Bank of England Page 1
Expectations, lags, and the
transmission of monetary
policy - speech by
Catherine L. Mann
Given at the Resolution Foundation
23 February 2023
Bank of England Page 2
Speech
1. Introduction
Economists often reference the ‘long and variable’ lags of monetary policy, first introduced
by Milton Friedman in 1961. In the central banking world, 18 to 24 months is often quoted
as how long it takes for changes in monetary policy to feed through to inflation, even as
certainly this effect accumulates over that timeframe. Although this has by now become a
sort of folk wisdom, the economic and policy environment over the past few years has
prompted me to re-examine these long and variable lags.
As I’ve noted in numerous previous speeches
1
, the speed and magnitude of monetary
transmission depends on the underlying structure of the economy, shocks the economy
faces, and on the behaviour of financial markets, firms and households. Monetary
transmission will change when the economy and the economic environment changes.
Empirical estimates of the effect of monetary policy on macroeconomic aggregates are
strictly speaking only valid in-sample – unless we believe that the structure of the economy
has not changed in a way that would invalidate our estimates.
We have been raising Bank Rate for more than a year now and by 390 basis points in
total. Should we have seen more of an effect on the real economy and inflation already?
Perhaps the ‘long and variable’ lags are influenced by how monetary policy is transmitted
through financial markets or via the expectations of participants in the real economy.
Certainly the sequence of shocks that we have encountered must also matter.
In the following examination of the a) data and research, b) presentation of a new financial
conditions index, and c) modelling of sequential shocks and expectations in a theoretical
model, I will argue that 1) financial markets have absorbed a substantial degree of the
tightening to date; 2) that the sequence of shocks and embedding of inflation risks a
troubling change in expectations formation via an increase in the share of
backward-looking participants in the real economy; which 3) risks a worse inflation and
output outcome in the longer term. This leads me to my conclusion that further tightening
and sooner rather than later likely is needed to ensure the effectiveness of monetary policy
to achieve the objective of 2% sustainably in the medium term.
1
See Mann, 2022a and 2022b.
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2. What is the transmission mechanism?
To structure the content of this speech, let me start with ‘the monetary transmission
mechanism’. The Bank’s Monetary Policy Committee uses a single interest rate –
Bank Rate – that affects only a narrow set of financial institutions.
2
How does that narrow
conduit affect the behaviour of households and firms, and ultimately output and prices in
the economy? Central banks rely on financial markets to pass through their policy choices
in a way that is consistent with their intended consequences, alongside the role for
expectations. Households and firms then react to these changed financial conditions and
in light of their own expectations, which subsequently affects output and prices.
Chart 1 shows a stylised representation of the main channels through which monetary
policymakers expect changes in policy rates to transmit through the economy. The
effectiveness of monetary policy is influenced by the functioning of these individual
channels, and the interactions between them, denoted by the arrows.
2
Of course, we also have conducted Quantitative Easing and engaged in forward guidance in order to
influence risk-free rates further along the yield curve but these are less direct policy tools. Our main
monetary policy instrument at the moment is certainly Bank Rate.
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Chart 1: Stylised representation of the main channels of the
monetary policy transmission mechanism
Source: Adapted from ECB (n.d.) ‘Transmission mechanism of monetary policy’.
Factors outside of the central bank’s control and interactions among the channels can
amplify or dampen the pass-through of any given policy choice. I’d like to highlight several
stages through which the transmission mechanism works in each of the following sections
of this speech.
The first stage comprises the transmission from a change in the policy rate through
financial markets. The overall transmission mechanism is often summarised in a ‘financial
conditions index’. But, as with many other cases of aggregation, it is important to look
under the bonnet for where changes in the policy rate feed through to specific financial
market variables, such as the exchange rate, the interest rates that firms and households
face, as well as other asset prices. Changes in the policy rate don’t transmit
Bank rate
Shocks outside
the control of the
central bank
Changes in risk
preferences
Changes in the
global economy
Changes in fiscal
policy
Changes in
commodity
prices
Expectations
Money market
interest rates
Money &
credit
Asset prices
and risk
premia
Exchange
rate
Wage and
price-setting
Supply and
demand in goods
and labour markets
Domestic
prices
Import
prices
Price developments
Stage 1:
transmission
through
financial
markets
Stage 2:
transmission
to the real
economy
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instantaneously though, but rather at different speeds to different financial market
variables, which is one source of lags in monetary policy.
