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Interest rates and Inflation
MPBIM 1
A Study on
TESTING THE EXISTENCE OF A
RELATIONSHIP BETWEEN INFLATION
AND INTEREST RATES
Submitted in Partial fulfillment of the requirements of the M B
A degree course of Bangalore University
Submitted By
NAMRATA RAO S
( Reg No : 05 XQCM 6050 )
Under the guidance and supervision of
Dr.T V Narasimha Rao
M P Birla Institute of Management
Associate Bharatiya Vidya Bhavan
#43, Race Course Road
Bangalore 560001
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DECLARATION
I hereby declare that the project report titled Testing the
existence of a relationship between inflation and interest ratesis a
record of independent work carried out by me, towards the partial
fulfillment of the requirement for MBA course of Bangalore
University at M P Birla Institute of Management. This has not been
submitted in part or full towards any other degree or diploma.
Place : Bangalore Namrata Rao S
Date : 18th May 2007 ( 05 XQCM 6050 )
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GUIDES CERTIFICATE
This is to certify that the dissertation titled Testing the relationship
between Interest Rates and Inflation is an original study conducted
by Namrata Rao S,bearing register number 05XQCM6050, of M. P.
Birla Institute of Management, Associate Bharatiya Vidya Bhavan,
under my guidance. This has not formed the basis for the award of
any Degree/Diploma by Bangalore University or any other
University.
Date: May 18, 2007
Place : Bangalore Dr. T. V. Narasimha Rao
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PRINCIPALS CERTIFICATE
This is to certify that this report titled, Testing the
relationship between Interest Rates and Inflation is the result of
project work undertaken by Namrata Rao S, bearing the
Register Number 05XQCM6050, under the guidance of
Dr. T.V. Narasimha Rao. This has not formed a basis for
the award of any Degree/ Diploma for any University.
Place: Bangalore ( Dr. N. S.
Malavalli)
Date : 19 . 05 . 07
PRINCIPAL
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ACKNOWLEDGEMENT
Any successful work is always a product of many hands
coming together in co-operation and assistance. This work is no
different. A number of people are responsible for accomplishment
of this work. Their guidance and suggestions were highly helpful
during the course.
I whole-heartedly extend my deep and sincere gratitude to
Dr. T.V. Narasimha Rao, (Faculty Finance), MPBIM, for his
continuous guidance and help provided for completing this
research study. I am also grateful to Dr N S Malavalli, Principal,
M.P Birla Institute of Management for his full support and
encouragement while I was conducting this research.
I would also like to thank my colleagues who helped me a lot
during the project period.
Thank you all
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Table of Contents
Executive Summary
Introduction 1
- Fisher Relation 3
- International Fisher Relation 4
- Interest Rate 4
- Inflationary expectations 6
Literature Review 8
Research Methodology 12
- Study Background 13
- Problem Statement 13
- Need and Importance 13
- Objectives 14
- Limitations 14
- Data Source 15
- Research Tools
15
Data Analysis 18
- Data 19
- Testing of stationarity 20
- Co-integration test 21
Conclusions 24
References and Bibliography
26
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List Of Tables
Long Term Yield data 16
Short Term Yield Data
17
Inflation data 18
Augmented Dickey Fuller Test Long term yield 18
Augmented Dickey Fuller Test Short Term Yield 19
Augmented Dickey Fuller Test - Inflation rates 19
Regression statistics of long term yield on inflation
21
Augmented Dickey Fuller Test Regression residuals 22
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EXECUTIVE SUMMARY
The study, Testing of the relationship between Interest rates and
Inflation is done with an intention to understand if there is any influence of
Inflation on long term interest rates. The study has used the redemption yield
of the Government of India securities for long term yields. An effort was made
to study the short term yield influences by inflation. The 91 day treasury bill
was used as proxy for short term yields. The inflation rates were collected from
www.inflatiodata.com . The period of 1998 2007 is considered for study
purposes. The data is collected, tabulated and annual percentages are
calculated.
The long run yield and inflation satisfy Dickey Fuller Test, but the
short run does not. Later, the dependent variable long term yield is regressed
with the independent variable inflation. The obtained residuals are again
subject to Augmented Dickey Fuller test. The result shows that the residuals
are stationary.
But, the significance of the test is very low. Hence, the study concludes that
during the period of study, there is no significant relationship.
