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Answer all of the following questions and submit your assignment by 4:00 pm on the due date through UM Learn. Submit 1 Excel file and 1 .pdf or Word document. Please get in touch with me via email with any questions. 1. Throughout this semester, we have been working with the so-called “household income – food expenditure model” (HI-FE model) where food expenditure for a household is a function of the level of household income. Our dataset can be found in the file Table 3-1.dat on the course homepage. (a) We have discussed how there may be heteroskedasticity in this model. Using the data found in Table 3-1.dat on our course homepage, test for heteroskedasticity in the model using the Goldfeldt-Quandt test. But instead of using the method found in the Excel manual, review the Lecture 11 notes and video and carry out all parts of the test by hand (show all your work; you may use a calculator). You may use Excel to run any needed regressions for this question but all parts of the test itself must be written out. (10 marks) (b) Find generalized least squares estimates for the HI-FE model assuming the following variance structures: (i) var (et) = (ii) var (et) = s2xt (10 marks each) (c) Mathematically show, in writing, why the heteroskedasticity correction you chose for each of the variance structures in part (b) would work (5 marks each) 2. Consider the investment function It = b1 + b2Yt + b3Rt + et, where It is the level of investment in the economy, Yt is gross national product (a measure of income) and Rt is the interest rate. The file inv.dat on the course homepage contains 30 years’ data for these variables. (a) Estimate the equation above and report your findings. Do the estimates for b1 and b2 have the expected signs? (10 marks) (b) Plot the residuals from your model in part (a). Does there appear to be autocorrelation? Why or why not? (5 marks) (c) Use the Durbin-Watson test to check for autocorrelation. Be sure to carry out all parts of the hypothesis test. Show all your work. (10 marks) (d) Use a Lagrange Multiplier test to check for autocorrelation. Be sure to carry out all parts of the hypothesis test. (5 marks) (e) Re-estimate the model after correcting for autocorrelation. (10 marks)
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