Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
The E¤ectiveness of Alternative Monetary Policy Tools
in a Zero Lower Bound Environment
James D. Hamilton
Jing (Cynthia) Wu
Department of Economics
UC San Diego
Hamilton and Wu (UCSD)
ZLB
1 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
What more can monetary policy do when:
the fed funds rate is 0.18%
reserves are over a trillion dollars?
Hamilton and Wu (UCSD)
ZLB
2 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
One possible answer:
change in maturity structure of outstanding Treasury debt
Hamilton and Wu (UCSD)
ZLB
3 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
One possible answer:
change in maturity structure of outstanding Treasury debt
1) Is there evidence this made any di¤erence historically?
Hamilton and Wu (UCSD)
ZLB
3 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
One possible answer:
change in maturity structure of outstanding Treasury debt
1) Is there evidence this made any di¤erence historically?
2) Is there reason to think it could work at the ZLB?
Hamilton and Wu (UCSD)
ZLB
3 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Maturity structure: December 31, 2006
Hamilton and Wu (UCSD)
ZLB
4 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Average maturity in weeks
320
300
280
260
240
220
200
180
160
1990
Hamilton and Wu (UCSD)
1992
1994
1996
1998
2000
ZLB
2002
2004
2006
2008
2010
5 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Yield data
Use a¢ ne-term-structure model to summarize weekly bond yields in terms
of 3 observable factors:
2
3
level
ft = 4 slope 5
curvature
Estimate 1990-2007.
Hamilton and Wu (UCSD)
ZLB
6 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
pnt = log price of n-period pure discount bond
0
pnt = an + b n ft
znt = fraction of my portolio in bond of maturity n
0
znt b n 1 εt +1 = risk exposure
Hamilton and Wu (UCSD)
ZLB
7 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Setup
Suppose a single mean-variance investor held all the publicly-held Treasury
debt
γ = weight on variance in preferences
E (εt εt0 ) = ΣΣ0
qt = equilibrium price of risk:
qt = γΣΣ0 ∑n =2 znt b n
N
1
(3 1 )
Hamilton and Wu (UCSD)
ZLB
8 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Excess holding returns
Excess holding return
e.g. hold 5 year bond over 1 year
h5,1,t = log
Hamilton and Wu (UCSD)
ZLB
P4,t +1
P5,t
y1,t
9 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Excess holding returns
Excess holding return
e.g. hold 5 year bond over 1 year
h5,1,t = log
P4,t +1
P5,t
y1,t
Regression
0
0
hnkt = cnk + βnk
ft + γnk
xt + unkt .
Hamilton and Wu (UCSD)
ZLB
9 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Excess holding returns
Excess holding return
e.g. hold 5 year bond over 1 year
h5,1,t = log
P4,t +1
P5,t
y1,t
Regression
0
0
hnkt = cnk + βnk
ft + γnk
xt + unkt .
.
Expectation hypothesis: excess holding returns are unpredictable
ATSM: ft contains all the information at t
Hamilton and Wu (UCSD)
ZLB
9 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Excess holding return regressions
ztA : average maturity; ztL :
vt : Cochrane-Piazzesi; qt :
Hamilton and Wu (UCSD)
fraction 10 years; ztPC : 3 principal components
Treasury factors
ZLB
10 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Endogeneity
Goal: if maturities of outstanding debt change, how would yields change?
Hamilton and Wu (UCSD)
ZLB
11 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Endogeneity
Goal: if maturities of outstanding debt change, how would yields change?
Conventional regression
ft = c + βqt + εt
Hamilton and Wu (UCSD)
ZLB
11 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Endogeneity
Goal: if maturities of outstanding debt change, how would yields change?
Conventional regression
ft = c + βqt + εt
Concerns:
Is ft responding to qt , or is qt responding to ft ?
Hamilton and Wu (UCSD)
ZLB
11 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Endogeneity
Goal: if maturities of outstanding debt change, how would yields change?
Conventional regression
ft = c + βqt + εt
Concerns:
Is ft responding to qt , or is qt responding to ft ?
Spurious regression
Hamilton and Wu (UCSD)
ZLB
11 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Yield factor forecasting regressions
Our approach:
ft +1 = c + ρft + φqt + εt +1
Hamilton and Wu (UCSD)
ZLB
12 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Yield factor forecasting regressions
Our approach:
ft +1 = c + ρft + φqt + εt +1
Advantages:
answers forecasting question of independent interest
Hamilton and Wu (UCSD)
ZLB
12 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Yield factor forecasting regressions
Our approach:
ft +1 = c + ρft + φqt + εt +1
Advantages:
answers forecasting question of independent interest
avoids spurious regression problem
Hamilton and Wu (UCSD)
ZLB
12 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Yield factor forecasting regressions
Our approach:
ft +1 = c + ρft + φqt + εt +1
Advantages:
answers forecasting question of independent interest
avoids spurious regression problem
nonzero φ does not re‡ect response of qt to ft
Hamilton and Wu (UCSD)
ZLB
12 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Yield factor forecasting regressions
Our approach:
ft +1 = c + ρft + φqt + εt +1
Advantages:
answers forecasting question of independent interest
avoids spurious regression problem
nonzero φ does not re‡ect response of qt to ft
estimate incremental forecasting contribution of qt beyond that in ft
Hamilton and Wu (UCSD)
ZLB
12 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Signi…cance of Treasury factors
level
F test that φ = 0
slope
ft +1 = c + ρft + φqt + εt +1
curvature
Hamilton and Wu (UCSD)
ZLB
F test
3.256
(0.023)
4.415
(0.005)
2.672
(0.049)
13 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Quantitative illustration
Fed sells all Treasury
securities < 1 year, and
uses proceeds to buy up
long-term debt
E.g. in Dec. 2006, the
e¤ect would be to sell
$400B short-term
securities and buy all
bonds > 10 year
Hamilton and Wu (UCSD)
ZLB
14 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Quantitative illustration
Fed sells all Treasury
securities < 1 year, and
uses proceeds to buy up
long-term debt
level
slope
E.g. in Dec. 2006, the
e¤ect would be to sell
$400B short-term
securities and buy all
bonds > 10 year
Hamilton and Wu (UCSD)
curvature
φi0 ∆
0.005
(0.112)
0.250
(0.116)
0.073
(0.116)
∆: average change in qt
ZLB
14 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Impact on yield curve 1-month ahead
Hamilton and Wu (UCSD)
ZLB
15 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Financial Crisis and Zero Lower Bound
Hamilton and Wu (UCSD)
ZLB
16 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Zero Lower Bond
Short term yields near zero
Longer term yields considerable ‡uctuation.
