NBP Working Paper No. 215
In search for appropriate lower bound.
Zero lower bound vs. positive lower bound
under discretion and commitment
Piotr Ciżkowicz, Andrzej Rzońca, Andrzej Torój
NBP Working Paper No. 215
In search for appropriate lower bound.
Zero lower bound vs. positive lower bound
under discretion and commitment
Piotr Ciżkowicz, Andrzej Rzońca, Andrzej Torój
Economic Institute
Warsaw, 2015
Piotr Ciżkowicz – Warsaw School of Economics; [email protected]
Andrzej Rzońca – Monetary Policy Council in Narodowy Bank Polski,
Warsaw School of Economics; [email protected]
Andrzej Torój – Warsaw School of Economics; [email protected]
Acknowledgments
We would like to thank Leszek Balcerowicz for inspiring discussions on the topic, as well as
an anonymous referee and participants of 46 Konstanz Seminar for Monetary Theory and
Policy on the Island of Reichenau at the Lake of Constance and various seminars at Narodowy
Bank Polski, the University of Economics in Katowice, the University of Economics in Łódź
and Warsaw School of Economics for helpful comments. The usual caveats apply.
Published by:
Narodowy Bank Polski
Education & Publishing Department
ul. Świętokrzyska 11/21
00-919 Warszawa, Poland
phone +48 22 185 23 35
www.nbp.pl
ISSN 2084-624X
© Copyright Narodowy Bank Polski, 2015
Contents
Abstract 4
1. Introduction 5
2. Related literature and context 13
3. Model description 20
3.1 The model 20
3.2 Shock definition 22
3.3 Solution under commitment 23
3.4 Solution under discretion 25
3.5 Calibration 25
4. Results 29
5. Conclusions 37
References 38
Figures and tables 46
NBP Working Paper No. 215
3
Abstract
Abstract
We lay a ground for a simple comparison of positive and possible side (adverse)
effects of zero interest rate policy (ZLB policy) on welfare. Using a standard New
Keynesian dynamic stochastic general equilibrium model, we show that if one
assumes that the ZLB policy has no side effects, then this policy is welfare
enhancing relative to positive lower bound (PLB) policy, except for the case where
PLB policy is pursued under commitment, while the ZLB policy is discretionary.
However, moderate side effects of the ZLB policy usually suffice for the PLB policy
to pay off in terms of welfare. Only if the ZLB policy was pursued under
commitment, while PLB policy was discretionary, would the PLB policy dominance
over the ZLB policy, in terms of welfare, require strong side effects of ZLB policy.
Otherwise PLB policy could dominate the ZLB policy in terms of welfare, even if
restructuring, fostered by the PLB policy, entailed some costs, which could be
reduced (or avoided) through slow restructuring. For given side effects of the ZLB,
the larger and the more persistent the shock that makes the ZLB bind, the more
likely PLB policy dominance over the ZLB policy. The findings holds for
economies with both fast and slow potential output growth, with low and high
inflation target, flexible and rigid.
Keywords: zero lower bound, positive lower bound, restructuring, uncertainty,
discretion, commitment
JEL classification: D80, E52, E58, G34
2
4
Narodowy Bank Polski
1. Introduction
Until recently, an effective lower bound on interest rate was 2% or more (for details
Chapter 1
see, Homer and Sylla, 2005). In 20th century, interest rates were kept below that
1. Introduction
bound virtually only after the Great Depression, during war economy and its
Until
recently,occasionally
an effective in
lower
bound
on interest
rate was
2% or more
(for details
withdrawal,
some
centrally
planned
economies,
in Switzerland
th
coping
with and
excessive
in 1977-1978
1996-1999
andbelow
in Japan
see,
Homer
Sylla, capital
2005). inflows
In 20th century,
interestand
rates
were kept
that
after speculative
bubbleafter
bursting
at the Depression,
beginning ofduring
the 1990s.
experience
of
bound
virtually only
the Great
war The
economy
and its
central
banksoccasionally
shifted
tocentrally
the interest
rates
close1993
to zero,
forward
Japan, where
interest aggressively
ratesinhave
remained
below
2% since
and
below
0.5%
withdrawal,
some
planned
economies,
intheir
Switzerland
guidance
hashas
provided
forecasts
of likely
interest
rateand
path,
instead
making
the
since
attracted
attention
of in
many
economists
to
the
zeroofand
lower
coping1995,
with
excessive
capital
inflows
1977-1978
1996-1999
in bound
Japan
3
commitment
to respond
future1,demand
suchofa
after speculative
bubble
bursting
at thetobeginning
of topic
the pressure.
1990s.
TheWithout
experience
(ZLB).
Since not
Eggertsson
andpromptly
Woodford
(2003)
the
has been
studied
mostly
commitment,
forward
guidance
reassure
the2%
public
in 1993
thegeneral
belief
that
growth
through
the lens
of New
Keynesian
(NK)
dynamic
stochastic
equilibrium
Japan, where
interest
rates
havecould
remained
below
since
and below
0.5%
2
prospects
arehas
poor.
models,
which
meanwhile
became the
toolto for
banks.bound
The
since 1995,
attracted attention
of basic
many analytical
economists
thecentral
zero lower
However,
there are
few
economists,
monetary
policy
NK
analytical
framework
implies
that
the(2003)
ZLB who
is11, not
necessarily
a serious
constraint
(ZLB).
Since Eggertsson
and
Woodford
thewarn
topicagainst
has been
studied
mostly
extremely
bytohistorical
standards.
For
example,
(2010,
2012,
through
theaccommodative
lens ofcapability
New Keynesian
(NK)
stochastic
equilibrium
on central
bank’s
stabilize
thedynamic
economy.
In
fact, general
if BIS
a central
bank
is
22quite
2013,
claims
that
such
policy
promote
forbearance
lending,
which
highly2014)
credible,
then
costs
ofa the
ZLB
are,
according
to
thefor
NK
framework,
models,
which
meanwhile
became
thecan
basic
analytical
tool
central
banks.keeps
The
unproductive
firms
afloat,can
crowds
viable
firms
out necessarily
of by
credit,
thwarts
capital
and
NK
analytical
framework
implies
the ZLB
is not
a serious
constraint
limited.
The central
bank
still that
stabilize
the
economy
affecting
expectations
of
labor
reallocation.
It thus
strengthens
financial
frictions
and
deters
post-crisis
future
interest
ratescapability
and
inflation
(see, e.g.
Walsh,
2009,
theifpapers
that
Walsh
on
central
bank’s
to stabilize
the
economy.
Inand
fact,
a central
bank
is
restructuring.
In turn,
Meltzer
andare,
Taylor
(2014),
others,
contend
that
refers to).
However,
after the
Lehman
collapse
in 2008,
the
ZLB
became
highly
credible,
then costs
of (2014)
the
ZLB
according
toamong
thewhen
NK
framework,
quite
unprecedented
nature
ofcanmonetary
policy
(and
other
kinds
of
policy),
its
binding
allcentral
major
economies,
economic
performance
turned out
to
be poorer
limited. in
The
bank
stilltheir
stabilize
the economy
by affecting
expectations
of
unpredictability
and
failure
rulesWalsh,
can persistently
heighten
futureexpected
interest (see
rates
and
inflation
(see, e.g.
2009, and the
papersuncertainty,
that Walsh
than
Figure
1). to follow
4
which
economic
agents
defer more
serious
refers invites
to). However,
after
the toLehman
collapse
in adjustments.
2008, when the ZLB became
evidence
supportstheir
the(Figure
minority
view. In particular,
bindingSome
in all major
economies,
economic
turned outeven
to be though
poorer
1) performance
recovery
of the
economy
has been sluggish by historical standards, the
than expected
(see US
Figure
1).
utilization
labor and link
capital
been growing
faster than
overtoprevious
Mostof economists
thathas
disappointing
performance
either
factors
recoveries.
In contrast,
growth
in productivity
abovereluctance
all, in capital
stock (in
beyond
reach
of monetary
policy,
or
to central
to rigorously
(Figure
1) and,banks’
spite
rapid development
of capital
intensive (see,
shale e.g.
gas Eggertsson
and oil industry)
has been
followofprescriptions
from the
NK framework
and Krugman,
5
Interestingly,
the current
recovery
haseither
two features
in
very
2012;slow
Gali
et economists
al.,Figure
2012;2).
Mian
and
2011;
Stockperformance
and
Watson,
2012;
Summers,
Most(see
link
thatSufi,
disappointing
to
factors
common
with two
previous
recoveries.
all these
recoveries
preceded
by
beyond
of monetary
policy,
or First,
toWoodford
central
banks’
reluctance
rigorously
2014 or reach
Woodford,
2012). For
example,
(2012)
argues were
that,toeven
though
interest
rate being
cutfrom
to a the
lower
thaninterest
in the
previous
easing
cycle.
Secondly,
follow prescriptions
NKlevel
framework
(see,rates
e.g.close
Eggertsson
and
Krugman,
central
banks
shifted
aggressively
to the
to zero,
their
forward
ofGali
them
outanalyzed
toMian
be more
than
therate
previous
2012;
etturned
al.,ZLB2012;
andofsluggish
Sufi,
and
Watson,
2012;
Summers,
guidance
has
provided
forecasts
likely
path,
instead
of inmaking
the
1each
For the
first
time
the
was
through
the
lens 2011;
of interest
the
NKStock
model
by
Jung
andone.
his co-authors
a Hitotsubashi
University working paper in 2001. The modified version of the paper was published as Jung et al. (2005).
3
Obviously,
the term
NK2012).
model refers
toexample,
very wide to
group
of models,
inclusivepressure.
of
open economy
models. though
Hereafter
2014
or Woodford,
For
Woodford
(2012)
argues
that,
even
commitment
notof to
respond
promptly
future
demand
Without
such
a
however, it applies to simple models of closed economy, which are commonly used to study the issue of ZLB.
(Figure 2)
commitment, forward guidance could reassure the public in the belief that growth
2
prospects
1
time
the
11 For
For the
the first
first are
time poor.
the ZLB
ZLB was
was analyzed
analyzed through
through the
the lens
lens of
of the
the NK
NK model
model by
by Jung
Jung and
and his
his co-authors
co-authors in
in aa Hitotsubashi
Hitotsubashi
University working
working paper
paper in
in 2001.
2001. The
The modified
modified version
version of
of the
the3paper
paper was
was published
published as
as Jung
Jung et
et al.
al. (2005).
(2005).
University
Obviously,
the
model
refers
to
wide
of
models.
However,
there
economists,
who inclusive
warn against
monetary
policy
Obviously,
the term
term of
of NK
NK
modelare
refersfew
to very
very
wide group
group of
of models,
models,
inclusive
of open
open economy
economy
models. Hereafter
Hereafter
however, it
it applies
applies to
to simple
simple models
models of
of closed
closed economy,
economy, which
which are
are commonly
commonly used
used to
to study
study the
the issue
issue of
of ZLB.
ZLB.
however,
3
Using the taxonomy
by Campbell et al. (2012),
the forward guidance
was more
of Delphic
than of Odyssean
nature. 2012,
extremely
accommodative
by historical
standards.
For
example,
BIS (2010,
4 We leave aside the most frequent criticism of extremely accommodative monetary policy, centered on risk misjudgment,
excessive risk taking, and asset bubbles creation (see, e.g. Adrian and Shin, 2010 and 2014; Altunbas et al., 2014; Bordo and
2013,
2014) claims that such a policy can promote forbearance lending, which keeps
Landon-Lane, 2013; Borio and White, 2003;Borio and Zhu, 2012; Diamond and Rajan, 2009; Farhi and Tirole, 2012; Issing,
3
2012, Jarocinski and Smets, 2008; Jiménez et al., 2012 and 2014 Maddaloni and Peydró, 2013, Rajan, 2005; Taylor, 2009 or
unproductive
firms
afloat,
crowds
viable
of credit,
thwarts
capital
White, 2010), not to mention inflationary pressure. This criticismfirms
refers toout
an economy
which has
no slack rather
than toand
one
hit
by Working
a crisis andPaper
struggling
to recover, which is focus of interest in this paper
NBP
No. 215
5
labor
reallocation.
thus
financial
frictions
post-crisis
TFP growth
was rapid in the It
acute
phase strengthens
of the global financial
crisis, that is
in the fourthand
quarterdeters
2008 and the
first quarter
2009. However since the end of the Great Recession, i.e. the second quarter 2009, as dated by the NBER, productivity has been
almost flat. Its cumulative
increase
until the end
of 2014 amounts
to mere 1.3%
(cf. Fernald,
2014).
restructuring.
In turn,
Meltzer
(2014)
and Taylor
(2014),
among
others, contend that
2
2
5
central banks shifted aggressively to the interest rates close to zero, their forward
guidance has provided forecasts of likely interest rate path, instead of making the
commitment not to respond promptly to future demand pressure.3 Without such a
commitment, forward guidance could reassure the public in the belief that growth
central banks shifted aggressively to the interest rates close to zero, their forward
central banks
shifted aggressively to the interest rates close to zero, their forward
prospects
are poor.
guidance has provided forecasts of likely interest rate path, instead of making the
guidance
has provided
likely interest
path,
instead
of making
the
However,
there forecasts
are few of
economists,
whorate
warn
against
monetary
policy
commitment not to respond promptly to future demand pressure.33 Without such a
commitment
not to respondbypromptly
future demand
pressure.BIS
Without
extremely
accommodative
historicaltostandards.
For example,
(2010,such
2012,a
commitment, forward guidance could reassure the public in the belief that growth
commitment,
forward
couldcan
reassure
theforbearance
public in the
belief which
that growth
2013,
2014) claims
thatguidance
such a policy
promote
lending,
keeps
prospects are poor.
prospects
are poor.
unproductive
firms afloat, crowds viable firms out of credit, thwarts capital and
However, there are few economists, who warn against monetary policy
However, there
are few
economists,
who frictions
warn against
monetary
policy
labor reallocation.
It thus
strengthens
financial
and deters
post-crisis
extremely accommodative by historical standards. For example, BIS (2010, 2012,
extremely
accommodative
by (2014)
historical
For example,
BIS (2010,
restructuring.
In turn, Meltzer
andstandards.
Taylor (2014),
among others,
contend2012,
that
2013, 2014) claims that such a policy can promote forbearance lending, which keeps
2013,
2014) claims
that such
a policy can
promote
forbearance
lending,
keeps
unprecedented
nature
of monetary
policy
(and
other kinds
of which
policy),
its
unproductive firms afloat, crowds viable firms out of credit, thwarts capital and
unproductive
firms
viable
firms
of credit,heighten
thwarts uncertainty,
capital and
unpredictability
and afloat,
failurecrowds
to follow
rules
can out
persistently
labor reallocation. It thus strengthens financial frictions and4 deters post-crisis
labor
It thus
strengthens
financial
and deters post-crisis
which reallocation.
invites economic
agents
to defer more
seriousfrictions
adjustments.
restructuring. In turn, Meltzer (2014) and Taylor (2014), among others, contend that
restructuring.
turn, Meltzer
(2014)
Taylor view.
(2014),Inamong
others,even
contend
that
Some In
evidence
supports
the and
minority
particular,
though
unprecedented nature of monetary policy (and other kinds of policy), its
unprecedented
of monetary
policysluggish
(and other
kinds ofstandards,
policy), the
its
recovery of thenature
US economy
has been
by historical
unpredictability and failure to follow rules can persistently heighten uncertainty,
unpredictability
and failure
to follow
persistently
uncertainty,
utilization of labor
and capital
has rules
been can
growing
faster heighten
than over
previous
which invites economic agents to defer more serious adjustments.44
which
invites
more serious
recoveries.
Ineconomic
contrast, agents
growthtoindefer
productivity
and,adjustments.
above all, in capital stock (in
Some evidence supports the minority view. In particular, even though
evidence supports
the intensive
minority shale
view.gasInand
particular,
evenhas
though
spite ofSome
rapid development
of capital
oil industry)
been
recovery of the US economy
has
been
sluggish
by
historical
standards,
the
recovery
theFigure
US economy
has beenthesluggish
by historical
standards,
current recovery
has two
featuresthe
in
very slow of(see
2).5 Interestingly,
utilization of labor and capital has been growing faster than over previous
utilization
of two
laborprevious
and capital
has First,
been all
growing
faster than
over
previous
common with
recoveries.
these recoveries
were
preceded
by
recoveries. In contrast, growth in productivity and, above all, in capital stock (in
recoveries.
contrast,
productivity
and,
above easing
all, in capital
stock (in
interest rateInbeing
cut togrowth
a lowerinlevel
than in the
previous
cycle. Secondly,
spite of rapid development of capital intensive shale gas and oil industry) has been
spite
of them
rapidturned
development
capital
intensive
gas and one.
oil industry) has been
each of
out to beofmore
sluggish
thanshale
the previous
very slow (see Figure 2).55 Interestingly, the current recovery has two features in
the current
recovery
has twoproductivity
features in
very slow
(see Figure
2). Interestingly,
Proponents
of majority
view respond
to the data
on stagnant
common with two previous recoveries. First,
all
these
recoveries
were
preceded
by
(Figure 2)
common
two recovery
previous by
recoveries.
First,they
all these
recoveries
were
preceded
by
during
thewith
current
evoking what
call inverse
Say’s
Law.
It follows
interest rate being cut to a lower level than in the previous easing cycle. Secondly,
interest
rateofbeing
cut creates
to a lower
than inpotential’
the previous
easinghave
cycle.
that
‘lack
demand
lacklevel
of supply
as firms
no Secondly,
reason to
each of them turned out to be more sluggish than the previous one.
each of in
them
be more(Summers,
sluggish than
the previous
one.
invest
anyturned
typeout
of tocapital
2015).
Note however
that stagnant
3
productivity
during
the etcurrent
is in stark
the
US experience
of
Using the taxonomy
by Campbell
al. (2012),recovery
the forward guidance
was more
of Delphicto
than
of Odyssean
nature.
(Figure
2) contrast
4 We leave aside the most frequent criticism of extremely accommodative monetary policy, centered on risk misjudgment,
(Figure
2)
excessive
taking, and
asset bubbles
creation
(see, e.g. Adrian
and Shin,stagnation’
2010 and 2014; Altunbas
et al.,1939).
2014; Bordo
and
the
laterisk
1930s,
which
first was
labelled
as ‘secular
(Hansen,
Even
Landon-Lane, 2013; Borio and White, 2003;Borio and Zhu, 2012; Diamond and Rajan, 2009; Farhi and Tirole, 2012; Issing,
2012, Jarocinski and Smets, 2008; Jiménez et al., 2012 and 2014 Maddaloni and Peydró, 2013, Rajan, 2005; Taylor, 2009 or
though
interest rate was then close to zero too, it couldn’t delay post-crisis
White, 2010), not to mention inflationary pressure. This criticism refers to an economy which has no slack rather than to one
hit by a crisis and struggling to recover, which is focus of interest in this paper
5
restructuring
for intwo
reasons.
interest
2% 2008
late,andthat
is quarter
after
TFP growth was rapid
the acute
phase ofFirst,
the global
financial rate
crisis, was
that is cut
in thebelow
fourth quarter
the first
3
UsingHowever
the taxonomy
by Campbell
al. (2012),
the forward
guidance
was more
Odyssean
nature. has been
2009.
since the
end of the et
Great
Recession,
i.e. the second
quarter
2009,ofasDelphic
dated bythan
theof
NBER,
productivity
34
GDP
had
finally
stopped
falling
(cf.amounts
Homer
and
Sylla,
2005,
Ch.on
Second,
We
aside
the
frequent
ofofof
extremely
accommodative
monetary
policy,
centered
risk
misjudgment,
Using
the
taxonomy
by
Campbell
etcriticism
al. the
(2012),
the
forward
guidance
was
more
of Delphic
than
of Odyssean
nature.
4almost
Weleave
leave
aside
themost
most
frequent
criticism
extremely
accommodative
monetary
policy,
centered
on17).
risk
misjudgment,
flat.
Its
cumulative
increase
until
end
2014
to mere
1.3%
(cf.
Fernald,
2014).
4 We leave
aside
the and
mostasset
frequent
criticism
of (see,
extremely
accommodative
monetary
policy,Altunbas
centeredeton
misjudgment,
excessive
risk
taking,
bubbles
creation
e.g. Adrian
and Shin, 2010
and 2014;
al.,risk
2014;
Bordo and
excessive risk
taking,
and asset
bubbles
creation
(see,
Adrian
2010
and 2014;
Altunbas
et al.,
2014;
Bordo
and
Landon-Lane,
2013;close
Borio
and
ande.g.
Zhu,
2012;
Diamond
and fraction
Rajan,
2009;
Farhi
and
Tirole,
2012;
Issing,
interest
rate
toWhite,
zero2003;Borio
applied
only
to and
a Shin,
small
of
banks
allowed
to
Landon-Lane,
2013;
White,
2003;Borio
and Zhu,
2012;Maddaloni
Diamond and
and2005;
Tirole,
2012;2009
Issing,
2012,
Jarocinski
and Borio
Smets,and
2008;
Jiménez
et al., 2012
and 2014
and Rajan,
Peydró,2009;
2013,Farhi
Rajan,
Taylor,
or
2012, Jarocinski
Smets, 2008;
Jiménezpressure.
et al., 2012
2014 Maddaloni
Peydró,
2013,has
Rajan,
2005;
Taylor,
or
White,
2010), notand
mention
inflationary
Thisand
criticism
refers to anand
economy
which
no slack
rather
than2009
one
participate
into
operations
with
the
Fed.
Its
effects
were
additionally
limited
bytothe
4 in
White,
not struggling
to mentiontoinflationary
pressure.
This
refers
to an economy which has no slack rather than to one
hit
by a2010),
crisis and
recover, which
is focus
of criticism
interest
this paper
5
hitTFP
by agrowth
crisis and
to acute
recover,
which
is focus
offinancial
interest incrisis,
this paper
wasstruggling
rapid in the
phase
of the
global
that is in the fourth quarter 2008 and the first quarter
5
stigmatizing
nature
of
support
fromcrisis,
thethat
Fed.
For
both
interest
TFP However
growth was
rapid
theof
acute
phaseRecession,
of the
global
financial
is inas
thedated
fourth
2008productivity
andthe
the first
quarter
2009.
since
the in
end
theliquidity
Great
i.e. the
second
quarter
2009,
by quarter
thereasons,
NBER,
has
been
2009.
since the end
of theuntil
Greatthe
Recession,
i.e. amounts
the second
2009,
dated by2014).
the NBER, productivity has been
almostHowever
flat. Its cumulative
increase
end of 2014
to quarter
mere 1.3%
(cf.asFernald,
rate
to zero increase
coulduntil
notthepromote
forbearance
lending,
which
almost close
flat. Its cumulative
end of 2014 amounts
to mere 1.3%
(cf. Fernald,
2014). largely conditions
its adverse effect on post-crisis restructuring,
6
4
It is hardly possible to settle, without
any doubts, which
of these two
4
Narodowy Bank Polski
opposite views is correct. Such a settlement is certainly beyond the scope of this
paper, which deals with a much less ambitious problem. It evaluates how strong
invest in any type of capital (Summers, 2015). Note however that stagnant
productivity during the current recovery is in stark contrast to the US experience of
the late 1930s, which first was labelled as ‘secular stagnation’ (Hansen, 1939). Even
Introduction
though interest rate was then close to zero too, it couldn’t delay post-crisis
restructuring for two reasons. First, interest rate was cut below 2% late, that is after
Proponents of majority view respond to the data on stagnant productivity
GDP had finally stopped falling (cf. Homer and Sylla, 2005, Ch. 17). Second,
during the current recovery by evoking what they call inverse Say’s Law. It follows
interest rate close to zero applied only to a small fraction of banks allowed to
that ‘lack of demand creates lack of supply potential’ as firms have no reason to
participate in operations with the Fed. Its effects were additionally limited by the
invest in any type of capital (Summers, 2015). Note however that stagnant
stigmatizing nature of liquidity support from the Fed. For both reasons, the interest
productivity during the current recovery is in stark contrast to the US experience of
rate close to zero could not promote forbearance lending, which largely conditions
the late 1930s, which first was labelled as ‘secular stagnation’ (Hansen, 1939). Even
its adverse effect on post-crisis restructuring,
though interest rate was then close to zero too, it couldn’t delay post-crisis
It is hardly possible to settle, without any doubts, which of these two
restructuring for two reasons. First, interest rate was cut below 2% late, that is after
opposite views is correct. Such a settlement is certainly beyond the scope of this
GDP had finally stopped falling (cf. Homer and Sylla, 2005, Ch. 17). Second,
paper, which deals with a much less ambitious problem. It evaluates how strong
interest rate close to zero applied only to a small fraction of banks allowed to
(weak) possible side effects of holding interest rates close to zero would have to be,
participate in operations with the Fed. Its effects were additionally limited by the
so that setting an effective lower bound at a higher level (and avoiding those effects)
stigmatizing nature of liquidity support from the Fed. For both reasons, the interest
would pay off in terms of welfare.
rate close to zero could not promote forbearance lending, which largely conditions
This evaluation is based on the approach developed by Jung et al. (2005),
its adverse effect on post-crisis restructuring,
which we generalize in two ways. Firstly, we allow the lower bound to be any real
It is hardly possible to settle, without any doubts, which of these two
number, not only zero. As the baseline case, we consider PLB at 2%. 6 This was the
opposite views is correct. Such a settlement is certainly beyond the scope of this
floor for policy rate of Bank of England since its foundation in 1694 until 2009 (see
paper, which deals with a much less ambitious problem. It evaluates how strong
Figure 3). Secondly, we allow for trend inflation. In the baseline case, it is set at 2%.
(weak) possible side effects of holding interest rates close to zero would have to be,
This level matches the inflation target most frequently seen in advanced economies.
so that setting an effective lower bound at a higher level (and avoiding those effects)
Besides, it implies real interest rate at PLB similar to this considered in the literature
would pay off in terms of welfare.
on the ZLB.
This evaluation is based on the approach developed by Jung et al. (2005),
The rational for the second generalization relates to the fact that raising
which we generalize in two ways. Firstly, we allow the lower bound to be any real
3) the problem of the ZLB (see, e.g.
inflation target has been promulgated(Figure
to alleviate
number, not only zero. As the baseline case, we consider PLB at 2%. 6 This was the
Blanchard et al., 2010). Hence, we want to check to what extent various inflation
6
floor
for policy
rate of
Bank
of range
England
since
foundation
in We
1694
until
Simulations
for other PLB’s
values
from the
from 0 to
2% areits
available
upon request.
do not
report2009
them, as(see
they
target’s
values
can alter
on the size of ZLB policy side effects required for
have no impact
(qualitatively)
on the findings
conclusions drawn.
Figure 3). Secondly, we allow for trend inflation. In the baseline case, it is set at 2%.
setting PLB to pay off in terms of welfare.
This level matches the inflation target most frequently seen in advanced economies.
We choose the approach developed
5 by Jung and his co-authors, because it
Besides, it implies real interest rate at PLB similar to this considered in the literature
models the expiration of shock that makes the lower bound bind, in a way which can
on the ZLB.
be easily linked with various narratives on side effects of interest rates close to zero
(see below). However, we are aware of shortcomings of this approach. The most
(Figure 3)
serious one is that the approach implies the length of period during which the lower
6
bound
binds
toPLB’s
be known
on 0impact
of shock.
This We
shortcoming
can
be
Simulations
for other
values fromalready
the range from
to 2% are available
upon request.
do not report them,
as they
have no impact (qualitatively) on the conclusions drawn.
addressed using the approach developed by Eggertsson and Woodford (2003). We
are going to apply this alternative approach in an extension to the paper.
5
The evaluation comprises two steps. Firstly, effects of positive lower bound
NBP Working Paper No. 215
(PLB) policy are studied and compared to those of ZLB policy. Four possible
combinations of these polices are under scrutiny, i.e.
7
We choose the approach developed by Jung and his co-authors, because it
models the expiration of shock that makes the lower bound bind, in a way which can
be easily linked with various narratives on side effects of interest rates close to zero
(see below). However, we are aware of shortcomings of this approach. The most
serious one is that the approach implies the length of period during which the lower
bound binds to be known already on impact of shock. This shortcoming can be
addressed using the approach developed by Eggertsson and Woodford (2003). We
are going to apply this alternative approach in an extension to the paper.
The evaluation comprises two steps. Firstly, effects of positive lower bound
(PLB) policy are studied and compared to those of ZLB policy. Four possible
combinations of these polices are under scrutiny, i.e.
(a)
both PLB and ZLB policies are discretionary,
(b)
both of them are pursued under commitment,
(c)
PLB policy is pursued under commitment,
while ZLB is
discretionary,
(d)
PLB policy is discretionary, whereas ZLB is pursued under
commitment.
We use the definition of discretion and commitment by Adam and Billi (2007) and
Jung et al. (2005) respectively. Secondly, we check how much less persistent a
shock under PLB policy would have to be, compared to one dealt with ZLB policy,
so that the welfare losses under the PLB did not exceed those incurred under the
ZLB.
The rationale to approximate possible side (adverse) effects of the ZLB
policy by an increase in inertia of shock to natural interest rate is the flowing. There
are three main types of those effects:
 forbearance lending which strengthens financial frictions related to collateral
constraints and capital requirements;
 delays in restructuring, which postpone recovery of potential output, and
 heightened uncertainty.
6
All of them appear, indirectly or even directly, in the equation of natural interest
rate, and can inhibit its return after a shock to the steady state.
The NK model has been criticized for its alleged uselessness to analyze postcrisis reality, characterized by strong financial frictions, a need of restructuring, and
a heightened uncertainty.7 We show that this criticism has been excessive. True,
financial frictions have been introduced to the NK model only after the outburst of
global financial crisis, the framework does not model restructuring and accounts for
uncertainty in very imperfect way at best. Consequently, careful study of possible
side effects of very accommodative monetary policy would indeed require other
8
tools. However, the NK model allows to assess how strongly (weakly)
these
effects
Narodowy
Bank
Polski
would have to differ across various policy responses to crisis so as to offset
differences in impact of these responses on aggregate demand. Hence, it helps
All of them appear, indirectly or even directly, in the equation of natural interest
rate, and can inhibit its return after a shock to the steady state.
The NK model has been criticized for its alleged uselessness to analyze postIntroduction
crisis reality, characterized by strong financial frictions, a need of restructuring, and
a heightened uncertainty.7 We show that this criticism has been excessive. True,
 forbearance lending which strengthens financial frictions related to collateral
financial frictions have been introduced to the NK model only after the outburst of
constraints and capital requirements;
global financial crisis, the framework does not model restructuring and accounts for
 delays in restructuring, which postpone recovery of potential output, and
uncertainty in very imperfect way at best. Consequently, careful study of possible
 heightened uncertainty.
side effects of very accommodative monetary policy would indeed require other
All of them appear, indirectly or even directly, in the equation of natural interest
tools. However, the NK model allows to assess how strongly (weakly) these effects
rate, and can inhibit its return after a shock to the steady state.
would have to differ across various policy responses to crisis so as to offset
The NK model has been criticized for its alleged uselessness to analyze postdifferences in impact of these responses on aggregate demand. Hence, it helps
crisis reality, characterized by strong financial frictions, a need of restructuring, and
establish a weight that academics and policy makers should attach to possible side
a heightened uncertainty.7 We show that this criticism has been excessive. True,
effects of very accommodative monetary policy in their research agenda and
financial frictions have been introduced to the NK model only after the outburst of
struggle to maximize social welfare respectively. That is what this paper aims at.
global financial crisis, the framework does not model restructuring and accounts for
Even though a medium scale NK model, with very rich dynamics, has been
uncertainty in very imperfect way at best. Consequently, careful study of possible
developed elsewhere (see, e.g. Smets and Wouters, 2007), we use a small scale NK
side effects of very accommodative monetary policy would indeed require other
model for two reasons. First of all, this is the first study which compares effects of
tools. However, the NK model allows to assess how strongly (weakly) these effects
the PLB with those of the ZLB. Thus, it is reasonable to provide results as
would have to differ across various policy responses to crisis so as to offset
comparable as possible to previous research on the ZLB, which in vast majority is
differences in impact of these responses on aggregate demand. Hence, it helps
based on NK models with output gap, inflation, natural interest rate and interest rate
establish a weight that academics and policy makers should attach to possible side
only. Second, the extension (by this paper) of otherwise benchmark model to allow
effects of very accommodative monetary policy in their research agenda and
trend inflation complicates computations, whereas it does not significantly affect
struggle to maximize social welfare respectively. That is what this paper aims at.
results of the comparison. This leads us to the conjecture that a focus on medium
Even though a medium scale NK model, with very rich dynamics, has been
scale NK model would not alter them either, but it would make the computations
developed elsewhere (see, e.g. Smets and Wouters, 2007), we use a small scale NK
even more complex. We leave its verification for further research. Even if it is
7
NK model
been reasons.
also criticizedFirst
for itsof
failure
predict
financial
crisis. See,
in particular
Wielandeffects
and Wolters
model
forhastwo
all,tothis
isglobal
the first
study
which
compares
of
(2011) who gradual
show that it extension
would not haveofhelped
predict any of would
the previous
four recessions
in the United States
1980,
refuted,
the toframework
facilitate
understanding
of (in
where
1980-81, 1990-91 and 2001) either. In this case we cannot help but notice that as indicated by those authors other models were
the
PLB NK
with
those score
of and
theunderperform
ZLB. Thus,
it isrecoveries
reasonable to provide results as
not better thansignificant
model on that
it in predicting
possible
differences
in effects
of the
PLB and ZLB stem from. This
comparable as possible to previous research on the ZLB, which in vast majority is
would be hardly possible to verify otherwise.
based on NK models with output gap, inflation, natural interest rate and interest rate
Our calibration strategy is also ancillary
to hold the model (and results) as
7
only. Second, the extension (by this paper) of otherwise benchmark model to allow
comparable as possible to previous papers. Thus, we take parameters’ values from
trend inflation complicates computations, whereas it does not significantly affect
those papers, but then we check the robustness of the results to changes in
results of the comparison. This leads us to the conjecture that a focus on medium
parameters’ value.
scale NK model would not alter them either, but it would make the computations
Our main findings are as follows.
7
First, if the ZLB policy has no side effects, then such a policy is better in
NK model has been also criticized for its failure to predict global financial crisis. See, in particular Wieland and Wolters
(2011) who show that it would not have helped to predict any of the previous four recessions in the United States (in 1980,
terms
of welfare
comparison
thebutPLB
policy,
unless
the
PLB
is
1980-81, 1990-91
and 2001)in
either.
In this case we with
cannot help
notice that
as indicated
by those
authors
otherpolicy
models were
not better than NK model on that score and underperform it in predicting recoveries
pursued under the commitment, while the ZLB policy is discretionary. Put it
differently, commitment may matter more than the value of effective lower bound
7
(provided
that this value remains reasonably low).
NBP Working Paper No. 215
Second, as long as central bank’s ability to commit does not depend on
value of lower bound, moderate side effects could be enough for the PLB policy to
9
Our calibration strategy is also ancillary to hold the model (and results) as
comparable as possible to previous papers. Thus, we take parameters’ values from
those papers, but then we check the robustness of the results to changes in
parameters’ value.
Our main findings are as follows.
First, if the ZLB policy has no side effects, then such a policy is better in
terms of welfare in comparison with the PLB policy, unless the PLB policy is
pursued under the commitment, while the ZLB policy is discretionary. Put it
differently, commitment may matter more than the value of effective lower bound
(provided that this value remains reasonably low).
Second, as long as central bank’s ability to commit does not depend on
value of lower bound, moderate side effects could be enough for the PLB policy to
pay off in terms of welfare. This is particularly true when central bank fails to
commit (and welfare losses are large irrespective of the value of effective lower
bound).
Third, side effects of the ZLB would have to be strong for the PLB policy to
outperform the ZLB policy in terms of welfare, only if the ZLB policy was pursued
under the commitment, while the PLB policy was discretionary. In other words, the
commitment could weigh on welfare more than possible side effects of the ZLB,
however mainly under the condition that it would be more likely under the ZLB
policy than PLB policy.
Fourth, when the above condition is not met, then PLB policy could
dominate the ZLB policy in terms of welfare, even if restructuring, fostered by the
PLB policy, entailed some costs, which could be reduced (or avoided) through slow
restructuring.
Sixth, with given side effects of the ZLB policy, PLB policy is more likely to
be welfare improving as compared to ZLB policy, when a shock that makes the ZLB
bind, is particularly large and persistent. This result implies that central bank should
be particularly cautious about cutting interest rates to zero in circumstances that
other papers consider to call for aggressive8 cuts.
Seventh, all above findings hold for economies with both fast and slow
potential output growth, with low and high inflation target, flexible and rigid. Any
differences in results between those economies are small, but if anything, they
advocate for more cautiousness about cutting interest rates to zero in countries with
slow potential output growth, low inflation target, and strong rigidities: nominal and
in labor supply, although tough competition.
The paper makes four main contributions to the literature.
Firstly, it studies effects of PLB. The possibility of positive lower bound
10
instead of being zero is noticed in other studies on ZLB.8 However,Narodowy
it has only
been
Bank Polski
analysed, if at all, in the context of ‘lack of confidence’ shock and self-fulfilling
deflations (see, e.g. Benhabib et al., 2001; Schmitt-Grohé and Uribe, 2010 or
differences in results between those economies are small, but if anything, they
advocate for more cautiousness about cutting interest rates to zero in countries with
slow potential output growth, low inflation target, and strong rigidities: nominal and
Introduction
in labor supply, although tough competition.
The paper makes four main contributions to the literature.
bind, is particularly large and persistent. This result implies that central bank should
Firstly, it studies effects of PLB. The possibility of positive lower bound
be particularly cautious about cutting interest rates to 8zero in circumstances that
instead of being zero is noticed in other studies on ZLB. However, it has only been
other papers consider to call for aggressive cuts.
analysed, if at all, in the context of ‘lack of confidence’ shock and self-fulfilling
Seventh, all above findings hold for economies with both fast and slow
deflations (see, e.g. Benhabib et al., 2001; Schmitt-Grohé and Uribe, 2010 or
potential output growth, with low and high inflation target, flexible and rigid. Any
Schmitt-Grohé and Uribe, 2012). We analyze ‘fundamental’ shock instead, which is
differences in results between those economies are small, but if anything, they
extensively used in the literature on ZLB.
advocate for more cautiousness about cutting interest rates to zero in countries with
Secondly, the paper develops a simple analytical framework, which allows to
slow potential output growth, low inflation target, and strong rigidities: nominal and
compare benefits with possible costs of interest rate close to zero. Both these effects
in labor supply, although tough competition.
have so far been analysed in complete isolation from each other. We facilitate
The paper makes four main contributions to the literature.
breaking this isolation and thereby better exploiting knowledge acquired from the
Firstly, it studies effects of PLB. The possibility of positive lower bound
above analyses.
instead of being zero is noticed in other studies on ZLB.8 However, it has only been
Thirdly, the paper puts into question an important policy advice from the
analysed, if at all, in the context of ‘lack of confidence’ shock and self-fulfilling
literature on the ZLB. From Eggertsson and Woodford (2003) onwards, this
deflations (see, e.g. Benhabib et al., 2001; Schmitt-Grohé and Uribe, 2010 or
literature has unanimously advocated for very aggressive interest rates cuts in
Schmitt-Grohé and Uribe, 2012). We analyze ‘fundamental’ shock instead, which is
response to severe negative shocks or anticipation thereof. Our findings suggest,
extensively used in the literature on ZLB.
instead, that the more severe a shock, the more cautious the central bank should be
Secondly, the paper develops a simple analytical framework, which allows to
about cutting interest rates to zero. The main reason for the suggested caution is the
compare benefits with possible costs of interest rate close to zero. Both these effects
risk of side effects of ZLB policy, whereas in some older papers it is a preservation
have so far been analysed in complete isolation from each other. We facilitate
of some powder dry for future emergencies.
breaking this isolation and thereby better exploiting knowledge acquired from the
Fourthly, the paper highlights significance of central bank’s credibility from
above analyses.
different
perspective
than
other studies
on ZLB
do.onlyThey
a
8a Obviously,
papers
warning against
very accommodative
monetary
policy not
notice consider
the possibilitycredibility
of lower bound as
being
Thirdly,
theitspaper
puts into
question
important
advice
fromeven
theif
positive, but
postulate such
value. However,
they do
not analyzean
its effects
using thepolicy
NK analytical
framework,
condition
forrefer
central
bank’s(see
capability
toRzońca,
stabilize
some
of the papers
to this framework
Ciżkowicz and
2014). the economy when ZLB binds.
literature on the ZLB. From Eggertsson and Woodford (2003) onwards, this
We add that central bank has strong reasons to cut interest rates to zero only if such
literature has unanimously advocated for very aggressive interest rates cuts in
cuts condition its credibility.
9
response to severe negative shocks or anticipation thereof. Our findings suggest,
The remainder of the paper is organized in four sections and an appendix.
instead, that the more severe a shock, the more cautious the central bank should be
Section 2 reviews related literature and sets the context of the analysis. Its primary
about cutting interest rates to zero. The main reason for the suggested caution is the
goal is to elaborate on why possible side effects of the ZLB policy can be
risk of side effects of ZLB policy, whereas in some older papers it is a preservation
approximated in the NK analytical framework by an increase in inertia of shock to
of some powder dry for future emergencies.
natural interest rate. Section 3 describes the model used and its calibration. Section 4
provides main findings and verifies their robustness. It briefly discusses their policy
88 Obviously,
Obviously, papers
papers warning
warning against
against very
very accommodative
accommodative monetary
monetary policy not only notice the possibility of lower bound being
implications
too.
5 concludes.
appendix
including
figures
and tables
positive,
but postulate
suchSection
its value. However,
they do notThe
analyze
its effects using
the NK analytical
framework,
even if
some of the papers refer to this framework (see Ciżkowicz and Rzońca, 2014).
follows.
NBP Working Paper No. 215
9
11
The remainder of the paper is organized in four sections and an appendix.
Section 2 reviews related literature and sets the context of the analysis. Its primary
goal is to elaborate on why possible side effects of the ZLB policy can be
approximated in the NK analytical framework by an increase in inertia of shock to
natural interest rate. Section 3 describes the model used and its calibration. Section 4
provides main findings and verifies their robustness. It briefly discusses their policy
implications too. Section 5 concludes. The appendix including figures and tables
follows.
10
12
Narodowy Bank Polski
Chapter 2
2. Related literature and context
Our findings relate to that strand of the literature on the ZLB, which envisages
‘fundamental’ shock using the NK analytical framework. Leading examples of such
research include Adam and Billi (2006 and 2007), Eggertsson (2003 and 2006),
Eggertsson and Woodford (2003), Jung et al. (2005), Levin et al. (2010), Nakov
(2008) or Walsh (2009). In this literature a severe shock, which is usually a
preference shock, hits natural interest rate, rt,. Literally interpreted, it means that all
of a sudden everybody wants to save more. However, given that natural interest rate
may also depend on other variables than discount factor, more sophisticated
interpretations are also possible, and indeed they are used. In particular, they have
recently been referring to financial frictions (cf., e.g. Eggertsson, 2011). Even
though financial frictions are not modelled in versions of NK framework commonly
used in analyses of the ZLB, it has been shown elsewhere that NK model with those
frictions can be reduced to a form quite similar to its standard version (see, e.g.
r , defined as follows:
Christiano et al., 2011) with modified natural interest rate, ~
t
~

