Hello Please reply only if you are sure about the precise complete answer . This

Question

Hello Please reply only if you are sure about the precise complete answer . This is exam ! Please consider my questions limit. don’t write incomplete answers ! 3. (a) Explain what is heteroscedasticity, and discuss its implications for OLS estimat (b) (c) of an econometric model Describe the tests that may be applied for heteroscedasitity. A saving function was tested for a country using the data over 31 years and the results are given below: S =-6641 + 0.08s, (117.6) (0.005) R2=0.903 The saving function was again estimated by OLS for two subsets of data relating to relating to 11 larger values of Y and 11 smaller values of Y, omitting the nine central observations, yielding RSSLow 144,771.5 and RSSIGH 769,899.2. Use this information to test for heteroscedasiticity and discuss your findings

Explanation / Answer

a) Heteroscedasticity refers to the situation when error variance is not constant. This implies Var(ui2) = i2 where ui is the error term.

The implication will be that the OLS estimators will not be BLUE anymore. The variance will be higher as a result there will very few significant t-values or the confidence interval will be widen.

b) One can use various tests to check for heteroscedasticity. I am describing white test for heteroscedasticity. Follow the steps given below.

We will run this test under the null hypothesis that there is not heteroscedasticity i.e. H0: No heteroscedasticity.

Step 1: Run the original OlS model and obtain the residuals ui.

Step 2: Now obtain ui2 and run the regression of ui2 on the X’s their cross product and the X squared. And obtain the R2

Step 3: Now the nR2 ~2(k-1) where k is no. of unknown parameters in Step 2.

Step 4: If the chi-square value obtained under step 3 is greater than the critical chi-square value, reject H0 else do not reject.

c) The part c) involves use of Goldfeld-Quandt test

Calculate =RSSHIGH/[(31-9)/(2-k)]/RSSLOW/[(31-9)/(2-k)]~ F((22/2-k),(22/2-k))

If the > than critical F-value then reject the null hypothesis of no heteroscedasticity.

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