1) Government spending multipliers are generally small when the economy is not at the zero lower bound (ZLB), and are increased only slightly by higher uncertainty. 2) When the economy is at the ZLB due to large negative shocks to bond returns or discount rates, multipliers can be substantially above one and increase further with higher spending or productivity volatility. 3) Different types of shocks can drive the economy to the ZLB, but bond return and monetary policy shocks are the primary drivers, while productivity shocks yield relatively small multipliers.

1. Government spending in a volatile economy at
the zero lower bound
Harri Turunen
University of Helsinki
University of Cambridge
February 16, 2015

2. Outline
Motivation
The model
Generalized Stochastic Simulation
Results

3. Outline
Motivation
The model
Generalized Stochastic Simulation
Results

4. Ramey (JEL 2011)
Reasonable people can argue, however, that the data do
not reject 0.5 or 2.0.
Blanchard & Perotti (2002): SVAR-identified tax shocks
imply multiplier of 0.9 to 1.29
Cogan, Cwik, Taylor & Wieland (2010): estimated
Smets-Wouters model implies 0.64 at peak

5. ECB refi rate, Fed Funds rate, BoJ overnight rate,
2004-2014

6. Intuition on the multiplier at the ZLB
Multiplier depends on response of hours worked to spending
increase
New Keynesian special case: when interest rates are low, the
multiplier can be large
With interest rates stuck, consumption level adjusted by
working more

7. This paper/presentation
How does uncertainty affect the multiplier at the ZLB?
Uncertainty modeled as stochastic volatility in government
spending and aggregate productivity
Model solved using a global method that accommodates the
ZLB
Multipliers computed by simulating the model
Not an explanation of causes of business cycles

8. This paper/presentation
How does uncertainty affect the multiplier at the ZLB?
Uncertainty modeled as stochastic volatility in government
spending and aggregate productivity
Model solved using a global method that accommodates the
ZLB
Multipliers computed by simulating the model
Not an explanation of causes of business cycles

9. What is spending uncertainty? What causes it?
Household uncertainty about government behavior
Greek commitment to cuts and reforms (also in 2010!)
U.S. government shutdown in 2013
More generally
Uncertainty about a new party or politician
Uncertainty about commitment
Uncertainty about general economic conditions

10. Justiniano and Primiceri (AER 2008)
DSGE-based estimate of volatility of U.S. government spending with confidence intervals

11. Baker et al (AER P&P 2014)
Economic policy uncertainty index based on newspaper word count

12. Previous literature on multipliers at ZLB
Christiano, Eichenbaum & Rebelo (2011): multiplier above 1
in a linearized model
Aruoba & Schorfheide (2013): multiplier greater than 1 - if
economy is in non-deflationary equilibrium
Braun, K¨orber & Waki (2013): multiplier 1 or less, depending
on parametrization
Fernandez-Villaverde, Gordon, Rubio-Ramirez &
Guerron-Quintana (2013): above bound 0.6, at bound 1.5

13. My results
Volatility matters:
1. Spending volatility has a positive effect; high volatility
increases the multiplier
2. Productivity volatility has a negative effect; high volatility
decreases the multiplier
Different shocks can take the economy to the bound; the multiplier
depends on the shock
1. Shocks to discount rate result in large multipliers
2. Shocks to productivity yield small multipliers
3. Bond return shock and monetary policy shock in between
Size of spending increase strongly affects size of multiplier

14. Outline
Motivation
The model
Generalized Stochastic Simulation
Results

15. Model foundations
Representative household
Calvo pricing in production
Central bank follows Taylor rule
Government levies lump sum taxes and spends, has balanced
budget
No capital, no distorting taxes

16. Shocks
Discount rate (ut), labor preference (lt), bond return (bt),
productivity (at), government spending (gt), monetary policy
(rt)
All follow ht = hρh
t−1 exp (σhεh,t), εh,t ∼ N (0, 1)
Two volatility shocks: productivity (σa,t), government
spending (σg,t)
log σj,t = (1 − j ) log σj + j log σj,t−1 + ςj ηj,t, ηj,t ∼ N (0, 1)

17. Central bank
Nominal rate constrained by ZLB
Rt = max {1, φt}
Central bank follows Taylor rule:
φt = rtR1−ρ
(Rt−1)ρ πt
π∗
φπ Yt
Y ∗
φY
1−ρ
Due to kink Rt non-differentiable =⇒ perturbation methods
inapplicable!