rt
rt   t
(1)
where ψt is a measure of financial frictions (and σ is the parameter of relative risk
aversion of households). Our analysis uses this latter interpretation.
Our findings also relate to the literature on possible side effects of very
accommodative monetary policy (see in particular BIS, 2010, 2012, 2013, 2014). It
draws first and foremost from the experience of Japan in the 1990s and 2000s, that is
from the very same experience that renewed interest of economists in the ZLB. After
the asset bubble bursting in the early 1990s, troubled Japanese banks were allocating
scarce credit to impaired, debt-ridden firms, rather than to viable ones. However,
credit flowing to otherwise insolvent firms did not improve their performance (Peek
and Rosengren, 2005). On the contrary, their poor financial conditions further
worsened (Sekine et al., 2003). Banks imposed discipline on viable firms only
(Arikawa and Miyajima, 2007). Insolvent firms kept afloat lowered viable firms’
profitability, which discouraged their development and entries of new firms
(Caballero et al., 2008). Still worse, while support to non-viable firms was
11
NBP Working Paper No. 215
13
maintained, many productive firms, especially new entrants, exited (Nishimura et
al., 2005). In industries where non-viable firms were heavily present, they increased
their market share (Ahearne and Shinada, 2005). Payment uncertainty discouraged
specialization (Kobayashi, 2007). Technology spillovers declined (Fukao, 2013).
Political leadership resisted capital and labor reallocation as well. A significantly
softened budget constraint enabled government to delay necessary adjustments
(Dugger and Ubide, 2004). Good lending opportunities for solvent banks diminished
(Caballero et al., 2008). Information effectiveness of the asset markets decreased
(Hamao et al., 2007). In summary, distortions in capital and labor reallocation
increased and prolonged disappointing economic performance of Japan (Nishimura
et al, 2005).
Even though the literature in question has been developed far from the
mainstream economics, it is likely to bring policy relevant lessons. It argues that
qualitatively similar distortions to those in Japan have appeared in other major
economies after the outburst of the global financial crisis. Evidence of forbearance
lending was found in Italy (Albertazzi and Marchetti, 2010) and the UK
(Arrowsmith et al., 2014). Even though in the UK it was of limited scale, corporate
insolvencies remained historically low there, while in early phase of previous
recoveries they had spiked (R3, 2013). At the same time, the share of firms suffering
losses exceeded 30%, reaching the highest level since at least the 1980s (Deutsche
Bank, 2013). Because firms of low productivity continued to operate, in spite of
being on the brink of insolvency, differences in productivity across firms became
wider than ever. Contribution of reallocation to productivity growth fell during the
crisis and became almost negligible in 2010-2012, whereas it had accounted for
more than two thirds thereof prior to the crisis. Correlation between profitability and
investment across firms weakened considerably. Share of both product and process
innovators decreased (Barnett et al., 2014a and 2014b). In the US, increase in
insolvencies after the outburst of the crisis was very short-lived (Deutsche Bank,
2013). Churn decreased significantly (Lazear and Spletzer, 2012). Reallocation not
only became less intensive, but also enhanced productivity by less than over
previous recessions (Foster et al., 2014). Both in Europe and the US, central banks’
12
14
Narodowy Bank Polski
Related literature and context
interventions distorted asset prices and, thereby, weakened market signals (Borio,
interventions distorted asset prices and, thereby, weakened market signals (Borio,
2014).
2014).
Cross-country comparisons of post-crisis economic performance also
Cross-country comparisons of post-crisis economic performance also
suggests that possible side effects of a very accommodative monetary policy should
suggests that possible side effects of a very accommodative monetary policy should
not be neglected. Bech et al. (2014) find that the benefits of such a policy, during a
not be neglected. Bech et al. (2014) find that the benefits of such a policy, during a
downturn, for a subsequent recovery disappear, if the downturn follows a financial
downturn, for a subsequent recovery disappear, if the downturn follows a financial
crisis. At the same time, the deeper the private sector deleveraging during a
crisis. At the same time, the deeper the private sector deleveraging during a
downturn, the stronger the subsequent recovery. Kannan et al. (2013) confirm that
downturn, the stronger the subsequent recovery. Kannan et al. (2013) confirm that
accommodative monetary policy is of limited effectiveness in advancing recovery
accommodative monetary policy is of limited effectiveness in advancing recovery
when financial crisis burst. In turn, Chen et al (2015) corroborate that the larger and
when financial crisis burst. In turn, Chen et al (2015) corroborate that the larger and
the quicker the private sector deleveraging, the more sizable medium-term output
the quicker the private sector deleveraging, the more sizable medium-term output
gains. In line with those results, Laeven and Valencia (2013) find that advanced
gains. In line with those results, Laeven and Valencia (2013) find that advanced
economies, which relied on macroeconomic policies as crisis-management tools
economies, which relied on macroeconomic policies as crisis-management tools
more heavily than emerging economies, were much slower to resolve banking
more heavily than emerging economies, were much slower to resolve banking
crises, which lasted on average two times longer than in emerging economies. It
crises, which lasted on average two times longer than in emerging economies. It
follows from the study that, while accommodative macroeconomic policies help to
follows from the study that, while accommodative macroeconomic policies help to
avoid disorderly deleveraging, they can also weaken incentives for financial
avoid disorderly deleveraging, they can also weaken incentives for financial
restructuring, with the risk of entrenching weak economic performance.
restructuring, with the risk of entrenching weak economic performance.
It is possible to break the isolation between the literature on the ZLB and
It is possible to break the isolation between the literature on the ZLB and
possible side effects of very accommodative monetary policy, because all main
possible side effects of very accommodative monetary policy, because all main
types of those effects, namely: forbearance lending, delayed restructuring and
types of those effects, namely: forbearance lending, delayed restructuring and
heightened uncertainty appear, indirectly or even directly, in the natural interest rate
heightened uncertainty appear, indirectly or even directly, in the natural interest rate
equation which is at the center of the literature on the ZLB.
equation which is at the center of the literature on the ZLB.
Forbearance lending, facilitated by the ZLB policy, can be considered to
Forbearance lending, facilitated by the ZLB policy, can be considered to
inhibit a return of the natural interest rate to the steady state, since it strengthens
inhibit a return of the natural interest rate to the steady state, since it strengthens
financial frictions (see Eq. 1) related to collateral constraints and capital
financial frictions
(see Eq. 1) related to collateral constraints and capital
requirements.99 First, it distorts publicly available signals that help to assess financial
requirements. First, it distorts publicly available signals that help to assess financial
credibility of firms, and expands the range of information required for such an
credibility of firms, and expands the range of information required for such an
assessment. As non-viable borrowers are able to demonstrate positive credit history,
assessment. As non-viable borrowers are able to demonstrate positive credit history,
9 Collateral constraints and capital requirements represent two out of three main types of financial frictions started to be
introduced
the NK analytical
framework
after represent
the
outburst
ofout
global
financial
(see,
e.g. Andrés
and Arce,
2009to
constraints
and capital
requirements
represent
two
out
types
of financial
frictions
started
toand
99 Collateral
Collateralinto
constraints
capital
requirements
two
of three
three
maincrisis
financial
frictions
started
be
Angeloni and
introduced
intoFaia,
the 2013).
NK analytical framework after the outburst of global financial crisis (see, e.g. Andrés and Arce, 2009 and
Angeloni and Faia, 2013).
NBP Working Paper No. 215
13
13
15
viable firms have to manifest their credibility in ways other than by being monitored
by banks. They can differentiate themselves from non-viable firms by deleveraging,
as the non-viable firms are hardly able to deleverage, but this perverse composition
of deleveraging firms magnifies problems of information asymmetry. Secondly,
forbearance lending forces banks to rely heavily on retained earnings to rebuild their
capital. It reduces their valuation, for it exposes potential investors to the burden of
undisclosed losses from the past and reduces expected profits from future
operations, until entire banking sector undergoes restructuring. Hence, the rebuilding
of capital takes a long time (additionally prolonged by compression of banks’
interest margin). Capital-constrained banks cannot offer new credit to viable firms.
Note that the very limited access of banks to new capital strengthens, in turn, their
incentives to delay balance sheet repair, as this delay helps them to meet capital
requirements.
Decelerated return of natural interest rate to the steady state can also be
associated with delays in restructuring that the ZLB policy can cause. It suffices to
assume that restructuring drives productivity growth or, more generally, potential
output growth (see Eq. 2).