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INTRODUCTION
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INTRODUCTION
Whenever there is any news on Interest rates, it is accompanied by
inflation. It is a known fact that there exists a relationship between interest rates
and inflation. But, the extent to which one affects the other for different time
periods is not certain. Mathematically, the relationship is given by Fisher
Hypothesis.
The well-known Fisher hypothesis was introduced by Irving Fisher in
1930. It maintains that the nominal interest rate is the sum of the constant real
rate and the expected decline in the purchasing power of money. Starting with
Fisher and extending to the present, this seemingly simple and intuitivehypothesis has found limited empirical support.
Fisher hypothesis provides the relationship between the expected inflation
and interest rates. Fishers hypothesis is that the nominal interest rate (R t) can be
taken to be the sum of real rate of interest (Pt) and the rate of inflation anticipated
by the public (t).
Rt = Pt + t
This means, the real interest rate equals the nominal rate minus inflation.
Therefore, if Rt rises, so must t , if you assume Pt to be constant. If an economic
theory or model has this property, it shows the Fisher effect.
Previous studies shows that there is a positive relationship between
interest rates and inflation. But, it is not a perfect one, which suggests that the
interest rates are influenced by other factors also.
Let us first have a brief understanding of various concepts in this report.
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Fisher Effect:
According to the principle of monetary neutrality, an increase in the rate
of money growth raises the rate of inflation but does not affect any real variable.
An important application of this principle concerns the effect of money oninterest rates. Interest rates are important variables for macroeconomists to
understand because they link the economy of the present and the economy of the
future through their effects on saving and investment. The relationship between
inflation and nominal interest rate and real interest rate put in simple words is;
Real interest rate= Nominal Interest Rate - Inflation Rate
Nominal Interest Rate= Real interest Rate + Inflation Rate
Illustration:
If inflation permanently rises from a constant level, let's say 4%per yr, to a
constant level, say 8% per yr, that currency's interest rate would eventually catch
up with the higher inflation, rising by 4 points a year from their initial level.
These changes leave the real return on that currency unchanged. The Fisher
Effect is evidence that in the long-run, purely monetary developments will have
no effect on that country's relative prices.
International Fisher Relation
The international Fisher relation predicts that the interest rate differential
between two countries should be equal to the expected inflation differential.
Therefore, countries with higher expected inflation rates will have higher
nominal interest rates, and vice versa.
This work concentrates on the relationship that exists between interest rates and
the inflation rates, which are main components of the Fishers effect. The interest
rate constitutes two components nominal interest rate and real interest rate. The
same are explained below.
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Interest rate
An interest rate is the price a borrower pays for the use of money he does
not own, and the return a lender receives for deferring his consumption, by
lending to the borrower. Interest rates are normally expressed as a percentageover the period of one year on the principle amount or capital employed.
Nominal interest rate
It is the amount, in money terms, of interest payable. For example,
suppose A deposits Rs100 with a bank for 1 year and they receive interest ofRs10. At the end of the year their balance is Rs110. In this case, the nominal
interest rate is 10% per annum.
Real interest rate
The real interest rateis the nominal interest rate minus the inflation rate. It
is a measure of cost to the borrower because it takes into account the fact that the
value of money changes due to inflation over the course of the loan period.Except for loans of a very short duration, the inflation rate will not be known in
advance. People often base their expectation of future inflation on an average of
inflation rates in the past, but this gives rise to errors. The real interest rate after
the fact may turn out to be quite different from the real interest rate that was
expected in advance. Conversely, when inflation was on a downward trend in
most countries, lenders fared well, while borrowers ended up paying much
higher real borrowing costs than they had expected.
The complexity increases for bonds issued for a long term, where the
average inflation rate over the term of the loan may be subject to a great deal of
uncertainty. In response to this, many governments have issued real return (also
known as inflation indexed bonds), in which the principle value rises each year
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with the rate of inflation, with the result that the interest rate on the bond is a real
interest rate.
Interest rates are set by a government institution, usually a central bank, as the
main tool of monetary policy. The institution offers to buy or sell money at thedesired rate and, because of their immense size, they are able to effectively set
the nominal interest rate on a short-term risk-free liquid bond (such as Govt
Treasury Bills).
Inflationary expectations
Most economies generally exhibit inflation, meaning a given amount ofmoney buys fewer goods in the future than it will now. The borrower needs to
compensate the lender for this.
According to the theory of rational expectations, people form an expectation of
what will happen to inflation in the future. They then ensure that they offer or
ask a nominal interest rate that means they have the appropriate real interest rate
on their investment.
