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Measures and Policy Applications of the
Equilibrium Neutral Real Interest Rate
FRBNY DSGE Team
2016 PBOC-FRBNY Joint Symposium
The views expressed here do not necessarily reflect those
of the Federal Reserve Bank of New York or the Federal Reserve
System
Disclaimer:
Outline
This presentation will focus on one specific definition of “neutral real
interest rate”, namely the so-called natural rate of interest r ∗ featured in
New Keynesian models, and will discuss estimates of r ∗ from one such
model – the FRBNY DSGE model – and their use in policy analysis.
1
The FRBNY DSGE Model
2
r ∗ – What is it, and what is it for?
3
Estimates of r ∗ for the US, or why are interest rates so low?
4
r ∗ as a Benchmark for Monetary Policy
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
2
Commentary
• In spite of the broad title, this presentation will focus on one specific
definition of “neutral real interest rate”, namely the so-called natural rate
of interest r ∗ featured in New Keynesian models, and will discuss
estimates of r ∗ from one such model – the FRBNY DSGE model.
• We start by quickly introducing the FRBNY model, and discussing its
main features.
• We continue by elaborating on why the New Keynesian natural rate of
interest r ∗ is a conceptually useful measure of the “neutral real interest
rate”.
• Next, we discuss empirical estimates of r ∗ obtained from the FRBNY
DSGE model, and focus on the question - Why have interest rates been so
low for so long in the US?
• We conclude with some policy applications, discussing the pace of interest
rate renormalization from the perspective of r ∗ .
The FRBNY DSGE Model
FRBNY DSGE Model
• New Keynesian DSGE model á la Smets-Wouters (2007)
• Stochastic growth model
+ ...
real rigidities
nominal rigidities
investment adjustment costs
price stickiness (ζp )
variable capital utilization
wage stickiness (ζw )
partial indexation
to lagged inflation
+ habit persistence
• Model is estimated on the several observables: output (both GDP
and GDI), consumption, investment, and wage growth, total hours
worked, inflation (both headline and core PCE), the federal funds
rate, TFP, 10-year rate
• Many shocks: TFP .. .
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
3
The FRBNY DSGE Model
FRBNY DSGE Model
• New Keynesian DSGE model á la Smets-Wouters (2007)
• Stochastic growth model
+ ...
real rigidities
nominal rigidities
investment adjustment costs
price stickiness (ζp )
variable capital utilization
wage stickiness (ζw )
partial indexation
to lagged inflation
+ habit persistence
• Model is estimated on the several observables: output (both GDP
and GDI), consumption, investment, and wage growth, total hours
worked, inflation (both headline and core PCE), the federal funds
rate, TFP, 10-year rate
• Many shocks: TFP .. .
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
3
Commentary
• We start by briefly describing the FRBNY DSGE model because this is the
model used to extract our measure of r ∗ , hence it is important to
understand its main features.
• The FRBNY DSGE model is based on the seminal work of Smets and
Wouters (2007) with a number of additions: shocks/observables/features
that are in our model but not in Smets and Wouters (2007) are in blue in
the previous slides. The most important addition is financial frictions
(next slide).
• The FRBNY DSGE model is broadly discussed in the Liberty Street post
“A Bird’s Eye View of the FRBNY DSGE Model” (De Paoli et al.) LINK
and its most recent version in “The FRBNY DSGE Model Forecast April
2015” (Del Negro et al.) LINK.
The FRBNY DSGE Model
Financial Frictions
• Modeled along the lines of Bernanke, Gertler, and Gilchrist (1999),
Christiano, Motto, and Rostagno (2003, 2014).
• No arbitrage condition between safe assets and risky investment
implies that
spread in the return
= f ( leverage ,
between risky and safe assets
| {z }
endogenous
shock
| {z } )
exogenous
• Spread is treated as observed and measured as the difference
between the Baa Corporate rate and the 10 year Treasury
• Del Negro, Giannoni, and Schorfheide (2015)
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
4
Commentary
• Financial frictions are introduced as in Del Negro, Giannoni, and
Schorfheide (2015) LINK.
• They are very important both in terms of the model’s dynamics
(propagation of financial shocks) and the information set (BAA-Treasury
spread contains information about the state of the economy, and
specifically of financial conditions).
• They are key in terms of forecasting performance (next slide).
