INFLUENCE OF ANTICIPATED INFLATION ON SHORT TERM INTEREST RATES
A dissertation submitted in partial fulfillment of the requirement for the award of M.B.A Degree of Bangalore University. By
AVINASH S HUKKERI 04XQCM6011
Under the guidance of Dr. T V N Rao Professor MPBIM
M P Birla Institute of Management Associate Bharatiya Vidya Bhavan #43, Race Courese road, Bangalore-01.
The study “influence of anticipated inflation on short term interest rates” is done with an intention to understand the impact of inflation in the short run over the interest rates. We have made use of composite yield of 91-day Government T-bills and urban non manual employee consumer price index. We have considered the period from April 1995 to March 2006. This is post liberalization period in India. The data collected tabulated is arranged and quarterly percentages are calculated. Data used satisfies both the stationarity Dickey-Fuller unit root test and Johansen cointegration test, which supports the requirements for using regression analysis. The dependent variable short term interest rate is regressed with independent variable anticipated inflation rate. One quarter lag of interest rate and interest rate is considered for anticipated inflation rate. The regression and correlation analysis show that short term interest rates do not adjust for changes for inflation rates which is anticipated. Both interest rates and inflation are linearly independent at one to one lag. Thus we conclude that short term interest rates do not adjust for anticipated inflation rates. However this work has its own limitations due to time constrain and lack of individual expertise also. The limitations of this work are as under 1. The study do not considers the money supply in the economy which also influences the inflationary changes. We assume that all other parameters remain constant 2. The inflation index used is not unique and other indices can also be made use to consider the inflation rates. The use of other indices may vary the accuracy of the results interpreted here. Similarly other short term interest rates can also influence in the same way.
CHAPTER 1 INTRODUCTION
Irving Fisher (1930) provided the relationship between the expected inflation and interest rates. Fisher’s doctrine is that nominal interest rate can be taken as the sum of real rate of interest and inflation anticipated by the market. Fisher’s hypothesis is that the nominal interest rate (rt) can be taken to be the sum of real rate of interest (pt) and the rate of inflation anticipated by the public (πt). rt = pt + πt This means, the real interest rate equals the nominal rate minus inflation therefore, if rt rises, so must πt , if you assume pt to be constant. If an economic theory or model has this property, it shows the Fisher effect. Fisher Effect: The one for one adjustment of the nominal interest rate to the inflation rate. 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 on interest 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 Fisher’s effect. The interest rate constitutes two components nominal interest rate and real interest rate. The same are explained below.
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 percentage over the period of one year on the principle amount or capital employed. The nominal interest rate 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 of Rs10. 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 rate is 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 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 the desired 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 of money 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 3. Risks of investment 4. Liquidity preference.
CHAPTER 2 LITERATURE REVIEW
Thomas J Sargent i in his work “Anticipated Inflation and the Nominal Rate of Interest” proposed his work to estimate whether the Fisher’s equation rt = a + Пt +et 1 can in general be taken to characterize correctly the relationship between inflation and nominal rate of interest. In his studies he studied the relationship between the rt (nominal rate of interest) and Пt (rate of inflation at time t) within the context of simple linear dynamic macroeconomic model. The model used is a Keynesian in structure and has assigned important roles to price level adjustments and anticipations of inflation effects frequently emphasized by monetarists. The factors that determine the appropriateness of above said equation were the same factors that within the standard IS-LM framework determine the relative short-term potency of money and fiscal policy in affecting the level of aggregate output. Sargent’s conclusion is that the relationship between inflation and nominal rate of interest is in principal more complex than is depicted by Fisher. However the correctness of the equation is true and it can be expected that an increase in anticipated inflation to drive the nominal interest rate upward by the entire amount of increase it may take a very long time for the adjustment to occur. Sergeant also considers the money supply as a determinant of nominal interest rate which is not included in the Fisher’s equation
rt is nominal rate on bonds, Пt is rate of inflation anticipated by public, et is a stochastic term which represents numerous factors affecting rt and are not included in ‘a’ or in Пt . ‘a’ is a constant which can be interpreted as the longrun equilibrium real rate of interest.