The second stage of the transmission mechanism describes the pass-through of changes
in financial conditions to the real economy, through the price-setting decisions of firms,
wage negotiation behaviour of firms and households, as well as their spending, saving,
and investment decisions. This is the stage in the transmission mechanism where lags
arguably are most obvious because of agents’ partial attentiveness and the staggered
nature of contracts, among other factors. Prices and wages are influenced by, and may
spill back into demand and supply, and labour markets.
But to start the transmission process, a tightening in financial conditions should mean
households cut back on consumption as the cost of borrowing rises, and the opportunity
cost of spending increases as saving rates rise. Firms may reduce investment, both in
response to rising borrowing costs, and in anticipation of worsening demand conditions.
Conditional on their pricing power and debt conditions, they may reduce prices or hold off
on increasing them in order to preserve their market share, or they may even increase
them to try to preserve cash flow.
Expectations – that is expectations of everything: policy, prices, demand, supply –
influence both financial and real-side channels but with different lags and with different
degrees of forward- versus backward-looking assessments of the current data and the
future. An often underappreciated feature of macroeconomics is that expectations about
the future can influence the present.
3
Expectations can affect wages and prices directly,
possibly before demand and supply conditions in goods and labour markets have changed
(Mann, 2022b).
However, there are also shocks, illustrated on the right-hand side of this diagram, that are
outside of the control of a central bank and can influence the key channels of the
transmission mechanism. These include for instance changes in fiscal policy, trade
linkages in the global economy, commodity prices, and risk preferences. In recent years,
economies and central banks across the world have faced a series of these shocks, which
most probably have influenced the long and variable lags – that is the effectiveness – of
how changes in Bank Rate affect the real economy and inflation.
3
In this current framework, in which central banks try to explain, as best as they can, the aim of and
reasoning for their policy choices, the stance of monetary policy is as much about Bank Rate today as it is
about Bank Rate tomorrow. Or even, as Woodford (2005) put it: “Not only do expectations about policy
matter, but, at least under current conditions, very little else matters.”
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3. The transmission of monetary policy through financial markets
In the next few minutes, I would like to focus entirely on the first stage of the transmission
mechanism, the transmission of monetary policy through financial markets.
Chart 2 shows the level of Bank Rate compared to a so-called “shadow rate”
(Wu & Xia, 2016). This shadow rate can be thought of as showing the unobserved level of
the short rate that could prevail, taking into account the effects of the policy rate as well as
of unconventional monetary policy tools. Since the Global Financial Crisis (GFC), central
banks have employed a range of conventional und unconventional monetary policy tools.
So far, I have only focused on the transmission mechanism of Bank Rate, which has been
the MPC’s active policy tool. The use of forward guidance and quantitative easing (QE) are
unconventional tools that were essential to the easing of the monetary stance while the
policy rate was restricted by its effective lower bound, but these may work through different
channels.
4
Chart 2: Wu-Xia shadow rate and Bank Rate
Source: Wu and Xia (2020) and Bank of England. Notes: The orange dotted line constrains the shadow rate
to the level of Bank Rate as suggested by the authors. Latest observation: February 2023.
4
For more information on QE and its transmission channels, see Busetto et al. (2022).
-10
-8
-6
-4
-2
0
2
4
6
8
10
94 98 02 06 10 14 18 22
Percent
Bank Rate
Wu-Xia shadow rate
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As a first step to assess the effectiveness of the monetary transmission mechanism, a
policymaker needs to understand how accommodative or tight the monetary stance is.
This is not as straightforward to determine in light of the unconventional tools and the
time-varying nature of r*. For a variety of reasons, the policy rate alone does not always
provide an accurate read on the monetary policy stance.
5
Over the last year and a half, monetary conditions have tightened significantly over a short
period of time, in response to the MPC’s Bank Rate increases. But, are the conditions
tight? Not just the speed and size of tightening matter here, but the starting point does
too. The MPC started tightening from what was a record-accommodative policy stance due
to the Bank’s response to the Covid-19 pandemic.
There is an obvious question on the interpretation of this shadow rate: Should monetary
policy stance be judged by the level or the change? Which one (or both) matter for overall
financial conditions and the real economy? To make an assessment on the level, you
would need a relevant reference point. Is an historical average a good reference point,
given the ‘structural break’ present in the data around the GFC? Compared to historical
average, the monetary stance is still loose. Compared to a post-GFC period, monetary
stance is tighter. But research also finds that the extent to which monetary policy affects
inflation depends on thresholds: that is, tightening from a loose stance has less of an effect
on inflation than tightening from a tight stance (Calza and Sousa, 2005).
