms in a debt
overhang".
F SOE with exogenous monetary policy
I Arce, Hurtado and Thomas (2015): "Policy Spillovers and Synergies in
a Monetary Union"
F 2-country model with endogenous ZLB
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8. Outline
1 Introduction
2 Model
3 Baseline deleveraging scenario
4 Fiscal consolidation
Consolidation size
Gradualism
5 Concluding remarks
6 Appendix
8 / 32

9. Model structure
Small open economy in a monetary union
) monetary policy exogenous ZLB.
Four main agents
I Patient households (lenders)
I Impatient households (borrowers)
I (Impatient) entrepreneurs (borrowers)
I Government: consumes, sets taxes and issues debt.
Three production sectors
I Consumption goods (entrepreneurs + retailers)
I Equipment capital producers
I Construction
Trade with rest of MU: consumption goods and foreign debt.
Standard real and nominal frictions: investment adjustment costs,
nominal price and wage rigidities
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10. Impatient households
Maximize
E0
∞
∑
t=0
βt
(
log ct + ϑ log ht χ
Z 1
0
nC
t (i)1+ϕ
1 + ϕ
di
)
subject to
(1 + τc
t ) ct + ph
t [ht (1 δh) ht 1] = bt
Rt 1
πt
bt 1 Tt
+ (1 τw
t )
Z 1
0
Wt (i)
Pt
nC
t (i) di
and an asymmetric debt constraint ...
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11. Long-run private debt and borrowing constraints
We assume long-run debt
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12. Long-run private debt and borrowing constraints
We assume long-run debt
I A constant fraction 1 γ of outstanding nominal principal is amortized
each period ( Woodford, 2001).
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13. Long-run private debt and borrowing constraints
We assume long-run debt
I A constant fraction 1 γ of outstanding nominal principal is amortized
each period ( Woodford, 2001).
Dynamics of real outstanding debt:
bt =
bt 1
πt
|{z}
initial debt
1 γ
πt
bt 1
| {z }
amortization
+ bnew
t
|{z}
gross new credit
net of voluntary prepayments
=
γ
πt
bt 1 + bnew
t .
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14. Long-run private debt and borrowing constraints
We assume long-run debt
I A constant fraction 1 γ of outstanding nominal principal is amortized
each period ( Woodford, 2001).
Dynamics of real outstanding debt:
bt =
bt 1
πt
|{z}
initial debt
1 γ
πt
bt 1
| {z }
amortization
+ bnew
t
|{z}
gross new credit
net of voluntary prepayments
=
γ
πt
bt 1 + bnew
t .
In ’normal times’, borrowing is subject to a collateral constraint
(Kiyotaki & Moore 97; Iacoviello 05)
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15. Long-run private debt and borrowing constraints
We assume long-run debt
I A constant fraction 1 γ of outstanding nominal principal is amortized
each period ( Woodford, 2001).
Dynamics of real outstanding debt:
bt =
bt 1
πt
|{z}
initial debt
1 γ
πt
bt 1
| {z }
amortization
+ bnew
t
|{z}
gross new credit
net of voluntary prepayments
=
γ
πt
bt 1 + bnew
t .
In ’normal times’, borrowing is subject to a collateral constraint
(Kiyotaki & Moore 97; Iacoviello 05)
I but debtors cannot be forced to repay faster than at contractual rate
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16. Long-run private debt and borrowing constraints
We assume long-run debt
I A constant fraction 1 γ of outstanding nominal principal is amortized
each period ( Woodford, 2001).
Dynamics of real outstanding debt:
bt =
bt 1
πt
|{z}
initial debt
1 γ
πt
bt 1
| {z }
amortization
+ bnew
t
|{z}
gross new credit
net of voluntary prepayments
=
γ
πt
bt 1 + bnew
t .
