Download Fiscal Stimulus and Distortionary Taxation Harald Uhlig Thorsten Drautzburg January 8, 2010

Fiscal Stimulus and Distortionary Taxation
Harald Uhlig1
Thorsten Drautzburg2
1 University of Chicago
Department of Economics
[email protected]
2 [email protected]
January 8, 2010
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
1 / 70
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
2 / 70
Introduction
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
3 / 70
Introduction
Question and Answers
Question:
What is the effect of a fiscal stimulus as the ARRA?
What are the resulting fiscal multipliers?
Answers: ...
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Introduction
Bernstein-Romer, Appendix: Multipliers
Romer−Bernstein output effects of a permanent stimulus of 1% of GDP
1.6
government spending
1.4
output effect
1.2
1
0.8
tax cut
0.6
0.4
0.2
0
2009
Harald Uhlig (University of Chicago)
2010
2011
Date
2012
Fiscal Stimulus and Distortionary Taxation
2013
January 8, 2010
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Introduction
What I do:
Build on: Cogan-Cwik-Taylor-Wieland (2009), using
Smets-Wouters (CCTW-SW). Lump-sum taxes.
This paper:
!
!
!
!
Medium-to-long term effects.
Distortionary labor taxation ...
... plus: rule-of-thumb consumers.
... plus: binding zero lower bound.
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Introduction
Key insights
Output response is modest. Fiscal multipliers are typically below
1.
Consumption response is typically negative or, at most, feebly
positive.
In the medium-to-long term:
!
!
Pronounced output loss due to increased tax burden.
Output losses large relative to initial increase.
Note: No or only moderate inflation tax on initial bond holders, i.e. no
“stealing from the Chinese”.
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
7 / 70
The model
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
8 / 70
The model
Smets-Wouters (2007): overview
Elaborate New Keynesian model.
Continuum of households. They supply household-specific labor
in monopolistic competition. They set wages. Wages are
Calvo-sticky.
Continuum of intermediate good firms. They supply intermediate
goods in monopolistic competition. They set prices. Prices are
Calvo-sticky.
Final goods use intermediate goods. Perfect competition.
Habit formation, adjustment costs to investment, variable capital
utilization.
Monetary authority: Taylor-type rule.
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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The model
Application to ARRA
CCWT: path for government spending. Government consumption.
Perhaps additively separable in utility.
CCWT: Fed-Funds = 0 for four quarters. “Jump” to “switched-off”
Taylor rule.
This paper:
!
!
!
!
!
Distortionary labor taxation, consumption taxes, capital income
taxes. Steady state levels: Trabandt-Uhlig (2009).
Details. Eg: all of labor income or without “union profits”? The
former.
Speed to return to steady state debt level: ψτ ∈ [0, 1].
... plus: rule-of-thumb consumers: φ ∈ [0, 100%].
... plus: binding zero lower bound per discount shock, causing
recession.
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
10 / 70
The model
Tax rule
Remaining deficit, prior to new debt and labor taxes ...
ft = gov.spend.+subs.+old debt repaym.−cons.tax rev.,cap.tax rev.
... needs to be financed:
lab.tax rev. + new debt = ft
Steady state debt level, steady state taxes: f̄ .
Tax rule:
lab.tax rev.t − lab.tax rev. = ψτ (ft − f̄ )
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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The model: Details
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
12 / 70
The model: Details
Equations
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
13 / 70
The model: Details
Equations
Extensions of Smets-Wouters (2007): Investment &
Consumption
Shadow price of investment – original SW with τ k = 0:
Q̂t = −q̂tb − (R̂t − Et [πt+1 ]) +
1
×
r∗k (1 − τ k ) + δτ k + 1 − δ
k
× [r∗k (1 − τ k )Et (r̂t+1
) + (1 − δ)Et (Q̂t+1 )], (1)
Consumption growth – SW with τ j = 0, j = l, c and “ex-dividend” wage
w∗h instead of w∗ :
ĉt =
1
h/µ
1 − h/µ
Et [ĉt+1 ] +
ĉt−1 −
(q̂ b + R̂t − Et [π̂t+1 ])
1 + h/µ
1 + h/µ
σ[1 + h/µ] t
[σ − 1][w∗ n∗ /c∗ ] 1 − τ l
−
(Et [n̂t+1 ] − nt ), (2)
σ[1 + h/µ] 1 + τ c
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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The model: Details
Equations
Extensions of Smets-Wouters (2007): Wages
Evolution of wages:
(1 + β̄µ)ŵt − ŵt−1 − β̄µEt [ŵt+1 ]
!