Turning to a key part of the transmission mechanism – household debt-servicing costs.
Chart 3 shows the levels of mortgage rates at 2-year and 5-year horizons, alongside
maturity-matched OIS reference rates. The difference between mortgage rates (in the
dotted lines) and the maturity-matched OIS rate (in solid lines) is referred to as the
mortgage spread. Up until the GFC, mortgage and reference rates co-moved closely – a
relationship that broke down in the financial crisis. Spreads widened as reference rates fell
in response to falling policy rates and QE. But mortgage rates fell only very slowly over the
next decade, and never recovered the level of pre-crisis spreads. This is evidence, at least
over the sample period we are looking at, of lagged pass-through from changes in policy
rates to the rates households face on their mortgages.
5
Typically, shadow rates in the literature are constrained to be near or equal to the level of the policy rate
when it is above its effective lower bound (ELB). This made sense when the goal was to measure the easing
effect of unconventional monetary policy. Arguably, however, also in times when the policy rate is far above
the ELB, it is not a clean measure of the monetary policy stance. See for example Choi et al. (2022) who
construct a less restrictive measure of the monetary policy stance for the US.
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Chart 3: Mortgage rates and OIS rates
Solid lines show OIS rates, and dotted lines the maturity-matched 75% LTV
mortgage rates
Source: Bank of England, Bloomberg Finance L.P, Moneyfacts and Bank calculations. Notes: For OIS data
pre-2008, a Gilt-OIS spread is applied to the equivalent-maturity gilt yield data. Data is monthly until July
2018, and daily thereafter. Latest observation: 7
th
February 2023.
Zooming in on the time since we started increasing Bank Rate, we see that mortgage rates
tracked reference rates quite closely, initially, on the way up. They have also somewhat
retraced their recent spike around the mini-budget turmoil of September 2022 – but not as
much as have reference rates. Interest rates spiked sooner than mortgage rates did,
reflecting again the lag in the pass-through from changes in reference rates to mortgage
rates.
It appears that pass-through from changes in risk-free rates to mortgage rates is highly
state-dependent, suggesting more rapid transmission as interest rates rise and slower
transmission as interest rates fall. Whereas the level of mortgages rates is higher than the
trough, they are about back to pre-GFC levels, and importantly, have loosened from last
autumn. Is this a tight stance for 2-year and 5-year mortgage rates? Notably, mortgage
rates are definitely looser than they were last autumn, even as Bank Rate has risen further
since.
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Turning now to the equity market, Chart 4 shows a decomposition of moves in equity
prices into underlying components through the lens of a Dividend Discount Model. The
MPC’s tightening in monetary policy has had a considerable downward effect on equity
prices over the last twelve months. This is the direction monetary policy makers would
expect the transmission mechanism to work in a hiking cycle: higher interest rates weigh
on equity prices as future earnings and cash flows are discounted using a higher discount
factor. It would also make sense that higher interest rates would signal a worsening
economic outlook to financial markets, which should dampen expected shareholder
payouts, and potentially increase risk premia.
Chart 4: Decomposition of equity price moves of the FTSE All-Share
6
Cumulative percentage changes
Source: Bloomberg Finance L.P, Tradeweb, Refinitiv Eikon and I/B/E/S from LSEG, IMF WEO and Bank
calculations. Latest observation: 1
st
February 2023.
But Chart 4 shows that, in fact, shareholder payout and most notably the equity risk
premium have made a positive contribution to equity prices since the beginning of last
year. These have outweighed the effects of monetary policy tightening through interest
rates. Shareholder payout, in aqua, captures a combination of realised cash flows to
investors, and their expectations for future payout, and is often used as a proxy for
market-implied views on the economic outlook. So, equity markets seem to have a reason
to believe the outlook has improved since the beginning of 2022, or at least some
6
The decomposition uses the Bank’s Dividend Discount Model. For more information, see Dison and Rattan
(2017).