In ’normal times’, borrowing is subject to a collateral constraint
(Kiyotaki & Moore 97; Iacoviello 05)
I but debtors cannot be forced to repay faster than at contractual rate
Borrowing constraint,
bnew
t maxf0,
collateral value
z }| {
mt
1
Rt
Etπt+1ph
t+1ht
contractual amort. path
z }| {
γ
πt
bt 1
| {z }
’excess’collateral
g
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17. Long-run private debt and borrowing constraints
In equilibrium, no voluntary early payments: bnew
t 0 ) An
asymmetric debt regime:
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18. Long-run private debt and borrowing constraints
In equilibrium, no voluntary early payments: bnew
t 0 ) An
asymmetric debt regime:
I ’Normal’regime (excess collateral > 0) =) bnew
t > 0 and bt equals
collateral value,
bt = mt
1
Rt
Etπt+1ph
t+1ht
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19. Long-run private debt and borrowing constraints
In equilibrium, no voluntary early payments: bnew
t 0 ) An
asymmetric debt regime:
I ’Normal’regime (excess collateral > 0) =) bnew
t > 0 and bt equals
collateral value,
bt = mt
1
Rt
Etπt+1ph
t+1ht
I ’Deleveraging’regime (excess collateral < 0) =) bnew
t = 0 and
bt follows the contractual amortization path,
bt =
γ
πt
bt 1
) Net debt ‡ows: bt
Rt 1
πt
bt 1 = (Rt 1 1)+(1 γ)
πt
bt 1 (interest +
amortization payments)
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20. Fiscal policy
Budget constraint (CPI-de‡ated),
b
g
t =
Rt 1
πt
b
g
t 1 +
PH,t
Pt
gt τw
t wtnt τc
tcTOT
t τk
t ∑
s=e,r,h,k
Πs
t Tt.
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21. Fiscal policy
Budget constraint (CPI-de‡ated),
b
g
t =
Rt 1
πt
b
g
t 1 +
PH,t
Pt
gt τw
t wtnt τc
tcTOT
t τk
t ∑
s=e,r,h,k
Πs
t Tt.
Fiscal rule,
fit = fit 1 + φb b
gy
t 1
¯bgy
+ φ∆b b
gy
t b
gy
t 1 ,
fit 2 fgt, τw
t , τc
t, τk
t , Ttg, where b
gy
t
Ptb
g
t
PH,tgdpt
: gov’t debt/GDP.
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22. Fiscal policy
Budget constraint (CPI-de‡ated),
b
g
t =
Rt 1
πt
b
g
t 1 +
PH,t
Pt
gt τw
t wtnt τc
tcTOT
t τk
t ∑
s=e,r,h,k
Πs
t Tt.
Fiscal rule,
fit = fit 1 + φb b
gy
t 1
¯bgy
+ φ∆b b
gy
t b
gy
t 1 ,
fit 2 fgt, τw
t , τc
t, τk
t , Ttg, where b
gy
t
Ptb
g
t
PH,tgdpt
: gov’t debt/GDP.
Fiscal consolidations consist of reductions in ¯bgy
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23. Fiscal policy
Budget constraint (CPI-de‡ated),
b
g
t =
Rt 1
πt
b
g
t 1 +
PH,t
Pt
gt τw
t wtnt τc
tcTOT
t τk
t ∑
s=e,r,h,k
Πs
t Tt.
Fiscal rule,
fit = fit 1 + φb b
gy
t 1
¯bgy
+ φ∆b b
gy
t b
gy
t 1 ,
fit 2 fgt, τw
t , τc
t, τk
t , Ttg, where b
gy
t
Ptb
g
t
PH,tgdpt
: gov’t debt/GDP.
Fiscal consolidations consist of reductions in ¯bgy
I Size: ∆¯bgy
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24. Fiscal policy
Budget constraint (CPI-de‡ated),
b
g
t =
Rt 1
πt
b
g
t 1 +
PH,t
Pt
gt τw
t wtnt τc
tcTOT
t τk
t ∑
s=e,r,h,k
Πs
t Tt.
