Discussion
“Global Dynamics at the Zero Lower Bound”
Brent Bundick
Federal Reserve Bank of Kansas City
April 2014
The opinions expressed in this discussion are those of the author and do not reflect the views of the Federal Reserve
Bank of Kansas City or the Federal Reserve System.
Global Dynamics at the Zero Lower Bound
Very interesting and well-executed paper
Contribution: Rigorous modeling of a zero lower bound economy
Effects of recent downturn lasting longer than expected
Rigorous modeling is key first step to explaining recent outcomes
Why can technological improvements be contractionary?
Aggregate demand curve has positive slope at zero lower bound
Use linearized AS-AD model to build intuition
πt = βEt πt+1 + ψy yt − (1 − η) ψzt − ψat
yt = Et yt+1 − (rt − r) − Et πt+1 + (1 − ρa ) at
rt = max 0, r + φπ πt + φy yt
Aggregate Demand Away From Zero Lower Bound
ψy
1 + φy +
β
!
yt
AD
1
= Et yt+1 − φπ −
πt + Shocks
β
AS
Y
Declines in πt offset with lower real rates which raises Yt
Technology Shock Away From Zero Lower Bound
ψy
1 + φy +
β
!
yt
AD
1
= Et yt+1 − φπ −
πt + Shocks
β
AS
Y
Higher technology lowers πt & raises Yt with policy accommodation
Aggregate Demand At Zero Lower Bound
ψy
1+
β
!
yt = Et yt+1 +
AD
1
πt + Shocks
β
AS
Y
Declines in πt cannot be initially offset which raises real rates
Technology Shock At Zero Lower Bound
ψy
1+
β
!
yt = Et yt+1 +
AD
1
πt + Shocks
β
AS
Y
Higher technology can cause larger disinflation & output losses
Discussion: Focus on Expectations About Future
ψy
1+
β
!
yt = Et yt+1 +
AD
1
πt + Shocks
β
AD(Yt+1 )
AS
Y
Expectations about future crucial in determining effects of shocks
in high technology states. Higher labor demand raises equilibrium hours, which mitigates the
decline in the real wage. In short, a tension exists at the ZLB between the supply-side effects of
technology and the demand-side effects of the real interest rate. When the central bank responds
less aggressively to the steady-state output gap when the ZLB does not bind (i.e., a lower φy ), the
demand-side effects at the ZLB are weaker and both real and nominal variables are less volatile.
Assumptions About Zero Lower Bound Duration
Steady−State Scenario
ZLB Scenario
!
Real Interest Rate (r/E[π])
Adjusted Output (ŷ adj )
0.75
0.6
0.5
0.4
0.25
0.2
0
−0.25
0
0
5
10
15
Inflation Rate (π̂)
20
0
5
10
15
Nominal Interest Rate (r̂)
20
0.5 preference shock is constant1 in impulse responses
Assume
0.75
⇒ Agents
expect zero lower bound
exit within 1-2 periods
0
0.5
0.25
−0.5
0
Economy
surprised
by zero
lower
bound
duration
every period
0
5
10
15
20
0
5
10
15
20
Labor Hours (n̂)
0
Real Wage Rate (ŵ)
0.8
Comment:
What is the “right” zero
lower bound scenario?