-80
-60
-40
-20
0
20
40
60
80
Jan 22 Apr 22 Jul 22 Oct 22 Jan 23
Percent
Interest rates
Shareholder payout
Other
Equity risk premium
Cumulative change
in FTSE All-Share
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remaining elevated tail risks from the Covid period seem to have receded. This could be a
result of their forward-looking nature, that inflation is expected to fall steadily this year, or
reflective of the fact that long term interest rates are expected to be lower than short term
ones.
Either way, this chart tells an interesting story about the net effectiveness of the monetary
tightening so far. The positive contribution of a falling equity risk premium implies that an
improving outlook is not enough to explain equity performance. Indeed, it implies that
equities have performed significantly better given what we know about interest rates and
growth expectations. It seems that the MPC’s tightening efforts have been in part offset by
this risk premium.
Moving now to how global factors affect the transmission mechanism as measured by the
exchange rate. Chart 5 decomposes the moves in the Sterling-Dollar exchange rate into
contributions by monetary policy, macroeconomic factors and risks. All other things being
equal, a rise in UK interest rates should cause Sterling to appreciate relative to other
currencies – but we see a marked depreciation instead.
Chart 5: Decomposition of bilateral Sterling-Dollar exchange rate
Cumulative percentage changes
Source: Bloomberg Finance L.P, Refinitiv Eikon from LSEG and Bank calculations. Notes: For more
information on the model see Appendix A1. Latest observation: 17
th
February 2023.
The chart covers the entire MPC tightening cycle, and Sterling has depreciated by 10%
versus the Dollar. Up until the end of 2022, the contribution of US policy and
macroeconomic factors have outweighed the MPC’s tightening. This in part reflects the
Federal Reserve tightening, particularly at a quicker pace than the MPC, but also a better
-28
-24
-20
-16
-12
-8
-4
0
4
8
Jan 22 Apr 22 Jul 22 Oct 22 Jan 23
Percent
UK-specific risk-off
UK policy and macro factors
US policy and macro factors
Global risk-on
Cumulative change in GBP/USD
(solid line) and Sterling ERI (dotted)
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macroeconomic outlook in the US. More recently, the orange US bars have come off as
the Fed had been expected to reduce their pace of tightening.
On the other hand, the aqua bars, reflecting the pricing of UK policy and domestic
macroeconomic factors, have increased, suggesting that had the MPC not tightened, the
exchange rate likely would have been even weaker. Another factor weighing on Sterling,
as seen through the lens of this model, is a persistent UK-specific risk premium which
captures the reduced appetite for Sterling assets more broadly, that is, apparently,
unrelated to direct pricing of monetary policy and future macroeconomic conditions.
To summarise this section on the first stage of the transmission mechanism, Chart 6
shows a new measure of aggregate financial conditions in the UK. There are numerous
such indices which all emphasise different aspects of the transmission mechanism. In my
view, this measure is particularly useful as it was constructed by explicitly controlling for
the non-stationarity in many underlying series, so for example should not be affected by a
falling r*. Its average level should, therefore, be able to better capture a notion of “neutral”.
That said, the distinctions among the transmission channels in the decomposition should
not be considered so bright-lined given the endogeneity among the components.
Chart 6: A UK financial conditions index
7
Source: Bloomberg Finance L.P, ICE, Moneyfacts, Refinitiv Eikon from LSEG, Tradeweb and Bank
calculations. Latest observation: January 2023.
7
More information can be obtained in a forthcoming Bank Underground post and in Appendix A2.
Bank of England Page 12
This new financial conditions index implies that UK financial conditions are, at the moment,
not much tighter than on average, relative to historical standards. But, coming out of an
entire decade of short rates at the effective lower bound, and relatively loose financial
conditions, we have had to come a long way. We are left with the conundrum of to what
extent tightening or tightness matters for the transmission to the real economy and
inflation.
In my view, we have more to do. Because, as markets have looked forward to the
soon-to-be expected peak in policy rates, financial conditions have again begun to loosen.
Financial conditions are looser relative to what they might be otherwise, due to the
depreciation of Sterling and a falling equity risk premium, which have global factors
embedded in them. To me, as both the level as well as the delta matter in assessing the
effectiveness of transmission of monetary policy, this implies that the forward-looking
nature of financial markets has been absorbing some of the intended tightening, which
impact the long and variable lags of folk wisdom. Even more important is the apparently
premature loosening of conditions, given prospects for inflation formation. A topic to
which I now will turn.
4. The transmission of monetary policy to the real economy and inflation
Now that I have outlined some of the ways in which the transmission through financial
markets can be assessed, I would like to turn the focus to the second stage. The
transmission to the real economy, specifically, inflation.
