POLS 6482 ADVANCED MULTIVARIATE STATISTICS
Fifth Assignment
Due 8 October 2001

1. The aim of this problem is to learn how do coefficient tests in EVIEWS and STATA using the Refrigerator data discussed in Epple Notes IV pp.15-19. Download the data and bring it up in EVIEWS.
   
   Refrigerator Data
   
   
   1. Replicate the analyses performed in Epple Notes IV pp.15-19.
      
      
   2. Answer questions 4.3 and 4.4 on page IV-22. With respect to question 4.4, generate an appropriate variable in EVIEWS and run the regression.
      
      
   3. Paste the dataset into STATA, insert the appropriate names and labels, do the d and summ commands and report the results.
      
      
   4. In STATA run the regression shown on page IV-15.
      
      
   5. In STATA perform the Wald Test discussed on page IV-19:
      
      test Opcost=-9.385
      
      
2. This problem is a continuation of 1.c of the 3^rd homework and 2 of the 4^th homework. I made some corrections in the file so download the new version:
   
   105th Elections Data by Congressional District (HDMG105Y.DTA)
   
   
   1. Bring up the HDMG105Y.DTA in STATA. Do the d and summ commands and report the results.
      
      Note that there are three types of variables: personal characteristics of the representative (e.g., female, aamer, himem, rep, catholic, etc.); demographics of the congressional district (e.g., black, hisp, asian, etc.); and election results (e.g., clint96, dole96, bush92, etc.).
      
      The variable dwnom1 is a measure of the economic liberalism/conservatism of the member of Congress and it ranges from approximately -1 (liberal) to +1 (conservative). The variable dwnom2 is a measure of the social liberalism/conservatism of the member of Congress and it ranges from approximately -1 (social-liberal) to +1 (social-conservative).
      
      
   2. Paste HDMG105Y.DTA into EVIEWS. Run the regression:
      
      ls clint96 c black south hisp income dwnom1 dwnom2 female aamer himem
      
      Do the results make sense to you? Specifically, should the personal characteristics of the representative have any effect upon the Clinton vote in the congressional district? Justify your answer.
      
      
   3. If we believe that the personal characteristics of the member of the House should have no effect upon the presidential vote, then this is tantamount to testing the following null hypothesis:
      
      b_female = b_aamer = b_himem = 0
      
      We can test this null hypothesis using the method discussed in Epple Notes V. The method is a more elaborate version of the simple Wald test done on the refrigerator data. Follow the same steps discussed on page IV-19. For example, if the variable female is C(3) in the Estimation Equation and aamer and himem are C(4) and C(5) respectively, in the Estimation Equation, then the command in EVIEWS is
      
      WALD C(3)=C(4)=C(5)=0
      
      (WARNING! Note that WALD C(3)=C(4)=C(5) tests whether or not the coefficients have the same value! This is different from testing whether or not they all are equal to zero!)
      
      
   4. In STATA, to perform the Wald test first run the regression and then type:
      
      test female aamer himem
      
      This tests b_female = b_aamer = b_himem = 0
      
      An alternative way to perform the test that sometimes is very convenient is to first type:
      
      test female=0
      
      then type:
      
      test aamer=0, accumulate
      
      This tests b_female = b_aamer = 0. Then if you type:
      
      test himem=0, accumulate
      
      You get the full test b_female = b_aamer = b_himem = 0. The keyword "accumulate" causes STATA to test the joint restriction that the coefficients on female, then aamer, and then himem are all equal to zero.
      
      (Note that, to test b_female = b_aamer = b_himem you would use the commands:
      
      test female=aamer
      
      then:
      
      test female=himem, accumulate)
      
      
   5. In EVIEWS run the above regression without the personal characteristics of the representative; namely:
      
      ls clint96 c black south hisp income dwnom1 dwnom2
      
      The sum of squared error should be larger for this regression (Sum squared resid in the EVIEWS regression table). How much larger is it? Compute the difference and divide by 3 ("3" is the number of restrictions -- see Epple notes V pp.1-7 -- the formula is (SSE_R - SSE_UR)/number of restrictions ). This number is the numerator of the formula shown in Epple notes V-1. Now, take the sum of squared error from the full regression with the personal characteristics (this is SSE_UR in Epple notes V) and divide it by 425. This is the denominator of the formula shown in Epple notes V-1. Compute the resulting number and compare it to the value shown in the Wald tests (show all of your work). The two numbers should be the same. This is the F-Statistic for the Wald test.
      
      
   6. Take the above result and calculate the P-Value using EVIEWS. Suppose the F value is .55. In EVIEWS enter the command:
      
      scalar pval=@fdist(.55,3,425)
      
      "pval" will now appear in the EVIEWS workfile. Double-Click on "pval" and the probability, .648389482496, will appear at the bottom of the window. The "3,425" in the fdist argument gives the degrees of freedom for the numerator and denominator, respectively.
      
      To calculate the P-Value using STATA enter the command:
      
      display fprob(3,425,.55)
      
      and the probability, .64838948, will appear in the "Stata Results" window.