  
      
(2)

where  is the household’s subjective discount factor and 
  is the growth
rate of potential output. This assumption is confirmed in numerous studies (for
more, see Caballero, 2007).
The ZLB policy can hamper restructuring, in particular through forbearance
lending. First, forbearance directs credit to the present borrowers, which reduces
exits of enterprises instead of promoting entries. Secondly, it supports current
operations instead of new ones, which could increase productivity of firms
continuing operations. Firms in receipt of forbearance have no incentive to
restructure because effort put into restructuring would bring benefits to their
creditors, not to them. Furthermore, they have to avoid any additional expenses (that
restructuring usually requires for some time), as new costs could be considered by
banks a signal of actions increasing creditors’ losses and thus result in an immediate
cut off from funding. This inspires their inaction and leads to betting for
14
16
Narodowy Bank Polski
Related literature and context
resurrection. Thirdly, forbearance lending hinders an increase in the market share of
resurrection. Thirdly, forbearance lending hinders an increase in the market share of
most productive businesses, as it helps non-viable firms, while pushing viable firms
most productive businesses, as it helps non-viable firms, while pushing viable firms
to deleverage (see Eq. 3).
to deleverage (see Eq. 3).
y tPP  y tPP
stXX1 atEE  atXX1  s tII1 atII  stEE  stXX1 atEE  s tII atII
(3)
1
y t  y t 
s
a

a

s

a

s

s
a


s
a
(3)
t 1 t
t 1
t 1
t
t
t 1 t
t t
1
where a is the logarithm of productivity in a given set of firms, s is the share of a
where a is the logarithm of productivity in a given set of firms, s is the share of a
given set of firms in output, and E, I, X superscripts indicate the set of firms entering
given set of firms in output, and E, I, X superscripts indicate the set of firms entering
the market, the set of firms continuing operation, and the set of firms exiting the
the market, the set of firms continuing operation, and the set of firms exiting the
market, respectively. Note, however, that even if only few non-viable firms were in
market, respectively. Note, however, that even if only few non-viable firms were in
receipt of forbearance, a deep fall in interest payments could have quite similar
receipt of forbearance, a deep fall in interest payments could have quite similar
effects to those of forbearance, for it facilitates non-viable firms to look solvent and
effects to those of forbearance, for it facilitates non-viable firms to look solvent and
banks to delay losses’ recognition and balance sheet’s repair (cf. Arrowsmith et al.,
banks 10
to delay losses’ recognition and balance sheet’s repair (cf. Arrowsmith et al.,
2014).10 Very accommodative monetary policy can also discourage government
2014). Very accommodative monetary policy can also discourage government
from reforms enhancing restructuring (Borio, 2014).
from reforms enhancing restructuring (Borio, 2014).
Ultimately, one can consider heightened post crisis uncertainty prolonged by
Ultimately, one can consider heightened post crisis uncertainty prolonged by
the ZLB policy to be responsible for slower return of natural interest rate to the
the ZLB policy to be 11responsible for slower return of natural interest rate to the
steady state (see Eq. 4)11.
steady state (see Eq. 4) .
1

rˆt
rt  1  2 vart ( ytP )
(4)

rˆt
rt  2  2 vart ( ytP )
(4)
2
By delaying post-crisis adjustments, the ZLB policy maintains uncertainty about
By delaying post-crisis adjustments, the ZLB policy maintains uncertainty about
timing, scope, and effects of restructuring, while narrowing possibilities for reducing
timing, scope, and effects of restructuring, while narrowing possibilities for reducing
uncertainty through information acquisition and processing, as its quality is low.12
uncertainty through information acquisition and processing, as its quality is low.12
At the same time, high risk persists that it will become obsolete. Even a small
At the same time, high risk persists that it will become obsolete. Even a small
negative shock may cease operations of non-viable firm for banks may confound
negative shock may cease operations of non-viable firm for banks may confound
effects of shock with debtor’s actions increasing their losses. Still worse, a positive
effects of shock with debtor’s actions increasing their losses. Still worse, a positive
economic development is not at all favorable for such firm either, because it
economic development is not at all favorable for such firm either, because it
increases the risk that banks stop forbearance lending and the firm loses funding.
increases the risk that banks stop forbearance lending and the firm loses funding.
The more non-viable firms there are, the more uncertain a positive economic
The more non-viable firms there are, the more uncertain a positive economic










10 It is sometimes recalled in favor of forbearance that it helped banks in advanced economies, and particularly in the US, to
10
overcome
solvency
problems
caused
by defaultsthat
of it
number
developing
countries
in the and
early
1980s. However,
ItItisissometimes
recalled
ininfavor
of
banks
in
economies,
particularly
to
10
sometimes
recalled
favor
offorbearance
forbearance
that
ithelped
helpedof
banks
in advanced
advanced
economies,
and
particularly
in the US,that
forbearance
was targeted
and conditional,
a deep
fall in interest
payments
due to interest
rate close
to zero
resembles
overcome solvency
problems
caused by while
defaults
of number
of developing
countries
in the early
1980s.
However,
that
general
and open-ended
forbearance
was targetedforbearance.
and conditional, while a deep fall in interest payments due to interest rate close to zero resembles
11
We take
relationship
from Barsky et al. (2014). It is generally neglected for two interrelated reasons. First, until recently
general
andthis
open-ended
forbearance.
11
only
first
Taylor expansion
of et
theal.model
hasIt been
considered.
Second,
it isinterrelated
usually assumed
thatFirst,
the until
second
order
Wethe
take
thisorder
relationship
from Barsky
(2014).
is generally
neglected
for two
reasons.
recently
terms
arefirst
smallorder
(see,Taylor
e.g. Gali,
2008). of the model has been considered. Second, it is usually assumed that the second order
only
the
expansion
12
Non-viable
afloat2008).
hinder assessment of financial credibility of any firm and its partners, existing and potential
terms
are smallfirms
(see, kept
e.g. Gali,
12
ones.
Non-viable firms kept afloat hinder assessment of financial credibility of any firm and its partners, existing and potential
ones.
NBP Working Paper No. 215
15
15
17
development becomes for other firms, as their important partners may turn out to be
development becomes for other firms, as their important partners may turn out to be
non-viable or collaborate with non-viable firms. All in all, firms do not know when
non-viable or collaborate with non-viable firms. All in all, firms do not know when
the structure of the economy will seriously change, and how it will change.
the structure of the economy will seriously change, and how it will change.
However, they should have no doubt that serious changes will come. If the economy
However, they should have no doubt that serious changes will come. If the economy
had not needed them, there would be no crisis. Unprecedented nature of the ZLB
had not needed them, there would be no crisis. Unprecedented nature of the ZLB
policy contributes to that risk, as signaled in the introduction.
policy contributes to that risk, as signaled in the introduction.
Therefore, we approximate possible side effects of ZLB policy by an
Therefore, we approximate possible side effects of ZLB policy by an
increase in inertia of a shock to natural interest rate.
increase in inertia of a shock to natural interest rate.
Technically, one may reach this approximation as follows. Let  be a shock
Technically, one may reach this approximation as follows. Let  be a shock
to natural interest rate with inertia parameter . In period 1  hits the economy and
to natural interest rate with inertia parameter . In period 1  hits the economy and
makes the ZLB bind. In period 2 it starts to expire. However, if side effects of the
makes the ZLB bind. In period 2 it starts to
expire. However, if side effects of the
ZLB policy materialize, another shock  occurs. It reflects financial frictions
ZLB policy materialize, another shock  occurs. It reflects financial frictions
strengthened by forbearance lending, productivity growth muted by delays in
strengthened by forbearance lending, productivity growth muted by delays in
restructuring or uncertainty heightened by these delays. Its dynamics is hard to
restructuring or uncertainty heightened by these delays. Its dynamics is hard to
specify. In particular, forbearance lending can be quite limited in the periods very
specify. In particular, forbearance lending can be quite limited in the periods very
close to period 1 and become widespread only later, given that it is fostered by two
close to period 1 and become
widespread only later, given that it is fostered by two
, which need time to fully work. The percentage of
strategic complementarities13
13
strategic complementarities , which need time to fully work. The percentage of
firms delaying restructuring can change accordingly to forbearance lending
firms delaying restructuring can change accordingly to forbearance lending
prevalence. In turn, uncertainty, albeit related to delays in restructuring, can increase
prevalence. In turn, uncertainty, albeit related to delays in restructuring, can increase
quicker, since it depends not only on intensity of its given source, but on its
quicker, since it depends not only on intensity of its given
source, but on its
‘novelty’ as well. Nevertheless at some point the shock  has to expire if the
‘novelty’ as well. Nevertheless at some point the shock  has to expire if the
steady state is not to change. We calibrate this shock so as to keep convenient
steady state is not to change. We calibrate this shock so as to keep convenient
constant inertia of total shock to natural interest rate:
constant inertia of total shock to natural interest rate:
(5)
     ~ 
(5)
     ~
where:
where:

~~    

(6)
       

(6)
~~  
 
13
Firstly, bank’s willingness to keep lending to over-indebted firms depend on other banks’ decisions with regard to such
13
clients,
as bank’s
these decisions
affect
both expected
of delayed
sale
of insolvent
and with
expected
profits
on
Firstly,
willingness
to keep
lending torevenue
over-indebted
firms
depend
on otherdebtors’
banks’ assets
decisions
regard
to such
credit expansion
that wouldaffect
require
a quick
repair
of bank’s
balancesale
sheet.
it also depends
on over-indebted
firms’
clients,
as these decisions
both
expected
revenue
of delayed
of Secondly,
insolvent debtors’
assets and
expected profits
on
restrain
from actions
that would
increase
pay-off
variance
and,sheet.
consequently,
expected
losses
of bank. Thefirms’
more
credit expansion
that would
require
a quicktheir
repair
of bank’s
balance
Secondly, the
it also
depends
on over-indebted
widespread
forbearance
lending,
the larger
chance
for such
a restrain
to be considered
by over
the
restrain fromtheactions
that would
increase
their the
pay-off
variance
and,
consequently,
the expected
lossesindebted
of bank.firms
Theasmore
most
effective
to continue
operations.
widespread
thestrategy
forbearance
lending,
the larger the chance for such a restrain to be considered by over indebted firms as the
most effective strategy to continue operations.
18
16
16
Narodowy Bank Polski
Related literature and context
Note that such a calibration is consistent with likely hump shape of expiration of
 . It also implies  to be weaker than , especially so in the case of large .
Under our baseline calibration of , as specified in the Table 1 (see the next
section), has to be more than five times as weak as  at least. The baseline
calibration of  implies that  should amount to less than 0.66 of (quarterly)
standard deviations of shock to natural interest rate in the US, as identified by Adam
and Billi (2006, 2007).
17
NBP Working Paper No. 215
19
Chapter 3
3. Model description
3. Model description
We use in the simulations the analytical framework developed by Jung et al. (2005)
We use in the simulations the analytical framework developed by Jung et al. (2005)
which we generalize in two ways, as specified in the introduction. Namely, we allow
which we generalize in two ways, as specified in the introduction. Namely, we allow
for PLB and trend inflation in the model. Most previous research on the lower bound
for PLB and trend inflation in the model. Most previous research on the lower bound
for interest rates was based on the standard New Keynesian Phillips Curve, which
for interest rates was based on the standard New Keynesian Phillips Curve, which
we have to modify accordingly, along with the algorithm for model solution.
we have to modify accordingly, along with the algorithm for model solution.
3.1 The model
3.1 The model
As in Jung et al. (2005) or Eggertsson and Woodford (2003), the central bank faces
As in Jung et al. (2005) or Eggertsson and Woodford (2003), the central bank faces
the following minimization problem:
the following minimization problem:
(7)
  
   



(7)
     
with the following one-period loss function  :
with the following one-period loss function  :
    