Fiscal rule,
fit = fit 1 + φb b
gy
t 1
¯bgy
+ φ∆b b
gy
t b
gy
t 1 ,
fit 2 fgt, τw
t , τc
t, τk
t , Ttg, where b
gy
t
Ptb
g
t
PH,tgdpt
: gov’t debt/GDP.
Fiscal consolidations consist of reductions in ¯bgy
I Size: ∆¯bgy
I Gradualism: φb
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25. Fiscal policy
Budget constraint (CPI-de‡ated),
b
g
t =
Rt 1
πt
b
g
t 1 +
PH,t
Pt
gt τw
t wtnt τc
tcTOT
t τk
t ∑
s=e,r,h,k
Πs
t Tt.
Fiscal rule,
fit = fit 1 + φb b
gy
t 1
¯bgy
+ φ∆b b
gy
t b
gy
t 1 ,
fit 2 fgt, τw
t , τc
t, τk
t , Ttg, where b
gy
t
Ptb
g
t
PH,tgdpt
: gov’t debt/GDP.
Fiscal consolidations consist of reductions in ¯bgy
I Size: ∆¯bgy
I Gradualism: φb
I (Composition: choice of instrument fit)
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26. Calibration
Calibrated to Spain pre-crisis (2007)
I Key ratios: HH & NFC debt/GDP, NFA position/GDP, etc.
Debt constraints:
I LTV ratios: ¯m = 0.85, ¯me = 0.69
I Amortization rates: 1 γ = 0.02, 1 γe = 0.03
) average age of outstanding debt: γ/ (1 γ) = 12,
γe/ (1 γe) = 8 years
Fiscal policy:
I Initial tax rates ¯τx, x = c, w, k, set as in Stähler & Thomas (2011,
FiMod model)
I Initial gov’t debt ratio: ¯bgy = 80%
I Fiscal rule coe¢ cients (φb, φ∆b) set to make the de…cit paths roughly
similar across instruments
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27. Outline
1 Introduction
2 Model
3 Baseline deleveraging scenario
4 Fiscal consolidation
Consolidation size
Gradualism
5 Concluding remarks
6 Appendix
15 / 32

28. Baseline scenario: a deleveraging shock
Gradual, permanent fall in LTV ratios: mt, me
t
mt = (1 ρm) ¯m + ρmmt 1
similarly for me
t
Set ρm = 0.75; shock size,
j∆ ¯mj = 5 pp
' Spanish experience
Economy enters on impact the slow deleveraging regime
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29. Baseline deleveraging scenario: debt dynamics
0 5 10 15 20 25 30 35 40
80
85
90
95
100
105
110
115
120
125
130
Entrepreneur debt
quarters
%ofSSGDP
0 5 10 15 20 25 30 35 40
40
45
50
55
60
65
70
75
80
85
90
quarters
%ofSSGDP
Household debt
contractual amortization path
collateral values
debt
end of deleveraging (T*,T**)
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30. Baseline deleveraging scenario: macroeconomic adjustment
0 10 20 30 40
-6
-4
-2
0
GDP
%
0 10 20 30 40
-4
-2
0
2
employment
%
0 10 20 30 40
50
60
70
80
90
household debt/annual GDP
pp
0 10 20 30 40
100
110
120
130
entrepreneurial debt/annual GDP
pp
0 10 20 30 40
-4
-3
-2
-1
0
real estate prices
%
0 10 20 30 40
-15
-10
-5
0
total investment
%
0 10 20 30 40
-4
-2
0
2
total consumption
%
0 10 20 30 40
-2
-1
0
1
CPI inflation
annualizedpp
0 10 20 30 40
-3
-2
-1
0
real wage
quarters
%
0 10 20 30 40
-1
-0.5
0
0.5
1
ex-ante real interest rate
quarters
annualizedpp
0 10 20 30 40
-2
0
2
4
terms of trade
quarters
%
0 10 20 30 40
-0.5
0
0.5
1
1.5
net exports
quarters
%ofSSGDP
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31. Outline
1 Introduction
2 Model
3 Baseline deleveraging scenario
4 Fiscal consolidation
Consolidation size
Gradualism
5 Concluding remarks
6 Appendix
19 / 32

32. Fiscal consolidation under private deleveraging
Against the background of this baseline scenario...