18. Spending
Government borrows Bt, levies lump-sum taxes Tt and spends
Budget always balanced
Spending shock gt subject to stochastic volatility:
gt = g
ρg
t−1 exp (σg,tεg,t)
log σg,t = (1 − g ) log σg + g log σg,t−1 + ςg ηg,t
Government expenditure computed as Gt = gt
¯GYt

19. Households
Households consume final good Ct, supply labor Lt to intermediate
goods producers, put savings into government bonds, maximize
max
Ct ,Bt ,Lt
E0
∞
t=0
βt
ut log (Ct) − lt
L1+ϑ
t
1 + ϑ
subject to
PtCt +
Bt
bt
≤ Rt−1Bt−1 + WtLt + Tt + Πt
Standard intertemporal optimality condition for bonds:
C−1
t = β
bt
ut
RtEt ut+1C−1
t+1
In equilibrium
Ct = 1 − gt
¯G atLt∆t

20. Firms
Competitive production of final good Yt using Dixit-Stiglitz
aggregation
Monopolistic production of intermediate goods with aggregate
productivity subject to stochastic volatility
Calvo pricing implies optimality condition for reset prices ˜Pt
˜Pt
Pt
≡
St
Ft
where
St =
utlt
at
Lϑ
t Yt + βθEt πε
t+1St+1
Ft = utC−1
t Yt + βθEt πε−1
t+1Ft+1

21. Calibration
Objective of calibration: model hits the bound in roughly 6% of
periods
Shocks central: variances set to 0.005 in steady state,
persistences 0.75, a = g = 0.9 and ςa = ςg = 0.1
Central bank reacts strongly to inflation: φπ = 2, φY = 0.15,
π∗ = 1.004 and ρ = 0.8
Households: β = 0.994, ϑ = 1
Firms: ε = 6, θ = 0.75

22. Outline
Motivation
The model
Generalized Stochastic Simulation
Results

23. Nutshell
Approximate equilibrium conditions with polynomials of state
variables
Polynomials found with fixed-point iteration:
1. Make a guess on parameters in polynomials
2. Simulate model for T periods using the polynomials
3. Regress “true” model outcomes on simulation outcome
4. Update guess using regression output. If no convergence, go
to 2.

24. Nutshell
Approximate equilibrium conditions with polynomials of state
variables
Polynomials found with fixed-point iteration:
1. Make a guess on parameters in polynomials
2. Simulate model for T periods using the polynomials
3. Regress “true” model outcomes on simulation outcome
4. Update guess using regression output. If no convergence, go
to 2.

25. My implementation
Third order polynomials for St, Ft and marginal utility
Vector of state variables
Xt = (∆t−1, Rt−1, at, bt, gt, lt, rt, ut, σa,t, σg,t)
Dimension of polynomials large - 286 parameters!
Initial values from second-order perturbation of Gomme and
Klein (2011)

26. Other technicalities
Problem: regression coefficients unstable between iterations
Solution: “stabilize” regression using singular value
decomposition
Use numerical integration to compute “true” model outcomes
of expectations
Iterate over structural parameters - even with stabilization
invertibility issues arise
10-20 minutes per iteration

27. Outline
Motivation
The model
Generalized Stochastic Simulation
Results

28. Results
Which shocks are important for hitting the bound?
What happens at the bound to output and inflation?
How large is the multiplier?

29. Which shocks drive the economy to the bound?
Probability of hitting the bound after a shock in the next 10 periods at least once
Size of innov. at bt ut rt
2 s.d. 0.31 0.43 0.23 0.22
1 s.d. 0.28 0.34 0.24 0.23
0 s.d. 0.26 0.26 0.26 0.26
-1 s.d. 0.24 0.2 0.28 0.28
-2 s.d. 0.22 0.15 0.3 0.36
Legend: at productivity, bt bond return,
ut discount rate, rt interest rate

30. Which shocks drive the economy to the bound?
Realized and theoretical distributions of shocks at bound
-0.03 -0.02 -0.01 0 0.01 0.02
0
1
2
3
x 10
4 Interest rate
-0.04 -0.02 0 0.02 0.04
0
1
2
3
x 10
4 Bond premium
-0.04 -0.02 0 0.02 0.04 0.06
0
1
2
3
x 10
4 Aggr. productivity
-0.04 -0.02 0 0.02 0.04
0
1
2
3
x 10
4 Discount factor

31. Which shocks drive the economy to the bound?
Realized and theoretical distributions of shocks at bound
-6.5 -6 -5.5 -5 -4.5 -4
0
1
2
3
x 10
4 Vol. of productivity
-6.5 -6 -5.5 -5 -4.5 -4
0
1
2
3
x 10
4 Vol. of spending
-0.04 -0.02 0 0.02 0.04
0
1
2
3
x 10
4 Gov. spending
-0.04 -0.02 0 0.02 0.04
0
1
2
3
x 10
4 Labor supply

32. “Primary” drivers of ZLB events bond return and monetary
policy shocks
5 s.d. shocks guarantee hitting bound
Productivity and discount rate shocks have lesser effects
10 s.d. shocks guarantee hitting bound
Spending, labor and volatility shocks seem to have no effect
Several different types of ZLB events!