"
d τtl
(1 − ζw β̄µ)(1 − ζw )
1
=
[ĉt − (h/µ)ĉt−1 ] + ν n̂t − ŵt +
]
ζw
1 − h/µ
1 − τl
− (1 + β̄µιw )π̂t + ιw π̂t−1 + µ̄Et [πt+1 ] + λ̂w ,t , (3)
In the flexible economy:
ŵt =
d τtl
1
[ĉt − (h/µ)ĉt−1 ] + ν n̂t +
.
1 − h/µ
1 − τl
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
(4)
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The model: Details
Equations
Extensions of Smets-Wouters (2007): Tax rate and
gov’t deficit
Financing the current deficit:
!
"
w∗ n∗ c∗ d τtl
+ ŵt + n̂t + ,τt
c∗ Ȳ τl
#
$
ψτ
b
b̂
−
π̂
c
k
∗
t
∗
∗
t−1
p
=
µ[ĝta + ĝ s ] +
− µτc ĉt − τ k [r∗k rtk + (rtk − δ)k̂t−1 ]
µ
π∗
Ȳ
Ȳ
Ȳ
τl
Budget:
ĝt +
1 b∗
1 b∗
c∗
[b̂t−1 − π̂t ] =
[b̂t − R̂t − q̂tb ] + τc ĉt +
µπ∗ Ȳ
R∗ Ȳ
Ȳ
! l
"
w∗ n∗ c∗ d τt
k∗
p
+ τl
+ ŵt + n̂t + τ k [r∗k rtk + (rtk − δ)k̂t−1
]
. (6)
c∗ Ȳ τl
µȲ
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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The model: Details
Equations
Unchanged SW equations: Cost and pricing equations
% t = (1 − α)ŵt + αr̂tk − γt ,
mc
(1 + β̄µιp )π̂t = ιp π̂t−1 + β̄µEt [π̂t+1 ]+ A
(7)
[1 − ζp β̄µ][1 − ζp ]
% t + λ̂p,t . (8)
mc
ζp
1 − ζp is the probability of (potential) price adjustment.
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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The model: Details
Equations
Unchanged SW equations: Capital services and
Capital Stock
Cost minimization yields:
k̂t = ŵt − r̂tk + n̂t .
(9)
From the FOC with respect to capacity utilization:
r∗k r̂tk = a## (1)ût
⇒ ût ≡
1 − ψu k
r̂ .
ψu t
(10)
The law of motion for capital implies:
!
"
x∗
x∗
x∗
p
p
k̂t = 1 − p k̂t−1
+ p q̂tx + p x̂t .
k∗
k∗
k∗
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
(11)
January 8, 2010
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The model: Details
Equations
Unchanged SW equations: Investment and FedFunds
The FOC for investment implies:
x̂t =
&
'
1
1
x̂t−1 + β̄µEt (x̂t+1 ) + 2 ##
[Q̂tk + q̂tx ],
µ
S
(µ)
1 + β̄µ
(12)
The interest rate rule:
R̂t = ρR R̂t−1 + [1 − ρR ][ψ1 π̂t + ψ2 (ŷt − ŷtflex )] + ψ3 [ŷt − ŷt−1 +
flex
− (ŷtflex − ŷt−1
)] + mst , (13)
Here: Introduce wedge between R̂t and the relevant interest rate for
the private sector for first periods.