William E Gibson ii in his study “Interest rates and Inflationary Expectations: New Evidence” alleviates the need to test the market determining the interest rates using directly observed data on price expectations. Gibson’s work made use of the data of Joseph Levingston 2 for the period of 1952 to 1970 for measuring the Fisher’s hypothesis. In his studies Gibson used the Joseph Levingstone data for constructing expected rates of price changes, which were related to market interest rates. Gibson used US treasury securities to measure market interest rates. He considered five different maturity categories of Us Treasury bills ranging from 3 month bills to 10years and longer term to maturity bond along with market yields. Estimates for 6 month and 12 month expected rates of inflation indicated a strong association between interest rates and measures of expectations. Interest rates have shown quick response to changes in expectations. The period before 1952 for US Treasury bill market was controlled and rates remained stable irrespective of inflation changes. After this period the market determined the interest rates even though the interest rates were not much adjusted for inflation till 1959. post 1959 was the period which showed the adjustments in interest rates towards the inflation changes. The results were calculated by regressing the actual prices on their earlier periods and for the pre and post 1959 sub-periods. Gibson’s studies show that when the rate of inflation increases to high rate, the expected rate of inflation increases for two reasons they are; firstly, At a constant rate of adjustment of expected to actual inflation rates, the expected rate rises because the actual rate rises and second the co-efficient of adjustment of expected to actual rises, rising the portion of actual rate incorporates with the expected rate. The results of the study say that, the real rate of interest is not affected by price expectation over six month period and that interest rates fully adjust to expectations
Joseph Levingston a nationally syndicated financial columnist has twice yearly since 1946 surveyed a group of business Government, labour and academic economists on their expectations of future values of selected aggregate economic variables. The latter include the consumer price index.
within six months. And expectations of given term have less influence on yields as the term to maturity increases beyond the term of the expectation.
study succeeded Eugene Fama’s study on Fisher’s theory. In his paper
titled “Interest Rates as Predictors of Inflation in a High-Inflation Semi-Industrialized Economy” suggests that Fama’s findings which are based on inflation where inflation has been mild and so has been at variability through time. Liderman’s study aimed at empherically assessing the role of interest rates as the predictors of inflation in different settings, one characterized by the co-existance of the high and volatile inflation and of less than well developed financial markets. Thus he selected the markets of Argentina for the same and used the data for period of 1964-1976. he supported the selection of Argentina as it is a semi-industrialised country, less than well developed financial market which have experienced relatively high degree of government intervention, which probably impair the operational efficiency of capital market as well as prediction of interest rates. Liderman’s Fisher type equation was it = αo+ α1 E (Пt / It-1) (1)
Where ‘it’ is nominal interest rate quoted at the end of (t-1) on a bill that matures at the end of ‘t’ and Пt is rate of inflation for period ‘t’. E (Пt / It-1) is the expected value of inflation rate implied by the information set available at time ‘t-1’ i.e. It-1 . Under the assumption that nominal interest rate equals the sum of real rate and expected rate of inflation, where the expected rate of inflation is given by
it- E (Пt / It-1) = αo+(α1-1) E (Пt / It-1)
Independence of real interest rate with respect to movements in anticipated inflation amounts to α1=1.
To study the role of interest rates as predictors of inflation equation (1) was rewritten as E (Пt / It-1) = βo + β1 it Where βo = (- αo) / α1 and β1=1 / α1. Since past inflation rates may help assess the expected inflation rates from ‘t-1’ to ‘t’. Thus equation (3) can be rewritten as E (Пt / It, Пt-1, Пt-2 …….) = βo + β1 it (4) (3)
Liderman inserted a prediction error in the above equation (4) as follows μt = Пt - E (Пt / It-1) So the equation (4) can be rewritten as Пt = βo+ β1 it+ μt (5)
Leat square estimations of equation (5) and the variants of equation were used in order to test the hypothesis of predominance of interest rates over past inflation as predictors of Пt. Liderman considered the quarterly Argentinean data from 1964 to 1976 (50 observations). He considered the bill brokerage yields which have very large market and this market is close to being a free financial market. The dependent variable was Пt, the inflation rate from‘t-1’ to ‘t’. the co-efficient of determinant indicate that the nominal interest rate contains nontrivial information about the rate of change in purchasing power from ‘t-1’ to ‘t’. Two major conclusions were made by his work. 1. markets use all information about subsequent inflation rates in setting quarterly inflation rates, and
2. An increase in expected inflation is not fully transmitted to nominal interest rate so it implies a reduction in the contemporaneous real interest rate.
