Small and Orthodox Fiscal Multipliers at the ZeroLower Bound
R. Anton Braun (FRB Atlanta)
Lena Körber (LSE)
Yuichiro Waki (University of Queensland)

End of Year Macroeconomics Conference
December 26, 2014
Disclaimer: The views expressed in this paper are our own personalviews and not those of the Federal Reserve System or Bank of EnglandOutline

1Introduction

2Model3

Our Parameterization

4

Results for the Great Recession

5Conclusions

2 / 34

Motivation

The nominal interest rate has fallen to (almost) zero in many
countries around the world.
Does fiscal policy have large and qualitatively different effects when
the nominal interest rate is zero?
An emerging consensus in the New Keynesian (NK) literature is thatthe answer is yes.

3 / 34

Labor tax increase

In normal times: labor tax ↑ → hours ↓At the ZLB: labor tax ↑ → hours ↑(“Paradox of Toil”, Eggertsson(2011))

4 / 34

Government spending multiplier

In normal times: government spending multiplier ≤ 1
At the ZLB: government spending multiplier >> 1
(Christiano, Eichenbaum and Rebelo (2011))−→ Policy implication: Fiscal stimulus is particularly effective whenmonetary policy is constrained by the ZLB.

5 / 34

Our paper
Provides new evidence that the properties of fiscal policy in the NK
model at the ZLB and away from the ZLB are generally quite similar :– labor tax ↑ → hours ↓, or hours are inelastic– government spending multiplier ≈ 1.

How do we reach this conclusion?
– Formulate a tractable, nonlinear, stochastic NK model with anoccasionally binding ZLB.
– Calibrate shock parameters to reproduce declines in GDP and inflationfrom the Great Recession and Great Depression.
– Analyze the global properties of the model using analytical andnumerical methods.

6 / 34

Fiscal multipliers are generally small

Great Recession
1

GDP government purchase multiplier is about 1.15 or less.

2

Employment generally falls or shows no response at all to an increase in
the labor tax.

Great Depression
1

GDP government purchase multiplier is 1.13 or less.

2

Employment falls when the labor tax is increased.

7 / 34

Fiscal multiplier asymptotes

Near asymptotes fiscal multipliers can be arbitrarily large and positiveor large and negative.
This region of the parameter space is small.
Woodford (2011) and Carlstrom, Fuerst and Paustian (2012) havealso documented asymptotes using loglinearized solutions.

8 / 34

What explains the difference between our results and theprevious literature?

Parameterization of the model– This paper uses parameterizations that can reproduce output andinflation responses from the Great Recession or the Great Depression.
– Some previous work uses parameterizations of the NK model thatcannot reproduce these responses.

Solution method– Loglinear solutions may get the local dynamics of the model wrong.

9 / 34

Outline

1Introduction

2Model3

Our Parameterization

4Results for the Great Recession

5Conclusions

10 / 34

Outline

1Introduction

2Model3

Our Parameterization

4

Results for the Great Recession

5Conclusions

11 / 34

2. ModelOverview

Standard New Keynesian model of a closed economy.
Nominal price rigidity á la Rotemberg (1996) adjustment costs.
No need to loglinearize.
Equilibrium employment and inflation in the ZLB state can be foundby solving two nonlinear equations.

12 / 34

1. Model

State of the economy

State s ∈ {H, L}.
2 state Markov chain with L as the initial state.
Stays in L with probability p. (Persistence)
H is the absorbing state.
Household’s one-step discount factor and firms’ technology depends on s.
Fiscal policy is also Markov in s.

13 / 34

1. ModelHouseholds
Momentary utility function:
ct1−σh1+ν
− t
1−σ 1+νOne-step preference discount factor β × dt+1 (t + 1 → t).
dt+1 = d L in the L state, dt+1 = 1 in the H state.
Labor income subject to linear tax τw ,t .
Optimality condition:"1= βdt+1 Et

wt=#−σct+11(1 + Rt )ct−σ 1 + πt+1htν
−σct (1 − τw ,t )14 / 34

2. Model

Final good firms
Produce the final foods using intermediate goods i ∈ [0, 1].
CES aggregator:
yt =

Z 1

θ

yt (i) θ−1 di θ−1θ.

0Profit maximizing input demand:ytd (i) =pt (i)
Pt

−θ
yt

R1
 1
where Pt = 0 pt (i)1−θ di 1−θ is the price of the final good and pt (i) is theprice of intermediate good i.

15 / 34

2. ModelIntermediate goods producers

Use linear production function:yt (i) = zt ht (i),which implies that the marginal cost is
wt /zt .
zt = z L in the L state, zt = 1 in the H state.

16 / 34

2. ModelIntermediate goods producers

Set prices {pt (i)}∞t=0 to maximize PV of profits subject to thedemand function.
Momentary profit function:pt (i)wt
γ(1 + τs )yt (i) −yt (i)−
Ptzt2



2
pt (i)− 1 yt .
pt−1 (i)yt = zt ht is the aggregate production.
In a symmetric equilibrium the fraction γ2 πt2 of agg. production isused for price adjustment.

17 / 342. Model

PolicyFiscal policy is Ricardian.
The Central Bank follows a Taylor rule:d )Rt = max(0, rt + φπ πt + φy gdpt
where rt = βd1t+1 − 1.

18 / 34

2. Model

Aggregate resource constraint

Aggregate resource constraint:
GDPt ≡ ct + gt = (1 − κt )zt ht .
κt ≡ γ2 πt2 represents the resource costs of price adjustment.
κt plays an important role in a severe, deflationary recession.
1
2
3
4

Magnitude and sign of employment and GDP responses can differ.
κ disappears when loglinearized about a constant price steady-state.
If the economy is far from the steady state this problem can be severe.
Same issue arises under Calvo pricing.

