CHAPTER 15
Interest Rates and Inflation
Troy Matheson
The conventional view among economists is that higher interest rates reduce infla-
tion. However, the prolonged period of low inflation and low interest rates in advanced
economies following the global financial crisis appears to be inconsistent with this
view. This situation has sparked a debate: do lower interest rates increase inflation (the
conventional view), or do they lead to lower inflation (the so-called Neo-Fisherian
view)? This chapter finds strong evidence in favor of the conventional view of mone-
tary policy transmission in Brazil. While lower inflation and lower nominal interest
rates can be achieved over the long term by targeting a lower level of inflation, this
outcome is likely to come at the cost of lower output (and employment) in the short
term—a cost that can be mitigated by enhancing monetary policy transparency and
credibility. Monetary policy transmission could be made more efficient by reducing
distortions and improving the allocation of resources in the financial sector.
INTRODUCTION
The conventional view among economists is that higher interest rates lead to
lower inflation. The rationale behind this view is that higher interest rates increase
the cost of borrowing and dampen demand across the economy, resulting in
excess supply and lower inflation. In this context, higher interest rates reduce
inflation through several channels, including the exchange rate channel, the credit
channel, and the bank–balance sheet channel (see Mishkin 1996). A central bank
facing the prospect of higher-than-targeted inflation would raise interest rates
enough to increase the real (inflation-adjusted) cost of borrowing, thereby reduc-
ing aggregate demand and returning inflation back toward the desired level.
Some debate has occurred about whether lower inflation can be achieved by
setting lower policy interest rates, the so-called Neo-Fisherian effect. At the heart
of the debate is a well-known equation in economics, the Fisher equation, that
relates the nominal interest rate R tto the real interest rate r t and expected inflation
E t π t+1 (all annualized):
Rt = r t + E t π t+1.
Taken at face value, and assuming that the real interest rate is fixed in the long
term, the equation implies that a lower long-term inflation rate can be achieved
by permanently setting the nominal interest rate to a lower level (see Cochrane
255
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256 Brazil: Boom, Bust, and the Road to Recovery
Figure 15.1. Headline Inflation and Policy Rate
45 Inflation (%, year over year) Interest rate (%, SELIC)
40
35
30
25
20
15
10
5
0
Jan. 11
Jan. 1998
Jan. 99
Jan. 2000
Jan. 01
Jan. 02
Jan. 03
Jan. 04
Jan. 06
Jan. 07
Jan. 08
Jan. 09
Jan. 10
Jan. 12
Jan. 13
Jan. 14
Jan. 15
Jan. 16
Jan. 17
Jan. 05
Source: Haver Analytics.
Note: SELIC = Sistema Especial de Liquidação e Custodia (Special Clearance and Escrow System).
2016). Indeed, proponents of this view often point to the positive relationship
between nominal interest rates and inflation seen across many countries as evi-
dence of Neo-Fisherian effects (see Figure 15.1).1
Would a commitment to fixing the policy interest rate to a lower level eventu-
ally lead to lower inflation? To answer this question, this chapter presents an
empirical analysis conducted to assess the impact of changes in Brazil’s policy rate
on inflation. The chapter then evaluates a simple model with long-term
Neo-Fisherian effects in the context of several countries’ historical experiences in
making the transition to lower levels of inflation. A summary of key findings and
policy conclusions rounds out the chapter.
EMPIRICAL ANALYSIS
The empirical analysis is based on vector autoregressions (VARs). The baseline
VAR is estimated using monthly data ranging from 2003 to 2016 and contains
six variables: monthly headline inflation, the nominal interest rate (Sistema
Especial de Liquidação e Custodia, or SELIC), the output gap, 12-month-ahead
inflation expectations, monthly percentage changes of commodity prices, and
monthly percentage changes of the real effective exchange rate. Inflation respons-
es to the interest rate are likely to differ across different sectors of the economy,
so in addition to the baseline VAR, five additional VARs are estimated as a robust-
ness check, including inflation for different sectors of the economy. Overall, the
1
Neo-Fisherian effects exist in standard models used by central banks under the assumption that
economic agents have perfect foresight and do not base their decisions on past observations. See
García-Schmidt and Woodford (2015) and Garín and Sims (2016).
©International Monetary Fund. Not for Redistribution
Chapter 15 Interest Rates and Inflation 257
Figure 15.2. Correlation: Headline Inflation and Interest Rate
(Correlation and 20th to 80th percentiles)
0.5
0.4
0.3
Lag interest rate→Inflation
0.2
0.1
0.0
–0.1
–0.2 Lag inflation→Interest rate
–0.3
–0.4
12 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12
Month (lag) Month (lag)
Source: IMF staff estimates.