Alexander B . Holmes and Myron L. Kwast
in their paper “Interest Rates and
Inflationary Expectations: Tests for Structural Changes 1952-1976” studied the relationship between the nominal interest rates and anticipated inflation rates during the structural changes i.e. during the period 1952-1976 in the US economy. Holmes and Kwast used Brown-Durbin tests for structural stability, for the data used and the results indicated were found significant. In their analysis Holmes and Kwast used CPI data, short term Treasury bill data and expected prices were constructed from Livingston survey, for the analysis. Their analysis found that there was radical upward shift in size of the coefficients at the estimated period and immediately after the period of estimated structural change, which confirms that market rates adjust more strongly to inflationary expectations in the late 1960s and there after than they had before. And also interest rates are estimated not to adjust to inflationary expectations before the period of structural change, but to make a significant positive adjustment after the estimated shift. Thus the work of Holmes and Kwast support the dating of structural change as determined by the Brown-Durbin technique and the hypothesis that the interest rates respond more strongly to inflationary expectations after the structural shift.
CHAPTER 3 RESEARCH METHODOLOGY
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. Fisher’s doctrine holds that nominal interest rate can be taken as the sum of real rate of interest and inflation anticipated by the market. Thomas J Sargent in his works has analyzed the Fisher’s doctrine. Sargent found that the relationship between the anticipated inflation and nominal rate of interest is in principle more complex than depicted in Fisher’s equation. It can be expected that an increase in anticipated inflation drives the nominal interest rate upward by the entire amount of increase, but this adjustment is not quick. In Indian context very less studies have been done in this regard as interest liberalizations are of recent past. Thenmozhi and Radha (2004) v have shown that Fisher’s hypothesis is true in India the context and have found that there is a long run relationship between interest rates and expected 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.
PURPOSE OF THE STUDY
The effects of expected inflation on market interest rates have been of great concern for decades. Irving Fisher’s description of interest rates relationship with expected inflation is convincing on the theoretical levels. I.Fisher’s doctrine holds that the nominal interest rate (rt) can be taken to be the sum of real rate of interest (pt) and the rate of inflation anticipated by the public (πt). Thus Fisher’s equation as proposed by him is rt = pt + πt (1)
In his works Fisher and group assume that real rate of return (pt) is unaffected by the change in anticipated inflation rate (πt). thus one can conclude that the term pt (real rate of return) in equation (1) is a constant and stochastic term et that is uncorrelated with πt. symbolically pt = a + et (2)
Where et represents numerous factors affecting rt, which are not included in ‘a’ or πt . From both the equations we can rewrite the equation (1) as follows rt = a + et + πt (3)
The purpose of this paper is to establish whether equation (3) can in general be taken to characterize correctly the relationship between anticipated inflation changes and nominal rate of interest.
SCOPE OF THE STUDY
Level of inflation always has a bearing on the short term 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. 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.
“To characterize the relationship between anticipated inflation changes and nominal rates of interest”
Correlation and regression analysis will be made use in order to analyze the relationship between interest rates and inflation. Regression and correlation analysis show us how to determine nature and strength of relationship between two variables. We need to find out the causal relationship between changes in interest rate to the changes in inflation. Regression analysis shows the relationship between the variables and correlation shows the degree of relationship between the variables.
The regression equation is given as follows Y = a + b (X) Where, Y is dependent variable, the value which is dependent on changes in X. X is the independent variable ‘a’ is the Y intercept, the value of Y is the value at which regression line crosses the Y –axis.
