Fishers Hypothesis and the UK Economy - Essay Example

Fishers Hypothesis and the UK Economy: This paper discusses the Fisher hypothesis that depicts a relationship between inflation and nominal interest rates, this model states that real interest rate is equal to nominal interest rate plus expected inflation rate. There are three major results which include a correlation coefficient analysis that shows a strong relationship between the variables, A co integration test shows that expected inflation rates will affect interest rates and a regression model I =α + βΠet where I is nominal interest rate and Πet is expected inflation that depicts the relationship between expected inflation and nominal interest rates. Introduction: This paper analysis the Fishers hypothesis using data for the UK over the last 20 years, the main aim of this paper is to analyze the relationship between interest rate and inflation, the main aim of this analysis is to show that real interest rate is equal to expected inflation rate plus nominal interest rates, the paper also analysis the underlying theories that depict the relationship between the variables. Interest rates and inflation are important economic variables, high levels inflation in an economy shows that there is something wrong in the economy and policy makers will try and reduce the high inflation rate. However the Fishers model may not hold in the short run given that the policy makers may alter interest rates in the short run, a study by Yuhn (1996) showed that the relationship between interest rate and inflation was stronger over the long run than in the short run. The Fishers hypothesis depicts that nominal interest rates do not depend on monetary policy measures and that there is a positive relationship between nominal interest rate and the expected inflation rate. The Fisher hypothesis model states that real interest rate is equal to nominal interest rate plus expected inflation rate stated as R = I + Πe where R is real interest rate, Πe is the expected inflation rate and I is nominal interest rate. The Fishers hypothesis model is also stated as I =α + βΠet where I is nominal interest rate and Πet is expected inflation. The value of β is expected to be positive and a value of β = 1 shows the strong version of the Fishers hypothesis. The paper analysis the correlation between the variables and help identify whether there is a strong positive relationship between inflation and nominal interest rate, however the correlation coefficient value only shows how two variables move together and this means that there is need to run a regression model that states the relationship between nominal interest rate, a cointergration test is also undertaken in order to analyse the relationship between real interest rate, nominal interest rate and inflation. Theories: There are theories that depict the relationship between of interest rates and prices, an increase or decline in interest rate will have an effect on the price level in the economy. An increase in interest rate will have an effect on the level of investment in an economy, according to Kandil (2005) an increase in interest rates will affect investment in two ways, increasing interest rate will reduce investment levels given that the cost of borrowed funds increase, on the other hand an increase in interest rate has a negative effect on the net present value of investment. The rate of interest rate also has an effect on the price level in an economy, when interest rate increase producers in the economy experience an increase in the cost of capital and this cost is transferred to consumers through higher prices, therefore the increase in interest rate will increase price levels in the economy. A study by Mishkin (1992) showed that interest rate and expected inflation are positively related over the long run, however his finding showed that in the long run this relationship did not hold for US data, Yuhn (1996) showed that the relationship between this variable was stronger over the long run than in the short run There exist other theories that oppose the effect of interest rate on inflation, from the discussion it is evident that an increase in interest rate will encourage savings in the economy and discourage borrowers. Ball (1990) states that increasing interest rates will encourage workers to work more hours in order to save at the high interest rate levels, this increases labour supply which increases the level of output in the economy and therefore prices will decline as the level of supply increases. The relationship between real interest rate, nominal interest rate and inflation is stated as R = I + Πe where R is real interest rate, Πe is the expected inflation rate and I is nominal interest rate, Mishkin (1992) states that if this