(8)
(8)
    
where  is the output gap at . Note that, under trend inflation,  is no longer the
where  is the output gap at . Note that, under trend inflation,  is no longer the
inflation rate, but deviation of inflation rate from the steady state. This has no
inflation rate, but deviation of inflation rate from the steady state. This has no
influence on the variance of  , and hence on policy ranking according to the loss
influence on the variance of   , and hence on policy ranking according to the loss
function values.
function values.
Policymakers are constrained by standard behavioral equations, i.e. the IS
Policymakers are constrained by standard behavioral equations, i.e. the IS
curve and the Phillips curve. The former is only slightly modified in a
curve and the Phillips curve. The former is only slightly modified in a
straightforward way to account for positive inflation in the steady state ():
straightforward way to account forpositive inflation in the steady state ():
(9)
              
(9)
               
where  is the nominal interest rate at . The Phillips curve under trend inflation has
where  is the nominal interest rate at . The Phillips curve under trend inflation has
been proven by multiple authors to contain additional dynamic components in
been proven by multiple authors to contain additional
dynamic components in
comparison to its counterpart under zero steady state14
(see Ascari, 2004; Bakhshi et
14
comparison to its counterpart under zero steady state (see Ascari, 2004; Bakhshi et
al., 2007; Cogley and Sbordone, 2008). A simple quasi-differencing operation
al., 2007; Cogley and Sbordone, 2008). A simple quasi-differencing operation
allows to present this equation in the following recursive form:
allows to present this equation in the following recursive form:
               
(10)
               
(10)
14
Specifically, the New Keynesian Phillips curve under trend inflation contains on the right-hand side the output gap (or real
14
marginal
cost), the
expected
inflation rate
at 1-period
lead, trend
but also
an infinte,
exponentially
weighted
further
of
Specifically,
New Keynesian
Phillips
curve under
inflation
contains
on the right-hand
sidesum
the of
output
gapleads
(or real
output
gap
and expected
inflation inflation
rate. Leading
equation
onealso
period,
multiplying
by the weighted
ratio of two
weights
marginal
cost),
rate atthis
1-period
lead,bybut
an infinte,
exponentially
sumsubsequent
of further leads
of
 gap
(
) and
subtracting
the original
equationby
yields
(8), after basic
output
and
inflation this
rate.from
Leading
this equation
one equation
period, multiplying
by simplifications.
the ratio of two subsequent weights
  ) and subtracting this from the original equation yields equation (8), after basic simplifications.
(
20
18
18
Narodowy Bank Polski
Model description
whereby the reduced-form parameters in (10) are derived as follows:

 



    
    
   
     







 
 
 
 

 

   
    

    
     
  
 


     
    
  

 
 



    
 
  
    
  





  
 
(11)
The notation for deep parameters used in equation (11) follows full derivation of the
standard New Keynesian Phillips curve in Gali (2008), i.e.  is households’
subjective discount factor as in equation (2),  is the Calvo probability,    is the
Cobb-Douglas exponent on labour in the production function,  is the Frisch
elasticity of labour supply, and  is the elasticity of substitution between goods
     is the gross inflation rate in the steady state. While the previous
varieties. 
literature on the ZLB refers to reduced form parameters of the Phillips curve, we
prefer to calibrate the structural parameters so as to ensure the consistency between
individual reduced-form parameters in extended equation (10).
Minimizing (8) subject to constraints (9) and (10), after skipping the
expectation operators (under perfect foresight, as in Jung et al., 2005), implies the
following Lagrange function:

   
 
                   
                 
(12)
where  and  are Lagrange multipliers. Note that in this setup, the central
bank sets  equal to    and the loss function is value zero as long as we ignore
further constraints on  . Turning to the case of any positive lower bound for interest
19
NBP Working Paper No. 215
21
rates requires a modification of Kuhn-Tucker conditions related to the constraint
   (instead of   ), which now takes the form:
    
(13)
  
(15)
  
(14)
This implies that, as in previous analyses of the ZLB, two states are possible: the
lower bound is non-binding (which implies zero loss and zero Lagrange multiplier
on IS curve) or binding (which leads to positive loss, i.e. non-fulfilment of equation
(9) and positive Lagrange multiplier on IS curve).
3.2 Shock definition
We start in period 0 and assume that all variables take their steady state values, i.e.
   and  =  . The steady state value
(net) inflation rate is equal to ,     
of the natural interest rate can be estimated from the equation (2), as in Jung et al.
(2005). In period 1, as stated in the section 2, a shock of size  occurs that brings
the natural interest rate down to a level which renders the lower bound binding
(   and   ):
    
(16)
      
(17)
Recall that the shock is assumed to exhibit serial correlation of order 1 with inertia
parameter :
Further shocks are not considered, i.e. equation (17) is valid for t=2,3,… . This
dying out pattern implies that, for some   , the lower bound will cease to bind.
Further analysis depends on whether the central bank can credibly commit to the
optimum rule (12), subject to (13)-(15), or acts under discretion.
20
22
Narodowy Bank Polski
Model description
3.3 Solution under commitment
When the central bank credibly commits to follow the optimum policy rule from 
onwards, the first order conditions from Lagrange problem (10) take the following
form:
                
(18)
                  (19)
Note that the generalization to positive steady state inflation, as in (10), implies the
inclusion of second-order dynamics into the model. This also emerges in (19) as the
second lag of Lagrange multiplier  .
The lower bound is binding from    to   . The last period when this
constraint is binding can be found on the basis of  , i.e.  is established so that
 is positive but  is not, according to conditions (13)-(15). In practice, a
relatively high value of  is considered at the beginning and it is iteratively
decremented until the abovementioned condition is met.
It should perhaps be mentioned that, due to the presence of second-order
dynamics and the resulting overshooting patterns, the algorithm had to be slightly
modified as compared to e.g. Jung et al. (2005). It is insufficient to consider a distant
T and decrement it until a positive value of  appears for the first time; instead,
one needs to keep track of this condition coupled with another one, stating that for
t=1,…,T,   .
Accordingly, the model solution consists of the following phases:
1. Equations (9), (10), (18) and (19) for       with   .
2. Equations (10), (18) and (19) for      with   , but   .
3. Equations (10), (18) and (19) for          with    and
  , etc.
In phases 2 and 3,  is additionally derived from equation (9).
Phase 1 takes as initial conditions   ,    and   . The
terminal conditions for this phase are  ,  and  .
In Phase 3, we use equation (18) to express  as a function of  and
 . After substitution into (10), we obtain a difference equation in  , ,
21
NBP Working Paper No. 215
23
 ,  ,  and  . This equation, coupled with (19), forms a dynamic
system of forward-looking equations that can be cast into matrix form as:




 
    





with    



  














  



(20)
      
  
 and


   
  
.


This system contains 2 variables predetermined at  ( ,  ) and can be solved
with Klein’s (2000) method as a law of motion for these two variables:



 


 


 
(21)
The upper block of (21), coupled with (19) – and with the fact that all relevant lags
of  are zero in phase 3 – yields the following system of equations:

    
    


     




(22)
As a result, phase 3 takes  and  as initial conditions.
Phase 2 is simulated on the basis of initial conditions on Lagrange multipliers and
terminal conditions on  and . In both cases, the system of equations can be
expressed in a matrix form as:



            
     



(23)
Note that for      , i.e. in phase 2,  is equal to zero vector. Also,
     
            ,
    
        
              
       
   
    
  
22
24
Narodowy Bank Polski
Model description
 
and        

 
 

 
  .

3.4 Solution under discretion
The first order conditions do not read as (18) and (19) when the central bank cannot
credibly commit to follow the same optimum policy rule in the future. In such case,
the timing to terminate the lower bound on interest rates is exogenous to the model
(as in the special case of ZLB, cf. Jung et al., 2005) and can be determined by the
following rule:
    
    
(24)
In (24), and per analogy to the case of commitment,  is the last period of the lower
bound binding, and    is the first period after the constraint has ceased to bind.
The solution for      and later is straightforward: the central bank sets
     so as to keep     .
For       the model consists of equations (9), (10), along with the constraint
equation:
  
(25)
The model is completed by the terminal conditions on  and :
  
  
  
(26)
3.5 Calibration
Our calibration strategy is to hold our model (and results) as comparable as possible
to Jung et al. (2005) based on the parameter set from Woodford (1999), similar to
the calibration made by Eggertson and Woodford (2003). However, due to the
changes in the structure of the model, this can be accomplished in a straightforward
23
NBP Working Paper No. 215
25
way only for a subset of parameters. Following Woodford (1999) and Jung et al.
way only for a subset of parameters. Following Woodford (1999) and Jung et al.
(2005), we set    and   .
(2005), we set    and   .
Following Adam and Billi (2006), we set  according to a micro-founded loss
Following Adam and Billi (2006),
we set  according to a micro-founded loss

criterion. Note, however, that    does not hold any more under trend inflation.15
criterion. Note, however, that    does not hold any more under trend inflation.15
To see this, consider the standard definition of the price level at t in the pricesetting
To see this, consider the standard definition of the price level at t in the pricesetting
model à la Calvo:
model à la Calvo:


 


(27)
        


(27)
  
    
This can be transformed into:
This can be transformed into:
      
(28)
      
(28)
with  denoting gross inflation rate at t, while    . This implies the
with  denoting gross inflation rate at t, while    . This implies the


 
  . Log-linearizing around this steady state yields
steady state value   
 

steady state value      . Log-linearizing around this steady state yields


  
   
  
(29)
   
 
  
       
  
(29)
  , expression (29) collapses to the standard formula  
Note that under 
  , expression (29) collapses to the standard formula  
Note that under 
   . Now denote the parameter accompanying  in (29) as c for convenience
   . Now denote the parameter accompanying  in (29) as c for convenience
of exposition. Expression (29) shall be used in the derivation of recursive definition
of exposition. Expression (29) shall be used in the derivation of recursive definition
of intratemporal, cross-section variance of prices between producers. Woodford
of intratemporal, cross-section variance of prices
between producers. Woodford
(2003, p. 695, formula E.8) substitutes     , which shall now be replaced by
(2003,
p. 695, formula E.8) substitutes     , which shall now be replaced by
   . This leads to replacing equation (2.20) in Woodford (2003, p. 399) with the
   . This leads to replacing equation (2.20) in Woodford (2003, p. 399) with the
following (up to terms of order higher than 2 and terms independent of policy):
following (up to terms of order higher than 2 and terms independent of policy):


(30)
    
 

(30)
      
Following Woodford (2003, p. 400), as a result of the forward iterative solution we
Following Woodford (2003, p. 400), as a result of the forward iterative solution we
obtain:
obtain:

 

 

(31)
     
   

 




   
    
(31)


This leads to the following welfare criterion (cf. Eq. (2.22) in Woodford (2003, p.
This leads to the following welfare criterion (cf. Eq. (2.22) in Woodford (2003, p.
400), up to a scaling constant, terms of higher orders and terms independent of
400), up to a scaling constant, terms of higher orders and terms independent of
policy):
policy):
15
 is the slope of the New Keynesian Phillips curve for  = 0.
 is the slope of the New Keynesian Phillips curve for  = 0.
15
26
24
24
Narodowy Bank Polski
Model description



   
    
 
 