‘b’ is the slope of the equation, it represents how much each unit of change in independent variable X changes the dependent variable Y.
b = Y2 –Y1 X2-X1
n ∑ XY – (∑ X) (∑ Y) n ∑ X2 - (∑ X)2
Where ‘n’ is the number of observations In our study the interest rate will be denoted by Y since it is a dependent on inflation. The variable X explains the inflation. To find out the variability of values around the regression line standard error of estimate is calculated. Standard error of estimate is given by Se = ∑ Y2 – a ∑ Y- b∑ XY (n-2)
To find out degree to which one variable is linearly related to another is calculated using correlation. There are two measures to analyze the same viz coefficient of determination and coefficient of correlation. Coefficient of determination is used to measure the extent or strength of association between the two variables X and Y. it is denoted by r2. it is calculated as follows
r2 = a ∑ Y + b∑ XY - n ∑ Y2 ∑ Y2 – n Y2 Coefficient of correlation (r) is also a measure which describes how well one variable is explained by the other. It is square root of coefficient of determination. The sign of r indicates that the direction of relationship. If r2 is positive the root will be positive and it
indicates the direct relationship and if the r2 is negative its root will be negative and indicates an inverse relationship Unit Root Test A test of stationarity (or nonstationarity) that is well known is the UNIT ROOT TEST. The starting point of unit root test is Y t=þY (t-1) +Ut Where, Ut=white noise term. Yt= random variable at discrete time interval t. If ρ=1, then the unit root exist. That is: the time series under consideration is nonstationary or follows a random walk. If ρ! = 1, then unit root does not exist. That is: the time series under consideration is stationary. Theoretically ‘ρ’ value can be calculated by regressing Y t with one period lag values.
Augmented Dickey Fuller (ADF) Test: ADF Test is used for calculating δ, where δ= ρ-1. Hypothesis: H0= Time series is non stationary. H1= Time series is stationary.
Decision Rule: 1) If T* >ADF critical value 2) If T* <ADF critical value exist. not reject the null hypothesis i.e., unit root exists. reject the null hypothesis i.e., unit root does not
Cointegration Cointegration is an econometric technique for testing the correlation between nonstationary time series variables. If two or more series are themselves non-stationary, but a linear combination of them is stationary, then the series are said to be cointegrated. It is often said that cointegration is a means of valid hypothesis testing between two variables having unit roots (Integrated of order one). In practise, cointegration is used for such series in typical econometric tests, but it is more generally applicable and can be used for variables integrated of higher order (to detect correlated accelerations or other second differencing effects).
T-Test: To find how closely historical and implied volatilities are related T –test is conducted.
The T- distribution has a number of applications in statistics like 1. T-Test for the significance of single mean, population variance being unknown. 2. T-Test for the significance of the difference between two sample means, the population variances being equal but unknown.
3. T-Test for the significance of an observed sample correlation coefficient. T-Test for significance of an observed sample correlation coefficient This test is conducted to find the significance of observed samples. Hypothesis: H0 = sample correlation does not differ significantly. (Tcal<Ttab) H1 = sample correlation differ significantly. (Tcal>Ttab)
The study for the study of mentioned objective will be on the basis of secondary data collected from various websites 3 . For calculations software are used.
The sources of data are mentioned in the bibliography.
PERIOD OF STUDY
The proposed period for the study is from April 1995 to March 2006 and data from the Indian economy. The data earlier to the period will not support the studies due to controlled market.
CHAPTER 4 RESULTS AND ANALYSIS
Interpretation of ADF test: For series X (Inflation rate changes) The computed ADF test-statistic (-3.158648) at none, is smaller than the critical values (-2.6182) @1%, (-1.9488) @ 5% level, -1.6199 @ 10% level. Thus the hypothesis is rejected for unit root; the data for inflation series is stationary. It is clear that data has passed the Dickey –Fuller test and we can continue further tests.
For series Y (Interest rate changes) The computed ADF test-statistic (-5.943633) at none, is smaller than the critical values (-2.6182) @1%, (-1.9488) @ 5% level, (-1.6199) @ 10% level. Thus the hypothesis is rejected for unit root; the data for interest rates is stationary. It is clear that data has passed the Dickey –Fuller test and we can continue further tests.