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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The model: Details
Equations
Unchanged SW equations: Production and
Expenditure
The production technology for final goods:
ŷt =
Ȳ + Φ
[αk̂t + (1 − α)n̂t + γt ],
Ȳ
(14)
Spending identity with costs of capacity utilization:
ŷt = ĝt +
Harald Uhlig (University of Chicago)
c∗
x∗
r k k∗
ĉt + x̂t + ∗ ût .
Ȳ
Ȳ
Ȳ
Fiscal Stimulus and Distortionary Taxation
(15)
January 8, 2010
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The model: Details
Parameters
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
21 / 70
The model: Details
Parameters
Parameters: Estimated SW parameters I
Parameter
δ
λw
g
µ
β
π∗
α
σ
Ȳ +Φ
= λp
Ȳ
S ## (µ)
h
Ξw
Value
0.025
1.5
0.18
1 + 0.4312
100
100
0.1657+100
1 + 0.7869
100
0.1901
1.3808
1.6064
0.5187
5.7606
0.7133
0.7061
Harald Uhlig (University of Chicago)
Description
depreciation rate
markup labor market
exogenous gov’t spending/GDP
trend growth rate
discount factor
inflation rate
capital share in production
1/intertemporal elasticity of substitution
fixed cost and goods market markup
net exports/gov’t exp. reaction to techn.
investment adjustment cost
habit persistence
calvo parameter labor market
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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The model: Details
Parameters
Parameters: Estimated SW parameters II
Parameter
ν
Ξp
ιw
ιp
ψ1
ρR
ψ2
ψ3
Value
1.8383
0.6523
0.5845
0.2432
0.5462
2.0443
0.8103
0.0882
0.2247
Harald Uhlig (University of Chicago)
Description
labor supply elasticity
calvo parameter goods market
indexation labor market
indexation goods market
capital utilization elasticity
Taylor rule reaction to inflation
Taylor rule interest rate smoothing
Taylor rule long run reaction to output gap
Taylor rule short run reaction to output gap
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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The model: Details
Parameters
Parameters: Calibration and Implications
Parameter
Value
Description
b
Ȳ
τk
0.63
0.36
0.28
0.05
0.1059
0.0097
0.2268
0.0335
0.0353
Debt to GDP ratio
capital tax
wage tax rate
consumption tax rate
implied transfer payment
Interest payments relative to GDP
Labor tax revenue relative to GDP
Capital tax revenue relative to GDP
Consumption tax revenue relative to GDP
τl
τc
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
24 / 70
Results
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
25 / 70
Results
Comparison to neoclassical growth.
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
26 / 70
Results
Comparison to neoclassical growth.
A neoclassical growth model
Comparison to a neoclassical growth:
standard, but ..
... add distortionary labor taxes, capital income taxes,
consumption taxes.
Frisch elasticity: 1.
Calibration: Trabandt-Uhlig (2009).
Consider an anticipated permanent increase in government
spending.
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Comparison to neoclassical growth.
Neoclass. vs SW-DU: announced, ψτ = 0.03.
Neoclass.
SW-DU
Impulse response to gov.spending announcement shock ,ψτ=0.03
government spending (% ini
1
1.5
government
spending(%init.output)
0.5
output
1
output
τn (wage tax,perc. points)
0
percent
percent
0.5
τ (wage tax rate, perc. points)
0
−0.5
consumption
−1
−0.5
−1.5
2009
2010
2011
Year
Harald Uhlig (University of Chicago)
2012
2013
−1
consumption
2009
2010
Fiscal Stimulus and Distortionary Taxation
2011
2012
year
2013
January 8, 2010
2014
28 / 70
Results
Comparison to neoclassical growth.
Neoclass. vs SW-DU: perm., ann., ψτ = 0.03. Long
run.
Neoclass.