Measuring the effects of the transmission of monetary policy, or more importantly the
causal effect of monetary policy on the macroeconomy and the price level is challenging.
Not least because the causality runs both ways. Monetary policy can affect the state of the
macroeconomy by changing the interest rate, changing borrowing costs in the economy,
and thereby influencing spending, investment and saving behaviour, including
expectations, wage and price setting. But through the reaction function, monetary policy
will be affected by developments in the macroeconomy: if a central bank observes high
inflation, policymakers should react by setting tighter monetary policy.
Failing to properly account for this empirical modelling challenge resulted in the famous
‘price puzzle’: Empirical models predicted that tightening monetary policy resulted in an
increase, not a decrease in inflation, at least in the short run. Sims (1992) argued this was
because policy shocks used to identify the causal effects also included the endogenous
policy responses to forecasts of future inflation. Ramey (2016) showed that identifying
monetary policy shocks to measure the transmission to macroeconomic outcomes is
Bank of England Page 13
essential in order to estimate causal effects – we require deviations from the monetary rule
to identify the response of the economy to monetary policy.
To confront this endogeneity, we need structural models to estimate the transmission of
monetary policy to the real economy and inflation. Using the results of just one empirical
model as an example, Chart 7 shows the impulse response functions to a 1 percentage
point monetary policy shock, replicated using a method adapted and extended from
Cesa-Bianchi, Thwaites and Vicondoa (2020)
8
. The authors – one of whom is now at the
Resolution Foundation – use a high-frequency identification approach to measure UK
monetary policy surprises, which they use as instruments to identify the transmission to
the real economy. The model is estimated over the entire period of inflation targeting in the
UK excluding the Covid period.
Chart 7: Impulse response functions to a 100 basis point monetary policy shock
Source: Cesa-Bianchi, Thwaites and Vicondoa (2020) and Bank calculations. Notes: sample period
1992-2019, monthly. The solid lines and shaded areas report the median and the 68% confidence intervals,
computed using moving block bootstrap with 5000 replications. For the full set of impulse responses, see
Appendix A3.
Starting by looking at the top left panel, a 100 basis point monetary policy shock has a
persistent effect on the 1-year nominal interest rate, lasting for around twelve months after
the shock hits. The top right-hand panel shows the monetary policy shock also
appreciates the Sterling exchange rate index, with a peak effect at two to three months
8
More information on methodology, and robustness checks can be obtained in Appendix A3.
-1
-0.5
0
0.5
1
1.5
2
0 4 8 12 16 20 24 28 32 36
1-year nominal interest rate
Percentage points
-4
-2
0
2
4
6
8
10
0 4 8 12 16 20 24 28 32 36
Percent
£ exchange rate index
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
0 4 8 12 16 20 24 28 32 36
Percent
GDP
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0 4 8 12 16 20 24 28 32 36
Percent
CPI
Bank of England Page 14
following the shock, consistent with the effect on the 1-year nominal interest rate. This
follows from the standard theory of interest rate differentials explaining exchange rate
movements when only the home central bank tightens.
The monetary policy shock also has a significant, delayed response on the level of real
GDP, which is consistent with the story on monetary policy lags, but also New Keynesian
theory that GDP lags inflation. Real GDP barely moves on impact, and slowly falls with a
statistically significant peak response of -1.25% after around two years – consistent with
the 18 to 24 months of the long and variable lags story. The results also suggest a
permanently negative effect of contractionary monetary policy on the level of output
relative to trend. This shouldn’t be interpreted as monetary policy scarring activity forever,
as in growth rate space, GDP recovers.
However, the lags on inflation are quite different in this simple set-up. Turning now to the
bottom right panel, the effect on the level of CPI is not only statistically significant and
negative, but also instantaneous. In the model, the fast pass-through of the monetary
tightening likely relies on the exchange rate appreciating on impact.
Of course, this is a simplified version of the world, as the impulse response functions show
the impact of a single monetary policy surprise, and only by UK policymakers, as indicated
by the role for the exchange rate in financial conditions. In reality, the economy has faced
a sequence of these shocks in the past year which have overlapped before we have seen
the full effect of any of them. And, other central banks have also been tightening policy.
