Relationship Between Inflation and Interest Rates

8/7/2019 Relationship Between Inflation and Interest Rates

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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

Documents

Relationship Between Inflation and Interest Rates