Money and inflation: Loans, bonds, and shares have some of the characteristics of
money and are included in the broad money supply. By setting the nominal
interest rate on a short-term risk-free liquid bond (such as Govt Treasury Bills).
The Government institution can affect the markets to alter the total of loans,
bonds and shares issued. Generally speaking, a higher real interest rate reduces
the broad money supply. Through the quantity theory of money, increases in the
money supply lead to inflation. This means that interest rates can affect inflation
in the future.
The other factors that influence the interest rates are
1. Deferred consumption
2. Alternative investments
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3. Risks of investment
4. Liquidity preference.
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LITERATURE
REVIEW
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Long run relationship between nominal interest rates and
inflation : The Fisher equation revisited
William J Crowder
Dennis L Hoffman
This paper recognizes that the persistence in nominal interest rates and
inflation can be modeled under the unit root hypothesis. A fully efficient
estimator that separates estimation of long run equilibrium relationship from
nuisance parameters is applied. The study finds considerable support for the tax-
adjusted Fisher effect. It reveals a long run relationship between interest rates
and inflation. However, it also finds that the short term interest rates may not be
good predictors of future inflation.
Is the Real Interest Rate stable?
Rose, Andrew
Rose analyses the time series properties of the variables that constitute the
Fisher paradigm and concludes that interest rates possess a unit root in their
autoregressive representation, but inflation does not. If this is true, then a
regression of interest rates on inflation is necessarily spurious because it attempts
to link variables that maintain different orders of integration. Hence, the Fisher
relation may be rejected. But, Roses conclusions must be viewed carefully as it is
widely recognized that conventional univariate unit root tests have difficulty in
distinguishing unit and near unit root processes and may not be able to provide a
definitive test of proposition.
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Do expected shifts in inflation affect estimates of the long run
Fisher relation?
Evans, Martin and Karen Lewis
This paper observes co-integration between nominal interest rates and
inflation in a sample of post war data and applies the DOLS estimator to estimate
the long run response of nominal interest rates with respect to inflation. They
support their case with Monte Carlo evidence. They conclude that the Fisher
hypothesis is generally consistent with postwar data once we recognize that
agents have been forced to form expectations from an inflation process that has
undergone several structural changes in the post war period and that their
results simply suffer from small sample bias.
Is the Fisher effect for real?
Mishkin, Frederic S
This paper takes inflation and nominal interest rates to be nonstationary
and applies the Engle Granger methodology to test for common stochastic
trends. The simple Fisher relation predicts that the two series share a common
stochastic trend and a long run unitary response of nominal interest rates to
movements in expected inflation rate. Mishkins analysis does not provide
particularly sharp statistical inference because his estimate of the relation
between inflation and nominal interest rates is very imprecise. However, his
analysis serves as an important first step to obtain better measures of the long
run relation.
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RESEARCH
METHODOLOGY
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STUDY BACKGROUND
Ever since Irving Fisher (1930) provided the relationship between the
expected inflation and interest rates; considerable attention has been paid for it.
Many financial controversies and literatures have surrounded this relationship.In Indian context very less studies have been done in this regard as interest
liberalizations are of recent past. Studies have shown that Fisher Hypothesis is
true in India and that there is a long run relationship between interest rates and
inflation and interest rates can be modeled considering expected inflation and
other macroeconomic variable to arrive at a more valid model of forecasting
interest rates. However, the short run relationship does not have sufficient
support.
PROBLEM STATEMENT
This paper studies whether there is a relationship between inflation and
interest rates over long term and short term.
NEED AND IMPORTANCELevel of inflation always has a bearing on the interest rates. The
interest rate is a key financial variable that affects decisions of consumers,
business firms, financial institutions, professional investors and policy makers.
Timely forecasts of inflation rates can therefore provide valuable to financial
market participants. Forecasts of interest rates can also help to reduce interest
rate risks faced by individuals and firms.
In Indian context the relationship between anticipated inflation changes and
returns were not of much concern till the 1990,s due to administered interest rate
mechanism. Since the economic reforms and the liberalization of capital market
the interest rates are market determined.
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The earlier findings report that no relationship between interest rates observed at
point of time and rates of subsequently observed inflation exist. However the
general finding is that there are relationships between current rates of interest
and past rates of inflation.If interest rates are not adjusted for changes in inflation then the real rate of
return decreases. Expected price changes have a bearing on the purchasing
power, thus on the level of consumption also. Hence interest rate determination
in Indian context also needs focus.