• Financial frictions also play an important role in terms of estimates of r ∗ :
financial shocks are the key drivers of r ∗ in our model.
The FRBNY DSGE Model
Why Financial Frictions?
Forecasts of the Great Recession: 2008Q3 Data (Del Negro and Schorfheide 2014)
Plain SW
SW + Financial Frictions
Output Growth
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
−0.5
−0.5
−1
−1
−1.5
−1.5
−2
−2
2004 2005 2006 2007 2008 2009 2010 2011 2012
3
2.5
2
1.5
1
0.5
0
−0.5
−1
−1.5
3
2.5
2
1.5
1
0.5
0
−0.5
−1
−1.5
−2
−2
2004 2005 2006 2007 2008 2009 2010 2011 2012
Inflation
1.5
1.5
1
1
1.5
1
0.5
0.5
1
0.5
0.5
0
0
0
−0.5
−0.5
2004 2005 2006 2007 2008 2009 2010 2011 2012
FRBNY DSGE Team
1.5
r
∗
−0.5
0
−0.5
−1
−1
2004 2005 2006 2007 2008 2009 2010 2011 2012
in the FRBNY DSGE Model
PBOC
5
Commentary
• The figure is from Del Negro and Schorfheide, 2014 Handbook of
Economic Forecasting, section 7.2 LINK, and is commented in detail
therein.
• The two models are identical except for the inclusion of financial frictions.
The figure shows that financial frictions, and the inclusion of spreads in
the information set, change the forecasts dramatically using pre-Lehman
(2008Q3) data.
• Figure description: The panels show for each model the available real
GDP growth/core PCE inflation data as of Jan 10 2009 (black line), the
DSGE model’s multi-step mean forecasts (red line) and bands of its
forecast distribution (shaded blue areas; these are the 50, 60, 70, 80, and
90 percent bands, in decreasing shade), the Jan 10 2009 Blue Chip
forecasts (blue diamonds), and the actual realizations according to the
May 2011 vintage (black dashed line). All the data are in percent, Q-to-Q.
“Real” Real Time Forecasts from FRBNY-DSGE Model
Forecasts evolution over time: FRBNY DSGE vs SEP
Output Growth (Q4/Q4)
Core PCE Inflation (Q4/Q4)
2012
2012
2012
2.2
5
4.5
2
4
1.8
3.5
1.6
3
2.5
1.4
2
1.2
1.5
1
1
0.5
Unconditional
Conditional
SEP Central Tendency
0.8
0
Unconditional
Conditional
SPF
SEP Central Tendency
0.6
2010.25
2010.75
2011.25
2011.75
2012.25
2012.75
Vintage
2010.25
2010.75
2011.25
2011.75
2012.25
2012.75
Vintage
2015
2015
2015
2.2
5
4.5
2
4
1.8
3.5
1.6
3
2.5
1.4
2
1.2
1.5
1
1
0.5
Unconditional
Conditional
SEP Central Tendency
0.8
0
Unconditional
Conditional
SPF
SEP Central Tendency
0.6
2011
2012.25
2013.5
Vintage
2014.75
2011
2012.25
2013.5
Vintage
2014.75
Commentary
• r ∗ estimates from the FRBNY DSGE model are credible only to the
extent that the model has some empirical validity. Real (as opposed to
pseudo) real-time assessment of forecasting accuracy from the model may
provide some.
• The FRBNY model from the beginning (mid-2010) predicted a meek
recovery and inflation below the long run objectives. The forecasts in the
Summary of Economic Projections were substantially more optimistic.
This is because it believed that the headwinds from the financial crisis
would dissipate only slowly. The FRBNY model was broadly correct in
terms of output growth. It under-predicted inflation in 2012 (Arab spring)
but did well for 2015 inflation.
• Figure description: The plots show the evolution over time of the
forecasts for 2012 (top panels) and 2015 (bottom panels) for output
growth (Q4/Q4, left panels) and core PCE inflation (Q4/Q4, right
panels). The forecasts are the FRBNY DSGE forecast (dark blue), the
FRBNY DSGE forecast conditional on the judgmental nowcast for output
and inflation (light blue), the upper and lower bounds of the “central
tendency” of the FOMC’s Summary of Economic Projections (green), and
the Survey of Professional Forecasters’ forecasts (red). These plots are
update versions of the charts shown in the Liberty Street post “An
Assessment of the FRBNY DSGE Model’s Real-Time Forecasts” (Cocci et
al.) LINK
The FRBNY DSGE Model
Caveats
• Long run trends misspecified (balanced growth path)
• No external sector (only exogenously captured via “demand
shocks”)
• No term premia
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
7
Commentary
• The FRBNY DSGE model – in spite of arguably being at the frontier – is
still badly misspecified and misses important features of the US economy.