0.4
−0.25
−0.5
Unexpected Long Zero Lower Bound Episode
Output
Inflation
0
3
0.4
−0.5
2.5
0.2
0
−0.2
−0.4
−0.6
−0.8
4
8
12
16
−1.5
1.5
−2
1
−2.5
0.5
−3
20
2
Percent
−1
Percent
Percent
Nominal Interest Rate
0.6
Real Interest Rate
4
8
12
16
0
20
4
Preference Shock
2
12
16
20
Technology
−0.01
2
Gavin et al (2014)
Unexpected ZLB Length
−0.02
1.5
8
1.5
0.5
Percent
Percent
Percent
−0.03
1
−0.04
1
−0.05
0.5
0
−0.5
−0.06
4
8
12
16
20
−0.07
4
8
12
16
20
0
4
8
12
16
20
Expected Long Zero Lower Bound Episode
Output
Inflation
1
0
0
−1
−1
Percent
Percent
−4
−5
1.5
1
−6
−6
0.5
−7
−7
4
8
12
16
−8
20
Real Interest Rate
4
8
12
16
0
20
−0.02
5
−0.04
4
−0.06
Percent
6
3
−0.1
1
−0.12
0
−0.14
8
12
16
20
−0.16
12
16
20
2
Gavin et al (2014)
Unexpected ZLB Length
Large AR(1) Shock
Expected ZLB Length
1.5
−0.08
2
8
Technology
0
4
4
Preference Shock
7
Percent
Percent
−4
−5
Percent
2
−3
−3
−1
2.5
−2
−2
−8
Nominal Interest Rate
3
1
0.5
4
8
12
16
20
0
4
8
12
16
20
Central Bank Responds to Output Gap
Output
Inflation
Nominal Interest Rate
0.7
0
4
0.6
−0.2
3.5
0.5
−0.4
3
0.4
0.3
Percent
Percent
Percent
2.5
−0.6
−0.8
2
1.5
0.2
−1
0.1
−1.2
0
4
8
12
16
−1.4
20
Real Interest Rate
1
0.5
4
8
12
16
0
20
4
Preference Shock
1
0
0.8
−0.01
8
12
16
20
Technology
2
Output Gap
1.5
0.4
0.2
−0.03
1
−0.04
0
0.5
−0.05
−0.2
−0.4
Percent
−0.02
Percent
Percent
0.6
4
8
12
16
20
−0.06
4
8
12
16
20
0
4
8
12
16
20
Central Bank Responds to Steady State Output
Output
Inflation
1
Nominal Interest Rate
0
4
3.5
0.8
−0.5
3
0.4
0.2
2.5
−1
Percent
Percent
Percent
0.6
−1.5
2
1.5
0
1
−2
−0.2
−0.4
0.5
4
8
12
16
−2.5
20
Real Interest Rate
4
8
12
16
0
20
4
Preference Shock
2
12
16
20
Technology
0
2
Output Gap
Steady State Output
−0.01
1.5
8
1.5
0.5
Percent
Percent
Percent
−0.02
1
−0.03
1
−0.04
0.5
0
−0.5
−0.05
4
8
12
16
20
−0.06
4
8
12
16
20
0
4
8
12
16
20
Output Gap Response - Longer Zero Lower Bound Episode
Output
Inflation
0.5
Percent
−0.5
−0.5
3.5
−1
3
−1.5
2.5
−2
−2.5
−1
−1.5
−2
4
4
8
12
16
−3
1
−3.5
0.5
−4
20
Real Interest Rate
0
2.5
−0.02
8
12
16
0
20
4
8
12
16
20
Technology
2
Output Gap
Steady State Output
Output Gap
Longer ZLB Episode
1.5
2
−0.04
Percent
Percent
4
Preference Shock
3
1.5
1
−0.06
1
−0.08
0.5
0.5
−0.1
0
−0.5
2
1.5
Percent
Percent
0
Nominal Interest Rate
0
Percent
1
4
8
12
16
20
−0.12
4
8
12
16
20
0
4
8
12
16
20
Expectations About Current Zero Lower Bound Duration
Figure 8: The Expected Path of Nominal Interest Rates
Gust, Lopez-Salı́do, and Smith (2013)
Model-implied (Red) & Futures Markets (Gray)
Financial Market Federal Funds−Rate Expectations
6
6
5
5
4
4
Percent
Percent
68% confidence bands
median
3
3
2
2
1
1
0
2009
2010
2011
2012
2013
2014
0
2010
Expectations as of 2009:Q1
2011
2012
2013
2014
Expectations as of 2010:Q2
Blue Chip
3−month
Treasury
Bill“late-2014”
Expectations
Expected duration
increased
markedly
with
language
6
6
Comments
Use an alternative zero lower bound scenario
1. Use expectations from data at a given point
2. Use “average” scenario from model simulations
3. Show robustness under variety of scenarios
Decomposing differences between linear & nonlinear model
1. Role of quadratic adjustment costs
2. Precautionary labor supply
I
I
Away from zero lower bound
Additional downside risk implied by the zero lower bound
Solve linear with nonlinear costs or nonlinear with quadratic utility
Very nice and well-executed paper
Additional Details
Precautionary Labor Supply
Wt
LS (λt )
LD (Kt , Zt
Nt
)
Precautionary Labor Supply Without Capital
Wt
LS (!t )
LD (
)
LD (µt )
Nt