Note: Dotted lines show 20th and 80th percentiles.
empirical analysis examines the impact of policy interest rate changes on headline
inflation, non-regulated-price inflation, regulated-price inflation, service-price
inflation, tradables inflation, and nontradables inflation.2
Cross-correlations show that higher inflation leads to higher interest rates and
higher interest rates lead to lower inflation, consistent with the conventional view.
The estimated cross-correlation function from the baseline VAR is displayed in
Figure 15.2; the results for all inflation rates can be found in Annex 15.1. The
results show a statistically significant positive relationship between past levels of
inflation and the interest rate, and a statistically significant negative relationship
between past levels of the interest rate and inflation. These results broadly reflect
the standard view of the transmission of monetary policy to inflation. Because
inflation tends to lead the policy interest rate, it appears that the central bank has
responded to inflation developments over this sample, partly as the result of
unanticipated demand and supply shocks (such as food and regulated-price
shocks, and exchange rate shocks). The results also suggest a peak correlation
between leads and lags of inflation and leads and lags of the interest rate of
about six months.
Structural VARs also support the conventional view that an unexpected cut in
the policy interest rate increases inflation in the short term. Responses of headline
inflation to a 100 basis point cut in the policy interest rate are displayed in
Figure 15.3; the results for all other inflation rates can be found in Annex 15.1.
2
VAR lag lengths are selected using the Schwarz-Bayesian Inflation Criterion. Parameter uncer-
tainty is captured in the analysis using bootstrapping methods, where for each VAR is resam-
pled 1,000 times.
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258 Brazil: Boom, Bust, and the Road to Recovery
Figure 15.3. Headline Inflation after 100 Basis Point Cut in Policy Rate
(Percent, annualized)
0.8
0.6
0.4
0.2
0.0
–0.2
–0.4
–0.6
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
Months
Source: IMF staff estimates.
Note: Dotted lines show 20th and 80th percentiles.
Here, the uncertainty about the responses relates both to uncertainty about the
parameters of the VARs and to the recursive ordering used to identify the mone-
tary policy shock.3 Examining all possible recursive identification schemes allows
the analysis to be indifferent to whether an interest rate shock has a contempora-
neous or a lagged impact on inflation. The results show that an unexpected cut
in the policy interest rate tends to increase inflation over time, with the magni-
tude of the impact dependent on the sector of the economy. The peak impact
generally occurs about nine months after the shock. The short-term impact of a
lower interest rate on inflation is less clear-cut, with identification schemes that
allow for a cut in the interest rate to immediately affect inflation (within the same
month) sometimes suggesting a positive relationship between inflation and inter-
est rate shocks. Overall, however, the results from the structural VARs strongly
support the standard view of monetary policy transmission.
HOW CAN LOWER INFLATION BE ACHIEVED
OVER THE LONG TERM?
Although little evidence suggests that a lower interest rate leads to lower infla-
tion in Brazil in the short term, the long-term Fisher equation can still help
inform policy advice. The long-term Fisher equation is
3
Each VAR contains six variables, so there are 720 different ways to order the variables to identify
shocks; 69 of these orderings lead to unique inflation responses to an interest rate shock. Using
bootstrapping methods, 1,000 parameterizations of each reduced-form model are simulated, leading
to 69,000 different estimates of the response of inflation to an interest rate for each VAR examined.
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Chapter 15 Interest Rates and Inflation 259
Figure 15.4. Simulated Responses to a Change in the Inflation Target from
4.5 Percent to 2 Percent
Output gap Inflation Policy rate
1. Forward Looking 2. Partially Forward Looking 3. Backward Looking
(Percent) (Percent) (Percent)
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
–5 –5 –5
–10 –10 –10
–8 –4 0 4 8 12 –8 –4 0 4 8 12 –8 –4 0 4 8 12
Quarters from inflation-targeting Quarters from inflation-targeting Quarters from inflation-targeting
announcement announcement announcement
Source: IMF staff calculations.
R * = r * + π *,
in which the steady-state nominal interest rate is equal to the steady-state real
interest rate plus the inflation target. Assuming the long-term neutrality of money
(that is, nominal variables do not affect real variables in the long term), the infla-
tion target determines the steady-state nominal interest rate. This relationship can
easily be inserted into a simple (and standard) New Keynesian model (see Annex
15.1).