Interpretation of DW statistics: The results of Dublin and Watson tests are close to 2 for both the series viz 1.89 for X series and 2.01 for Y series. The DW statistics indicate that there is no autocorrelation existing.
Tests ADF test D-W Statistics
Series X (inflation rates) Stationary No autocorrelation
Series Y ( interest rates) Stationary No autocorrelation
Interpretation of cointegration test: The cointegration test for series X and series Y at 1 to 1 lag intervals has critical value of 15.41@ 5%, 20.04 @ 1%, which leads to rejection of the hypothesis Ho which says no cointegration exists, thus the result indicates the cointegration of both the series X and Y. thus the existence of cointegration further supports the study methodology.
Variables Entered/Removed Model 1 a b Variables Entered INF All requested variables entered. Dependent Variable: INTREST Variables Removed . Method Enter
Model Summary Adjusted R Square -0.009 Std. Error of the Estimate 9.8367
Model 1 a
R 0.122 Predictors: (Constant), INF
R Square 0.015
Coefficients Unstandardized Coefficients Model 1 (Constant) INF Dependent Variable: INTREST B -2.501 0.949 Std. Error 2.344 1.203 Standardized Coefficients Beta 1.067 0.789 0.292 0.434 t Sig.
-30 -2 -1 0 1 2 3 4 5
Regression results a = -2.501 b = 0.949 The constant term ‘a’ = (-2.501) is Y–intercept, the negative sign indicates that real rate of return does not compensate for the inflation rate. The other term ‘b’ indicates the slope of the regression equation which is 0.949. The test results indicate that for the considered series there is no significant relationship existing.
Correlations INF INF Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N 1 . 43 0.122 0.434 43 INTREST 0.122 0.434 43 1 . 43
Correlation r = 0.0122 and r2 = 0.015 r2 explains the percentage of influence that is explained by the inflation. Thus it says that 1.5% of the change in interest rate is due to the inflation change. Thus the interest rates and inflation rates are linearly independent at lag 1.
CHAPTER 5 SUMMARY AND CONCLUSIONS
SUMMARY AND CONCLUSION
The study considers the secondary data of the Indian economy from April 1995 to March 2006. The data constitutes of 91 day Government T-Bills’ composite yields and Consumer Price Index is used for the purpose of inflation rates. The quarterly changes in the inflation rates and interest rates are calculated for the ten years. The inflation rates constitute the independent variable in the regression equation and interest rates form the dependent variable. One period lag is taken between the interest rate and inflation so that the lag in the inflation forms the anticipated inflation. The variables are regressed to find out the relationships that both have and results are interpreted. From the statistical analysis it can be interpreted that in Indian context the relationship between the short term interest rates and the anticipated inflation doesn’t show any significant relationship. The interest rates in short terms have been unable to compensate for the inflation changes that occur in the short run. From the study we can say also say that in short term the investors are not compensated for the inflationary changes. In total interest rates and inflation are linearly independent at lag one. No relationship is observed between the said variables in short term.
The sources of the data are as follows
Websites used www.rbi.org.in www.reservebank.org.in www.eaindustry.nic.in www.mospi.nic.in
Software used SPSS Eviews
Books Referred Statistical methods Levin and Rubin Econometrics Damodaran Gujarati
Thomas J Sargeant “anticipated inflation and nominal interest rates” quarterly journal of finance pg no 212, 1972
“Interest Rates And Inflationary Expectations: New Evidences” American Economic Review (December 1972, pg no 854-865)
“Interest Rates as Predictors of Inflation in a High Inflation Semi Industrialized Economy”. Leonardo Leiderman , Journal of finance, vol XXXIV, September 1979. “Interest Rates and Inflationary Expectations: Tests for Structural Change 1952-1976”, Journal of finance, vol. XXXIV No.3, June1979. v “Short Term Interest Rates and Macroeconomic Variables an OSL Model” M Thenmozhi and Radha S, The ICFAI university press, January 2006. pg no 5-16.