Further, the period over which the model was estimated had generally low and stable
inflation. Might these results be affected a period of surging and persistently high inflation
such as we have experienced over the last 18 months? Could high inflation itself affect
the monetary transmission mechanism? Using an event study, Bank researchers show
some evidence for a direct expectations channel of monetary policy which could affect
price setting already within the period of the shock.
9
To examine these questions, I need to
turn to a different kind of model that allows us to control and vary deep parameters about
expectations formation.
9
See Di Pace et al. (2023) who analyse firm expectations in particular, and find that announced changes in
the monetary policy rate induce firms to revise their price expectations, with rate hikes inducing a decrease
in price expectations and uncertainty surrounding them.
Bank of England Page 15
5. A stylised example of forward- versus backward-looking expectations
formation and the monetary policy transmission mechanism
This section presents a so-called “toy model” in which we can vary the share of
backward-looking price-setters in the economy. At its core, it is a very simple, calibrated,
textbook New Keynesian model.
10
It is designed to capture a certain mechanism that we
are interested in but, as these models tend to do, it disregards many other features of the
real world. It shouldn’t be thought of as quantifying the behaviour of any particular real-life
economy. For example, it is not COMPASS, the Bank’s large and complex structural
model that is used, among others, in our forecasting exercise every quarter (Burgess et al,
2013). Although, as a dynamic and stochastic general equilibrium model, it does share the
underlying modelling paradigm.
This model focuses and formalises a concern that I flagged in a previous speech
(Mann, 2022b): What happens to the behaviour of macroeconomic aggregates if people
begin to form backward-looking inflation expectations? In this model, I find that, indeed, a
higher degree of “backward-lookingness” generates more inflation persistence even if the
underlying shock is the same. But, crucially, it also changes the effectiveness of monetary
policy to control inflation. A given monetary tightening has less of an effect on inflation if
expectations formation is mainly backward-looking, detached from demand and supply
conditions, which thereby worsens any inflation-activity trade-off in the face of a shock.
Stepping back from the model exercise, is there evidence that the degree of forward- and
backward-lookingness changes? In a previous speech (Mann, 2022b), I cited research
which estimated the share of forward- versus backward-looking agents using switching
forecast rules. Cornea-Madeira and Madeira (2022) show empirically that for the UK the
share of backward-looking agents has varied significantly over time, in particular being
higher when energy prices surge.
11
Returning to the model, we can trace out the response of our model economy to the same
underlying shock: a so-called cost-push shock which exogenously increases prices over
and above what would be implied by domestic demand conditions. It is, of course,
intended to stand in for the global goods price shock of 2021 or the energy price shock of
2022.
10
It is a generalisation of the model described in Chapter 3 of Galí (2015), enriched with backwards- and
forward-looking price-setters as in Galí and Gertler (1999). For more information, please see Appendix 4.
11
For a fully structural model with endogenous forecast switching, see Fischer (2022).
Bank of England Page 16
Consider Chart 8: it shows the reactions for a model economy which differs only by the
share of backward-looking price-setters.
12
The baseline, where all firms form fully
forward-looking and model-consistent expectations, is shown in the aqua line. In this
economy, the cost-push shock has a very limited and short-lived impact on activity and
prices. The output gap jumps on impact but quickly returns to zero. Because of the lagged
nature of year-on-year inflation (Mann, 2023), it peaks after four quarters and then reverts
towards target.
Chart 8: Responses to an inflationary cost-push shock, given a central bank
using a balanced Taylor Rule
Output gap (LHS) and year-on-year inflation (RHS)
Source: Bank calculations. Notes: Responses are generated using a New Keynesian model with varying
degrees of backward-looking expectations formation. For more information, see Appendix A4.
The behaviours of the output gap and inflation change dramatically when we introduce a
modest degree of backward-looking inflation expectations formation. The output gap is
more negative for longer which is mirrored in inflation peaking higher and remaining above
target for an extended period of time.
Increasing the share of backward-looking agents even more takes this pattern to the
extreme. Both output and inflation display a pronounced hump-shaped pattern and are
away from equilibrium for the entirety of the plotted period (4 years). Remember that I
12
The three lines refer to models in which the share of backward-looking firms is calibrated to be zero, 40,
and 80 percent respectively. The choice of these values, away from the fully forward-looking baseline, is
motivated by the range of the share of fundamental agents in Cornea-Madeira and Madeira (2022) which
find that for most of the last 50 years, this share has fluctuated between 20 and 80 percent with a median of
about half.