Model-based simulations show that lower long-term inflation and nominal
interest rates can be achieved by lowering the inflation target, but this strategy is
likely to be costly in the short term when the central bank has limited policy
credibility. The results show that a reduction in the inflation target reduces both
the nominal interest rate and inflation in the long term (Figure 15.4). If house-
holds and firms in the economy have expectations that are either partially
forward-looking or entirely backward-looking, the transition to the new inflation
target requires lower output to move inflation expectations to the new target; the
real interest rate must rise to reduce demand in the short term. On the other
hand, in a purely forward-looking model the central bank is fully credible, and
households and firms fully understand the future implications of monetary policy
actions and immediately embed this knowledge in their expectations. In this case,
the transition of inflation and nominal interest rates to the new target is instan-
taneous once the target is announced, and output is unaffected.
Disinflation episodes across countries show that inflation was slow to adjust to
lower levels and the transition to lower inflation was costly to output, reflecting
unanchored inflation expectations and limited monetary policy credibility before
©International Monetary Fund. Not for Redistribution
260 Brazil: Boom, Bust, and the Road to Recovery
the disinflation. Figure 15.5 shows the behavior of inflation, interest rates, and
the output gap in the two years before the adoption of inflation targeting in the
first five countries that formally adopted the practice, in addition to the Volker
disinflation episode in the United States, beginning in 1981.4 The behavior of
inflation, interest rates, and the output gap follow broadly similar trends across
countries. Nominal interest rates and inflation rates were positively correlated and
tended to decline together once the central bank formally adopted inflation tar-
geting; output gaps generally moved into negative territory. These results are
qualitatively (and quantitatively) very similar to the simulation results obtained
when households’ and firms’ expectations for inflation and output are not
assumed to be entirely forward-looking. The large output losses during disinfla-
tion across these countries likely reflect a high degree of inflation persistence and
limited policy credibility before the adoption of inflation targeting. Changing the
inflation target would likely be less costly if the central bank had more policy
credibility and more-anchored inflation expectations before the target change.
CONCLUSIONS
There is strong evidence of the conventional view of monetary policy trans-
mission in Brazil, suggesting that a cut in the policy interest rate leads to higher
inflation in the short term. Cross-correlations show that higher inflation leads to
higher nominal interest rates, and higher interest rates result in a reduction in
inflation. Because inflation tends to lead the policy interest rate examined in the
sample, it appears that the central bank has responded to inflation developments,
partly as the result of unanticipated demand and supply shocks (such as food and
regulated-price shocks, and exchange rate shocks). Structural VARs also suggest
that an unexpected cut in the policy interest rate leads to a broad-based rise in
inflation across the sectors examined, with the peak impact on inflation occurring
about nine months after a monetary policy shock.
Model-based simulations and cross-country evidence suggest that lower infla-
tion and lower nominal interest rates can be achieved over the longer term if the
central bank commits to a lower inflation target. If households and firms base
their output and inflation expectations on the past (even partially), the transition
to the new inflation target comes at the cost of lower output in the short term,
with larger output losses and more prolonged transition periods occurring when
expectations are more backward-looking. An examination of disinflation episodes
across several countries broadly supports the key findings from model simulations
that assume that expectations were at least partially backward-looking
before disinflation.
Although permanently lowering inflation in Brazil will not be easy, a lower
inflation target could be achieved at less cost with enhanced monetary policy
4
For each country, the output gap is defined as the percentage deviation of real GDP from
a linear trend.
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Chapter 15 Interest Rates and Inflation 261
Figure 15.5. Disinflation Episodes across Countries
Output gap Interest rate Inflation
1. United States 2. New Zealand
(Percent, annual average) (Percent, annual average)
20 20
15 15
10 10
5 5
0 0
–5 –5
–10 –10
–8 –6 –4 –2 0 2 4 6 8 10 12 –8 –6 –4 –2 0 2 4 6 8 10 12
Quarters from Volker disinflation (1981) Quarters from inflation-targeting announcement
3. Canada 4. Australia
(Percent, annual average) (Percent, annual average)
20 20
15 15
10 10
5 5
0 0
–5 –5
–10 –10
–8 –6 –4 –2 0 2 4 6 8 10 12 –8 –6 –4 –2 0 2 4 6 8 10 12
Quarters from inflation-targeting announcement Quarters from inflation-targeting announcement
5. United Kingdom 6. Sweden
(Percent, annual average) (Percent, annual average)
20 20
15 15
10 10
5 5
0 0
–5 –5
–10 –10
–8 –6 –4 –2 0 2 4 6 8 10 12 –8 –6 –4 –2 0 2 4 6 8 10 12
Quarters from inflation-targeting announcement Quarters from inflation-targeting announcement
Source: IMF staff estimates.