OBJECTIVES
To check the relationship between inflation and interest rates for long
term and short term
LIMITATIONS
The study is limited to a period of 10 years only due to non-availability of
data.
DATA SOURCE
This study has been carried out on the basis of secondary data collected
from Reserve Bank of India (RBI). The short term interest rates have been taken
from Treasury bill yields and the Government of India securities yields act as
long term interest rates.
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RESEARCH TOOLS
Unit Root Test
A test of stationarity (or non-stationarity) that has been widely popular
over the past several years is the Unit root test. The two widely used standard
unit root test statistics are Augmented Dickey fuller test and Phillips Perron test.
Drawbacks of Unit Root Test :
Conceptually the unit root tests are straightforward. In practice, however,
there are a number of difficulties:
Unit root tests generally have nonstandard and non-normal asymptoticdistributions.
These distributions are functions of standard Brownian motions, and donot have convenient closed form expressions. Consequently, critical
values must be calculated using simulation methods.
The distributions are affected by the inclusion of deterministic terms, e.g.constant, time trend, dummy variables, and so different sets of criticalvalues must be used for test regressions with different deterministic
terms.
Augmented Dickey Fuller (ADF) Test
Many economic and financial time series have a more complicated
dynamic structure than is captured by a simple AR(1) model.
Said and Dickey (1984) augment the basic autoregressive unit root test toaccommodate general ARMA(p, q) models with unknown orders and
their test is referred to as the augmented Dickey-Fuller (ADF) test
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Basic Model
The ADF test tests the null hypothesis that a time series Yt is I(1) against the
alternative that it is I(0), assuming that the dynamics in the data have an ARMA
structure. The ADF test is based on estimating the test regression
Yt= 1+ 2t + Yt-1+ iYt-i + t
Where t is a pure white noise error term, Yt-1 = (Yt-1-Yt-2), Yt-2 = (Yt-2 Yt-3), etc.
In ADF we test whether = 0
Hypothesis:
H1 : Time Series Data is Stationary
H0 : Time Series Data is Non Stationary
=
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DATA ANALYSIS
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DATA
Long Term Yield:
The redemption yields of the Government of India Securities are takes as
proxy for long term yields. The data is collected for every month from Oct 1998
to Apr 2007. This data is tested for stationarity.
Long Term Yields
Year Rates
1998 11.3950
1999 9.3988
2000 11.3050
2001 10.4421
2002 7.8843
2003 6.02232004 5.4445
2005 6.8373
2006 7.4038
2007 7.7219
A plot of the annualized data is given below.
Long Term Yield
0.0000
2.0000
4.0000
6.0000
8.0000
10.0000
12.0000
1 2 3 4 5 6 7 8 9 10
From 1998 - 2007
Averageyield
Series1
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Short Term Yield
The 91 day treasury bill yield from Oct 1998 to Apr 2007 is taken as the
short term yield. This data is also tested for stationarity.
Short term yields
Year Avg Yield
1998 7.3465
1999 8.4713
2000 9.0129
2001 8.7430
2002 7.4110
2003 5.6109
2004 4.8623
2005 4.99332006 5.7420
2007 6.3935
A graphical representation of the variations in the data for the study
period is depicted below.
Short Term Yield
0.0000
2.0000
4.0000
6.0000
8.0000
10.0000
1 2 3 4 5 6 7 8 9 10
Year from 1998-2007
AvgYiel
Series1
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Inflation
TESTING OF STATIONARITY
To start with, the stationarity of Long term yield, short term yield and
inflation rates are tested using the Augmented Dickey fuller test.
The results of the test carried for first difference, lag 0 for Long term yields
are as follows.
ADF Test Statistic -2.19980556885
1% Critical Value*
-2.9676749557
5% Critical Value
-1.9890499413
10% Critical Value
-1.6382249891
Interpretation
The data is stationery at 5% critical value for long term yields.
Annual Inflation
Year Rates
1998 13.131999 4.69
2000 4.01
2001 3.85
2002 4.15
2003 3.98
2004 3.63
2005 4.28
2006 6.16
2007 5.66
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The results of test carried for first difference, lag 0 for Short term yields are
as follows;
ADF Test Statistic -1.2536141 1% Critical Value* -2.9676749557
5% Critical Value
-1.9890499413
10% Critical Value -1.6382249891
Interpretation
The data is nonstationary at 5% critical value. Hence, we have two
options. One is to convert the data into stationary and another is to rule out any
relationship between short term interest rates and inflation.
