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Safety, Liquidity, and the Natural Rate of Interest
by Marco Del Negro, Domenico Giannone,
Marc P. Giannoni, Andrea Tambalotti
Jing Cynthia Wu
Chicago Booth & NBER
Cynthia Wu (Chicago & NBER)
1 / 19
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Comment 1: Decomposing long term yield into
expectation and term premium
This is one core question in the term structure literature
ytn = ȳtn + tptn
where
ȳtn =
1
Et [rt + rt+1 + . . . rt+n−1 ]
n
Expectation ȳtn is the trend.
Cynthia Wu (Chicago & NBER)
2 / 19
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Comment 1: Expectation
The short rate
rt
= δ0 + δ10 Xt
Dynamics for factors
Xt+1 = µ + ρXt + Σεt+1 ,
εt+1 ∼ N(0, I )
Pricing equation
Et [exp(−mt+1 )Pn−1,t+1 ]
Pnt
=
ynt
1
= − log(Pnt )
n
Expectations
Et [rt+n ] = δ0 + δ10 Et [Xt+n ]
Cynthia Wu (Chicago & NBER)
3 / 19
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Comment 1: Bias correction
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Estimation: OLS for VAR. Highest eigenvalue of ρ: 0.95.
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However, the persistence is underestimated.
YLabelRight
14
12
Use
as d.g.p.
and estimate
10
8
6
4
2
0
0.6
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0.8
1.0
Bias correction: Bauer, Rudebusch, and Wu (2012, 2014).
Cynthia Wu (Chicago & NBER)
4 / 19
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Comment 1: Downward trend in expectation
U.S.
10
Percent
Percent
10
5
0
1990
5
0
1995
2000
2005
2010
1990
Germany
Cynthia Wu (Chicago & NBER)
10
ent
ent
black: five-by-five-year forward rate
Red: OLS
10
blue: Bauer, Rudebusch, and Wu (2012, 2014) bias corrected
5 / 19
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Comment 2: How negative can nominal rates be?
real r *
10
6.5
nominal r *
6
15
5.5
5
5
10
4.5
4
0
5
3.5
3
-5
0
2.5
Q1-60
Q1-80
Q1-00
Cynthia Wu (Chicago & NBER)
2
Q1-60
Q1-80
Q1-00
Q1-60
Q1-80
Q1-00
6 / 19
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Comment 2: How negative can nominal rates be?
Nominal r ∗ was as negative as -5%.
Is it plausible?
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We do not observe negative interest rates in the US.
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The SNB’s deposit rate is at record low of -75 basis points. But that’s still
far away from -5%.
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The negative interest rates in Europe were due to interventions by central
banks, but r ∗ is in the conterfactual world where there is no central bank.
Frictions that potentially allow a negative nominal rate
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take physical currency out of circulation
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highly unlikely
storage cost
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there is a limit
Cynthia Wu (Chicago & NBER)
7 / 19
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Comment 2: What causes implausibly negative nominal
rate?
Lack of proper treatment for ZLB
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In the reduced form: discard short rate after 2008 Q3
Consequences
I internal inconsistency
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remove short rate and its ZLB
forward looking agents factor the ZLB in the future into yields at
longer maturities.
the same lower bound should constrain the nominal trend and r ∗ .
less information leads to less accurate estimation
Cynthia Wu (Chicago & NBER)
8 / 19
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Comment 2: Shadow rate – a treatment for ZLB
Black (1995)
rt = max(st , r ),
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Allow the model to be internally consistent
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short rate, trend on nominal rates, and expectations in longer rates are
subject to the same lower bound.
Does not allow nominal rates to be (too) negative.
Cynthia Wu (Chicago & NBER)
9 / 19
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Comment 2: Shadow rate – a treatment for ZLB
Wu and Zhang (2016)
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DSGE linear in st
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rt = max(st , r )
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A negative st accommodates unconventional monetary policy
Potential consolidating negative nominal rates by relabeling rt as st
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s ∗ + Et πt+1 < 0
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r ∗ + Et πt+1 > 0
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A downward trend in s ∗ instead of r ∗ at the ZLB.
Cynthia Wu (Chicago & NBER)
10 / 19
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Comment 2: Shadow rate – a treatment for ZLB
Puzzle remaining: what happened in the 1970s?
Cynthia Wu (Chicago & NBER)
11 / 19
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Comment 3: Trend in convenience yield
4.5
4
3.5
3
2.5
2
1.5
1
Q1-60
Q1-70
Q1-80
Q1-90
Q1-00
Q1-10
Main result: a trend in convenience yield from late 1990s explains the
decline in r¯.
Cynthia Wu (Chicago & NBER)
12 / 19
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Comment 3: No trend in the data
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No trend is present in the data
Spread jumps up during the Great Recession
Cynthia Wu (Chicago & NBER)
13 / 19
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Comment 3: No trend in the data
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No trend is present in the data
Spreads jump up during the Great Recession
Cynthia Wu (Chicago & NBER)
14 / 19
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Comment 4: Model dependent results
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For the first 70% of the sample, the correlation is 0.37
The difference was 0.8% at the beginning
Different cyclical behaviors
Cynthia Wu (Chicago & NBER)
15 / 19
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Comment 4: Model dependent results
LW r *
DGGT 5-year forward r *
6
5
4
3
2
1
0
Q1-60
I
I
Q1-70
Q1-80
Q1-90
Q1-00
Q1-10
For the first 70% of the sample, the correlation is -0.57
The difference was 4.8% at the largest
Cynthia Wu (Chicago & NBER)
16 / 19
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Comment 4: Model dependent results
10
5
0
LW r *
-5
DGGT 5-year forward r *
DGGT r *
Q1-60
I
I
Q1-70
Q1-80
Q1-90
Q1-00
Q1-10
r ∗ is much more volatile than the other two series
There is hardly a common pattern across the three
Cynthia Wu (Chicago & NBER)
17 / 19
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Comment 4: Should the natural rate of interest be more
volatile than observed rates?
r*
r
10
5
0
-5
Q1-60
Q1-80
Q1-00
The variance of r ∗ is 3 times the variance of r .
Cynthia Wu (Chicago & NBER)
18 / 19
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Conclusion
Overall, this is a very interesting, timely, and well written paper!
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Comment 1: downward trend in expectation.
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Comment 2: is very negative nominal r ∗ a shadow rate?
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Comment 3: there isn’t a trend in convenience yield in the data.
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Comment 4: model dependent results.
Cynthia Wu (Chicago & NBER)
19 / 19