SW-DU
Impulse response to gov.spending announcement shock ,ψ =0.03
τ
1.5
2
government
spending(%init.output)
output
1
0.5
τn (wage tax,perc. points)
0
0.5
percent
percent
government spending (% init. output)
1
1.5
0
output
τ (wage tax rate, perc. points)
−0.5
−0.5
consumption
−1
−1
consumption
−1.5
−1.5
−2
2010
2015
2020
Year
Harald Uhlig (University of Chicago)
2025
2030
2010
2015
Fiscal Stimulus and Distortionary Taxation
2020
2025
year
2030
2035
January 8, 2010
29 / 70
Results
No rules-of-thumb, no binding zero lower bound.
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
30 / 70
Results
No rules-of-thumb, no binding zero lower bound.
Short-run. ψτ = .03 vs lump-sum.
ψτ = 0.03
Lump-sum (CCWT)
0.6
0.4
0.2
0.8
Stimulus
GDP
τ (wage tax rate, perc. points)
0
−0.2
Investment
Consumption
0.6
Stimulus
GDP
0.4
0.2
0
−0.2
2009 2010 2011 2012 2013 2014 2015 2016
year
Harald Uhlig (University of Chicago)
% of init. output/perc. points
% of init. output/perc. points
0.8
τ (wage tax rate, perc. points)
Consumption
Investment
2009 2010 2011 2012 2013 2014 2015 2016
year
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
No rules-of-thumb, no binding zero lower bound.
Medium-run. ψτ = .03 vs lump-sum.
ψτ = 0.03
Lump-sum (CCWT)
0.6
0.4
0.8
Stimulus
GDP
τ (wage tax rate, perc. points)
0.2
0
−0.2
Investment
Consumption
2010
2015
2020
% of init. output/perc. points
% of init. output/perc. points
0.8
0.6
GDP
0.4
0.2
Harald Uhlig (University of Chicago)
2030
2035
τ (wage tax rate, perc. points)
0
−0.2
2025
year
Stimulus
Consumption
Investment
2010
2015
Fiscal Stimulus and Distortionary Taxation
2020
2025
year
2030
2035
January 8, 2010
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Results
No rules-of-thumb, no binding zero lower bound.
Fiscal stimulus: medium run. ψτ = 0.03.
% of init. output/perc. points
0.8
0.6
0.4
Stimulus
GDP
τ (wage tax rate, perc. points)
0.2
0
−0.2
Investment
Consumption
2010
Harald Uhlig (University of Chicago)
2015
2020
2025
year
2030
Fiscal Stimulus and Distortionary Taxation
2035
January 8, 2010
33 / 70
Results
No rules-of-thumb, no binding zero lower bound.
Spending increase, short-run output dynamics:
various ψτ .
0.5
ψ= 0.03
0.4
0.3
ψ= 0.10
0.2
percent
0.1
0
Lumpsum
−0.1
ψ= 0.30
−0.2
ψ= 1.00
−0.3
−0.4
2008
Harald Uhlig (University of Chicago)
2010
2012
year
2014
Fiscal Stimulus and Distortionary Taxation
2016
January 8, 2010
34 / 70
Results
No rules-of-thumb, no binding zero lower bound.
Spending increase, short-run fiscal multipliers
0.6
ψ= 0.03
0.4
Lumpsum
ψ= 0.10
0.2
ψ= 0.30
0
ψ= 1.00
−0.2
−0.4
−0.6
2008
Harald Uhlig (University of Chicago)
2010
2012
year
2014
Fiscal Stimulus and Distortionary Taxation
2016
January 8, 2010
35 / 70
Results
No rules-of-thumb, no binding zero lower bound.
Spending increase, short-run tax dynamics: various
ψτ .
1
percentage points
0.8
ψ= 0.30
0.6
ψ= 0.10ψ= 1.00
0.4
0.2
0
2008
Harald Uhlig (University of Chicago)
ψ= 0.03
2010
2012
year
Lumpsum
2014
Fiscal Stimulus and Distortionary Taxation
2016
January 8, 2010
36 / 70
Results
No rules-of-thumb, no binding zero lower bound.