The results of test carried for first difference, lag 1 for inflation are as
follows;
ADF Test Statistic-2.1488946771
1% Critical Value*
-3.0506979154
5% Critical Value
-1.9961570841
10% Critical Value
-1.6414571319
Interpretation
Inflation rates are stationary at 5% critical value.
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CO-INTEGRATION
Since long term yield and inflation data series are proved to be Stationary,
now test for co-integration is executed to evaluate if these two are linearlyrelated. Engel-Granger Co-integration technique is utilized in this study due to its
simplicity and reliability. The residuals obtained are tested for Stationarity using
ADF test. If this residual series is proved to be stationary then it can be said that
a relationship exists between interest rates and inflation over a long term.
Regression
A regression of long term yields on inflation is run using both MS Exceland SPSS. The output of the regression is as follows.
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OUTPUT LT on Inf
Regn stats
Multiple R 0.46121
R Square 0.21272Adjusted R
Square 0.11430
Standard Error 2.01171
Observations 10
ANOVA
df SS MS F Significance
Regression 1 8.7475 8.74752 2.1615 0.179707
Residual 8 32.3757 4.04696Total 9 41.1232
Co-Eff Std Err t StatP-
value Lower 95%Upper95%
Lower95.0%
Upper95.0%
Intercept 6.5344 1.4106 4.6323 0.0017 3.2815 9.7874 3.2815 9.7874
X Variable 1 0.3457 0.2352 1.4702 0.1797 -0.1965 0.8880 -0.1965 0.8880
RESIDUALS
ObservationPredicted
Y Residuals
1 11.0739 0.3211
2 8.1559 1.2428
3 7.9208 3.3842
4 7.8655 2.5766
5 7.9692 -0.0849
6 7.9105 -1.8882
7 7.7894 -2.3449
8 8.0142 -1.1769
9 8.6641 -1.2604
10 8.4913 -0.7694
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Next, we check the stationarity of the residuals obtained. If the residuals
are stationary, then the two variables are said to co-integrate with each other. i.e.,
there exists a relationship between inflation and interest rates.
The results obtained are as follows.
ADF Test Statistic -3.86596541
1% Critical Value*
-2.9676749557
5% Critical Value
-1.9890499413
10% Critical Value
-1.6382249891
The above results show that it is stationary at 5% critical value. Hence,
there might be some relationship between the two. However, also keeping in
view the regression statistics, i.e., the values of F-test and significance of the test,
it can be said that there in no significant relationship between interest rates and
inflation on long term.
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CONCLUSIONS
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This paper has attempted to study the existence of relationship between
long run interest rates and inflation. The data that has been collected was tested
for stationarity and then put to further use. The stationarity was tested using the
Augmented Dickey Fuller test (ADF ) which revealed that the data wasstationary for long term yields and inflation, but not so for short term yields. The
persistence of a relationship between interest rates and inflation was tested using
the Engle Granger co-integration test. This test involves running a regression of
long term interest rates on inflation. The test throws up a list of residuals. These
residuals are then tested for stationarity, the result of which proves the existence
of a relationship or otherwise. This test showed feeble relationship between the
two for the particular study period.From the above ADF and Granger co-integration test, it can be said the
there is no significant relationship between long term interest rates and inflation
during the period of study .i.e., from Oct 1998 to Mar 2007.
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REFERENCES
AND
BIBLIOGRAPHY
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References
1. William J Crowder and Dennis L Hoffman. Long run
relationship between interest rates and inflation,
Journal of Money, credit and Banking, Vol 28, No.1, pp,
102-118.
2. Rose, Andrew. Is the interest rate for real?, Journal
of Finance 43, (Dec 1998), pp 1092 112.
3. Fredric S Mishkin. Is the Fisher effect for real? : A re-
examination of the relationship between inflation
and interest rates, Journal of Monetary economics 30
(Nov 1992), pp 195 - 215.
4. Evans, Martin and Karen Lewis. Do expected shifts
in inflation affect estimates of the long run Fisher
relation?, Journal of Finance 50,( Mar 1995), pp. 225
53.
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Bibliography
TEXT BOOKS
Multinational Business Finance by David K Eiteman,
Arthur K Stonehill and Michael H Moffett.
Basic Econometrics by Damodhar Gujarathi.
WEBSITES
www.google.com
www.finance.yahoo.com
www.rbi.org.in
www.inflationdata.com