-2
-1.5
-1
-0.5
0
0.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Quarters after shock
Many backward-
looking firms
Fully forward-looking
baseline
Few backward-
looking firms
Percentage points
-2
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Quarters after shock
Many backward-
looking firms
Fully forward-looking
baseline
Few backward-
looking firms
Percentage points
Bank of England Page 17
have not changed the size of the shock – just the degree of backward-lookingness of the
firms in the economy.
These pictures also reveal an important non-linearity generated by changes in the
formation of inflation expectations. Even though I have increased the share of
backward-looking firms by equally sized increments step-by-step from aqua to orange to
purple, the change in behaviour is increasingly stark. Not only does more
backward-lookingness worsen the trade-off between inflation and output, every additional
step worsens the trade-off by more than the last.
The outcomes in the previous charts are determined also by what central banks are doing.
Chart 9 shows the nominal (left side) and real interest (right side) rates associated with the
central bank that follows a Taylor rule balanced between output and inflation deviations
from target. In the model, this trade-off is reflected in the reaction of interest rates to the
shock.
Chart 9: Responses to an inflationary cost-push shock, given a central bank
using a balanced Taylor Rule
Annualised nominal (LHS) and real interest rates (RHS)
Source: Bank calculations. Notes: Responses are generated using a New Keynesian model with varying
degrees of backward-looking expectations formation. For more information, see Appendix A4.
In the baseline case with fully forward-looking agents, the central bank raises nominal
rates on impact which, due to benign inflation dynamics is sufficient to raise the real rate,
which dampens inflation, and quickly both interest rates (and the real economy and
-2
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Quarters after shock
Many backward-
looking firms
Fully forward-looking
baseline
Few backward-
looking firms
Percentage points
-2
-1.5
-1
-0.5
0
0.5
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Quarters after shock
Many backward-
looking firms
Fully forward-looking
baseline
Few backward-
looking firms
Percentage points
Bank of England Page 18
inflation) return to baseline. In the two less benign cases, however, despite the central
bank raising the nominal rate sharply and persistently, the real rate actually falls initially.
Since it is the real rate that determines output in this model, the falling real rate adds to
inflation persistence so that, in the latter half of the simulation, the central bank must keep
restrictive real rates longer in order to stabilise the economy. In the case of many
backward-looking firms, the nominal interest rate rises even more and the restrictive real
rates last for much longer.
However, the problems of the central bank in the orange or the purple economy do not
stop there. As a result of the increased share of backward-looking firms, the speed at
which monetary policy can affect realised inflation also changes. In other words, the lags
of the monetary transmission mechanism lengthen as shown by the increasingly long
period away from the neutral line in the charts, which is particularly dramatic for the purple
economy. The share of backward-looking firms in the purple economy is 80%, which is
what Cornea-Madeira and Madeira (2022) find in their work for years when energy prices
surged.
13
Finally, given the monetary response, what happens to inflation? Chart 10 plots the
inflation response to a monetary policy shock in the three types of economies. All three
lines are indexed to yield the same amount of output losses. As shown in the appendix
(Chart A4.2), the path for output and the nominal interest rate is very similar for each
case, which implies that the monetary transmission mechanism into economic activity is
not meaningfully affected by backward-looking inflation expectations.
13
In this simple model, we abstract from the behaviour of financial conditions discussed above. In that
sense, the model here simplifies away the challenges of transmitting monetary policy through financial
markets, the focus of the first half of the speech.
Bank of England Page 19
Chart 10: Inflation responses to a contractionary monetary policy shock, given
same output costs
Year-on-year inflation
Source: Bank calculations. Notes: Responses are generated using a New Keynesian model with varying
degrees of backward-looking expectations formation. For more information, see Appendix A4.
However, what does change is the transmission of monetary policy into prices. By
construction, in the chart, the tightening yields the same outcome in activity, so we can
read the lines as a dynamic slope of the Phillips curve under conditions of changing
expectations formation.
14
An increasing degree of backward-lookingness implies a
shrinking share of price-setters in the economy that consider supply and demand
conditions when making decisions. Therefore, their importance for aggregate inflation
falls. Inflation becomes persistent because firms that set prices and generate inflation
expect it to be persistent. With a high share of backward-looking agents, monetary policy
effectiveness – whether directly on expectations or through the output gap channel – is
greatly diminished.