Spending increase, short-run debt dynamics: various
ψτ .
6
percent of init. output
5
4
ψ= 0.10
3
2
ψ= 0.03
ψ= 0.30
1
0
2008
Harald Uhlig (University of Chicago)
2010
ψ= 1.00
Lumpsum
2012
year
2014
Fiscal Stimulus and Distortionary Taxation
2016
January 8, 2010
37 / 70
Results
Including Rule-of-Thumb Consumers.
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
38 / 70
Results
Including Rule-of-Thumb Consumers.
Consumption of the two agents
Modify consumption Euler equation to account for Rational Agents
only:
ĉtRA =
1
h/µ
1 − h/µ
Et [ĉt+1 ]+
ĉt−1 −
(q̂ b + R̂t −Et [π̂t+1 ])
1 + h/µ
1 + h/µ
σ[1 + h/µ] t
[σ − 1][w∗ n∗ /c∗RA ] 1 − τ l
−
(Et [n̂t+1 ] − nt ), (16)
σ[1 + h/µ]
1 + τc
The consumption of the Rule-of-Thumb consumer is determined from
their budget constraint:
!
"
dτl
RoT
l w∗ n∗
ĉt
= (1 − τ ) RoT ŵt + n̂t −
,
(17)
c∗
1 − τl
using n̂t = n̂tRoT = n̂tRA and n∗ = n∗RoT = n∗RA .
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
39 / 70
Results
Including Rule-of-Thumb Consumers.
Aggregating consumption
Aggregate consumption:
ĉt =
c∗RA
c RoT
(1 − φ)ĉtRA + ∗ φĉtRoT ,
c∗
c∗
(18)
where
w∗ n∗ (1 − τ l ) + s∗
,
1 + τc
c∗ − φc∗RoT
=
.
1−φ
c∗RoT =
c∗RA
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
40 / 70
Results
Including Rule-of-Thumb Consumers.
Distorting taxation and Rule-of-Thumb Consumers:
ψτ = 0.03, φ = 0.50.
0.6
output
government spending (% init. output)
percent
0.4
0.2
0
τ (wage tax rate, perc. points)
consumption
−0.2
−0.4
2008 2009 2010 2011 2012 2013 2014 2015
year
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
41 / 70
Results
Including Rule-of-Thumb Consumers.
Medium run.
φ=0
φ = 0.5
0.8
0.6
0.6
0.2
0
government spending (% init. output)
government spending (% init. output)
output
0.4
percent
percent
0.4
τ (wage tax rate, perc. points)
output
0.2
0
τ (wage tax rate, perc. points)
consumption
−0.2
−0.2
−0.4
consumption
−0.4
2010
2015
2020
2025
year
Harald Uhlig (University of Chicago)
2030
2035
2010
2015
Fiscal Stimulus and Distortionary Taxation
2020
2025
year
2030
2035
January 8, 2010
42 / 70
Results
Including Rule-of-Thumb Consumers.
Comparing consumption patterns, ψτ = 0.03.
φ = 0:
φ = 0.5:
0.5
0.6
0.4
percent
percent
output
0
Rule of Thumb
output
0.2
0
Rule of Thumb
consumption
−0.2
Rational Agent
consumption
−0.4
−0.5
2007 2008 2009 2010 2011 2012 2013 2014
year
Harald Uhlig (University of Chicago)
Rational Agent
2007 2008 2009 2010 2011 2012 2013 2014
year
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Including Rule-of-Thumb Consumers.
Short run: ψτ = 0.03, vary rules-of-thumb fraction φ.