   
(32)
.
Equation (32) allows to calibrate  on the basis of , , , ,  and 
As regards the parameters of the Phillips curve, it is sufficient for the
abovementioned authors to calibrate only    (i.e. the parameter on one-
period-ahead expected inflation rate) and    (i.e. the parameter for current
output gap) under the assumption of zero steady state inflation. This is not a feasible
solution with our altered structure of the model and four reduced-form parameters in
equation (10). Note that these parameters are interdependent and cannot vary freely,
being based on the same subset of structural parameters.
All 4 parameters are based on  and , but also on (i) Calvo probability , (ii)
Cobb-Douglas exponent on labour in the production function   , (iii) Frisch
elasticity of labour supply  and (iv) elasticity of substitution between goods
varieties . We calibrate ,  and  in line with literature standards and,
conditionally upon that, then set  so as to match Woodford’s (1999)    in
the standard Phillips curve.
In particular, we calibrate   ,  and  based on the works of Smets and
Wouters (2002, 2003). The value of      taken by the exponent on labour in
the production function is widespread in the literature, resulting both from direct
estimation attempts of production function and from a direct calibration based on
labour share in national income. The value of Frisch elasticity of labour supply at
   seems to be relatively low, but the calibrations in the literature are quite
scattered. For example Christiano et al. (2005) assume a value of unity. However, in
our case, such a change has only marginal effect on the reduced form parameters in
(10), and hence on our results. The calibration of    in the New Keynesian
monopolistic competition model is typically set so as to imply a markup of 50%.
Also, even large changes in  (that we consider carrying the robustness check) have
no significant effect on our results. Ultimately, the set of 3 structural parameters
based on Smets and Wouters (2002, 2003) and Woodford’s (1999) calibration of
   together imply the calibration of Calvo parameter at   .
The calibration of the shock size and persistence follows the previous
literature on the ZLB with serially correlated disturbance of natural interest rate. We
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NBP Working Paper No. 215
27
set    like Adam and Billi (2006, 2007). This value is also the central point of
set    like Adam and Billi (2006, 2007). This value is also the central point of
the interval from 0.75 to 0.85 considered by Levin et al. (2010). In our sensitivity
the interval from 0.75 to 0.85 considered by Levin et al. (2010). In our sensitivity
analysis, we consider a wider range from 0.5 (the baseline value of Jung et al., 2005)
analysis, we consider a wider range from 0.5 (the baseline value of Jung et al., 2005)
to 0.9 (maximum value considered by Adam and Billi, 2006, 2007). The initial
to 0.9 (maximum value considered by Adam and Billi, 2006, 2007). The initial
shock size, , is calibrated to  as in the case of Levin et al. (2010). Note that
shock size, , is calibrated to  as in the case of Levin et al. (2010). Note that
this is 3.3 of (quarterly) standard deviations of this type of shock, as identified by
this is 3.3 of (quarterly) standard deviations of this type of shock, as identified by
Adam and Billi (2006, 2007).
Adam and Billi (2006, 2007).
We calibrate the steady state natural interest rate in line with Eq. 2 at the level
We calibrate the steady state natural interest rate in line with Eq. 2 at the level
consistent with ,  and the growth rate of potential output equal to 0.02/4. The
consistent with ,  and the growth rate of potential output equal to 0.02/4. The
latter figure corresponds to the average growth rate of real GDP in the US economy,
latter figure corresponds to the average growth rate of real GDP in the US economy,
according to Penn’s World Tables 8.0 (since 1950). As a result,   . Steady
according to Penn’s World Tables 8.0 (since 1950). As a result,   . Steady
state inflation is set at   . The same value is proposed as the PLB. Note
state inflation is set at   . The same value is proposed as the PLB. Note
that these calibrations, as well as the previous ones, are expressed in quarterly terms.
that these calibrations, as well as the previous ones, are expressed in quarterly terms.
This corresponds to annual values of  at , and  and PLB at . As
This corresponds to annual values of  at , and  and PLB at . As
mentioned in the introduction, 2% matches inflation target most frequently seen in
mentioned in the introduction, 2% matches inflation target most frequently seen in
advanced economies, as well as the floor for policy rate of Bank of England since its
advanced economies, as well as the floor for policy rate of Bank of England since its
foundation in 1694 until 2009 (and of most other central banks too). Note that such a
foundation in 1694 until 2009 (and of most other central banks too). Note that such a
floor usually implied clearly positive real interest rates. When it was binding, it was
floor usually implied clearly positive
real interest rates. When it was binding, it was
often accompanied by a deflation.16
In
our setting real interest rate at PLB is lower.
often accompanied by a deflation.16 In our setting real interest rate at PLB is lower.
It is similar to this from most other studies on the ZLB (where both steady state
It is similar to this from most other studies on the ZLB (where both steady state
inflation and the floor for interest rates are nil).(see Table 1).
inflation and the floor for interest rates are nil).
(Table 1)
(Table 1)
16
16
28
At the end of 19th century the price level in the UK was about a third of the level from the beginning of the century
At the end of 19th century the price level in the UK was about a third of the level from the beginning of the century
26
26
Narodowy Bank Polski
Chapter 4
4. Results
4. Results
As indicated in the introduction, four combinations of ZLB and PLB policies
As indicated in the introduction, four combinations of ZLB and PLB policies
varying in terms of their credibility are considered:
varying in terms of their credibility are considered:
(a)
both policies are discretionary,
(a)
both policies are discretionary,
(b)
both policies are pursued under commitment,
(b)
both policies are pursued under commitment,
(c)
PLB policy is pursued under commitment, while ZLB is discretionary,
(c)
PLB policy is pursued under commitment, while ZLB is discretionary,
(d)
PLB policy is discretionary, whereas ZLB is pursued under commitment.
(d)
PLB policy is discretionary, whereas ZLB is pursued under commitment.
We scrutinize all four combinations, because one cannot prejudge which type of the
We scrutinize all four combinations, because one cannot prejudge which type of the
policy, ZLB or PLB, is more likely to be credible. On the one hand, the ZLB policy
policy, ZLB or PLB, is more likely to be credible. On the one hand, the ZLB policy
signals dovish bias. By contrast PLB can be considered as a sign of hawkish bias,
signals dovish bias. By contrast PLB can be considered as a sign of hawkish bias,
limiting the actual probability of the bank allowing inflation to exceed the target.
limiting the actual probability of the bank allowing inflation to exceed the target.
On the other hand, the empirical evidence, albeit very scarce, suggests that the ZLB
On the other hand, the empirical evidence, albeit very scarce, suggests that the ZLB
policy can undermine the trust in central bank (Albinowski at al., 2014).
policy can undermine the trust in central bank (Albinowski at al., 2014).
We start the comparison of the ZLB and PLB policies as if the ZLB policy
We start the comparison of the ZLB and PLB policies as if the ZLB policy
had no side (adverse) effects such as strengthened post-crisis financial frictions,
had no side (adverse) effects such as strengthened post-crisis financial frictions,
delayed restructuring or heightened uncertainty. It is not a surprise that under this
delayed restructuring or heightened uncertainty. It is not a surprise that under this
assumption the ZLB policy is, in general, welfare enhancing relative to the PLB
assumption the ZLB policy is, in general, welfare enhancing relative to the
PLB
policy. That being said, the central bank’s credibility is of crucial importance.17
17
policy. That being said, the central bank’s credibility is of crucial importance.
In the case (a), when both policies fail to prevent severe and long recession,
In the case (a), when both policies fail to prevent severe and long recession,
the difference in the depth of negative output gap and resulting deflation is large. In
the difference in the depth of negative output gap and resulting deflation is large. In
the case (b), the difference is less profound. Still the ZLB policy allows to clearly
the case (b), the difference is less profound. Still the ZLB policy allows to clearly
reduce the output gap in comparison with the PLB policy. Moreover, the subsequent
reduce the output gap in comparison with the PLB policy. Moreover, the subsequent
overshooting and accompanying inflation needed to alleviate the recession are
overshooting and accompanying inflation needed to alleviate the recession are
weaker and more short lived than under the PLB policy. By contrast, in the case (c)
weaker and more short lived than under the PLB policy. By contrast, in the case (c)
the ZLB policy underperforms the PLB policy, in terms of welfare. Although the
the ZLB policy underperforms the PLB policy, in terms of welfare. Although the
former implies lower average nominal interest rates, it is the latter that results in
former implies lower average nominal interest rates, it is the latter that results in
milder and shorter recession. This result suggests that when the economy is hit by a
milder and shorter recession. This result suggests that when the economy is hit by a
severe shock, the commitment, if credible, counts more for the welfare performance
severe shock, the commitment, if credible, counts more for the welfare performance
17
When the baseline model’s calibration is applied, the micro funded loss function amounts to 0.0096519 under the ZLB and
17 0.027677 under the PLB if both policies are discretionary, as compared to 0.0012064 under the ZLB and 0.0019718 under
to
When the baseline model’s calibration is applied, the micro funded loss function amounts to 0.0096519 under the ZLB and
the
PLB, if they
arethe
pursued
to 0.027677
under
PLB ifunder
bothcommitment.
policies are discretionary, as compared to 0.0012064 under the ZLB and 0.0019718 under
the PLB, if they are pursued under commitment.
NBP Working Paper No. 215
27
27
29
than the exact value of the effective lower bound does (as long as this value is
reasonably low). It is true that the weight of central bank’s credibility is already
highlighted in many other studies on the ZLB (see, e.g. Adam and Billi, 2006 or
Eggertsson
and value
Woodford,
However,
they
prove
provides
central
than the exact
of the2003).
effective
lowerwhile
bound
does
(as that
longit as
this value
is
than the exact value of the effective lower bound does (as long as this value is
reasonably
low). It isto true
that economy
the weightwhen
of central
bank’s
is already
bank
with capability
stabilize
the ZLB
binds,credibility
we go a step
further
reasonably low). It is true that the weight of central bank’s credibility is already
and
argue that
the credibility
can on
deprive
central
strong
highlighted
in many
other studies
the ZLB
(see,bank
e.g. of
Adam
andjustification
Billi, 2006 for
or
highlighted in many other studies on the ZLB (see, e.g. Adam and Billi, 2006 or
aggressive
rates cuts
all the
way towhile
zero. they
Lastly,
in that
the case
(d), both
the
Eggertsson interest
and Woodford,
2003).
However,
prove
it provides
central
Eggertsson and Woodford, 2003). However, while they prove that it provides central
bank
capability
to stabilize
economy
when the
ZLB
we go a of
stepthefurther
lowerwith
bound
value and
an inability
to commit
work
to binds,
the detriment
PLB
bank with capability to stabilize economy when the ZLB binds, we go a step further
and argue
thatit the
credibility
deprive
central
justification
for
policy.
Thus,
generates
muchcan
larger
welfare
lossesbank
thanof
thestrong
ZLB policy
does (see
and argue that the credibility can deprive central bank of strong justification for
aggressive
Figure
4). interest rates cuts all the way to zero. Lastly, in the case (d), both the
aggressive interest rates cuts all the way to zero. Lastly, in the case (d), both the
lower bound value and an inability to commit work to the detriment of the PLB
lower bound value and an inability to commit work to the detriment of the PLB
policy. Thus, it generates much larger(Figure
welfare
4)losses than the ZLB policy does (see
policy. Thus, it generates much larger welfare losses than the ZLB policy does (see
Figure 4).
Figure 4).
Next we relax the assumption of no side effects of the ZLB policy. We
(Figureof4)shock to  under the ZLB policy, for
approximate them instead, as larger inertia
(Figure 4)
reasons explained in section 2. We check how much less persistent a shock under
we would
relax the
of no to
side
of thetheZLB
the PLBNext
policy
haveassumption
to be, compared
oneeffects
dealt with
ZLBpolicy.
policy,We
so
Next we relax the assumption of no side effects of the ZLB policy. We
approximate
them
instead,
larger
of shock
to incurred
 underunder
the ZLB
policy, for
that the welfare
losses
of theasPLB
didinertia
not exceed
those
the ZLB.
approximate them instead, as larger inertia of shock to  under the ZLB policy, for
reasonsItexplained
section
2. as
Weboth
check
how much
persistent
a shock
under
turns out in
that
as long
policies
are of less
similar
credibility,
i.e. in
the
reasons explained in section 2. We check how much less persistent a shock under
the PLB
policy
have to be,
to one
dealt policy
with the
ZLBoff
policy,
so
case
(a) and
(b),would
the difference
in compared
required for
the PLB
to pay
is quite
the PLB policy would have to be, compared to one dealt with the ZLB policy, so
that the welfare
of the PLB
did not exceed
those to
incurred
ZLB.
moderate.
Underlosses
the baseline
calibration
it amounts
0.063 under
in thethe
case
(a) and
that the welfare losses of the PLB did not exceed those incurred under the ZLB.
It turns
out (b).
that Thus,
as longit asis both
policies
of similar
credibility,
i.e. in(and
the
0.092 in
the case
lower
when are
central
bank fails
to commit
It turns out that as long as both policies are of similar credibility, i.e. in the
case (a) losses
and (b),arethelarge)
difference
in  required
forthat
the PLB
policy to pay
off baseline
is quite
welfare
than otherwise.
Note
the dispersion
in the
case (a) and (b), the difference in  required for the PLB policy to pay off is quite
moderate.
the baseline
0.063and
in Billi,
the case
(a)2007
and
value
of  Under
considered
in variouscalibration
papers on it
theamounts
topic (cf.toAdam
2006,
moderate. Under the baseline calibration it amounts18to 0.063 in the case (a) and
0.092
in the
case
(b).isThus,
lower
when
centralThe
bank
fails todifference
commit (and
and
Jung
et al.,
2005)
threeittoisfive
times
as large.
required
in 
0.092 in the case (b). Thus, it is lower when central bank fails to commit (and
welfare
losses
large) than
otherwise.
Note
that the
dispersion
in theof baseline
seems also
quiteare
moderate
if related
to some
empirics.
It implies
the ratio
shock’s
welfare losses are large) than otherwise. Note that the dispersion in the baseline
value
of under
considered
in various
papers
on the
topic (cf. of
Adam
and
2006,
half-lives
the ZLB
and PLB
policy
respectively
1.368
in Billi,
the case
(a)2007
and
value of  considered in various papers on the topic (cf.
Adam
and
Billi,
2006,
2007
and
Jung
2005)
three
to five timestheas period
large.18
The required
in 
1.548
in et
theal.,case
(b).is By
comparison,
since
the enddifference
of the Great
and Jung et al., 2005) is three to five times as large.18 The required difference in 
seems alsoisquite
moderate
related
to some
It implies
ratiogap
of shock’s
Recession
already
1.750 iftimes
longer
than empirics.
the average
time ofthe
output
closing
seems also quite moderate if related to some empirics. It implies the ratio of shock’s
half-lives under the ZLB and PLB policy respectively of 1.368 in the case (a) and
half-lives under the ZLB and PLB policy respectively of 1.368 in the case (a) and
1.548 in the case (b). By comparison, the period since the end of the Great
18
We do not
the case(b).
(c) hereBy
because
in this case PLBthe
policyperiod
dominates since
the ZLB policy
in termsof
of welfare,
even if
1.548
in describe
the case
comparison,
the end
the Great
the
ZLB policy has
side effects
at all. times longer than the average time of output gap closing
Recession
is no
already
1.750
Recession is already 1.750 times longer than the average time of output gap closing
18
28
We do not describe the case (c) here because in this case PLB policy dominates the ZLB policy in terms of welfare, even if
18 ZLB policy has no side effects at all.
the
We do not describe the case (c) here because in this case PLB policy dominates the ZLB policy in terms of welfare, even if
the ZLB policy has no side effects at all.
30
28
28
Narodowy Bank Polski
(Figureof5)the initial gap needs to be closed20 (cf.
after previous recessions19, and still 35.4%
Figure 5).
Results
Only in the case (d), the required difference in  would have to be large for
19
(Figure
after
previous
, andthe
stillZLB
35.4%
of5)the
needs toThis
be closed
(cf.
the PLB
policyrecessions
to outperform
policy
in initial
terms gap
of welfare.
is the20
only
19
after previous recessions , and still 35.4% of the initial gap needs to be closed20 (cf.
Figurewhen
5). the break-even  under the PLB policy (0.425) is out of the range
case
Figure 5).
Onlyininthe
theliterature
case (d),onthe
difference
 would
to be
large
for
considered
therequired
ZLB (see
Figure 6).inThis
is so have
because
PLB
policy
(Figure
the
PLBhigher
policy interest
to outperform
ZLB
policy
in terms
of welfare.
This until
is thelower
only
implies
rates asthe
compared
to5)the
ZLB policy
not only
(Figure 5)
case
break-even
underlater
the as
PLB
policy
is out of again
the range
boundwhen
bindsthebut
for sometime
well.
This(0.425)
case highlights
the
Onlyinof
inthe
theliterature
casebank’s
(d),onthe
difference
 rates
would
have
be
large
for
considered
therequired
ZLB (see
Figureinterest
6).inThis
is socuts
because
PLB
policy
significance
central
credibility.
Should
to to
zero
condition
Only in the case (d), the required difference in  would have to be large for
the
PLBhigher
policy
to outperform
ZLB policy
in
terms
ofpossible
welfare.
This
is theof
only
it, central
bank interest
would
not
have
tocompared
attach
much
weight
effects
the
implies
rates
asthe
to the
ZLBtopolicy
notside
only
until
lower
the PLB policy to outperform the ZLB policy in terms of welfare. This is the only
case
when
break-even
underlater
the as
PLB
policy
is out of again
the range
bound
bindsthebut
for sometime
well.
This(0.425)
case highlights
the
ZLB policy.
case when the break-even  under the PLB policy (0.425) is out of the range
significanceinofthe
central
bank’s
Should
rates
to zero
condition
considered
literature
on credibility.
the ZLB (see
Figureinterest
6). This
is socuts
because
PLB
policy
considered in the literature on the ZLB (see Figure 6). This is so because PLB policy
it, centralhigher
bank interest
would not
have
attach
much
weight
possible
the
implies
rates
as tocompared
to6)the
ZLBtopolicy
notside
onlyeffects
until of
lower
(Figure
implies higher interest rates as compared to the ZLB policy not only until lower
ZLB policy.
bound
binds but for some time later as well. This case highlights again the
bound binds but for some time later as well. This case highlights again the
significance
of centralthe
bank’s
cuts to the
zerolower
condition
Interestingly,
morecredibility.
persistentShould
or theinterest
larger rates
the shock,
the
significance of central bank’s credibility. Should interest rates cuts to zero condition
it, centraldifference
bank would
havethereby
to attach
much
weightinto relative
possibleterms,
side effects
of the
(Figure
6)
 and
more
limited,
the implied
required
in not
it, central bank would not have to attach much weight to possible side effects of the
ZLB
policy.
difference
in half-life of  (see table 2). This relationship casts doubt on aggressive
ZLB policy.
more
or severe
the larger
the shock,
lowersince
the
interestInterestingly,
rates cuts tothezero
in persistent
response to
negative
shock,the
which
(Figure
required
difference
in  and
thereby
more
limited,
in relative
terms,bythe
Eggertsson
and Woodford
(2003)
have
been6)
unanimously
advocated
theimplied
whole
(Figure 6)
This relationship
casts doubt
aggressive
difference
in half-life
of on
 (see
strand of the
literature
the table
ZLB 2).
envisaging
‘fundamental’
shock.onThe
results
persistent
or shock,
theargued.
larger
the
shock,
lower
the
interest
rates
cuts that
tothezero
insome
response
to
severe
negative
shock,
since
suggests,
instead,
themore
more
severe
the
more
cautious
the
central
dry
for Interestingly,
future
emergencies,
as
older the
papers
It
is the
risk the
ofwhich
side
effects
Interestingly, the more persistent or the larger the shock, the lower the
required
difference
in be,
and
thereby
in credibility
relative
terms,
Eggertsson
and Woodford
(2003)
havemore
been
unanimously
advocated
bythe
theimplied
whole
of
ZLB response
policy.
bank’s
should
and
especially
solimited,
when its
is dubious.
Note
required difference in  and thereby more limited, in relative terms, the implied
difference
in half-life
 (see
2).
This
relationship
casts
doubt
aggressive
that theofreason
for theofsuggested
caution
is not
the
need to
preserve
some
powder
strand
the
literature
on
the table
ZLB
envisaging
‘fundamental’
shock.on
The
results
difference in half-life of  (see table 2). This relationship casts doubt on aggressive
suggests,
instead,
the as
more
severe
the
the
more
cautious
the central
(Table
dry
for future
emergencies,
older
papers
argued.
It
is the
risk ofwhich
side
effects
interest
rates
cuts that
to zero
insome
response
to2)shock,
severe
negative
shock,
since
interest rates cuts to zero in response to severe negative shock, which since
of
ZLB response
policy.
Eggertsson
and Woodford
have been
advocated
by the whole
bank’s
should be,(2003)
and especially
so unanimously
when its credibility
is dubious.
Note
Eggertsson
and
Woodford
(2003)
have
been
unanimously
advocated
by
the
whole
19
In thethe
calculation
the
recession
ofsuggested
q1 1980:q3
1980
is combined
with
recession
q3preserve
1981:q4
1982some
due
to the
fact that
that
reason
for
thesensitivity
is not
the
need oftothat
powder
We
check
for
ofcaution
our
results
tothe
assertion
certain
costs
related
strand
of
the
literature
on
the ZLB
envisaging
‘fundamental’
shock.
The
results
the output gap after the former was not closed till the beginning of the latter. The end of the former is taken as the starting
strand
of gap
theclosing.
literature on the ZLB envisaging ‘fundamental’ shock. The results
point
of output
to
fast
restructuring
could
be avoided
orthe
reduced
ifthe
restructuring
wasgap
slow.
We
(Table
2)shock,
suggests,
instead,
that
the
more
severe
more
cautious
the
central
The
period
since
the end of the
Great
Recession
would
be
2.161
times
longer than
the
average time
of output
closing
after
suggests,
instead,
severe
central
previous
recessions,
if the that
averagethe
time more
was measured
sincethe
the shock,
bottom of the
outputmore
gap andcautious
not the end the
of recession
as
bank’s
response
andincrease
especially
whenthe
itsPLB
credibility
dubious.
approximate
theseshould
costs be,
by an
in sounder
policy.isWe
verify Note
how
announced
by the NBER.
20
Please note
that this comparison
notand
by a long
sight prejudge
in when
what partits
if any
interest rates close
to zero have been
bank’s
response
shouldofdoes
be,
especially
sowith
credibility
is
dubious.
Note
19
In thethe
calculation
the for
recession
q1
is combined
the
ofto
q3previous
1981:q4
1982some
due
to the
fact that
responsible
for
deceleration
ofthe
output
gap1980:q3
closing 1980
after
the
Great
Recession
asrecession
compared
to
recoveries.
We
check
for
sensitivity
of
our
results
to
assertion
that
certain
costs
related
that
reason
suggested
caution
is
not
the
need
preserve
powder

would
have
to
be
under
this
policy
so
as
to
push
the
break-even
large
the
implied

the output gap after the former was not closed till the beginning of the latter. The end of the former is taken as the starting
that ofthe
reason
for the suggested caution is not the need to preserve some powder
point
output
gap closing.
to
fast
restructuring
could
be avoided
or times
reduced
ifthe
restructuring
wasgapslow.

out
of
the
range
in the
literature
onthan
ZLB.
It of
follows
from
the
The period since the end of the considered
Great
Recession
would
be 2.161
longer
the
average time
output
closingWe
after
previous recessions, if the average time was measured since the bottom of output gap and not the end of recession as
approximate
these costs
an increase
under the
PLB
verifytimes
how
announced
by calibration
the NBER.
baseline
thatbythe
implied in29
 would
have
to policy.
exceed We
several
20
Please note that this comparison does not by a long sight prejudge in what part if any interest rates close to zero have been
19
In the calculation
recession
of q1
is combined
with theasrecession
oftoq3previous
1981:q4recoveries.
due to the fact that
responsible
deceleration
gap1980:q3
closing 1980
after
the
Great
Recession
compared
would
have
to
be
under
this
policy
so
as the
to
push1982
theidentified
break-even
large
theforimplied
of output
(quarterly)
thethestandard
deviations
of
the
shock
consideration,
as
by
19 output gap after the former
the
closed till
the
theunder
latter.
The
end
former1982
is taken
as the
the fact
starting
In the calculation the recessionwas
of not
q1 1980:q3
1980
isbeginning
combinedofwith
the
recession
of of
q3 1981:q4
due to
that
point
of output
the output
gap gap
afterclosing.
the former was not closed till the beginning of the latter. The end of the former is taken as the starting

out
ofsincethe
range
in the
literature
onthan
the
It the
follows
from
Adam
and
Billi
(2006,
2007).
Respective
ratio
amounts
6.0 in
casegap(a),
4.3the
in
The
period
theclosing.
end
of the considered
Great
Recession
would
be 2.161
times longer
thetoZLB.
average
time
of
output
closing
after
point
of output
gap
previous
if the
average
was measured
since the
of output gap and not the end of recession as
The periodrecessions,
since the end
of the
Great time
Recession
would be 2.161
timesbottom
longer
21 than the average time of output gap closing after
announced
by(b),
the NBER.
29
baseline
calibration
thewould
to and
exceed
times
the case
and
9.4average
inthat
thetimethe
case
(c)
(seesince
Figure
7). ofhave
previous
recessions,
if the
wasimplied
measured
bottom
output gap
not the several
end of recession
as
20
Please note
this comparison does not by a long sight prejudge in what part if any interest rates close to zero have been
announced
by that
the NBER.
20
responsible
forthat
deceleration
of output
gap
after
the
Great
Recession
aspart
compared
to previous
Please note
this standard
comparison
does
notclosing
by a long
sight
prejudge
in what
ifconsideration,
any interest
rates recoveries.
close
zero have beenby
(quarterly)
the
deviations
of
the
shock
under
astoidentified
responsible for deceleration of output gap closing after the Great Recession as compared to previous recoveries.
Adam and Billi (2006, 2007). Respective
ratio
(Figure
7) amounts to 6.0 in the case (a), 4.3 in
29 7).21
the case (b), and 9.4 in the case (c) (see Figure
We Paper
check
the
NBP Working
No. 215
29
robustness of our findings to changes in the model’s
(Figure
7) output growth has almost no impact
calibration (see table 3). It follows that
potential
on the required difference in . In the range considered of potential output growth
31
to out
fast ofrestructuring
could be avoided
or reduced
was slow.

the range considered
in the literature
on iftherestructuring
ZLB. It follows
from We
the
approximate
these costs
an increase
under the
PLB
verifytimes
how
baseline
calibration
thatbythe
implied in would
have
to policy.
exceed We
several
have toof
bethe
under
thisunder
policy
so as to pushas
theidentified
break-even
large the implied
 would
(quarterly)
the standard
deviations
shock
consideration,
by
dry
for
future
emergencies,
as
some
older
papers
argued.
It
is
the
risk
of
side
effects

out and
of the
range
considered
in the literature
on thetoZLB.
follows
from
Adam
Billi
(2006,
2007). Respective
ratio amounts
6.0 inIt the
case (a),
4.3the
in
of
baseline
calibration
 would
theZLB
casepolicy.
(b),
and 9.4 inthat
the the
case implied
(c) (see Figure
7).21 have to exceed several times
inflation targets should be discouraged from the use of ZLB policy by its possible
(quarterly) the
standard deviations of the shock under consideration, as identified by
side effects.22
(Table
2)
(Figure
7) amounts to 6.0 in the case (a), 4.3 in
Adam and Billi (2006, 2007). Respective
ratio
As far as parameters related to elasticity of
economy are concerned,  has
the case (b), and 9.4 in the case (c) (see Figure 7).21
almost no
on the required
difference to
in .
Even a that
significant
increase
in 
Weinfluence
check
of our
assertion
certain
costsmodel’s
related
We
checkfor
thesensitivity
robustness
of results
our findings
to changes
in the
leads
a limited risecould
in thebe
required
difference
in ,ifexcept
for the case
where
to
fasttorestructuring
avoided
or reduced
restructuring
was (c),
slow.
We
(Figure
7) output
calibration
(see table 3). It follows
that
potential
growth has almost
no impact
the relationship
is opposite
albeit
still very
Recall
that in
this case,
PLB
policy
approximate
these
costs byin
an.increase
in weak.
the PLB
policy.
We
verify
how
 under
on the required
difference
In the range
considered
of potential
output
growth
dominates
the ZLBpolicy
in terms
welfare,
irrespective
of to
any
sidethe
effects
of the
would
to of
be
under
policy
as
push
break-even
large
the
implied
We
check
the
robustness
oflimited
our this
findings
toso changes
in
the
model’s
this difference
increases
(tohave
a very
extent)
mainly
when
potential
output
latter.
this dominance
is ainbitthe
weaker,
when
the
is lower
than
in thefrom
baseline

out True,
ofis the
considered
literature
on
ZLB. has
It
follows
calibration
(seerange
tableor
3).above).
It follows
thatifpotential
growth
almost
no impact
growth
high
(3%
Thus,
the ZLBoutput
policy
entails
side
effects,
thenthe
it
calibration,
but
still
holds
comfortably.
The
case
of

is
not
significantly
different.
would
exceed
severalgrowth
times
baseline
the
and
on
the required
difference
in .implied
the fast
range
considered
oftopotential
should
becalibration
avoided
by that
countries
ofInboth
slow have
economic
growth.output
Its
impact on
the
required
difference
in shock
is primarily
related to changes
in  and
(quarterly)
standard
deviations
ofsignificant,
the
under
consideration,
asimpact
identified
by
this difference
increases
(toa amore
very
limited
extent)
mainly
output
The the
value
of  has
however
still when
limitedpotential
on
the
floppy
(at Billi
least (2006,
as long2007).
as it Respective
does not fall
below
1, i.e. 6.0
remains
with
Adam
and
ratio
amounts
inside
the consistent
case
(a),then
4.3
in
growth
isdifference
high (3%
or .
above).
Thus, if the
ZLB
policy
effects,
it
required
in
The difference
increases
whentoentails
the inflation
target
is set
23
21
empirical
studies
on
markups).
The
required
difference
in

very
feebly
increases
the
casebe
(b),
andincrease
9.4
the
case of
(c)both
(seeThis
Figure
should
avoided
byincountries
fast
and7).
slow economic
growth.
higher,
but
the
is very
weak.
weakness
ought to be
expected given the
with rising  (except for very high value of , when it decreases), if the ZLB policy
 has aamore
however
on the
findingsThe
on value
PLB, of
as 
setting
PLB significant,
is functionally
quite still
closelimited
in the impact
NK model
to
is discretionary. Otherwise, the relationship
is7)opposite and stronger, albeit still very
(Figure
required
in 
.
difference
increases
when the
inflation
target
set
downwarddifference
revision of
. The result
implies
that countries
with
both high
andislow
weak. First and foremost however, it strengthens, if anything, the conclusions drawn
higher, but
the increase
is very
weak. This
weakness
to be
expected
the
inflation
targets
should be
discouraged
from
the use ought
of ZLB
policy
by itsgiven
possible
under the
baseline
calibration.
Namely,
in
the
case
(b),
the
break-even