©International Monetary Fund. Not for Redistribution
262 Brazil: Boom, Bust, and the Road to Recovery
transparency and credibility. Enhanced credibility can better anchor inflation
expectations, reduce the persistence of inflation, improve the short-term trade-off
between inflation and output, and mitigate the associated cost should a lower
inflation target be desired over the medium term. As discussed in Domit and
others (2016), there are several dimensions along which Brazil’s inflation-targeting
framework can be improved to enhance transparency and credibility, including
increasing the autonomy of the central bank and changing the inflation target
from a range that needs to be met at the end of each year to a longer-term point
target. The National Monetary Council made a step in this direction in 2016 by
narrowing the target range from 4.5 percent +/–2 percent to 4.5 percent
+/–1.5 percent beginning in 2018. In 2017, it also announced that it would
reduce the inflation target to 4.25 percent for 2019 and to 4 percent for 2020.
Monetary policy transmission could also be made more efficient by reducing
distortions and improving resource allocation in the financial sector. There is
general agreement that the effectiveness of monetary policy in Brazil could be
improved by changing various credit policies that involve earmarking and credit
subsidies. As already planned by the authorities, the gap between the subsidized
interest rate on long-term lending (Taxa de Juros de Longo Prazo, or TJLP) and
market interest rates will be reduced over time. Linking the TJLP more tightly to
a market-determined rate will enhance the transmission of SELIC changes to
longer-term interest rates, will increase the potency of a given change in the
SELIC, and could contribute to lowering interest rate volatility over the business
cycle. Improving the efficiency of resource allocation in the financial sector could
also contribute to a lower long-term real interest rate in Brazil, allowing lower
nominal interest rates for a given inflation target.5
REFERENCES
Cochrane, John. 2016. “Michelson-Morley, Occam and Fisher: The Radical Implications of
Stable Inflation at Near-Zero Interest Rates?” Working Paper, Hoover Institution,
Washington, DC.
Domit, Sílvia, Douglas Laxton, and Joannes Mongardini. 2016. “Upgrading Brazil’s Inflation-
Targeting Framework.” IMF Country Report No. 16/349, Washington, DC.
García-Schmidt, Mariana, and Michael Woodford. 2015. “Are Low Interest Rates Deflationary?
A Paradox of Perfect-Foresight Analysis.” NBER Working Paper No. 21614, National Bureau
of Economic Research, Cambridge, MA.
Garín Julio, Robert Lester, and Eric Sims. 2016. “Raise Rates to Raise Inflation? Neo-Fisherianism
in the New Keynesian Model.” NBER Working Paper No. 22177, National Bureau of
Economic Research, Cambridge, MA.
International Monetary Fund (IMF). 2016. “Upgrading Brazil’s Inflation-Targeting Framework.”
IMF Country Report No. 16/349, Washington, DC.
Mishkin, Frederic. 1996. “The Channels of Monetary Policy Transmission: Lessons for
Monetary Policy.” NBER Working Paper No. 5464, National Bureau of Economic
Research, Cambridge, MA.
5
See Minutes of the 205th Meeting of the Monetary Policy Committee of the Central Bank of
Brazil for a discussion.
©International Monetary Fund. Not for Redistribution
Chapter 15 Interest Rates and Inflation 263
ANNEX 15.1. DATA AND ROBUSTNESS DATA
Annex Table 15.1.1. Data, Sources and Transforms
Series Source Transform*
Headline IPCA IGBE log(x)*1200
Nontradable IPCA IGBE log(x)*1200
Tradable IPCA IGBE log(x)*1200
Services IPCA IGBE log(x)*1200
Nonregulated IPCA IGBE log(x)*1200
Regulated IPCA IGBE log(x)*1200
Inflation expectations (12 months ahead) BCB x
Interest rate (SELIC) BCB x-hptrend(x)
Activity Index (IBC-BR) BCB log(x)*100-hptrend(log(x))*100
Commodity Price Index (IC-BR) BCB log(x)*1200
Real Effective Exchange Rate (broad) JP Morgan log(x)*1200
Source: IMF staff.
Note: * 5 first difference; BCB = Central Bank of Brazil; hptrend 5 Hodrick-Prescott
Filter; IGBE = Brazilian Institute of Geography and Statistics.
Empirical Results
See Figures 15.1.1 and 15.1.2.
Simple Model
The investment/saving (IS) curve relates the current level of the output gap,
yt ,to the lagged output gap, expectations of the future output gap, and the real
interest rate (deviation from the steady state):
yt = δE t yt+1 − σ(Rt − E t π t+1 − r *).