• Among the sources of misspecification are the long run trends (e.g., the
balanced growth path assumed in the model implies that output and
consumption grow at the same pace)
• Among the (many) missing features are the lack of an external sector,
term premia, a banking sector, non-linearities ...
r
∗
– What is it, and what is it for?
What is r ∗ ?
(in New Keynesian DSGE Models)
• r ∗ is the short term real rate of return in an hypothetical
economy without nominal (price and wage) rigidities, but
otherwise identical to the one we live in.
• In this economy monetary policy cannot affect real rates of return ...
• ... nor should it try to. The level of output (y ∗ ) is the optimal one –
given the environment.
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
8
Commentary
• r ∗ in New Keynesian models in general and in the FRBNY DSGE model in
particular is discussed in the Liberty Street post “Why Are Interest Rates
So Low?” (Del Negro et al.) LINK. See also the literature cited therein.
r
∗
– What is it, and what is it for?
What is r ∗ for?
1) Provide information on real rates of return – net of monetary
policy. (Positive)
• What would the real rate be in a parallel universe where monetary
policy had no effects?
• Real rates of return in the US are currently very low, and have been
so for many years. According to the model, monetary policy has very
little to do with this.
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
9
r
∗
– What is it, and what is it for?
What is r ∗ for?
2) Provide a benchmark for setting the short term rate.
(Normative)
• Why? A simple New Keynesian economy can be described by an AD
curve resulting from the interaction of monetary policy (the LM)
and the IS relationship:
yt = σrt + IE t [yt+1 ] + IS shifters
or
∗
(yt − yt∗ ) = σ(rt − rt∗ ) + IE t [(yt+1 − yt+1
)]
and by an AS curve
πt = κ(yt − yt∗ ) + βIE t [πt+1 ]
• In this simple economy setting r equal to r ∗ kills two birds with one
stone: 1) it closes the output gap (y = y ∗ ) and 2) stabilizes
inflation (π = 0).
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
10
r
∗
– Estimates for the US
A Time Series of r ∗
• r ∗ varies greatly over time and is pro-cyclical → Assumption of
constant r ∗ does not appear to be supported by the data.
• r ∗ fell in the Great Recession; it has been low ever since and only
recently started to rise.
15
10
5
0
−5
−10
Range
FRBNY DSGE
−15
1985
FRBNY DSGE Team
1990
1995
∗
r
2000
in the FRBNY DSGE Model
2005
2010
2015
PBOC
11
Commentary
• Figure description: The black line shows r ∗ (in real terms, quarterly
annualized) in the FRBNY DSGE model. The shaded areas show the
range of estimates of r ∗ from various DSGE models used across the
Federal Reserve System and shown in a December 2015 speech by Chair
Yellen LINK.
• Estimates of r ∗ in the FRBNY DSGE model are discussed in the Liberty
Street posts“Why Are Interest Rates So Low?” (Del Negro et al.) LINK
and more recently in “The FRBNY DSGE Model Forecast November
2015” (Del Negro et al.) LINK. The current estimates are based on data
up to 2015Q4.
• Since model misspecification is a serious issue, it may not be wise to rely
on a single model. Hence we look at estimates of r ∗ across different
DSGE models (although, in fairness, all these model share some of the
same sources of misspecification).
• Note that quarterly estimates of r ∗ tend to be quite volatile.
r
∗
– Estimates for the US
What Drives r ∗ ?
• The main forces driving r ∗ in the US in the recent period have been
financial headwinds, which lower investment and increase savings,
and productivity shocks, which affect the marginal product of
capital.
• Financial headwinds are expected to dissipate over time, but slowly.