remains
We
robustness
of functionally
our findings
to close
changes
in NK
the model
model’s
findings
on 22check
PLB, asthe
setting
a PLB is
quite
in the
to
side
effects.
within the range
considered
in thethat
literature
on output
the ZLB
even has
for almost
extremely
low 
calibration
(see
table
3)..It The
follows
potential
growth
noand
impact
downward
revision
of
result
implies
that
countries
with
both
high
As
far
as
parameters
related
to
elasticity
of
economy
are
concerned,
 low
has
21
We do not describe the case (d) here because in this case break-even  under the PLB policy is out of the range of 
(and,
a result,
very
high ),
while
in
the
case
(d)any
moderately
high  raises
itsgrowth
value
on
theasrequired
difference
.
In
range
considered
of
potential
output
considered
in the
literature
irrespective
whether
fastthe
restructuring
entails
extra costs
or
not.
almost
no
influence
on theofin
required
difference
in .
Even
a significant
increase
in 
to the level from
that range.
it differently,
even mainly
if the ZLB
policy is pursued
this
increases
(to required
aPut
very
limited
extent)
when
leadsdifference
to a limited
rise in the
difference
in , except for
thepotential
case (c), output
where
under commitment,
fairly
limited
side ifeffects
of the
ZLB entails
policy side
oughteffects,
to be enough
growth
is high (3%
or above).
the
ZLB
policy
it
30weak.
the relationship
is opposite
albeitThus,
still very
Recall
that in this
case, PLB then
policy
21
We do not describe the case (d) here because in this case break-even  under the PLB policy is out of the range of 
for PLBbe
to pay
off in terms
ofrestructuring
welfare.
holds
for or
anygrowth.
, if the PLB policy
should
avoided
by countries
of fast
both
fast andThis
slow
economic
considered
inpolicy
the
literature
any
extra
costs
dominates
the
ZLBirrespective
policyofinwhether
terms
of welfare,entails
irrespective
of not.
any side effects of the
is underThe
commitment
for moderately
high
, if central
banks fails
to commit
value
of too,
hasand
aismore
however
on the
latter. True,
this dominance
a bitsignificant,
weaker, when
 is still
lowerlimited
than inimpact
the baseline
under PLB.
Similarly
with
regard
to ,30increases
it has almost
on the
required
required
difference
in .
The
difference
whennotheimpact
inflation
target
is set
calibration, but still holds comfortably. The
case of  is not significantly different.
difference
if the ZLB
policy
discretionary.
however
weak,
higher,
but in
the,increase
is very
weak.is This
weakness Certain
ought toeffect,
be expected
given
the
Its impact on the required difference in  is primarily related to changes in  and
appears when
the as
ZLB
policy
is pursued
under commitment.
In the
such
case, the
findings
on PLB,
setting
a PLB
is functionally
quite close in
NKa model
to
floppy (at least as long as it does not fall below 1, i.e. remains consistent with
required difference
somewhat
withcountries
rising . with
This both
is irrelevant
the
downward
revision in
of .decreases
The result
implies that
high andin low
empirical studies on markups).23 The required difference in  very feebly increases
case (b), where break-even  remains within the range considered in the literature on
with rising  (except for very high value of , when it decreases), if the ZLB policy
the topic for any value of . Nevertheless in the case (d), a bit larger  than in the
is discretionary. Otherwise, the relationship is opposite and stronger, albeit still very
baseline calibration suffices to increase break-even  to the level from that range.
21
weak.
and the
foremost
however,
strengthens,
conclusions
drawn
We do First
not describe
case (d) here
because initthis
case break-evenif
 anything,
under the PLBthe
policy
is out of the range
of 
considered in the literature irrespective of whether fast restructuring entails any extra costs or not.
22
Note however
that this result
can be sensitiveNamely,
to changes ininthethe
assumptions
on thethe
pricebreak-even
setting. We leavetheremains
respective
under
the baseline
calibration.
case (b),
robustness check for future research.
23
Recall that
. We consider ain
wider
of  than justified
by results
empirical
studies
on markups,low
in order
within
the depends
rangeonconsidered
therange
literature
on the
ZLBofeven
for
extremely

to cover values of  that appears in the literature on the ZLB.
30
(and, as a result, very high ), while in the case (d) moderately high  raises its value
to the level from that range. Put it differently, even if the ZLB policy is pursued
32
31
Narodowy
Polski
under commitment, fairly limited side effects of the ZLB policy ought
to beBank
enough
for PLB policy to pay off in terms of welfare. This holds for any , if the PLB policy
Its impact on the required difference in  is primarily related to changes in  and
floppy (at least as long as it does not fall below 1, i.e. remains consistent with
empirical studies on markups).23 The required difference in  very feebly increases
Results
with rising  (except for very high value of , when it decreases), if the ZLB policy
is discretionary. Otherwise, the relationship is opposite and stronger, albeit still very
weak. First and foremost however, it strengthens, if anything, the conclusions drawn
under the baseline calibration. Namely, in the case (b), the break-even  remains
within the range considered in the literature on the ZLB even for extremely low 
(and, as a result, very high ), while in the case (d) moderately high  raises its value
to the level from that range. Put it differently, even if the ZLB policy is pursued
under commitment, fairly limited side effects of the ZLB policy ought to be enough
for PLB policy to pay off in terms of welfare. This holds for any , if the PLB policy
is under commitment too, and for moderately high , if central banks fails to commit
under PLB. Similarly with regard to , it has almost no impact on the required
difference
in , if the
ZLB
policy
is discretionary.
Certain should
effect, however
weak,
All in all, countries
with
both
flexible
and rigid economies
be discouraged
appears
when
policy
pursuedside
under
commitment.
In suchinaresults
case, the
from using
the the
ZLBZLB
policy
by itsispossible
effects.
Any differences
for
required
difference
 decreases
somewhat
with rising
Thisspecific,
is irrelevant
the
these economies
areinsmall.
However,
if one wants
to be.more
then in
more
case
 remains
within
the
range
considered
in the
on
valid
reasons
forbreak-even
avoiding
the
ZLB
policy
arerigid
displayed
by countries
with
more rigid
All in(b),
all,where
countries
with both
flexible
and
economies
should
be literature
discouraged
.
in
the
casealbeit
(d),
bit larger
than
in the
the
forthe
any
value
of
labor
supply
and
higher
degree
nominalside
rigidities,
more
fierceincompetition
fromtopic
using
ZLB
policy
byNevertheless
itsofpossible
effects.
Anyadifferences
results
for
(manifested
in lower
markups).
baseline
calibration
to increaseif break-even
 to
level
from that
these economies
aresuffices
small. However,
one wants to
be the
more
specific,
thenrange.
more
valid
for avoiding
the ZLB
policy
arerigid
displayed
by countries
more rigid
All inreasons
all, countries
with both
flexible
and
economies
should with
be discouraged
22
Note however that this result can be sensitive to changes in the assumptions on the price setting. We leave the respective
robustness check for future research.
(Table
3) effects.albeit
from
using
ZLB
policy
by itsofpossible
side
Any differences
results for
labor
supplythe
and
higher
degree
nominal
rigidities,
more fierceincompetition
23
Recall that  depends on . We consider a wider range of  than justified by results of empirical studies on markups, in order
to cover values of  that appears in the literature on the ZLB.
(manifested
in lower
these economies
are markups).
small. However, if one wants to be more specific, then more
Ultimately,
we check
change of
parameters
the level
valid reasons
for avoiding
thehow
ZLBsimultaneous
policy are displayed
byall
countries
withtomore
rigid
implying
the and
largest
required
difference
in31,rigidities,
as indicated
in more
the table
3, would
affect
(Table
3)
labor supply
higher
degree
of nominal
albeit
fierce
competition
(manifested
markups).
our
findings.inItlower
follows
that if central bank fails to commit under the ZLB policy,
Ultimately,ofwe
how simultaneous
change
of the
all parameters
level
then irrespective
itscheck
credibility
under the PLB
policy,
break-evento the
remains
(Table
3)
implying
largest
requiredindifference
in ,on
asthe
indicated
in the
table8).3, would affect
within thethe
range
considered
the literature
ZLB (see
Figure
our findings. It follows that if central bank fails to commit under the ZLB policy,
Ultimately,ofwe
how simultaneous
change
of the
all parameters
level
then irrespective
itscheck
credibility
under
the 8)
PLB
policy,
break-evento the
remains
(Figure
implying
largest
requiredindifference
in ,onasthe
indicated
in the
table8).3, would affect
within thethe
range
considered
the literature
ZLB (see
Figure
our findings.
It follows
that ifsome
central
bank fails
under
thebreak-even
ZLB policy,
The case
(b) requires
discussion.
In to
thiscommit
case there
is no


then
its credibility
the
PLBthe
policy,
 remains
(Figure
8)
underirrespective
the assumedofcalibration.
Theunder
reason
is that
fast the
  and high
 raise
 break-even
within
range considered
the literature
on the
ZLBthe
(see
Figure
8). As a result
nominaltheinterest
rate in theinsteady
state high
above
lower
bound.
casevalue
(b) requires
some0.69
discussion.
In this
case thereconsidered),
is no break-even

below under
calibration
the loss
below aThe
certain
of  (from

(Figure
8) the
and high
 raise
under
the under
assumed
calibration.
reason
isvalue
that
fast 
function
PLB
assumes The
a constant
regardless
of(while
remaining
nominal
interest
in theThis
steady
state
above
lower
bound.
a lower
result
larger than
under rate
the ZLB).
is due
to high
the fact
that the
at such
a value
of As
 the
The
case
(b)
some0.69
discussion.
In this
casetwo
there
is no break-even

below
certain
of  (from
below
under
calibration
considered),
the,loss
bound abinds
forvalue
onerequires
period
only
(from
0.70 already
for
periods).
For all
at


NBP Working
Paper No.
215
under
the
assumed
calibration.
The
reason
isvalue
that the
fast gap

inflation
and high
 raise
function
PLB
assumes
a only
constant
regardless
of
remaining
which
theunder
lower
bound
binds for
one period,
output
and
follow
the
(while
nominal
interest
in the
steady
state
above
the
lower
bound.
a of
result
larger
than
under
the
ZLB).
is due
to high
the
fact
that
at such
a value
of As
 the
lower
same path,
whichrate
results
in This
the
same
loss
function
values.
The
construction
the
33

under the assumed calibration. The reason is that the fast 
  and high  raise
nominal interest rate in the steady state high above the lower bound. As a result
below a certain value of  (from 0.69 below under calibration considered), the loss
function under PLB assumes a constant value regardless of  (while remaining
larger than under the ZLB). This is due to the fact that at such a value of  the lower
bound binds for one period only (from 0.70 already for two periods). For all , at
which the lower bound binds for only one period, output gap and inflation follow the
same path, which results in the same loss function values. The construction of the
model requires at least two periods of lower bound binding for relevance of  for
welfare losses due to the lower bound.
In summary, the findings provide support for cautiousness about cutting
interest rates to zero. Note that PLB would by no means rule out quantitative easing
in order to keep possible panic down in systemically important segments of financial
sector after the outburst of financial crisis. Such a policy would be in line with
Bagehot’s (1892) prescription of lending freely to solvent banks, against good
collateral and at penalty rates. It would 32
also contribute, in some sense, to central
banks’ return to their original task of interest rate stabilization (see, e.g. Goodhart,
1988; cf. figure 3).
The question arises whether establishing PLB suits the situation such as the
current one in major economies, where interest rates have already been close to zero
for many years. If the approach developed by Jung et al. (2005) correctly describes
how lower bound ceases to bind, then the answer is: not necessarily, for four
reasons, albeit with reservations.
Firstly, as periods go by since the ZLB has started to bind, a large part of
initial shock  can expire. In other words, even if interest rates close to zero
promoted forbearance lending, hindered post-crisis restructuring or contributed to
heightened uncertainty, then they would postpone the return of rt to the steady state,
but would not rule such return out. The state of modelled economy in a given period
k>0 can be fully described with help of a shock  , such as:

   ~
 
(33)
Recall the table 2 which reports that the milder the shock to rt, the less likely the
dominance of PLB over the ZLB in terms of welfare (the larger the side effects of
ZLB required for such dominance). One obvious caveat applies here. It follows from
Eq. 33 that  / depends not only on k, but on ~ as well. The larger the ~ , the less


weighing the passage of time on chances of PLB to dominate the ZLB. Put it
differently, raising interest rates from zero to PLB’s value in order to curb
forbearance lending or foster post-crisis restructuring is more likely to pay off in
economy where forbearance lending has been massive and post-crisis restructuring
34
Narodowy Bank Polski
slow and thus, far from being advanced in spite of long time k having been passed
since the outburst of crisis. These conditions are more likely to be met in economy
(5)
dominance of PLB over the ZLB in terms of welfare (the larger the side effects of
ZLB required for such dominance). One obvious caveat applies here. It follows from
Eq. 33 that  / depends not only on k, but on ~ as well. The larger the ~ , the less
Results


weighing the passage of time on chances of PLB to dominate the ZLB. Put it
sector after the outburst of financial crisis. Such a policy would be in line with
differently, raising interest rates from zero to PLB’s value in order to curb
Secondly,
in restructuring
are likely
to increase
fast
Bagehot’s
(1892) delays
prescription
of lending freely
to solvent
banks, costs
againstof good
forbearance lending or foster post-crisis restructuring is more likely to pay off in
restructuring
are avoided
mitigated
as long as in
restructuring
is slow.
The
collateral andwhich
at penalty
rates. Itorwould
also contribute,
some sense,
to central
economy where forbearance lending has been massive and post-crisis restructuring
delays return
lengthen
the period
capital
labour are(see,
used
a given
banks’
to their
originalfor
taskwhich
of interest
rateand
stabilization
e.g.inGoodhart,
slow and thus, far from being advanced in spite of long time k having been passed
application.
This3).lengthening gives at least some of the production factors a more
1988; cf. figure
since the outburst of crisis. These conditions are more likely to be met in economy
specificThe
nature.
Besides,
low
entry rate
reduces PLB
the share
fully such
adapted
to
question
arises
whether
establishing
suitsof
thefirms
situation
as the
with: banking based financial sector24, loans of recourse debt’s nature and high costs
the
current
conditions, where
while interest
strugglesrates
of many
existingbeen
firmsclose
to maintain
current
one economic
in major economies,
have already
to zero
of dealing with insolvency.
status
quoyears.
resultIfinthe
lower
and lower
percentage
of etentities
easily
adapting
to new
for many
approach
developed
by Jung
al. (2005)
correctly
describes
Secondly, delays in restructuring are likely to increase costs of fast
conditions.
such then
changes
production
specificity
and
how
lower Note
boundhowever
ceases that
to bind,
the in
answer
is: notfactors’
necessarily,
for four
24
restructuring
which
are
or mitigated
as long
aspromotes
restructuring
slow.
The
Simons (1936) was
probably
the avoided
first who claimed
that capital market
funding
adjustments’isspeed
relative
to
banking
funding.
In
turn,
Allard
and
Blavy
(2011)
were
among
the
first,
who
verified
this
claim
empirically.
One
has
to
notice
firms’
need
and
ability
to
adapt
increase
sensitivity
of
economy
not
only
to
the
reasons, albeit with reservations.
delays lengthen the period for which capital and labour are used in a given
establishment
but to
Firstly,ofasPLB,
periods
goany
by shock.
since the ZLB has started to bind, a large part of
application. This lengthening gives at least some of the production factors a more
Thirdly,
interest
to PLB’s
valuerates
can close
triggerto fiscal
33 zeroeven
initial shock
 raising
can expire.
In rates
otherfrom
words,
if interest
zero
specific nature. Besides, low entry rate reduces the share of firms fully adapted to
crisis, if government
has beenhindered
runningpost-crisis
primary deficit,
dp under
ZLB policy.
promoted
forbearance lending,
restructuring
or contributed
to
the current economic conditions, while struggles of many existing firms to maintain
Provided that
investors consider
probability
ofthe
stabilization
sovereign debt to
heightened
uncertainty,
then theythe
would
postpone
return of rof
t to the steady state,
status quo result in lower and lower percentage of entities easily
adapting to new
GDP
ratio
b
in
any
future
period
as
equal
to
δ,
and
assume
no
change
in dp period
before
t
but would not rule such return out. The state of modelled economy in a given
conditions. Note however that such changes in production factors’ specificity and
the stabilization,
then the value
sovereign
debt
stab they
as: expect at the moment of
k>0
can be fully described
with of
help
of a shock
 ,bsuch
firms’ need and ability to adapt increase sensitivity
of economy not only to the

the stabilization is given by the Eq. 34 (cf.~Blanchard,
1990):
(33)
 
establishment of PLB, but to any shock.
   


  ( t  k )
dp
dp
 i   y ( t  k )
toert, the
e the
Thirdly,
interest
frommilder
zero
candtless
trigger
fiscal
  raising
E the
b

 to
 likely
Recall
2 bwhich
reportsrates
that
thePLB’s
shockP value
the
stab table
k 
P 
i    y 
i    y 
k 
crisis, if government
deficit,
dp under
ZLB
policy.
dominance
of PLB overhas
thebeen
ZLB running
in terms primary
of welfare
(the larger
the side
effects
of

, for     y P  i
(34)
 that for
Provided
consider
theOne
probability
stabilization
of sovereign
debt
to
ZLB required
such
obviousof
caveat
applies here.
It follows
from
d p dominance).

  b investors

  k

don

depends
y P not
GDP
future
toonδ,~and
assume
change
before
p equal
 well.
 btin
period
as
The
larger
the in~ d, pthe
less
Eq. 33ratio
/iany
onlyas
k, but
P no
that
,
or


y
f
i





P
P

y
y
i
i











the
stabilization,
then the
debtPLB
bstabtothey
expect atthetheZLB.
moment
weighing
the passage
of value
time of
onsovereign
chances of
dominate
Put of
it
the
stabilization
is given by therates
Eq. 34
(cf. zero
Blanchard,
1990):value in order to curb
differently,
raising
from
to PLB’s
It follows that
in the interest
case of zero interest
rate, even
marginally
positive δ is enough

  or foster
 likely
d p post-crisis
d p is more
 i is
forbearance
lending
to pay
off in
( t  k ) 
 ( t  k )
y restructuring
to calm
unless
they
e expect
e  sustainable,
bk sovereign debt
dt the

E binvestors
 economy
stab 
k  that
P 
P 
i    y 
i    y 
forbearance
economy
where
hastime
beenyet,
massive
and low
post-crisis
to shrink in
nominal
terms. Atlending
the same
with very
value ofrestructuring
δ there is a
P

, for     y  i
(34)
slow
and
being
advanced in spite of long time k having been passed
substantial
risk far
thatfrom
any
 thus,
dafter
 increase of interest rate investors will lose their faith in
p
  b 
 These conditions are more likely to be met in economy
the
k
 outburst
since
ofcrisis.
d p however, that
sustainability
ofi sovereign
Note
in real world ZLB policy may

y P debt.
 