19 / 34

2. Model

ZLB Markov equilibrium of Eggertsson and Woodford(2003)

Markov equilibrium with state s ∈ {L, H}.
(Fiscal policy is also Markov in s.)Assume: Zero inflation steady-state occurs in state H.
Assume: ZLB binds in state L. (Taylor rule checked).
ZLB Equilibrium: (c L , hL , w L , π L ).
II

Eqm condition reduces to two equations with (π L , hL ).
”AD” and ”AS” equations.

20 / 34

2. Model

Equilibrium condition at the ZLB
1NKPC:π L (1 + π L ) =2

θ wL(− 1) + pβd L π L (1 + π L )γ zLEuler equation:(c L )−σ = pβd L

3(c L )−σ+ (1 − p)βd L c −σ
1 + πLLabor supply:w L = (c L )σ (hL )ν /(1 − τwL ).

4

Resource constraint:c L = (1 − η L − κL )z L hL . (g L = η L z L hL .)21 / 34

2. Model

Equilibrium employment and inflation at the ZLB

1AS: Price setting condition (+ labor supply and resource constraint)θπ (1 + π ) =γLL
(1 − κL − η L )σ (hL )σ+ν
− 1 + pβd L π L (1 + π L )(1 − τwL )(z L )1−σ2

AD: Euler equation (+ production function and resource constraint)



βd L
(1 − κL − η L )σ (hL )σL
1=p+ (1 − p)βd1 + πL(1 − η)σ hσ

3R Taylor < 022 / 34

Outline

1Introduction

2Model3

Our Parameterization

4Results for the Great Recession

5Conclusions

23 / 34

5. Our ParameterizationEstimated parameters
Key parameters are estimated by Bayesian methods using theloglinear equilibrium conditions.
Data: output gap, inflation and the FFR (1985:I-2007:IV).
Model: loglinearized three-equation model (quarterly)
Shocks: technology, demand, and monetary policy.

Parameter
ν Labour supply elasticity
γ Price adj. costs
φy TR coefficient on GDP
φπ TR coefficient on inflation
ρr TR coefficient on Rt−1

distribution
gamma
normalnormalnormal
beta

Prior
mean
0.5
150030.75

std. dev.
0.25
200110.1

Posteriormode 5% 95%
0.28 0.08 0.63458315 704
1.63 1.06 2.33
3.46 2.38 4.77
0.86 0.81 0.90

24 / 34

5. Our Parameterization

Other parameters

The remaining parameters are fixed a priori as follows:Parameterβ
Discount factorσRelative risk aversionθθ−1 Steady state gross markup

Value
0.997
1
1.15

Resulting slope of NK Phillips Curve is: 0.021.
Close to estimate of Rotemberg and Woodford (1997): 0.024.

25 / 34

5. Our Parameterization

Targets from the Great Recession and the Great
Depression

Great Recession (2008-09)
Great Depression (1929-30s)

Inflation-1%-10%GDP-7%-30%

Consider a wide range of p (duration of the ZLB) ∈ [0, 0.95].
For each p we adjust z L and d L to reproduce these numbers at ZLB.
This presentation focuses on the GR calibration.

26 / 34

Outline

1Introduction

2Model3

Our Parameterization

4Results for the Great Recession

5Conclusions

27 / 34

6. Results for the Great Recession

Three configurations for the AD-AS schedules

All equilibria are MSV solutions.
Left case doesn’t occur if loglinearized around zero inflation
steady-state.
Measure policy effects by perturbing fiscal policy in state L.

28 / 346. Results for the Great Recession

The response of hours to a labor tax increase

Labor tax ↑ ⇒ AS shifts up.
Employment ↓ for the left and the right cases.
Employment ↑ for the middle case.
29 / 34

6. Results for the Great Recession

The response of hours to a labor tax increase
1

1009
0.8

8
7

0.6

−5

6
5

0.4

4
−100.23LL
NL (target)
NL (non−target)

2
0

1
0.2

0.4
p

0.6

0.8

0.8

0.82

0.84
p−15

0.88 0.9 0.92 0.94
p

Third equilibrium can exist (red).
1
Labor tax multiplier proportional to slope(AD)/slope(AS)−1.

30 / 34

6. Results for the Great Recession

Government spending multiplier

Government spending ↑ ≈ AD shifts toward the right.
Inflation ↑ for the left and the middle cases. → C ↑ ⇒ Multiplier > 1.
Inflation ↓ for the right case → C ↓ ⇒ Multiplier < 1.
31 / 34

6. Results for the Great Recession

Government spending multiplier
3

1.15

42

2.5

1.1

02

1.05

−2
1.5

1

0.95

−4
1
0.2

0.4
p0.6

0.8

0.8

0.82

0.84
p−6LL
NL (target)
NL (non−target)
0.88 0.9 0.92 0.94
pVery large multiplier only around the asymptote.
Right panel corresponds to Mertens and Ravn (2014).

32 / 34

Outline

1Introduction

2Model3

Our Parameterization

4

Results for the Great Recession

5Conclusions

33 / 34

Conclusions

Our findings:
For a broad and empirically relevant range of parameter/shockconfigurations– labor tax ↑ → hours ↓ or hours are inelastic– government spending multiplier ≈ 1I

Fiscal multipliers can be very large and positive or large and negative
near asymptotes.
These properties also hold inI
ISpecifications with preference shock only, andSpecifications that are calibrated to Great Depression.

34 / 34