... consider a …scal consolidation of (baseline) size
∆¯bgy
= 20 pp
¯bgy falls from 80% to 60%
Fiscal instrument: gov’t spending (gt)
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33. Fiscal consolidation: macroeconomic impact
0 10 20 30 40
-8
-6
-4
-2
0
GDP
quarters
%
0 10 20 30 40
50
60
70
80
90
government debt/GDP
quarters
pp
0 10 20 30 40
-5
-4
-3
-2
-1
0
1
private consumption
quarters
%
0 10 20 30 40
50
60
70
80
90
household debt/annual GDP
quarters
pp
0 10 20 30 40
100
110
120
130
140
entrepreneurial debt/annual GDP
quarters
pp
0 10 20 30 40
-5
-4
-3
-2
-1
0
1
2
CPI inflation
quarters
annualizedpp
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34. Fiscal consolidation: the ’duration’channel
0 5 10 15 20 25 30 35 40
50
55
60
65
70
75
80
85
90
Household debt
quarters
%ofSSannualGDP
collateral value, baseline
debt, baseline
collateral value, fiscal cons.
debt, fiscal cons.
bt
= γ*bt-1
/πt
for t<T**
Tcons
**T**
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35. Consolidation size
Compare consolidations of di¤erent sizes in terms of GDP e¤ects
rescaled by size,
∆gdpt
∆¯bgy
,
∆gdpt gdpcons
t gdpbase
t
Similar to ’…scal sacri…ce ratio’(e.g. Erceg & Lindé, 2013)
Show e¤ects relative to baseline (no consolidation) scenario: ∆gdpt
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36. Small vs large …scal consolidation
0 5 10 15 20 25 30 35 40 45 50
-0.2
-0.15
-0.1
-0.05
0
0.05
GDP effect of fiscal consolidations
quarters
%/pp
size = 1 pp
size = 20 pp
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37. Small vs large …scal consolidation
Relative welfare and output losses
Size: 1 pp 20 pp
Rel. PV output losses * 0.070 0.081
Rel. welfare loss ** 0.024 0.027
[T , T ] [9, 17] [11, 19]
* ∑40
t=1 βt 1
∆gdpt/ ∑40
t=1 βt 1
∆¯bgy
** In % of permanent consumption
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38. Gradualism
Consider di¤erent coe¢ cients φb on debt ratio deviations from target
(b
gy
t 1
¯bgy) in …scal rule
Size …xed at baseline (20pp)
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39. Gradualism
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40. Gradualism
Welfare losses (% of perm. cons.)
Scenario welf. loss (T , T )
Front-loaded 0.67 (12 , 22)
Baseline 0.55 (11 , 19)
Gradual 0.42 (10 , 18)
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41. Outline
1 Introduction
2 Model
3 Baseline deleveraging scenario
4 Fiscal consolidation
Consolidation size
Gradualism
5 Concluding remarks
6 Appendix
29 / 32

42. Concluding remarks
Understand the interconnection between …scal consolidation and
private deleveraging
New channel of …scal consolidations: e¤ect on private deleveraging
dynamics
Key …nding: larger and front-loaded …scal consolidations are
(relatively) more costly
I by hampering the recovery of borrowers’net worth (collateral values,
debt de‡ation)
I and thus prolonging their deleveraging processes
Results speak in favor of “deleveraging-friendly” consolidation
strategies
30 / 32

43. Outline
1 Introduction
2 Model
3 Baseline deleveraging scenario
4 Fiscal consolidation
Consolidation size
Gradualism
5 Concluding remarks
6 Appendix
31 / 32

44. Alternative …scal instruments
Di¤erent …scal instruments have a potentially very di¤erent macro
impact, through the private-deleveraging channel
32 / 32