ψτ = 0.03, φ = 0:
ψτ = 0.03, φ = 0.25:
0.8
0.8
0.6
0.6
0.2
0
outputgovernment spending (% init. output)
government spending (% init. output)
output
τ (wage tax rate, perc. points)
0.4
percent
percent
0.4
0.2
0
−0.2
−0.2
τ (wage tax rate, perc. points)
consumption
consumption
−0.4
2008 2009 2010 2011 2012 2013 2014 2015
year
ψτ = 0.03, φ = 0.50:
−0.4
2008 2009 2010 2011 2012 2013 2014 2015
year
ψτ = 0.03, φ = 0.75:
1
0.6
output
output
government spending (% init. output)
0.5
0.2
0
τ (wage tax rate, perc. points)
consumption
percent
percent
0.4
government spending (% init. output)
consumption
0
τ (wage tax rate, perc. points)
−0.2
−0.4
2008 2009 2010 2011 2012 2013 2014 2015
year
Harald Uhlig (University of Chicago)
−0.5
2008 2009 2010 2011 2012 2013 2014 2015
year
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Including Rule-of-Thumb Consumers.
Short run: φ = 0.75, vary ψτ .
ψτ = 0.03
ψτ = 0.10
1
40
output
30
government spending (% init. output)
consumption
0
20
percent
percent
0.5
τ (wage tax rate, perc. points)
10
τ (wage
tax rate,
perc. points)
government
spending
(% init. out
output
0
−10
−0.5
2008 2009 2010 2011 2012 2013 2014 2015
year
Harald Uhlig (University of Chicago)
consumption
2008 2009 2010 2011 2012 2013 2014 2015
year
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
A binding zero Lower Bound.
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
A binding zero Lower Bound.
Zero nominal interest rates
Before (and following CCWT): for four quarters, “switch off” Taylor
rule and set nominal interest rate to zero instead.
SW/CCWT: steady state quarterly nominal interest rate is 1.55%
Now: recession per bond-premium-shock q̂tb : Consumers want to
save more at any given interest rate (Christiano, Eichenbaum and
Rebelo (2009)). Increase half-life of shock to one period (SW:
<0.5 periods).
Zero lower bound becomes binding with a bond-premium shock of
0.165, implying a (quarterly) change in GDP of -5.46%.
Assume shock of 0.20.
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
A binding zero Lower Bound.
Results
Extreme scenario.
Examine differences between “with” and “without” stimulus.
Results are practically the same as before.
Erceg-Lindé, 2009.
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
A binding zero Lower Bound.
Without stimulus, ψτ = 0.03.
Economic performance:
0
τ (wage tax rate, perc. points)
government spending (% init. output)
percent
−2
−4
output
−6
−8
consumption
Rates:
0
percentage points (quarterly rate)
2
inflation
−0.5
marginal cost
implied fed funds
−1
−1.5
actual fed funds
−2
2007 2008 2009 2010 2011 2012 2013 2014
year
Harald Uhlig (University of Chicago)
2005 2006 2007 2008 2009 2010 2011 2012
year
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
49 / 70
Results
A binding zero Lower Bound.
With stimulus, ψτ = 0.03.
Economic performance:
0
τ (wage tax rate, perc. points)
government spending (% init. output)
percent
−2
−4
output
−6
−8
consumption
Rates:
0
percentage points (quarterly rate)
2
inflation
−0.5
marginal cost
implied fed funds
−1
−1.5
actual fed funds
−2
−10
2007 2008 2009 2010 2011 2012 2013 2014
year
Harald Uhlig (University of Chicago)
2005 2006 2007 2008 2009 2010 2011 2012
year
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
50 / 70
Results
A binding zero Lower Bound.
Difference between with and without stimulus.
0.8
0.6
percent
0.4
government spending (% init. output)
output
0.2
0
τ (wage tax rate, perc. points)
−0.2
consumption
−0.4
2009 2010 2011 2012 2013 2014 2015 2016
year
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
A binding zero Lower Bound.
SW-DU, Bondpremium-Shock with binding ZLB:
Difference, compared to “switching off”.