What does the central banker need to do when faced with these different types of
expectations formation? The model in Chart 9 shows the extent to which monetary policy
needs to be increasingly restrictive to return the inflation rate to target when agents
increasingly are backward-looking.
We have to remember that the world has been hit by a sequence of large inflationary
shocks, which have increased the risk of being in the purple world in which troubling
14
It is also related to the Phillips multiplier of Barnichon & Meesters (2021) in that it attempts to capture the
trade-off between inflation and economic activity over time.
-0.3
-0.2
-0.1
0
0.1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Percent
Quarters after shock
Many backward-
looking firms
Fully forward-looking
baseline
Few backward-
looking firms
Bank of England Page 20
non-linearities are evident. I am not saying we are at that point yet or that we will
necessarily get there given what we know now. However we need to be aware of how
important the expectations formation process is for the effectiveness of monetary policy,
and position ourselves accordingly. To reduce the risk of ending up in the ‘purple’ world,
we should weigh inflation more highly in our reaction function.
15
6. What does this all mean for monetary policy?
So, what does this all mean for monetary policy? Typically, we assume that the world is
sufficiently stable such that the estimated relationships between, for example Bank Rate
and inflation also are stable and we can look to these when deliberating monetary policy
stance – the folk wisdom of 18 to 24 months.
In this speech, I have presented state-of-the-art evidence which shows that, in normal
times, the monetary transmission into inflation is in fact faster, peaking within the first year.
But, I have also reviewed factors that may change these relationships – change the long
and variable lags – including a) that there has been a sequence of shocks, b) that the
transmission from monetary policy to financial markets has been quick, but not all in the
direction of tightening, and c) that the degree of backward- or forward-lookingness in
expectations formation influences the effectiveness of monetary policy. Going forward,
how should this reassessment of lags determine the appropriate monetary policy strategy?
Looking back to my speech from just under a year ago (Mann, 2022a), in the face of two
shocks, and given what was already in-train regarding inflation expectations and the
collected research on policy effectiveness in the face of inflation uncertainties, a greater
degree of front-loading would have reduced the risk of an increasing share of
backward-looking households and firms.
In the end, monetary policy has taken a path which has been historically aggressive, but
perhaps insufficiently so relative to the multiple shocks, the behaviours pushing up
inflation, and the initial accommodative starting point. The stage was set for a
transmission of monetary policy to financial markets that has been quick, but also has
been partially absorbed. And also, having a shorter horizon and being more
15
Indeed, in an exercise of explicitly considering overlapping shocks and monetary reaction, I evaluate the
implied paths of inflation and the output gap according to the loss function of Mark Carney’s “Lambda”
speech of 2017. In that speech, he shows how this loss function can embody society’s preferred trade-off.
Given the shocks hitting our model economy, the inflation-biased policy rule delivers a combination of output
and inflation which is superior to those of the balanced policy rule.
Bank of England Page 21
forward-looking than households and firms, markets are already incorporating the
expected future inflection in monetary stance.
Collectively, all this adds up to financial conditions that are now looser than what likely will
be needed to moderate the embedding of on-going inflation into the wage- and
price-setting paths. I worry that this constellation could yield extended persistence of
inflation into this year and the next. The resulting long period of time above the 2% target
could increase the degree of backward-lookingness, or catch-up behaviour, in the system.
Given that the risk of increasingly persistent inflation rises disproportionately with the share
of backward-lookingness, I believe that more tightening is needed, and caution that a pivot
is not imminent. In my view, a preponderance of turning points (Mann, 2023) is not yet in
the data.
We have an inflation remit, and we will achieve it one way or another. Failing to do enough
now risks the worst of both worlds – the higher inflation and lower activity of the ‘purple’
regime – as monetary policy will have to stay tighter for longer to ensure that inflation
returns sustainably back to the 2% target.
The views expressed in this speech are not necessarily those of the Bank of England or
the Monetary Policy Committee.
I would like to thank in particular Lennart Brandt and Natalie Burr, as well as
Andrew Bailey, Nicolò Bandera, Lauren Barnes, Robin Braun, Alan Castle,
Matthieu Chavaz, Ambrogio Cesa-Bianchi, Johannes Fischer, Maren Froemel,
Robert Hills, Huw Pill, Silvana Tenreyro, and Chris Yeates for their comments and help
with data and analysis.
Bank of England Page 22
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Economics, 117, pp. 689-705.
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Bank of England Page 23
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