, for     y P  i

24
P
P

with:
banking
based
sector
,p,yloans
of recourse
debt’sbnature
and high costs
i increase
i   d

 yfinancial
to
 government
encourage
δ may
decline once
t becomes large (cf.
of dealing
insolvency.
Conesa
andwith
Kehoe,
2014), and large bt may give rise to fear of economy shrinking
It follows that in the case of zero interest rate, even marginally positive δ is enough
(cf. Reinhart et al., 2012). Thus, fiscal crisis may also outbreak under the ZLB
to
calm investors that sovereign debt is sustainable, unless they expect the economy
24
(5)
P
P
Simons (1936) was probably the first who claimed that capital market funding promotes adjustments’ speed relative to
banking
funding.
turn, Allardterms.
and BlavyAt
(2011)
among
the first,
verified
this low
claim empirically.
has to notice
to shrink
in Innominal
thewere
same
time
yet,who
with
very
value ofOne
δ there
is a
that although they found some support in the data to that claim, their findings are not unequivocal, given the differences in
product and labor market flexibility across analyzed countries.
substantial risk that after any increase of interest rate investors will lose their faith in
33
sustainability of sovereign debt. Note however,
that in real world ZLB policy may
encourage government to increase dp, δ34may decline once bt becomes large (cf.
NBP Working Paper No. 215
Conesa and Kehoe, 2014), and large bt may give rise to fear of economy shrinking
(cf. Reinhart et al., 2012). Thus, fiscal crisis may also outbreak under the ZLB
35

, for     y P  i
 
dp



   bk 
P 
dp
i    y 
 
, for     y P  i

P
P

y
y
i
i











(34)
It follows that in the case of zero interest rate, even marginally positive δ is enough
to calm investors that sovereign debt is sustainable, unless they expect the economy
to shrink in nominal terms. At the same time yet, with very low value of δ there is a
substantial risk that after any increase of interest rate investors will lose their faith in
sustainability of sovereign debt. Note however, that in real world ZLB policy may
encourage government to increase dp, δ may decline once bt becomes large (cf.
Conesa and Kehoe, 2014), and large bt may give rise to fear of economy shrinking
(cf. Reinhart et al., 2012). Thus, fiscal crisis may also outbreak under the ZLB
policy. In such a case bt is likely to be larger. Taylor (2012) (among others)
that although they found some support in the data to that claim, their findings are not unequivocal, given the differences in
documents that the larger the sovereign debt, the more costly the crisis.
product and labor market flexibility across analyzed countries.
Fourthly, a shift from the ZLB to PLB policy creates a risk that the public
would blame the central bank for the whole negative output gap (and not only for
34
costs of fast restructuring). Taking into account government’s willingness to keep
soft budget constraint, a general perception that central bank and not the crisis is
responsible for poor performance of the economy could put at risk central bank’s
independence and result in policy reversal. Note that raising interest rate from zero
to PLB’s value when inflation deviates from the target and output gap is deeply
negative could be presented as inconsistent with central bank’s mandate. Besides
such a shift requires from the central bank to admit that the previous monetary
policy was wrong. Image of erring institution would make it easier to attack the PLB
policy as unsound by the beneficiaries of the ZLB policy. At the same time, the ZLB
policy have provided them with funds for lobbying, which they would not have had,
had they been forced to restructure immediately after the crisis outburst. All in all,
late establishment of a PLB could be infeasible, even if it was desirable from social
welfare perspective.
36
Narodowy Bank Polski
Chapter 5
5. Conclusions
If the ZLB policy has no side effects such as strengthened post crisis
financial frictions, delayed restructuring or heightened uncertainty, it is, in general,
welfare enhancing relative to the PLB policy. However, credibility of central bank is
of crucial importance. If central bank failed to commit under the ZLB policy, while
its commitment under the PLB policy was perceived credible, the latter policy
would outperform the former in terms of welfare. In turn, under similar credibility of
both policies, quite moderate side effects of the ZLB policy are enough for the PLB
policy to pay off in terms of welfare. This held especially when central banks failed
to commit, and even if restructuring, fostered by the PLB policy, entailed some
costs, which
could be reduced or even avoided through slow restructuring.
Moreover, the larger and the more persistent the shock, the more moderate the side
effects required for PLB policy dominance over ZLB policy. Only if the ZLB helped
central bank to credibly commit, while the PLB policy undermined central bank’s
credibility, the required side effects would have to be large. Robustness check
suggests that the findings hold for economies with both fast and slow potential
output growth, with low and higher inflation target, flexible and more rigid. If
anything, they are more robust for economies with slow potential output growth, low
inflation target, strong rigidities: nominal and in labor supply, although tough
competition.
Our findings indicate that there are two directions of particular policy
relevance for future research on ZLB. Firstly, it should focus on what makes central
bank commitment credible and what harms its credibility. Secondly, quantitative
evaluation of ZLB policy effects on post crisis financial frictions, restructuring and
uncertainty should be given high priority in research agenda.
This paper is the first step to accommodating both positive and side effects of
the ZLB policy (or the extremely accommodative policy in general). However,
further steps should follow in order to establish optimal central bank’s response to
severe shock. The paper suggests that the aggressive interest rates cuts all the way to
zero may not be the right response. It might be that central bank should establish a
PLB instead and use quantitative easing to keep panic down in systemically
important segments of financial sector. Bagehot (1892) could be right.
36
NBP Working Paper No. 215
37
References
References
Adam K., Billi R. M. (2006) “Optimal Monetary Policy under Commitment with a
Zero Bound on Nominal Interest Rates.” Journal of Money, Credit and Banking.
38(7): 1877-1905
Adam K., Billi R. M. (2007) “Discretionary monetary policy and the zero lower
bound on nominal interest rates”, Journal of Monetary Economics 54(3): 728-752
Adrian T., Shin H. S. (2010) “Liquidity and leverage.” Journal of Financial
Intermediation. 19(3): 418-437
Adrian T., Shin H. S. (2014) “Procyclical Leverage and Value-at-Risk.” Review of
Financial Studies. 27 (2): 373-403
Ahearne A. G., Shinada N. (2005) “Zombie firms and economic stagnation in
Japan.” International Economics and Economic Policy. 2(4): 363-381
Albertazzi U., Marchetti D. J. (2010) “Credit supply, flight to quality and
evergreening: an analysis of bank – firm relationships after Lehman.” Banca
D’Italia Temi di Discussione (Working Paper.) 756
Albinowski M., Ciżkowicz P., Rzońca A. (2014) “Links between the trust in the
ECB and its interest rate policy.” Applied Economics. 46(25): 3090-3106
Allard J., Blavy R. (2011) “Market Phoenixes and Banking Ducks. Are Recoveries
Faster in Market-Based Financial Systems?” IMF Working Paper. 11/213
Altunbas Y., Gambacorta L., Marqués-Ibáñez D. (2014),”Does Monetary Policy
Affect Bank Risk?” International Journal of Central Banking. 10(1): 95-136
Andrés J., Arce O. (2009) “Banking Competition, Housing Prices and
Macroeconomic Stability”. Banco de España Working Paper. 0830
Angeloni I., Faia E. (2013) “Capital regulation and monetary policy with fragile
banks.” Journal of Monetary Economics. 60(3): 311-324
Arikawa Y., Miyajima H. (2007) “Relationship Banking in post Bubble Japan:Coexistence of soft-and hard budget constraint”, in: Corporate Governance in Japan:
Institutional Change and Organizational Diversity. Aoki M., Jackson G., Miyajima
H. [eds.] Oxford, New York: Oxford University Press
38
38
Narodowy Bank Polski
References
Arrowsmith M., Griffiths M., Franklin J., Wohlmann E., Young G., Gregory D.
(2014) “SME forbearance and its implications for monetary and financial stability.”
Bank of England Quarterly Bulletin. 2013 Q4: 296-303
Ascari, G. (2004), „Staggered price and trend inflation: some nuisances”, Review of
Economic Dynamics 7: 642–67
Bagehot W. (1892) Lombard Street: A Description of the Money Market. London:
Kegan Paul, French, Trübner & Co Ltd
Bakhshi H., Khan H., Burriel-Llombart P., Rudolf B. (2007) „The New Keynesian
Phillips curve under trend inflation and strategic complementarity”, Journal of
Macroeconomics 29: 37–59
Barnett A., Batten S., Chiu A., Franklin J., Sebastiá-Barriel M. (2014a) “The UK
productivity puzzle.” Bank of England Quarterly Bulletin. 2014 Q2: 114-128
Barnett A., Broadbent B., Chiu A., Franklin J., Miller H. (2014b) “Impaired capital
reallocation and productivity.” National Institute Economic Review. 228: R35-R48
Barsky R., Justiniano A., Melosi L. (2014) “The Natural Rate of Interest and Its
Usefulness for Monetary Policy.”
American Economic Revie: Papers and
Proceedings. 104(5): 37-43
Basu S., Fernald J., Fisher J., Kimball M. (2013) “Sector-Specific Technical
Change.” mimeo
Basu S., Fernald J., Kimball M. (2006) “Are Technology Improvements
Contractionary?” American Economic Review. 96(5): 1418-1448
Bech M. L., Gambacorta L., Kharroubi E. (2014): “Monetary Policy in a Downturn:
Are Financial Crises Special?”, International Finance, 17(1): 99-119
Benhabib J., Schmitt-Grohé S., Uribe M. (2001) “The Perils of Taylor Rules.”
Journal of Economic Theory. 96(1): 40-69
BIS (2010) BIS 80th Annual Report. Basel: Bank For International Settlements
BIS (2012) BIS 82nd Annual Report. Basel: Bank For International Settlements
BIS (2013) BIS 83rd Annual Report. Basel: Bank for International Settlements
BIS (2014) BIS 84th Annual Report. Basel: Bank for International Settlements
Blanchard
O.
J.
(1990)
“Comment
on
Giavazzi
and
Pagano.”
NBER
Macroeconomics Annual. 1990
39
NBP Working Paper No. 215
39
Blanchard O. J., Dell’Ariccia G., Mauro P. (2010) “Rethinking Macroeconomic
Policy.” Journal of Money, Credit and Banking. 42(s1): 199-215
Bordo M. D., Landon-Lane J. (2013) “Does Expansionary Monetary Policy Cause
Asset Price Booms? ; Some Historical and Empirical Evidence.” NBER Working
Paper. 19585
Borio C. E. V. (2014) "The financial cycle and macroeconomics: What have we
learnt?" Journal of Banking & Finance. 45(C): 182-198
Borio C. E. V., White W. R. (2003)"Whither monetary and financial stability: the
implications of evolving policy regimes," Federal Reserve Bank of Kansas City
Proceedings - Economic Policy Symposium - Jackson Hole. 2003:131-211.
Borio C. E. V., Zhu H. (2008) “Capital regulation, risk-taking and monetary policy:
a missing link in the transmission mechanism?” Journal of Financial Stability. 8(4):
236-251
Caballero R. J. (2007) Specificity and Macroeconomics of Restructuring.
Cambridge. London: MIT Press
Caballero R. J., Hoshi T., Kashyap A. K. (2008) “Zombie Lending and Depressed
Restructuring in Japan” American Economic Review. 98(5): 1943-1977
Campbell J. R., Evans Ch., Fisher J. D. M., Justiniano A. (2012) “Macroeconomic
Effects of Federal Reserve Forward Guidance.” Brookings Papers on Economic
Activity. 1(2012): 1-80
Chen S., Kim M., Otte M., Wiseman K., Zdzienicka A. (2015) “Private Sector
Deleveraging and Growth Following Busts.” IMF Working Paper. 15/35
Christiano L. J., Eichenbaum M., Evans C. L. (2005) „Nominal Rigidities and the
Dynamic Effects of a Shock to Monetary Policy”, Journal of Political Economy,
115(1): 1-45
Ciżkowicz P., Rzońca A. (2014) “Interest rates close to zero, post-crisis
restructuring and natural interest rate.” Prague Economic Papers. 3(2014): 315-329.
Claessens S., Kose M. A., Laeven L., Valencia F. [eds.] (2013) Financial Crises.
Causes, Consequences, and Policy Responses. Washington: International Monetary
Fund
40
40
Narodowy Bank Polski
References
Cogley T., Sbordone A. M. (2008), „Trend Inflation, Indexation, and Inflation
Persistence in the New Keynesian Phillips Curve”, American Economic Review
98(5): 2101–2126
Conesa J. C., Kehoe T. J. (2014) “Is It Too Late to Bail Out the Troubled Countries
in the Eurozone?” American Economic Review. 104(5): 88-93
Deutsche Bank (2013) Default Study 2013. Analysing a Decade of Record Low HY
Defaults. London: Deutsche Bank Markets Research. Deutsche Bank AG
Diamond D. W., Rajan R. G. (2009) “The Credit Crisis: Conjectures about Causes
and Remedies” American Economic Review. Papers and Proceedings. 99(2): 606610
Dugger R. H., Ubide A. (2004) “Structural Traps. Politics and Monetary Policy.”
International Finance. 7(1): 85-116
Eggertsson G. B. (2003) “How to Fight Deflation in a Liquidity Trap: Committing
to Being Irresponsible”. IMF Working Paper. 03/64
Eggertsson G. B. (2011) “What Fiscal Policy is Effective at Zero Interest Rates?”
2010 NBER Macroeconomic Annual 25: 59-112
Eggertsson G. B., Woodford M. (2003) “The Zero Bound in Interest Rates and
Optimal Monetary Policy” Brookings Papers on Economic Activity. 34(1): 139-235
Eggertsson G., Krugman P. (2012) “Debt, Deleveraging, and the Liquidity Trap: A
Fisher-Minsky-Koo Approach.” Quarterly Journal of Economics, 127: 1469-1513
Eggertsson, G. (2006), “The Deflation Bias and Committing to Being Irresponsible”,
Journal of Money, Credit and Banking, Vol. 38, Issue 2, pp. 283-321
Farhi E., Tirole J. (2012) “Collective Moral Hazard, Maturity Mismatch, and
Systemic Bailouts.” American Economic Review. 102(1): 60-93
Fernald J. (2014) “A Quarterly, Utilization-Adjusted Series on Total Factor
Productivity.” Federal Reserve Bank of San Francisco Working Paper. 2012-19
Foster L., Grim Ch., Haltiwanger J. (2014)”Reallocation in the Great Recession:
Cleansing or Not?.” NBER Working Paper. 20427
Fukao K. (2013)”Explaining Japan's Unproductive Two Decades.” Asian Economic
Policy Review. 8(2): 193-213
41
NBP Working Paper No. 215
41
Gali J. (2008), „Monetary policy, inflation, and the business cycle: an introduction
to
the
New
Keynesian
framework”,
Princeton
University
Press,
Princeton/Woodstock.
Gali J., Smets F., Wouters R. (2012) “Slow Recoveries: A Structural Interpretation.”
Journal of Money, Credit and Banking. 44(s2): 9-30.
Goodhart Ch. A. G. (1988) The evolution of central banks, Cambridge, MA: MIT
Press
Hamao Y., Mei J., Xu Y. (2007) “Unique Symptoms of Japanese Stagnation: An
Equity Market Perspective”. Journal of Money, Credit and Banking. 39(4): 901-923
Hansen A. H. (1939) “Economic Progress and Declining Population Growth.”
American Economic Review. 29(1): 1-15
Homer S., Sylla R. E. (2005) History of interest rates. Hoboken: Wiley
Issing O.(2012)”The Mayekawa Lecture: Central Banks – Paradise Lost.” Monetary
and Economic Studies. 30(2012): 55-74
Jarocinski M., Smets F. R. (2008) “House prices and the stance of monetary policy.”
Federal Reserve Bank of St. Louis Review, July: 339-366
Jiménez G., Ongena S., Peydró J. L., Saurina J. (2012) “Credit Supply and Monetary
Policy: Identifying the Bank Balance-Sheet Channel with Loan Applications.”
American Economic Review. 102(5): 2301-2326
Jiménez G., Ongena S., Peydró J. L., Saurina J. (2014) “Hazardous Times for
Monetary Policy: What Do TwentyThree Million Bank Loans Say About the
Effects of Monetary Policy on Credit RiskTaking?” Econometrica. 82(2): 463-505
Jung T., Teranishi Y., Watanabe T. (2005) „Optimal Monetary Policy at the ZeroInterest-Rate Bound”, Journal of Money, Credit and Banking 37(5): 813-835
Kannan P, Scott A., Terrones M. E. (2013) “From recession to Recovery: How Soon
and How Strong?” in: Claessens S. et al. [eds.] (2013a)
Klein P. (2000) „Using the Generalized Schur Form to Solve a Multivariate Linear
Rational Expectations Model”, Journal of Economic Dynamics and Control 24:
1405-1423.
Kobayashi K. (2007) “Payment Uncertainty and the Productivity Slowdown.”
Macroeconomic Dynamics. 11(2): 231-248
42
42
Narodowy Bank Polski
References
Laeven L., Valencia F. (2013) “Systemic Banking Crisis.” in: Claessens S. et al.
[eds.] (2013)
Lazear E., Spletzer R. (2012) “Hiring, Churn and the Business cycle.” American
Economic Review. 102(3): 575-79
Levin A., Lopez-Salido D., Nelson E., Yun T. (2010) “Limitations on the
Effectiveness of Forward Guidance at the Zero Lower Bound.” International
Journal of Central Banking 6(1): 143-189
Maddaloni A., Peydró J. L. (2013) ”Monetary Policy, Macroprudential Policy, and
Banking Stability: Evidence from the Euro Area" International Journal of Central
Banking. 9(1): 121-169
Meltzer A. H. (2014) “Slow Recovery with Low Inflation.” Book Chapters, in: Baily
M. N., Taylor J. B. (ed.), Across the Great Divide: New Perspectives on the
Financial Crisis. Chapter 8. Stanford: Hoover Institution, Stanford University
Mian A., Sufi A. (2011) “House Prices, Home Equity-Base Borrowing, and the U.S.
Household Leverage Crisis.” American Economic Review. 101(5): 2132-2156
Nakov A. (2008) “Optimal and simple monetary policy rules with zero floor on the
nominal interest rate.” International Journal of Central Banking. 4(2): 73-127
Nishimura K., Nakajima T., Kiyota K., (2005) “Does the natural selection
mechanism still work in severe recessions? Examination of the Japanese economy in
the 1990s.” Journal of Economic Behavior and Organization, 58(1), 53-78
Peek J., Rosengren E. S. (2005) “Unnatural selection: perverse incentives and the
misallocation of credit in Japan” American Economic Review 95(4): 1144-1166
R3 (2013) Are zombies really attacking the UK economy? London: Rescue,
Recovery, and Renewal (Association of Business Recovery Professionals)
Reinhart C. M., Reinhart V. R., Rogoff K. S. (2012) “Public Debt Overhangs:
Advanced-Economy Episodes Since 1800.” Journal of Economic Perspectives.
26(3): 69–86
Rajan R. G. (2005) “Has financial development made the world riskier?” NBER
Working Papers. 11728
Schmitt-Grohé S., Uribe M. (2010) “Liquidity Traps: An Interest-Rate-Based Exit
Strategy”. NBER Working Paper. 16514
43
NBP Working Paper No. 215
43
Schmitt-Grohé S., Uribe M. (2012) “ The Making Of A Great Contraction With A
Liquidity Trap and A Jobless Recovery.” NBER Working Paper. 18544
Sekine T., Kobayashi K., Saita Y. (2003) “Forbearance Lending: The Case for
Japanese Firms”. Monetary and Economic Studies. 21(2): 69-92
Simons H. C. (1936) “Rules Versus Authorities in Monetary Policy.” Journal of
Political Economy. 44(1): 1-30
Smets F., Wouters R. (2002) „Openness, imperfect exchange rate pass-through and
monetary policy”, Journal of Monetary Economics 49: 947-981.
Smets F., Wouters R. (2003) „An estimated Dynamic Stochastic General
Equilibrium model of the euro area”, Journal of the European Economic Association
1(5): 1123-1175.
Smets F., Wouters R. (2007) “Shocks and Frictions in US Business Cycles: A
Bayesian DSGE Approach.” American Economic Review. 97(3): 586-606
Stock J. H., Watson M. W. (2012)”Disentangling the Channels of the 2007-09
Recession” Brookings Papers on Economic Activity. 44(1): 81-156
Summers L. (2014) “U.S. Economic Prospects: Secular Stagnation, Hysteresis, and
the Zero Lower Bound.” Business Economics. 49(2): 65-73
Summers L. H. (2015) “Demand Side Secular Stagnation.” American Economic
Review. Papers and Proceedings. 105(5): 60-65
Taylor A. M. (2012) “The Great Leveraging.” NBER Working Paper. 18290
Taylor J. B. (2009), Getting off track: How government actions and interventions
caused, prolonged, and worsened the financial crisis, Stanford: Hoover Institution
Press
Taylor J. B. (2014) “Causes of the Financial Crisis and the Slow Recovery: A TenYear Perspective,” Book Chapters, in: Baily M. N., Taylor J. B. (ed.), Across the
Great Divide: New Perspectives on the Financial Crisis. Chapter 3. Stanford:
Hoover Institution, Stanford University
Walsh C. E. (2009) “Using monetary policy to stabilize economic activity”. Paper
prepared for the Jackson Hole Symposium on Financial Stability and
Macroeconomic Policy. May 18
44
44
Narodowy Bank Polski
References
White W. R. (2010) “The Mayekawa Lecture: Some Alternative Perspectives on
Macroeconomic Theory and Some Policy Implications.” Monetary and Economic
Studies. 28(2012): 35-58
Wieland V., Wolters M. (2011) “The Diversity of Forecasts from Macroeconomic
Models of the U.S. Economy.” Economic Theory. 47(2-3): 247-292
Woodford M. (1999) „Optimal Monetary Policy Inertia”, Proceedings, Federal
Reserve Bank of San Francisco.
Woodford M. (2003) Interest and Prices. Princeton: Princeton University Press
Woodford M. (2012) “Methods of Policy Accommodation at the Interest-Rate
Lower Bound.” Paper presented at the Jackson Hole Symposium “The Changing
Policy Landscape.” August 30 – September 1
45
NBP Working Paper No. 215
45
Figures and tables
Figures and tables
Figure 1. IMF GDP forecasts generated in the years 2007-2014 and actual GDP growth path (20072013)
a: United States
b: Euro area
Source: IMF WEO database, April 2007, 2008, 2011, 2013 and 2014. Note: This figure represents
actual (solid line) and forecasted (dotted lines) GDP growth paths in the United States (a) and Euro
area (b). It shows that actual GDP dynamics was turned out to be poorer than expected. 2009, 2010
and 2012 forecasts for the United States and 2009 and 2010 forecasts for the Euro area also indicated
faster GDP growth than actually recorded. They are not included in the graph to make it easier to read
(they crossed with other forecasts).
46
46
Narodowy Bank Polski
Figures and tables
Figure 2. Recovery after the Great Recession in the United States and previous recoveries since the
second world war
a: GDP
b: Utilization of capital and labour
c: TFP
d: Capital stock
Source: NBP Economic Institute, based on Fernald (2014). Note: This figure reports cumulative
change of GDP and its main components in the United States after the Great Recession and previous
recoveries since the second world war. End of 10 recessions considered is dated in accordance with
the NBER. In particular the second quarter 2009 is taken as the end of the Great Recession. The
evaluation of utilization of capital and labor follows Basu et al. (2006 and 2013) and TFP data are
utilization-adjusted. More details on computations’ methodology are provided by Fernald (2014).The
horizontal axis represents subsequent quarters, where the end of recession is labeled as t. The vertical
axis represents log percentage cumulative change of respective variable. The solid line depicts the
Great Recession. The dotted line shows the average values while the grey area minimum and
maximum values for the previous recoveries. The respective panels shows that though recovery of the
US economy has been sluggish by historical standards (a), the utilization of labor and capital has
47
NBP Working Paper No. 215
47
been growing
been faster
growing
than
faster
overthan
previous
over previous
recoveriesrecoveries
(b). In contrast,
(b). In contrast,
growth ingrowth
productivity
in productivity
(c) and in(c) and in
capital stock
capital
(d) stock
has been
(d) has
verybeen
slow.very slow.
16
14
14
12
12
10
10
8
6
6
4
4
2
2
0
0
Source:
Bank of England.
Note:
This
figurethe
reports
the base
of the
Bank of during
Englandtheduring the
Source: Bank
of England.
Note: This
figure
reports
base rate
of therate
Bank
of England
period 1694-2009.
refer rate
to bank
(for 1694-1972),
lending
(for 1972-1981),
period 1694-2009.
Data referData
to bank
(for rate
1694-1972),
minimumminimum
lending rate
(for rate
1972-1981),
band 1rate
dealing
(for 1981-1996),
rate (for 1997-2005)
andbank
official
minmum minmum
band 1 dealing
(for rate
1981-1996),
repo rate repo
(for 1997-2005)
and official
ratebank
(for rate (for
2006-2009).
Bank
Rate, Minimum
Lending
Rate,
Repo
andBank
Official
Bank
Rate arerates.
interest rates.
2006-2009).
Bank Rate,
Minimum
Lending Rate,
Repo
Rate
and Rate
Official
Rate
are interest
The Minimum
Band 1 Rate
Dealing
Rate is discount
to the minimum
The Minimum
Band 1 Dealing
is discount
rate and rate
refersand
to refers
the minimum
publishedpublished
rate at rate at
Bank discounted
bills tomoney
relievemarket
moneyshortages
market shortages
(excluding
late assistance
and
which thewhich
Bankthe
discounted
bills to relieve
(excluding
late assistance
and
repurchase
and sale agreements).The
figure
shows
that
Great Recession
the been
rate has been
repurchase
and sale agreements).The
figure shows
that
before
thebefore
Greatthe
Recession
the rate has
2%
and itsvalue
average
value amounted
never set never
belowset
2%below
and its
average
amounted
to 5.1%. to 5.1%.
48
48
48
Narodowy Bank Polski
1991
2000
2009
8
Rate (%)
16
1694
1703
1712
1721
1694
1730
1703
1739
1712
1748
1721
1757
1730
1766
1739
1775
1748
1784
1757
1793
1766
1802
1775
1811
1784
1820
1793
1829
1802
1838
1811
1847
1820
1856
1829
1865
1838
1874
1847
1883
1856
1892
1865
1901
1874
1910
1883
1919
1892
1928
1901
1937
1910
1946
1919
1955
1928
1964
1937
1973
1946
1982
1955
1991
1964
2000
1973
2009
1982
Rate (%)
Figure 3. Figure
Bank of
3.England
Bank of base
England
rate base
in therate
period
in the
of period
1694-2009
of 1694-2009
Figures and tables
Figure 4. Interest rate, output gap and inflation under various combinations of ZLB and PLB policies:
Interest rate path
a
Output gap
0,018
0,014
0,02
0
0,01
0
-0,2
-0,4
0,006
-0,6
0,002
b
0,2
0,01
-0,002
Inflation
0
5
10
15
20
25
30
0,018
0,014
-0,01
-0,02
-0,03
-0,8
-0,04
-1
-0,05
-1,2
-0,06
0
5
10
15
20
25
30
0,2
0,02
0
0,01
c
0
5
10
15
20
25
30
0,018
0,014
d
10
15
20
25
30
0,02
0
0,01
-1,2
5
10
15
20
25
30
0,006
-0,6
0,002
0
5
10
15
20
25
30
20
25
30
0
5
10
15
20
25
30
0
5
10
15
20
25
30
-0,04
-0,05
0
5
10
15
20
25
30
-0,06
0,02
0,01
0
-0,01
-0,02
-0,03
-0,8
-0,04
-1
-0,05
-1,2
15
-0,03
-0,2
-0,4
10
-0,02
0
0,01
5
0
0,2
0,014
0
-0,01
-1
0
-0,06
0,2
-0,8
0,018
-0,002
5
-0,6
0,002
-0,002
0
-0,4
0,006
30
-0,05
-0,2
0,01
25
-0,04
-1
-1,2
20
-0,03
-0,8
-0,002
15
-0,02
-0,6
0,002
10
-0,01
-0,4
0,006
5
0
-0,2
0,01
0
0
5
Zero lower bound (ZLB)
10
15
20
25
30
-0,06
Positive lower bound (PLB) = 0.02/4
Source: Authors. Note: This figure compares the model’s results for interest rate, output gap and inflation.The
vertical axis represents the steady state value of respective variable for t=0 and then their deviation from the
steady state. The horizontal axis depicts the quarters. Four combinations of ZLB and PLB policies varying in
terms of their credibility are considered: (a) ZLB and PLB under discretion; (b) ZLB and PLB under
49
NBP Working Paper No. 215
49
commitment;commitment;
(c) ZLB under
(c) ZLB
discretion
underand
discretion
PLB under
and PLB
commitment;
under commitment;
(d) ZLB under
(d) ZLB
commitment
under commitment
and PLB and PLB
under discretion.
under discretion.
Figure 5. Output
Figure
gap
5. in
Output
the United
gap inStates
the United States
8
6
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
1947
1949
1951
1953
1955
1947
1957
1949
1959
1951
1961
1953
1963
1955
1965
1957
1967
1959
1969
1961
1971
1963
1973
1965
1975
1967
1977
1969
1979
1971
1981
1973
1983
1975
1985
1977
1987
1979
1989
1981
1991
1983
1993
1985
1995
1987
1997
1989
1999
1991
2001
1993
2003
1995
2005
1997
2007
1999
2009
2001
2011
2003
2013
2005
2015
2007
2009
2011
2013
2015
8
Recessions as announced
Recessionsby
as the
announced
NBER by the NBER
Output gap (% Output
of potential
gap (%
output)
of potential output)
Source: NBP
Source:
Economic
NBP Institute,
Economicbased
Institute,
on data
based
from
on BEA
data and
fromCBO.
BEA Note:
and CBO.
This figure
Note: This
presents
figure presents
output gap in
output
the United
gap inStates
the United
over q1
States
1949:
over
q1q1
2015.
1949:
It is
q1expressed
2015. It isinexpressed
% of potential
in % of
output.
potential
Dataoutput. Data
on potential on
output
potential
and GDP
output
areand
taken
GDP
from
are CBO
takenand
from
BEA
CBO
respectively.
and BEA respectively.
Data on GDP
Data
for on
q1 GDP
2015 for
is q1 2015 is
its second estimate.
its second
Grey
estimate.
areas represent
Grey areasrecessions
representasrecessions
announced
as by
announced
the NBER.
by the
TheNBER.
figure shows
The figure shows
that output gap
that closing
output gap
afterclosing
the Great
afterRecession
the Greathas
Recession
been slower
has been
than slower
after any
than
previous
after any
recession
previous recession
after the second
afterworld
the second
war. Note
worldthat
war.
this
Note
slowdown
that thishas
slowdown
taken place
has in
taken
spiteplace
of a in
clear
spite
deceleration
of a clear deceleration
of
of
potential output
potential
growth.
output
Since
growth.
the end
Since
of the
theGreat
end ofRecession
the Greatpotential
Recession
output
potential
has been
output
growing
has been
on growing on
average by 1.3%
average
perby
year,
1.3%
while
per over
year,previous
while over
recoveries
previousitsrecoveries
average growth
its average
amounted
growthtoamounted
3.2%. to 3.2%.
50
50
50
Narodowy Bank Polski
Figures and tables
Figure 6. Comparison of loss function values between PLB and ZLB.
a
b
0,03
0,007
0,006
0,025
0,005
0,02
0,004
0,015
0,003
0,01
0,002
0,005
0
c
0,001
0
0
0,1
0,2
0,3
0,4
0,03
0,5