relationship holds then the changes in interest rate will reflect the changes in inflation expectations and therefore may be used to depict future inflation expectations. Mallick (2004) used UK data to test Fishers hypothesis and his analysis showed that the Johansen cointergration test was the most appropriate to analyze the relationship between the variable. The Fishers hypothesis model regarding the relationship between nominal interest rate and inflation is stated as I =α + βΠet whereby the value of β is expected to be positive, the strong version of the fishers hypothesis will yield the value of β = 1, however the weaker form of the fishers model will yield the value of β < 1. Darby (1975) depicts a model where β is greater than 1 and this due to the tax effect, the change in nominal interest rate in the case of tax will be greater than the change in inflation and therefore the value of the slope in the model will be greater than one. From the above analysis therefore it is evident that the all the theories depict the value of β being positive, the following is an analysis of the data and model specified. Data: Data used for this study is nominal interest rate for the UK for the period 1989 to 2008 and inflation rate for the same period, according to Mishkin (1992) some economic series such as the inflation rate series tend to possess unit root, this means that the current period data value depends on lagged variables or previous values of the variable, this means that applying regression on this variables will mean that regression assumptions will not hold, this means that we have to test for unit root using the Dickey Fuller test. Because expected inflation rate is unobservable we use past inflation rate to analyze the relationship, the following is the data used in this analysis: treasury bill data was used for the UK to represent nominal interest rates and data was retrieved from the Bank of England database, consumer index data that was used to calculate inflation rate was retrieved from the UK labour statistics database: year 3 month treasury bills annual average inflation (all products) 1989 13.29 0.051968504 1990 14.09 0.070359281 1991 10.82 0.074125874 1992 8.91 0.04296875 1993 5.21 0.024968789 1994 5.16 0.020706456 1995 6.33 0.026252983 1996 5.78 0.024418605 1997 6.5 0.01816118 1998 6.81 0.015607581 1999 5.04 0.013172338 2000 5.8 0.008667389 2001 4.76 0.011815252 2002 3.86 0.012738854 2003 3.56 0.013626834 2004 4.44 0.01344364 2005 4.55 0.020408163 2006 4.65 0.023 2007 5.53 0.023460411 2008 4.34 0.036294174 The following chart represents trend in inflation rate in the UK: From the chart it is evident that inflation rate declined for the period 1991 to 2000 where inflation rate increased gradually to the year 2008. The chart below shows the 3 year Treasury bill rate in the UK: From the above chart it is evident that the Treasury bill rate has a general downward trend, lowest values were recorded in 2003 where the rate started to increase gradually and in the period 2007 to 2008 the rate declined. From the two trends it is evident that they have a relatively similar shape meaning that there is a strong relationship between the variables. Methods: This section shows an analysis of the relationship between the variables using various techniques including correlation, the correlation coefficient is a statistical value that depicts the strength and nature of the relationship between two variables, a high positive correlation coefficient for our variables will depict that Fishers hypothesis holds. The other method is to estimate the model I =α + βΠet using the OLS method, this will involve including all the data variables and observing the value of β which is expected to have the value 1, however values greater or greater than one can be explained by the weak form of the Fisher hypothesis if the value is less than one or the tax effect explained by Darby (1975) if the value is greater than 1. Finally the Johansen cointergration test is applied in order to show the effect of changes in inflation on the interest rate, this method is applied on the data and the results will depict the percentage level of inflation rate that will increase interest rate by 1%, Results: Correlation coefficient: The following table summarizes the correlation coefficient between the two variables. INFLATION NOMINAL INTEREST RATE INFLATION  1.000000  0.857759 NOMINAL INTEREST RATE  0.857759  1.000000 From the above the correlation coefficient value is 0.857759, the positive value shows that there is a positive relationship between the two variables; this means that as one variable increases the other variable is also increasing and that if we reduce the values of one value the other value will also decline. The value 0.85 is close to