Eviews - L3

Question 1

What is the general formula for an F-test?

Answer 1

-use the Wald test on EViews

Question 2

how can we test for non-linearity?

Answer 2

• We firstly take a linear relationship
• We then add higher order powers (this is usually the squared values of each X variable and their cross products - all with their own β coefficient
• to the test for non-linearity we want to perform a hypothesis test under the null that all the β coefficients to the higher order powers = 0 (so the model would be the same as the original and is linear)
• if we reject the null then there is obvious some element of a non-linear relationship
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Question 3

What is the problem with testing non-linearity by adding high powers?

Answer 3

• increasing the number of explaintory variable:
• after the degrees of freedom
• the squared terms will mostly likely be highly correlated with the original regress variables –> we end up with multicollinearity which lead to very imprecise estimates of the coefficient

That why we use the Ramsey RESET test

Question 4

How does the Ramsey RESET test solve the problem faced when testing for non-linearity?

Answer 4

• It is able to test for the joint significance of the coefficients of the higher order powers without running into the problem of multicollinearity by including each of the variables separately
• In the Ramsey RESET test:
  
  • You find the fitted values of the regression equation
  • Then find the squared fitted values of the regression equation
  • by adding the two together you get the original fitted equation plus Y(hat)² which is the squared fitted values
  • its coefficient is γ which captures the statistical significance of all the high order β coefficient
  • Then we use either a t-test or F-test to see γ=0 or not

Question 5

How is the F-statistic related to the t-statistic?

Answer 5

• The F-statistic is the square of the t-statistic