ZLB, ψ = 0.03:
“switching off”, ψ = 0.03:
0.6
percent
0.4
0.2
0.8
Stimulus
GDP
wage tax rate
0
−0.2
Investment
Consumption
0.6
0.4
Stimulus
GDP
τ (wage tax rate, perc. points)
0.2
0
−0.2
2009 2010 2011 2012 2013 2014 2015 2016
year
Harald Uhlig (University of Chicago)
% of init. output/perc. points
0.8
Investment
Consumption
2009 2010 2011 2012 2013 2014 2015 2016
year
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
A binding zero Lower Bound.
Rates: Difference between with and without stimulus.
0.1
percent
0.05
0
implied fed funds
marginal cost
inflation
actual fed funds
−0.05
−0.1
2009 2010 2011 2012 2013 2014 2015 2016
year
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Chemotherapy
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
54 / 70
Results
Chemotherapy
i = 0 for 0 quarters (ψτ = 0.03).
0.8
0.6
percent
0.4
government spending (% init. output)
output
0.2
0
τ (wage tax rate, perc. points)
−0.2
consumption
−0.4
2009 2010 2011 2012 2013 2014 2015 2016
year
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Chemotherapy
i = 0 for 4 quarters (ψτ = 0.03).
0.8
0.6
percent
0.4
government spending (% init. output)
output
0.2
0
τ (wage tax rate, perc. points)
−0.2
consumption
−0.4
2009 2010 2011 2012 2013 2014 2015 2016
year
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Chemotherapy
i = 0 for 8 quarters (ψτ = 0.03).
0.8
output
0.6
government spending (% init. output)
percent
0.4
0.2
0
τ (wage tax rate, perc. points)
consumption
−0.2
−0.4
2009 2010 2011 2012 2013 2014 2015 2016
year
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Chemotherapy
i = 0 for 12 quarters (ψτ = 0.03).
1.4
output
1.2
1
percent
0.8
0.6
0.4
consumption
government spending (% init. output)
0.2
0
−0.2
τ (wage tax rate, perc. points)
−0.4
2009 2010 2011 2012 2013 2014 2015 2016
year
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
58 / 70
Results
Chemotherapy
i = 0 for 16 quarters (ψτ = 0.03).
5
output
4
consumption
percent
3
2
1
government spending (% init. output)
0
−1
τ (wage tax rate, perc. points)
2009 2010 2011 2012 2013 2014 2015 2016
year
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Chemotherapy
i = 0 for 20 quarters (ψτ = 0.03).
τ (wage tax rate, perc. points)
2
1
government spending (% init. output)
0
percent
−1
−2
−3
−4
−5
output
consumption
−6
2009 2010 2011 2012 2013 2014 2015 2016
year
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
60 / 70
Results
Chemotherapy
i = 0 for 16 quarters (ψτ = 0.03). Long run
output
5
4
consumption
percent
3
2
1
government spending (% init. output)
0
−1
τ (wage tax rate, perc. points)
2010
Harald Uhlig (University of Chicago)
2015
2020
2025
year
2030
Fiscal Stimulus and Distortionary Taxation
2035
January 8, 2010
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Results
Chemotherapy
i = 0 for 12 quarters (ψτ = 0.03). Long run
1.4
output
1.2
1
percent
0.8
0.6
0.4
consumption
government spending (% init. output)
0.2
0
−0.2
τ (wage tax rate, perc. points)
−0.4
2010
Harald Uhlig (University of Chicago)
2015
2020
2025
year
2030
Fiscal Stimulus and Distortionary Taxation
2035
January 8, 2010
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Results
Chemotherapy
Comparing binding ZLB, “switching off” with proper
ZLB. 12 quarters
ZLB, 12 qtrs:
1.4
switching off, 12 qtrs:
GDP
1.4
1
percent
0.8
0.6
0.4
Stimulus
Consumption
0.2
0
wage tax rate
Investment
−0.2
2009 2010 2011 2012 2013 2014 2015 2016
year
% of init. output/perc. points
1.2
GDP
1.2
1
0.8
0.6
0.4
Stimulus
Consumption
0.2
0
τ (wage tax rate, perc. points)
Investment
−0.2
−0.4
2009 2010 2011 2012 2013 2014 2015 2016
year
