Assignment Questions on Household Income and Investment Functions

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)