33. Not all shocks are created equal
Impulse responses to productivity and bond shocks that drive the economy to the ZLB
0 2 4 6 8 10
1
1.005
1.01
1.015
1.02
1.025
Aggr.product.
Output
0 2 4 6 8 10
0.98
0.985
0.99
0.995
1
1.005
Inflation
0 2 4 6 8 10
0.94
0.96
0.98
1
Bondreturn
0 2 4 6 8 10
0.97
0.98
0.99
1

34. Not all shocks are created equal
Impulse responses to productivity and bond shocks that drive the economy to the ZLB
together with a government intervention
0 2 4 6 8 10
1
1.005
1.01
1.015
1.02
1.025
Aggr.product.
Output
5 s.d. shock to spending
No increase
0 2 4 6 8 10
0.98
0.985
0.99
0.995
1
1.005
Inflation
0 2 4 6 8 10
0.94
0.96
0.98
1
Bondreturn
0 2 4 6 8 10
0.97
0.98
0.99
1

35. Not all shocks are created equal
Impulse responses to discount rate and monetary policy shocks that drive the economy to
the ZLB together with a government intervention
0 2 4 6 8 10
0.96
0.97
0.98
0.99
1
1.01
Discountrate
Output
0 2 4 6 8 10
0.985
0.99
0.995
1
1.005
Inflation
0 2 4 6 8 10
0.98
1
1.02
1.04
1.06
1.08
Interestrate
0 2 4 6 8 10
0.995
1
1.005
1.01
1.015

36. Simulation procedure for computing fiscal multipliers
1. Start from steady state. Hit the economy with a shock that
drives it to the bound, a shock to volatility and a shock to
spending.
2. Simulate 10 000 realizations for 10 periods.
3. Compute multiplier for period t as an average over
realizations with formula Yt −Yt ∗
G1−G∗
1
Five cases: economy not at bound, at bound due to
productivity, discount rate, bond return or monetary shock
Two volatility shocks: spending and productivity

37. Fiscal multiplier, not at bound
Volatility in spending

38. Fiscal multiplier, not at bound
Volatility in productivity
Productivity volatility shock
Spendingshock
-10 -5 0 5 10
20
15
10
5
1
0
0.5
1
1.5
2

39. When not at the bound...
Multipliers low
Larger spending packages have significantly smaller multipliers
Effects of uncertainty minor
Spending volatility seems to have no clear effect
Extremely low productivity volatility increases multiplier

40. Fiscal multiplier at ZLB
1. Bond return shock
Spending volatility shock
Spendingshock
-10 -5 0 5 10
20
15
10
5
1
0.7
0.8
0.9
1
1.1
1.2
Productivity volatility shock
Spendingshock
-10 5 0 5 10
20
15
10
5
1
0.4
0.6
0.8
1
1.2

41. Fiscal multiplier at ZLB
2. Discount rate shock
Spending volatility shock
Spendingshock
-10 -5 0 5 10
20
15
10
5
1 0
0.5
1
1.5
2
2.5
3
Productivity volatility shock
Spendingshock
-10 -5 0 5 10
20
15
10
5
1 -1
0
1
2
3

42. Some intuition
1. The economy is at the bound due to a high bond return shock
or a low discount rate shock and there is a change in
uncertainty
2. The government spends a portion of output greater than
normal
3. Households would like to save less, but the interest rate is
stuck
From the household’s point of view, spending is taxation - thus
uncertainty in spending is uncertainty in taxation

43. Fiscal multiplier at ZLB
3. Monetary policy shock
Spending volatility shock
Spendingshock
-10 -5 0 5 10
20
15
10
5
1 0.2
0.4
0.6
0.8
1
1.2
Productivity volatility shock
Spendingshock
-10 -5 0 5 10
20
15
10
5
1
0
0.2
0.4
0.6
0.8
1
1.2

44. Fiscal multiplier at ZLB
4. Productivity shock
Spending volatility shock
Spendingshock
-10 -5 0 5 10
20
15
10
5
1
-0.5
0
0.5
Productivity volatility shock
Spendingshock
-10 -5 0 5 10
20
15
10
5
1
-1.5
-1
-0.5
0
0.5

45. Conclusions
Size of the multiplier often, but not always, greater than 1,
when the economy is at the ZLB
Strong dependence on volatility: high spending volatility can
significantly increase the multiplier
Size of spending increase has a strong impact on multiplier
Different shocks lead to different types of ZLB events and
different multipliers
Caveats: lack of capital and distorting taxation probably skew
results