# Statistical Study Of Inflation Fluctuation

An in-depth study of Economic variables effecting Inflation. The use of forecasting and regression models with many Statistical tests and considerations. Off course, the content here is very messy as

Date : 26/7/2013

### Author Information Subject : Maths

Analysis of Inflation

### Dependent Variable

I have chosen Inflation as my dependent variable. As Milton Friedman states, Inflation is a ".steady and sustained increase in the general price level" (Friedman 1977). This then carries great implications on many aspects of the economy. It is particularly interesting as this variable is affected by many other variables and has a sceptical nature. Ever since the gold standard was abandoned and the fiat standard was put in place (with the expectations of better economic growth) there has been a major degree of instability with varying economic cycles and artificial money. However, under the new standard many economies have more leeway to grow but also have to face the many trade-offs (Rolnick and Weber 1997). As mentioned previously, there are many factors the affect inflation and its movement may sometime be unpredictable and sceptical. This off course carries a larger burden and challenge for me analysing this variable, but out of keenness I have chosen to proceed with it.

### Fluctuations of Inflation

The first apparent observation we could deduce is the rapid movements in the years 1975/80/90. A BBC article emphasised the desperate state of the economy in an article expressing many economic fears and implications that existed in 1975 (Stone Lee 2005). These rapid movements represent the cycles of the economy as we could also see in the most recent rapid movement was in 2009 when the UK economy suffered economic decline with inflation dropping to -0.5% namely deflation or near stagnation if it had persisted near 0%. From 1993 up till the recession the fluctuations seem to be moving around the 2% mark, which is the objective of the UK economy give/take 1%.

### Independent variables

As mentioned before, there could be many variables that could explain the variation in Inflation. I have chosen 3 independent variables that I think are most effective in assessing the variations in inflation and may also coincide with economic theories and government objectives which would make it more interesting.

### Income

This variable is worked as an average of UK salaries. It would interesting to observe the relationship between income and inflation as the common assumption would suggest that as income rises so does disposable income which leads to increased expenditure which then results in increased consumption which raises aggregate demand and thus increases inflation. However, as interest rates vary, this also affects expenditure as increased income may lead to increased savings and a decrease in consumption causing the opposite affect (interest rates were high in many early years of my data set).

### Interest Rate

The monetary policy manipulates interest rates to try to achieve inflation targets. An increase interest rate would encourage saving and less spending which would cause inflation to calm down and vice-versa. However, this is may be based on mere speculation and assuming other variables are fairly constant and there is a time lag in its effectiveness. This variable would therefore be very interesting to assess.

### Unemployment

The Phillips curve suggests a short-term trade-off between inflation and unemployment. When there is a large amount of consumption (high inflation rates) there will also be a higher demand for labour to meet consumption levels and aggregate demand, this will therefore decrease unemployment and vice-versa. When unemployment varies, this determines disposable income and therefore effects consumption and inflation. However, in the long term this model may become less effective as other forces and variables become present.

### Econometric Equation

multiple regression model is shown below:
Yt = ?0 + ?1 X1t + ?2 X2t + ?3 X3t + ?t
Where Yt is the annual inflation rate and ?0 is a constant value. X1 denotes income, X2 is the annual interest rate and X3 represents unemployment. The Et coefficient accounts for errors.

### 2.6 The Multiple Regression Model

An estimation output from Eviews presents the relationship that exists between the dependent and independent variables. The P-value suggests if the null hypothesis value were true, sampling variation would create an estimate that is further away from the hypothesised value than our data estimate (Statistics, 2011). If the p-value is below 0.05 (5% significance level) than the null hypothesis is rejected and the alternate hypothesis is accepted, however if it is above 0.05 then there is not enough evidence to reject the null hypothesis. From the model we could see that the P-value<0.05 is the case for each of my independent variables so H0 is rejected. The model with each independent variable is therefore useful in predicting Y.

The R value assesses the extent at which the independent variables explain the variations in the dependent variable. The value in the estimation output is 66%, so 66% of the variation is explained by my independent variables.

The change in interest rates takes up to 18months to affect inflation as established by the monetary policy so I think I could improve the model by lagging the interest rates one period.

### 2.7 Improved model (lag (-1) on interest rate)

Dependent Variable: INFLATION
Method: Least Squares
Date: 01/03/13 Time: 17:48

The P-Values have decreased significantly attesting further to the usefulness of the independent variables and the R value has increased considerably.

### Diagnostic testing

3.1 Multicollinearity test This test assesses the correlation that exists between 2 or more independent variables and it is preferable if the correlations are low to avoid possible prediction flaws.

### Decrease Multicollinearity correlation

I have tried many attempts to edit the variables to lower the relationship, the only possible change I could make without disrupting my estimation output and variables too much is to square the interest rates.

Dependent Variable: INFLATION
Method: Least Squares
Date: 01/04/13 Time: 17:28

### Breusch Godfrey - Serial Correlation LM test

Serial correlation exists when the variable is affected by its previous values in past periods. In my estimation output it shows the Durbin-Watson stat at 1.18 close to 1 so there is evidence that there is positive serial correlation in the model. Breusch-Godfrey Serial Correlation LM Test:

Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 01/04/13 Time: 19:41
Sample: 1971 2006
Included observations: 36
Presample missing value lagged residuals set to zero.

My initial model (with no edits made to variables) would have no serial correlation (as tried before), since edits have been made and significantly improved the models p-value and r-squared I will proceed with this model and opt for serial correlation present. 3.4 Heteroskedasticity This test identifies if the variance of the error term in a regression model is not constant between observations leading to more frequent occurrence of errors in forecasting. Heteroskedasticity Test: Breusch-Pagan-Godfrey

Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 01/04/13 Time: 19:28
Sample: 1971 2006
Included observations: 36

### Ramsey RESET Test

This test checks for non-linearity in the model. The model assumes a linear relationship between the independent and depend variable. In some cases there may be a non-linear relationship between the independent and dependent variable.

LR test summary: Value df
Restricted LogL -82.16592 32
Unrestricted LogL -77.14725 31

Unrestricted Test Equation: Dependent Variable: INFLATION Method: Least Squares Date: 01/04/13 Time: 19:36 Sample: 1971 2006 Included observations: 36

This resource was uploaded by: Ajay Vignesh