Question 1- State with reasons whether the following statements are true or false:
a. Despite perfect multicollinearity, OLS estimators are best linear unbiased estimators (BLUE).
b. In cases of high multicollinearity, it is not possible to assess the individual significance of one or more partial regression coefficients.
c. If an auxiliary regression shows that a particular Ri2 is high, there is definite evidence of high collinearity.
d. High pairwise correlations do not necessarily suggest that there is high multicollinearity.
e. Multicollinearity is harmless if the objective of the analysis is prediction only.
Question 2- In data involving economic time series such as unemployment, money supply, interest rate, or consumption expenditure, multicollinearity is usually suspected. Why?
Question 3- Consider the following set of hypothetical data:
| Y: |
-10 |
-8 |
-6 |
-4 |
-2 |
0 |
2 |
4 |
6 |
8 |
10 |
| X2: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
| X3: |
1 |
3 |
5 |
7 |
9 |
11 |
13 |
15 |
17 |
19 |
21 |
Suppose you want to do a multiple regression of Y on X2 and X3.
a. Can you estimate the parameters of this model? Why or why not?
b. If not, which parameter or combination of parameters can you estimate?
Question 4- You are given the annual data in Table 8-5 for the United States for the period 1971 to 1986. Consider the following aggregate demand function for passenger cars:
In Yi = B1 + B2lnX2t + 83ln X3t + B4ln X4t + B5In X5t + B6lnX6t + ut
where ln = the natural log
a. What is the rationale for the introduction of both price indexes X2 and X3?
b. What might be the rationale for the introduction of the "employed civilian labor force" (X6) in the demand function?
c. How would you interpret the various partial slope coefficients?
d. Obtain OLS estimates of the preceding model.
Question 5- Continue with question 4. Is there multicollinearity in the previous problem? How do you know?
Question 6- If there is collinearity in question 4, estimate the various auxiliary regressions and find out which of the X variables are highly collinear.
Question 7- Check that all R2 values in Table 8-4 are statistically significant.
Question 8- Table 8-7 on the textbook's Web site gives data on imports, GDP, and the Consumer Price Index (CPI) for the United States over the period 1975-2005. You are asked to consider the following model:
In Importst = β1 + β2In GDPt + β3ln CPIt+ ut
a. Estimate the parameters of this model using the data given in the table.
b. Do you suspect that there is multicollinearity in the data?
c. Regress: (1) In Importst = A1 + A2 In GDPt
(2) In Importst = B1 + B2 ln CPIt
(3) In GDPt = C1 + C2 In CPIt
On the basis of these regressions, what can you say about the nature of multicollinearity in the data?
d. Suppose there is multicollinearity in the data but β2^ and β3^ are individually significant at the 5% level and the overall F test is also significant. In this case, should we worry about the collinearity problem?
Question 9- Table 8-8 on the textbook's Web site gives data on new passenger cars sold in the United States as a function of several variables.
a. Develop a suitable linear or log-linear model to estimate a demand function for automobiles in the United States.
b. If you decide to include all the regressors given in the table as explanatory variables, do you expect to face the multicollinearity problem? Why?
c. If you do expect to face the multicollinearity problem, how will you go about resolving the problem? State your assumptions clearly and show all calculations.
Attachment:- Tables.rar