Explanation: when escape from ZLB (with a probability), interest
rates will respond to ft as before
Hamilton and Wu (UCSD)
ZLB
17 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Parsimonious Model of ZLB
Same underlying factors ft
ft +1 = c + ρft + Σut +1
same (c, ρ, Σ)
Hamilton and Wu (UCSD)
ZLB
18 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Parsimonious Model of ZLB
Same underlying factors ft
ft +1 = c + ρft + Σut +1
same (c, ρ, Σ)
Once escape from ZLB
ỹ1t = a1 + b10 ft
0
p̃nt = an + b n ft
an and b n calculated from the same di¤erence equations
Hamilton and Wu (UCSD)
ZLB
18 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Parsimonious Model of ZLB
At ZLB
y1t = a1
0
pnt = an + b n ft .
π Q : probability still at ZLB next period
No-arbitrage:
Can calculate b n (how bond prices load on factors at ZLB) as functions of
b n (how they’d load away from the ZLB) along with π Q (probability of
remaining at ZLB), ρ (factor dynamics), and Λ (risk parameters).
Hamilton and Wu (UCSD)
ZLB
19 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Parsimonious Model of ZLB
Assume: (c Q , ρQ , a1 , b1 , Σ) as estimated pre-crisis
) (an , bn ) same as before
Estimate two new parameters a1 , π Q to describe 2009:M3-2010:M7
data from
Y2t = A2† + B2† Y1t + εet
Y1t = 6-month, 2-year, 10-year
Y2t = 3-month, 1-year, 5-year, 30-year
A2† , B2† functions of (c Q , ρQ , a1 , b1 , Σ) and a1 , π Q
Estimation method: minimum chi square (Hamilton and Wu, 2010)
Hamilton and Wu (UCSD)
ZLB
20 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Parameter estimates for ZLB
Slightly better …t if allow new value for a1 after escape from ZLB
5200a1 = 0.068 (ZLB = 0.07% interest rate)
π Q = 0.9907 (ZLB may last 108 weeks)
5200a1 = 2.19 (compares with 5200a1 = 4.12 pre-crisis–
market expects lower post-ZLB rates than seen pre-crisis)
Hamilton and Wu (UCSD)
ZLB
21 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Actual and …tted values
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
06-Mar-2009
Hamilton and Wu (UCSD)
26-Aug-2009
15-Feb-2010
ZLB
07-Aug-2010
22 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Factor Loadings
Hamilton and Wu (UCSD)
ZLB
23 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
One-month-ahead predicted e¤ect of Fed swapping shortfor long-term
Hamilton and Wu (UCSD)
ZLB
24 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
One-month-ahead predicted e¤ect of Fed swapping shortfor long-term
Note: quantitative easing has almost identical e¤ect as swapping
maturities at the ZLB
Hamilton and Wu (UCSD)
ZLB
24 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Comparison of alternative estimates
Hamilton and Wu (UCSD)
ZLB
25 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
E¤ect of buying intermediate- instead of long-term debt
0.02
SWAP2-ZLB
SWAP1-ZLB
0
-0.02
-0.04
-0.06
-0.08
-0.1
-0.12
-0.14
-0.16
-0.18
0
200
Hamilton and Wu (UCSD)
400
600
800
ZLB
1000
1200
1400
1600
26 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Combined e¤ect of Fed’s QE2 and Treasury operations
Average
maturity
of publicly-held
Average
maturity
of publicly-held
Treasury debtTreasury
debt
228
226
224
222
220
218
216
214
212
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
2010
Long-term
debtpublicly-held
as a percent
of debt
total
-term
publicly-heldpublicly-held
Treasury debt as Treasury
a percent of total
Treasury
publicly-held Treasury debt
8.0
7.9
7.8
7.7
7.6
7.5
7.4
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
2010
Hamilton and Wu (UCSD)
ZLB
27 / 28
Introduction
Data
Risk measures
Results for monthly data, 1990-2007
ZLB
Discusssion
Why the Fed and not the Treasury?
Possible tool for signaling future short rate plans
Far from ideal instrument in normal times
Hamilton and Wu (UCSD)
ZLB
28 / 28