( ψτ = 0.03, scaling the interest rate down to 2/3 of actual value in interest
rate rule. High persistence, ρb = 0.9. Shocks: 2.38% for 16 qtrs, 2.02% for 12
qtrs, 1.57% for 8 qtrs, 1.43% for 5 qtrs. )
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Chemotherapy
Comparing binding ZLB, “switching off” with proper
ZLB. 16 quarters
ZLB, 16 qtrs:
3
switching off, 16 qtrs:
GDP
5
% of init. output/perc. points
2.5
percent
2
1.5
Consumption
1
0.5
Stimulus
Investment
0
−0.5
wage tax rate
2009 2010 2011 2012 2013 2014 2015 2016
year
GDP
4
3
Consumption
2
1
Stimulus Investment
0
−1
τ (wage tax rate, perc. points)
2009 2010 2011 2012 2013 2014 2015 2016
year
( ψτ = 0.03, scaling the interest rate down to 2/3 of actual value in interest
rate rule. High persistence, ρb = 0.9. Shocks: 2.38% for 16 qtrs, 2.02% for 12
qtrs, 1.57% for 8 qtrs, 1.43% for 5 qtrs. )
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Chemotherapy
Evaluation
What does it take for the ZLB to bind?
Disclaimer: based on linear extrapolation of the case of a non-binding ZLB.
This is a problem because it neglects the feedback – since the recession is
stronger if the ZLB binds, a smaller shock is needed for a given decline in
interest rates.
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
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Results
Chemotherapy
Necessary initial bond premium shock to make ZLB
exactly binding at x quarters
Necessary size of bond shock for binding ZLB at x quarters
100
0.3
=0.22
0.1
0.4
80 SW
0.5 0.6
0.7
Shock size (%)
ρ
0.8
60
40
20
used values
0.9
0
Harald Uhlig (University of Chicago)
5
10
quarters
15
Fiscal Stimulus and Distortionary Taxation
20
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Results
Chemotherapy
With a maximal contraction of 50%, ZLB of x quarters
obtains for ...
maximum horizon at which ZLB binds if peak GDP contraction < 50%
30
horizon (quarters)
25
20
15
10
SW
5
0
0
Harald Uhlig (University of Chicago)
0.2
0.4
rho
0.6
0.8
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1
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Results
Chemotherapy
Generating a binding ZLB at x horizons leads to...
Peak GDP response if ZLB binds at x quarters
0.9
0.8
0
ρ
GDP response (%)
−500
=0.22
SW
0.6
0.7
0.3
−1000
−1500
0.40.5
−2000
0.1
−2500
−3000
0
Harald Uhlig (University of Chicago)
5
10
quarters
15
Fiscal Stimulus and Distortionary Taxation
20
January 8, 2010
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Conclusions
Outline
1
Introduction
2
The model
3
The model: Details
Equations
Parameters
4
Results
Comparison to neoclassical growth.
No rules-of-thumb, no binding zero lower bound.
Including Rule-of-Thumb Consumers.
A binding zero Lower Bound.
Chemotherapy
5
Conclusions
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Fiscal Stimulus and Distortionary Taxation
January 8, 2010
69 / 70
Conclusions
Conclusions
In the context of this model, the impact of a government spending
stimulus ...
... is very sensitive to assumptions about taxes.
... on output is rarely larger than the government spending
increase
... is a comparatively larger output loss later on, due to the
increased tax burden.
Furthermore,
Consumption declines.
Rules-of-thumb agents do not change the results much.
Consumption may be feebly positive, the increase in output is
somewhat larger.
Binding zero lower bound: does not change the results much, if
temporary, and is extreme and fragile, if longer.
Therefore: tax considerations and medium-term impacts merit much
more attention!
Harald Uhlig (University of Chicago)
Fiscal Stimulus and Distortionary Taxation
January 8, 2010
70 / 70