one and this shows that there is a strong relationship between the two variables. Dickey Fuller test: Mishkin (1992) states that economic series tend to possess unit root whereby current period data value depends on previous values of the variable, therefore regression assumption on autocorrelation may not hold , we apply the Dickey Fuller test on the data. The following is a test of unit root whereby we determine whether the series has unit root, the ADF test null hypothesis states that the series exhibits unit, the following table summarises the test for the inflation variable: Null Hypothesis: D(INFLATION2) has a unit root Exogenous: Constant, Linear Trend Lag Length: 4 (Automatic based on SIC, MAXLAG=4) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -5.663985  0.0026 Test critical values: 1% level -4.800080 5% level -3.791172 10% level -3.342253 From the above table the ADF test statistics value is greater than the critical value at 1%, 5% and 10%, when T statistics > T critical value the null hypothesis is rejected , therefore the conclusion is that the series does not exhibit unit root. The following table summarizes the test for the interest rate series: Null Hypothesis: D(NOMINALINTERESTRATE) has a unit root Exogenous: Constant, Linear Trend Lag Length: 4 (Automatic based on SIC, MAXLAG=4) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -3.896858  0.0423 Test critical values: 1% level -4.800080 5% level -3.791172 10% level -3.342253 From the above table it is evident that the ADF critical value is greater than the critical value at 5% and 10%, when T statistics > T critical value the null hypothesis is rejected the null hypothesis that there is unit root, however this value is less than the 1% level of test, this means that the series does not exhibit unit root at the 5% and 10% level of test. Regression: The fishers model is stated as I =α + βΠet and the value of β is expected to be positive, we estimate this model using Eview, however according to Mishkin (1992) some economic series such as the inflation rate series tend to possess unit root therefore we apply the Dickey Fuller test to test unit root, the following table summarizes the results: Dependent Variable: NOMINAL INTEREST RATE Method: Least Squares Date: 05/06/09 Time: 10:26 Sample: 1989 2008 Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob.   C 2.738812 0.635009 4.313030 0.0004 INFLATION2 1.366872 0.193078 7.079369 0.0000 R-squared 0.735751     Mean dependent var 6.471500 From the above output we state our model as follows: I =2.738812+ 1.366872Πet The above estimated model depicts that the constant and the slope of the model is positive, a 95% level of test on the significance of these estimated coefficients shows that they are statistically significant, the model states that if expected inflation increases by 1% holding all other factors constant then the interest rates will increase by 1.367%. the correlation of determination value R squared is 0.7357 which shows a strong relationship between the dependent variable interest rate and the independent variable expected inflation, the value shows that 73.57% deviations in the dependent variable are explained by the changes in the independent variable. From the above equation it is evident that the value of β is greater than the value 1, this can be explained by Darby (1975) who states that nominal interest rates are taxed and therefore this means that a change in the nominal interest rate will be greater than the change in expected inflation rate and this is because the relationship that depict the relationship between the real interest rate, nominal interest rate and inflation expected (R = I + Πe where R is real interest rate, Πe is the expected inflation rate and I is nominal interest rate) to hold. Cointergration test: MacKinnon (1987) state that two variables that are non stationary may have a stationary linear equation and therefore the two variables are said to cointegrated, in this case therefore given that I and Πe are non stationary we determine whether the linear equation is stationary. Johansen cointergration test is applied and the following table summarizes the output: Sample (adjusted): 1991 2008 Included observations: 18 after adjustments Trend assumption: Linear deterministic trend (restricted) Series: NOMINALINTERESTRATE INFLATION2  Lags interval (in first differences): 1 to 1 Hypothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None *  0.787762  27.90082  19.38704  0.0023 At most 1  0.184987  3.681927  12.51798  0.7875 1 Cointegrating Equation(s):  Log likelihood -34.01156 Normalized cointegrating coefficients (standard error in parentheses) NOMINALINTERESTRATE INFLATION2 @TREND(90)  1.000000 -0.298561  0.159729  (0.17700)  (0.06048) From the above table we state