0,6
0,7
0,8
0,9
d
0
0,1
0,2
0,3
0,4
0
0,1
0,2
0,3
0,4
0,007
0,5

0,6
0,7
0,8
0,9
0,006
0,025
0,005
0,02
0,004
0,015
0,003
0,01
0,002
0,005
0
0,001
0
0
0,1
0,2
0,3
0,4

0,5
0,6
0,7
0,8
0,9
Loss function value at PLB = 0.02/4 and different ρ
0,5

0,6
0,7
0,8
0,9
Loss function value for ZLB and ρ = 0.8
Source: Authors. Note: This figure reports loss function values for PLB = 0.02/4 and different autocorrelation
coefficient (ρ) of a schock to natural interest rate. The values are compared with loss function value
calculated for ZLB and baseline ρ=0.8. The vertical axis represents loss function while horizontal axis
autocorrelation coefficient (ρ). The lowest value of ρ covered by the grey area represents the lowest value of
this coefficient considered in the literature on the ZLB, while the highest value equals the baseline calibration
in the paper. Four combinations of ZLB and PLB policies varying in terms of their credibility are considered:
(a) ZLB and PLB under discretion; (b) ZLB and PLB under commitment; (c) ZLB under discretion and PLB
under commitment; (d) ZLB under commitment and PLB under discretion.
51
NBP Working Paper No. 215
51
Figure 7. Line of equivalent loss under PLB:
-0,02
b
-0,06
-0,06
-0,08
-0,08
1
-0,04
-0,1
-0,1
-0,12
-0,12
-0,14
-0,14
-0,16
-0,16
0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9

-0,02
d

-0,06
-0,06
-0,08
-0,08
1
-0,04
-0,1
-0,1
-0,12
-0,12
-0,14
-0,14
-0,16
0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9
-0,02
-0,04
1
c
-0,02
-0,04
1
a
-0,16
0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9

0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9

Baseline parameters (1=-0.05 and 
Line of loss function equivlance
Source: Authors. Note: This figure reports combinations of 1 and ρ which produce equal values of
the loss function for PLB=0.02/4 (calculated for a given combination of 1 and ρ) and for ZLB
(calculated for baseline combination. 1=-0.05 and =0.8). The given combination equalize
possible costs of faster restructuring due to PLB policy (as compared to ZLB case) with possible
gains stemming from faster shock absorbtion (faster return of natural interest rate to its steady state
level). The costs are expressed in terms of initial shock to natural interest rate and are shown as the
difference beetwen baseline 1=-0.05 (solid line) and 1 value for a given  (dotted line). Four
combinations of ZLB and PLB policies varying in terms of their credibility are considered: (a)
ZLB and PLB under discretion; (b) ZLB and PLB under commitment; (c) ZLB under discretion
and PLB under commitment; (d) ZLB under commitment and PLB under discretion.
52
52
Narodowy Bank Polski
Figures and tables
Figure 8. Comparison of loss function values between PLB and ZLB. Robustness check.
a
0,02
0,0008
0,016
0,0006
0,012
0,0004
0,008
0,0002
0,004
0
c
b
0,001
0
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
0,0002
0,00016
0,00012
0,00008
0,00004
0
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
Loss function value at PLB = 0.02/4 and different ρ
Loss function value for ZLB and ρ = 0.8
Source: Authors. Note: This figure reports loss function values for PLB = 0.02/4 and different
autocorrelation coefficient (ρ) of a schock to natural interest rate. The values are compared with
loss function value calculated for ZLB and baseline ρ=0.8. The vertical axis represents loss
function while horizontal axis autocorrelation coefficient (ρ). The lowest value of ρ covered by the
grey area represents the lowest value of this coefficient considered in the literature on the ZLB,
while the highest value equals the baseline calibration in the paper. Four combinations of ZLB and
PLB policies varying in terms of their credibility are considered: (a) ZLB and PLB under
discretion; (b) ZLB and PLB under commitment; (c) ZLB under discretion and PLB under
commitment. The combinations are calibrated as follows. In the case (a) potential GDP growth rate

  ) is assumed at 4%, trend inflation () at 4%, Frisch elasticity of labour supply () at 5,
(
elasticity of substitution between goods varieties () at 10, Calvo probability () at 0,9. In the case


  is assumed at 4%,  at 4%,  at 5,  at 1,1,  at 0,4. In the case (c) 
  is
(b) 
assumed at 4%, at 4%,  at 0,1,  at 10,  at 0,9. Parameter values are selected so as to get a
highly reduced value of break-even ρ. The combination (d) (where ZLB policy is under
commitment while PLB policy is discretionary) is not analyzed because it implies already under
the baseline calibration the break-even ρ out of the range considered in the literature on the ZLB
(cf. Figure 7, panel (d)).
53
NBP Working Paper No. 215
53
Table 1. Baseline
Tablecalibration
1. Baseline
ofcalibration
the model’sofparameters
the model’sused
parameters
in the simulations
used in the simulations
Parameter Parameter
Value
Value Source
Source
Woodford (1999)
Woodford (1999)

 

Woodford (1999)
Woodford (1999)

 


Woodford
(1999)
Woodford (1999)

  

Smets and Wouters
Smets (2003)
and Wouters (2003)

   

Smets and Wouters
Smets (2003)
and Wouters (2003)




Smets and Wouters
Smets (2002)
and Wouters (2002)

 

implied from implied
other parameter
from other
values
parameter
and Woodford
values and
(1999)
Woodford (1999)

 

Adam and Billi
Adam
(2006,
and2007)
Billi (2006, 2007)

 

Levin et al. (2010)
Levin et al. (2010)

 




based on Penn’s
based
World
on Penn’s
TablesWorld Tables


  



Authors
Authors

 

PLB
PLB 
Authors
Authors

Source: Authors
Source: Authors
Table 2. Sensitivity
Table 2.
of Sensitivity
break-evenofbreak-even
to changes 
in to
thechanges
persistence
in theand
persistence
size of shock
and size
to natural
of shock
interest
to natural interest
rate
rate
Panel A
Panel
used A
in ZLB used in ZLB
0,5
0,55 0,5 0,6 0,550,65 0,6 0,7
0,65 0,750,7
0,8
0,75 0,850,8
0,9
0,85
model
model (1,000) (1,159)(1,000)
(1,357)
(1,159)
(1,609)
(1,357) (1,943)
(1,609) (2,409)
(1,943) (3,106)
(2,409) (4,265)
(3,106) (6,579)
(4,265)
(a)
ZLB and PLB
Break(a) ZLB and
0,324
PLB 0,3770,324
0,4750,377
0,5330,475 0,605
0,533 0,667
0,605 0,737
0,667 0,803
0,737 0,868
0,803
under
under discretion
even discretion
(0,615) (0,711)
(0,615)
(0,931)
(0,711)
(1,102)
(0,931) (1,379)
(1,102) (1,712)
(1,379) (2,271)
(1,712) (3,159)
(2,271) (4,896)
(3,159)
Breakeven 
(b) ZLB and PLB
(b) ZLB and
PLB 0,3390,257
0,257
0,4160,339
0,4930,416 0,565
0,493 0,637
0,565 0,708
0,637 0,779
0,708 0,85
0,779
under commitment
under commitment
(0,510) (0,641)
(0,510)
(0,790)
(0,641)
(0,980)
(0,790) (1,214)
(0,980) (1,537)
(1,214) (2,007)
(1,537) (2,775)
(2,007) (4,265)
(2,775)
(c) ZLB under(c) ZLB under
0,649 0,6840,649
0,7440,684
0,7970,744 0,851
0,797
discretion anddiscretion
PLB
and
PLB
(1,603) (1,825)
(1,603)
(2,344)
(1,825)
(3,055)
(2,344) (4,296)
(3,055)
under commitment
under commitment
(d) ZLB under(d) ZLB under
0,22
commitment and
commitment and
(0,458)
PLB under PLB under
discretion discretion
Panel B
Breakeven 
Panel
in ZLBand
used in ZLB and
 used B
-0.02 -0.03-0.02-0.04-0.03-0.05-0.04 -0.06
-0.05
PLB
PLB
0,994
(6,720)
(4,296) (14,091)
(6,720)(115,178)
(14,091)
(115,178)
0,868
(4,896)
0,85
(4,265)
0,308
0,22 0,421
0,308 0,512
0,421 0,605
0,512
0,605
(0,589)
(0,458) (0,801)
(0,589) (1,035)
(0,801) (1,379)
(1,035)
(1,379)
-0.06
-0.07
-0.07
-0.08
-0.08
-0.09
-0.1
-0.09
-0.1
(a)
ZLB and PLB
Break(a) ZLB and PLB 0,628
under
under discretion (1,490)
even discretion
0,7110,628
0,7370,711 0,749
0,737 0,757
0,749 0,762
0,757 0,766
0,762 0,769
0,766
0,769
(2,032)
(1,490)
(2,271)
(2,032) (2,398)
(2,271)
(2,639)
(c) ZLB under(c) ZLB under
0,8
discretion anddiscretion
PLB
and PLB(3,106)
under commitment
under commitment
0,843 0,80,920,843 0,952
0,92 0,969
0,952 0,982
0,969 0,992
0,982 0,999
0,992
0,999
(4,059)
(3,106)
(8,313)
(4,059)(14,091)
(8,313) (22,011)
(14,091) (38,161)
(22,011) (86,296)
(38,161)(692,801)
(86,296)
(692,801)
(b) ZLB and PLB
(b) ZLB and PLB 0,549
under commitment
under commitment(1,156)
(d) ZLB under(d) ZLB under
commitment and
commitment and
PLB under PLB under
discretion discretion
(2,490)
(2,398) (2,550)
(2,490) (2,600)
(2,550) (2,639)
(2,600)
0,6680,549
0,7080,668 0,729
0,708 0,742
0,729 0,751
0,742 0,757
0,751 0,762
0,757
0,762
(1,718)
(1,156)
(2,007)
(1,718) (2,193)
(2,007)
(2,550)
(2,323)
(2,193) (2,421)
(2,323) (2,490)
(2,421) (2,550)
(2,490)
0,347
0,4210,347 0,445
0,421 0,449
0,445 0,453
0,449 0,456
0,453 0,459
0,456
0,459
(0,655)
(0,801)
(0,655) (0,856)
(0,801)
(0,890)
54
54
0,902
0,851 0,952
0,902 0,994
0,952
0,9
(6,579)
(0,866)
(0,856) (0,875)
(0,866) (0,883)
(0,875) (0,890)
(0,883)
54
Narodowy Bank Polski
Figures and tables
Table 3. Robustness check of the findings to changes in the model’s calibration
Panel A
0
0.01
0.02
   (baseline: )
Break(a) ZLB and PLB under discretion
0.737 0.737 0.737
even 
(b) ZLB and PLB under commitment
0.709 0.709 0.708
(c) ZLB under discretion and PLB under
0.957 0.955 0.952
commitment
(d) ZLB under commitment and PLB
0.427 0.424 0.421
under discretion
Panel B
Breakeven 
Panel C
Breakeven 
Panel D
Breakeven 
Memo
Panel E
Breakeven 
0.03
0.04
0.736
0.733
0.707
0.706
0.949
0.947
0.418
0.415
0.02
0.03
0.04
(a) ZLB and PLB under discretion
0.737
0.732
0.722
(b) ZLB and PLB under commitment
(c) ZLB under discretion and PLB under
commitment
(d) ZLB under commitment and PLB
under discretion
0.708
0.703
0.696
0.952
0.932
0.908
0.421
0.408
0.38
0.1
0.25
0.5
1
2
3
5
(a) ZLB and PLB under discretion
0.737
0.737
0.737
0.736
0.736
0.736
0.735
(b) ZLB and PLB under commitment
(c) ZLB under discretion and PLB under
commitment
(d) ZLB under commitment and PLB
under discretion
0.712
0.708
0.702
0.692
0.675
0.658
0.621
0.935
0.952
0.969
0.985
0.997
0.469
0.421
0.356
0.274
0.1
1.1
2
3
5
10
100
(a) ZLB and PLB under discretion
0.741
0.739
0.738
0.737
0.735
0.732
0.735
(b) ZLB and PLB under commitment
(c) ZLB under discretion and PLB under
commitment
(d) ZLB under commitment and PLB
under discretion
Implied lambda
0.547
0.69
0.702
0.708
0.714
0.72
0.725
0.977
0.952
0.908
0.842
0.817
0.212
0.323
0.421
0.504
0.587
0.572
0.747
0.039
0.016
0.008
0.003
0.001
0.00001
0.4
0.5
0.6
0.7
0.8
0.9
0.743
0.743
0.741
0.738
0.735
0.731

 (baseline: )
(baseline: )
(baseline: )
(baseline: 0 )
(a) ZLB and PLB under discretion
(b) ZLB and PLB under commitment
0.661 0.674 0.688 0.702 0.714 0.722
(c) ZLB under discretion and PLB under
0.983 0.908 0.811
commitment
(d) ZLB under commitment and PLB
0.303 0.505 0.617
under discretion
Source: Authors. Note: This table displays the values of autocorrelation coefficient of a schock to
natural interest rate which equalizes loss function for PLB=0.02/4 and ZLB (break-even).
Simulations for other PLB’s values from the range from 0 to 2% are available upon request.


Respective panels show break-even  calculated for variuos potential GDP growth rates (

 from 0.0 to 0.04 as indicated by the table header of panel A), trend inflation (from 0.02 to 0.04
as indicated by the table header of panel B), Frisch elasticity of labour supply (from 0.1 to 5 as
55
NBP Working Paper No. 215
55
indicated by the table header of panel C), elasticity of substitution between goods varieties (from
0.1 to 100 as indicated by the table header of panel D) and Calvo probability (from 0.4 to 0.9 as
indicated by the table header of panel E). For each of the cases four types of ZLB and PLB policies
are concidered varying in terms of their credibility (as described by a-d). Lack of value for particular
crossection indicates that break-even  in this case would have to be lower than 0 or higher than 1 in
order to equalize PLB and ZLB loss function.
56
56
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www.nbp.pl