+ (1 − δ) yt−1
The Phillips curve relates the current level of inflation to inflation expecta-
tions, past inflation, and the output gap (where 0 ≤ α ≤ 1) :
π t = α Et π t+1 + (1 − α) π t−1 + γ yt .
The monetary policy rule relates the nominal interest rate to the steady-state
nominal interest rate and the expected deviation of inflation from the
inflation target:
Rt = R * + μ(Et π t+1 − π *) ,
where μ > 1to ensure a unique and stable solution, and the long-term
Fisher equation is
R * = r * + π *.
The parameter values are σ = 1,γ = 0.05, μ = 1.5, and r * = 6. The param-
eters in the Phillips and IS curves related to persistence are δ = α = 1in the
forward-looking model, δ = α = 0.5in the partially forward-looking model,
and δ = α = 0in the backward-looking model.
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264 Brazil: Boom, Bust, and the Road to Recovery
Figure 15.1.1. Range of Cross-Correlations between the Interest
and Inflation Rates
(Median and 20th and 80th percentiles)
1. Headline and Interest Rate 2. Nonregulated and Interest Rate
(Correlation) (Correlation)
0.5 0.4
0.4 0.3
Lag Lag
0.3
interest → Inflation interest → Inflation 0.2
0.2 rate rate 0.1
0.1
0.0
0.0
–0.1 –0.1
Lag Interest Lag Interest –0.2
–0.2 inflation→ rate inflation
→
rate
–0.3 –0.3
–0.4 –0.4
12 10 8 6 4 2 0 2 4 6 8 10 12 12 10 8 6 4 2 0 2 4 6 8 10 12
Month (lag) Month (lag) Month (lag) Month (lag)
3. Regulated and Interest Rate 4. Services and Interest Rate
(Correlation) (Correlation)
0.4 0.2
Lag
0.15
0.3 interest → Inflation
Lag 0.1
rate
0.2 interest → Inflation
0.05
rate
0.1 0.0
0.0 –0.05
Lag Interest
Lag Interest → –0.1
–0.1 inflation→ rate inflation rate
–0.15
–0.2 –0.2
12 10 8 6 4 2 0 2 4 6 8 10 12 12 10 8 6 4 2 0 2 4 6 8 10 12
Month (lag) Month (lag) Month (lag) Month (lag)
5. Tradable and Interest Rate 6. Tradable and Interest Rate
(Correlation) (Correlation)
0.4 0.3
0.3 Lag Lag 0.2
interest → Inflation interest → Inflation
0.2
rate rate 0.1
0.1
0.0 0.0
–0.1 –0.1
Lag Interest
–0.2 inflation→ rate Lag Interest
→ –0.2
–0.3 inflation rate
–0.4 –0.3
12 10 8 6 4 2 0 2 4 6 8 10 12 12 10 8 6 4 2 0 2 4 6 8 10 12
Month (lag) Month (lag) Month (lag) Month (lag)
Source: IMF staff estimates.
©International Monetary Fund. Not for Redistribution
Chapter 15 Interest Rates and Inflation 265
Figure 15.1.2. Range of Inflation Responses to 100 Basis Point Cut in
Policy Rate
(Median and 20th and 80th percentiles)
1. Headline Inflation 2. Nonregulated Inflation
(Percent, annualized) (Percent, annualized)
0.8 0.7
0.6 0.6
0.5
0.4
0.4
0.2 0.3
0.0 0.2
0.1
–0.2
0.0
–0.4 –0.1
–0.6 –0.2
1 6 11 16 21 26 31 36 1 6 11 16 21 26 31 36
Months Months
3. Regulated Inflation 4. Services Inflation
(Percent, annualized) (Percent, annualized)
0.8 0.3
0.6 0.2
0.4 0.1
0.2 0.0
0.0
–0.1
–0.2
–0.4 –0.2
–0.6 –0.3
–0.8 –0.4
–1.0 –0.5
1 6 11 16 21 26 31 36 1 6 11 16 21 26 31 36
Months Months
5. Tradable Inflation 6. Nontradable Inflation
(Percent, annualized) (Percent, annualized)
0.9 0.6
0.8 0.5
0.7
0.6 0.4
0.5 0.3
0.4
0.2
0.3
0.2 0.1
0.1 0.0
0.0
–0.1 –0.1
–0.2 –0.2
1 6 11 16 21 26 31 36 1 6 11 16 21 26 31 36
Months Months
Source: IMF staff estimates.
©International Monetary Fund. Not for Redistribution
