Financial Econometrics Coursework - Essay Example

In 2003, the U.S. Securities and Exchange Commission (SEC) mentioned that the R-square of the regression analysis was insufficient to determine the effectiveness of hedging. A speech by a professional accounting fellow from the office of the chief accountant of the U.S. Securities and Exchange Commission stated that determination of hedge effectiveness should consider the slope of the coefficient of the regression analysis. This coefficient reflects the minimum variance hedge ratio.

Question 2:

2. A.

The interpretation of the regression slope coefficient is the average change in the dependent variable: real total expenditure on food for a unit increase in the independent variable: Real total expenditure on goods and services. The slope coefficient is 0.32, thus for every 1 unit change in real total expenditure on goods and services, there is a 0.32 unit change in real expenditure on food.

2. B.

To test the null hypothesis that a 1% increase in real total expenditures on goods and services leads to 0.25% increase in real total expenditures on food:

Assuming:       100* Δ[ln(X )]≈ %ΔX

Therefore:       1% change = 100* Δ[ln(1 )] = 0

Null hypothesis: slope = 0,

Alternative hypothesis: slope not equal to 0.

Using the p-value approach, the p-value is given in the output = 0.0001.

Since the p-value is < 0.01 we reject the null hypothesis and accept the alternative hypothesis.

Conclusion:

A 1% increase in real total expenditures on goods and services leads to a 0.25% increase in real total expenditure on food using a significance level of 1%.

C.

95% confidence interval estimate for β2 = coefficient of β 2 +/- t_.005 * SE β 2

= 0.3224 +/- 0.11654 * 0.0194

= (0.320139, 0.324661)

2.D.

Ramsey's Regression Specification Error Test (RESET) = 2.748

Since p-value = 0.0064 which is less than < .01.

Then the null hypothesis that the coefficient is zero can be rejected at the 1% level.

E:

Omission of an important independent variable such as the real price of food relative to other goods will result in the decreased ability of the model to predict the real total expenditures on food given the real total expenditures on food.

The value of the slope coefficient would decrease.

The null hypothesis could not be rejected, and the confidence interval would become wider

 The statistical results are explained as follows:

The independent varia were les used to predict 99.9% of the dependent variable: real consumption expenditure as indicated by the value of the adjusted-R Squared. The Durbin-Watson value of 1.85 indicates tar are no signs of first-order serial correlation in the residuals of a time series regression. The values of Akaike info criterion (AIC) -268.2093 and Schwarz criterion -273.6530 are extremely low indicating the need for modification in the regression model by changing the independent variables. The t-statistic value could be compared with the critical t-value which is not available.

The reported Probability is the p-value, or marginal significance level. Since this probability value of the regression analysis (F-statistic) is less than the size of the test, say 0.05, the null hypothesis could be rejected. This indicates that the regression equation could be used to predict the real consumption expenditure based on personal shareholdings personal bond holdings, net liquid assets net of house loans, share prices, bond prices, real disposable income. This could be accomplished by using the following equation:

Real consumption expenditure = 7093 -0.0076 * personal shareholdings -0.1498 * personal bond holdings -0.0643 * net liquid assets net of house loans + 3.1394 * share prices + 8.3013 * bond prices + 0.7915 * real disposable income.

To refine and improve the model it is best to determine the relevance of each variable, it is best to omit the variable and examine the values of the t-test, adjusted R-Squared, and bias. The probability values for some of the independent variables are larger than .05. This is the case for the probability of the variables; personal shareholdings (AS) of 0.864, bond prices (BP) 0.520, and share prices (SP) 0.156. It is suggested to omit the personal shareholdings variable and then re-evaluate the values of probability of each independent variable and R-squared values. Then it is suggested to omit the independent variable BP, then SP.