4
4
2
2
0
0
−2
−2
−4
−4
1985
1995
2005
Productivity
FRBNY DSGE Team
r
∗
Financial
in the FRBNY DSGE Model
2015
Other
PBOC
12
Commentary
• Figure description: The black line shows r ∗ in deviations from its long run
mean. The red line shows the model’s forecast for r ∗ . The colored bars
show the contribution of various shocks to the evolution of the natural
rate.
• The DSGE model allows us to trace the evolution of the natural rate back
to the original shocks perturbing the economy.
• Financial and (to a lesser extent) productivity shocks are the main drivers
of r ∗ – both in the recent period and throughout the entire sample.
r
∗
as a Benchmark for Monetary Policy
The Monetary Policy Stance Through the Lenses of r ∗
• r (actual real rate of return) > r ∗ → monetary policy is
“restrictive”
• r > r ∗ → monetary policy is “accommodative”
• Caveat: r ∗ is not necessarily optimal in outside of simple models
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
13
Commentary
• Figure description: The figure shows the actual real short term interest
rate (black, computed as the federal funds rate minus expected inflation),
and r ∗ (red, 90% bands characterize estimation uncertainty).
• r ∗ – rather than the absolute level of interest rates – can serve as a gauge
as to whether policy is accommodative or not.
• According to this measure, policy was accommodative in the mid-2000’s,
but restrictive in the aftermath of the Great Recession. Currently, r ∗ and
the actual real rate are close to one another, indicating that policy is close
to “neutral.”
r
∗
as a Benchmark for Monetary Policy
The r ∗ Gap and Business Cycles in the US
• The gap between r and r ∗ is strongly countercyclical (negatively
correlated with CBO output gap).
• This does not mean the monetary policy “caused” recessions and
booms; only that it could have responded more forcefully –
according to the model
8
0.75
De-trended
10-Year Rate Gap
6
0.5
4
0.25
2
0
0
-2
-0.25
-4
CBO Output Gap
-0.5
-6
-8
1980
FRBNY DSGE Team
-0.75
1990
2000
r
∗
in the FRBNY DSGE Model
2010
PBOC
14
Commentary
• Figure description: The figure shows the gap between the 10-year r ∗ and
the 10-year real rate (red line), both computed using the expectation
hypothesis. This r ∗ gap is detrended using the HP filter. The orange line
shows the CBO output gap.
• Does the r ∗ gap matter? The figure shows that the r ∗ gap and the CBO
output gap are strongly negatively correlated. This does not mean the
monetary policy “caused” recessions and booms; only that it could have
responded more forcefully – at least, according to the model (see
Justiniano et al. 2013 LINK for a similar finding).
• Why do we use the 10-year rate gap? Because it is the long rate, rather
than the short rate, that affects economic conditions in New Keynesian
models (as can be seen by iterating the Euler/IS equation). We use the
HP filter to address the long run trends issues discussed before, but the
negative correlation is there even with non-detrended data, if slightly
weaker.
r
∗
as a Benchmark for Monetary Policy
Interest Rate Renormalization and Nominal r ∗ in the US
• r ∗ set to renormalize quite slowly
• The chances that nominal r ∗ become negative are not small →
asymmetric risks
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
15
Commentary
• Figure description: The figure shows the federal funds rate and the
median forecast for the federal funds rate from the December Summary of
Economic Projections (black line), the nominal natural rate (defined as r ∗
plus expected inflation, red lines), and the OIS (Overnight Interest Swaps,
blue line, as of February 9 2016).
• The figure makes two points. First, the nominal natural rate is currently
slightly higher than the federal funds rate, but renormalizes very slowly
(because of financial headwinds discussed before). The median SEP
forecast foresees a faster renormalization which, according to the model,
may change the stance of US policy from being mildly accommodative to
being restrictive.
• Second, there are non negligible chances that the nominal natural rate
may become negative → the risks are asymmetric, as negative nominal
rates are harder to achieve.
r
∗
as a Benchmark for Monetary Policy
Conclusions
• The FRBNY DSGE model has a reasonable forecasting track record
so far
• r ∗ is the real rate of interest “net” of monetary policy influences
•
It varied widely in the US over the past 30 years, mostly driven
by financial shocks
•
It provides a useful benchmark for monetary policy
• The gap between r and r ∗ is countercyclical
• r ∗ is expected to normalize slowly in the US
FRBNY DSGE Team
r
∗
in the FRBNY DSGE Model
PBOC
16