the model as: I = -0.159729 +0.298561 Π The above equation means that if we increase the level of expected inflation by one percent then interest rates will increase by 0.29856%, from the above table it is evident that cointergration exists and this means that all variables are stationary, from the above results therefore it is evident that policy makers can adjust the yield curve by adjusting interest rates, and given that interest rates are adjusted according to inflation expectations. Conclusion: From the above analysis it is evident that the nominal interest rates and inflation rates are related given that the value of their correlation is positive, the correlation coefficient for the two variables is 0.85 which shows a strong relationship between the variables. The regression model also shows that the two variables are positively related meaning that as inflation rate increases interest rates increase, the value of regression model from the estimated model is greater than one and this shows that the change in nominal interest rate is greater than the change in the rate of inflation, however this is explained by the fact that nominal interest rates are taxed. From cointergration test it is evident that an increase in inflation will affect the interest rates, from our analysis it is evident that a 1% increase in inflation rate will increase interest rates by 0.29%, this means that policy makers will adjust interest rates that will affect the yield curve given that interest rates are adjusted with reference to expected inflation. References: Bank of England (2009) 3 month treasury bills annual average rate data, retrieved on 4th May, from http://www.bankofengland.co.uk Ball, L (1990) Inter temporal substitution and constraints on labour supply, economic inquiry, 28, 706 to 724 Brigitte Granville and Sushanta Mallick (2004) ‘Fisher hypothesis: UK evidence over a century’ Applied Economics, 2004, 11, 87 to 90. Darby, M. (1975) ‘Financial and Tax effect of monetary policy on interest rates’, economic inquiry, 13, and 266 to 276 Kandil, M. (2005) ‘Money, Interest and Prices: some international evidence’, international review of economics and finance, 14, 129 to 147. MacKinnon, J. (1987) Critical values for co integration tests: Long run Economic relationships, Cambridge: Cambridge University Press. Mishkin, F. (1992) Is the Fisher Effect for real, Journal of monetary economics, 30, 195 to 215. UK Labour Statistics (2009) Consumer Price index data, retrieved on 4th May, from http://www.statistics.gov.uk/statbase/TSDdownload1.asp Yuhn, K. (1996) Is the Fisher effect robust: Further evidence, Applied Economics, 3, 41to 44. Appendixes: Dependent Variable: NOMINALINTERESTRATE Method: Least Squares Date: 05/06/09 Time: 10:26 Sample: 1989 2008 Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob.   C 2.738812 0.635009 4.313030 0.0004 INFLATION2 1.366872 0.193078 7.079369 0.0000 R-squared 0.735751     Mean dependent var 6.471500 Adjusted R-squared 0.721070     S.D. dependent var 2.996551 S.E. of regression 1.582593     Akaike info criterion 3.850646 Sum squared resid 45.08281     Schwarz criterion 3.950219 Log likelihood -36.50646     F-statistic 50.11747 Durbin-Watson stat 1.021532     Prob(F-statistic) 0.000001 Date: 05/06/09 Time: 23:24 Sample (adjusted): 1991 2008 Included observations: 18 after adjustments Trend assumption: Linear deterministic trend (restricted) Series: NOMINALINTERESTRATE INFLATION2  Lags interval (in first differences): 1 to 1 Unrestricted Cointegration Rank Test (Trace) Hypothesized Trace 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None *  0.787762  31.58274  25.87211  0.0087 At most 1  0.184987  3.681927  12.51798  0.7875  Trace test indicates 1 cointegrating eqn(s) at the 0.05 level  * denotes rejection of the hypothesis at the 0.05 level  **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None *  0.787762  27.90082  19.38704  0.0023 At most 1  0.184987  3.681927  12.51798  0.7875  Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level  * denotes rejection of the hypothesis at the 0.05 level  **MacKinnon-Haug-Michelis (1999) p-values  Unrestricted Cointegrating Coefficients (normalized by b*S11*b=I):  NOMINALINTERESTRATE INFLATION2 @TREND(90)  0.660034 -0.197060  0.105426 -1.071838  1.354643 -0.240860  Unrestricted Adjustment Coefficients (alpha):  D(NOMINALINTERESTRATE) -1.191317  0.087237 D(INFLATION2) -0.315437 -0.246345 1 Cointegrating Equation(s):  Log likelihood -34.01156 Normalized cointegrating coefficients (standard error in parentheses) NOMINALINTERESTRATE INFLATION2 @TREND(90)  1.000000 -0.298561  0.159729  (0.17700)  (0.06048) Adjustment coefficients (standard error in parentheses) D(NOMINALINTERESTRATE) -0.786309  (0.11480) D(INFLATION2) -0.208199  (0.10508) Read More