Question 1 Discuss the following specification issues: i) In the context of the regression model yo = B1 + 8z*zi + ByXsi + & (a) Explain the meaning of the following statement: an OLS regression suffers from a A. Explain the notion of heteroskedastic error. Illustrate your answer using a graph. multicollinearity problem. What are the implications of this problem and how might it be solved? How would you detect multicollinearity in the context of [7 marks] this regression model? [6 marks] B. With reference to the OLS estimator of the marginal effect of x2; on yr, discuss the potential problems that a heteroskedastic error will create. Use the graph of the distribution of the OLS estimator to illustrate your answer. (b) Suppose that a test based on the conventional -statistic suggests that the coefficient By [7 marks] is insignificant, albeit marginally (e.g., the f-statistic is 1.90). Suppose also that regressors x2i and x3: are correlated. Would you drop regressor x3: from the regression? Why or why not? ii) The following exhibit reports the sample autocorrelation (AC) function obtained for the [7 marks] residuals of the regression model yt = 8, + 82*+ + &, t=1,2,...,T. The regression has been estimated using a sample of 7-200 monthly observations. Discuss the outcome of a test at the 5% significance level for the hypothesis that there is no autocorrelation up to lag order 6. What is the name of the test statistic being used? Write clearly the null hypothesis and alternative hypothesis of the test. What is the probability distribution of the test statistic? [13 marks] Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.022 0.022 1.3224 0.250 2 -0.010 -0.011 1.5973 0.450 3 0.056 0.057 10.216 0.017 4 0.011 0.008 10.545 0.032 5 -0.015 -0.014 11.138 0.049 6 -0.006 -0.008 11.233 0.081 7 -0.012 -0.013 11.627 0.114 8 0.015 0.017 12.270 0.140 9 -0.014 -0.014 12.828 0.171 10 -0.015 -0.013 13.443 0.200 11 0.050 0.049 20.201 0.043 12 0.036 0.035 23.731 0.022 iii) The following regression model has been estimated using a cross-section sample ye = Bit Baxzi + Byxai + Bakmi + 6, i-1,2,...,N observations