ECON 120C, FALL 1998  --  HOMEWORK #1


This assignment should be done in three different parts, but a single
set of papers should be submitted.  It is due no later than 11:10 am,
Tuesday, October 20, 1998, and will carry a weight of 5% towards the
grade.  Papers turned in at the end of the class will carry a 10%
penalty.  AFTER CLASS, NO PAPERS WILL BE ACCEPTED.  As before, I
recommend that you team up with one or two more persons, do each
problem individually (otherwise you won't be well prepared for exams),
but submit a joint paper with all your names (max 3).  You are not
allowed to add your name later.  If you try to do that, I will consider
it a blatant attempt to cheat and give you zero points for the
assignment AND THE FIRST MID-TERM EXAM.  If your name appears on more
than one paper, the LOWER score will be recorded.

If you have not done the Practice Computer session posted in the
bulletin, do that right away.  Also, if you have installed ESL/ESLWIN
at home, by sure to download the updated files esl.exe, esl.cfg, and
esl.hlp and follow the directions in readme.txt in the Web page link.

This and the next part requires you to run things on the computer.  Use
different names for the input/output files from each session so that
you can recover from any mistakes.

Submit the computer output with annotations on the margin to answer the
questions.  All references are to the fourth edition only.  Although
the theory section is the same as in 3/e, the applications and examples
are quite different and there is more in 4/e.

The data you will be using here is DATA4-15.  For details on the
variables, see DATA4-15 in Appendix D.  The dependent variable is the
Gini coefficient, which is a measure of the income inequality in a
country.
    
Run ESL, choose whatever names you want for the input and output files,
and select the data set DATA4-15.  From ESLDOS, you would type 0 to exit
the default menu, then DATA4-15 for the data.  From ESLWIN, you use the
mouse to select the data file.

I.1   When you get the ? prompt, type the command:
             summary ;
      which computes summary statistics for all the variables.  Then
             square 2 3 4 5 6 7 8 ;
      to generate the squares of the independent variables.  Next
      estimate by ols the most general model with the linear and
      squares terms (ols 1 0 2 3 ...  15 ;).  Be careful in
      typing this line and make no mistakes.

I.2   Choose the variable (ignore the constant term in all this) that
      has the least significant coefficient (two-sided alternative) and
      use the omit command to exclude it and reestimate the new model. 
      Repeat this process until all variables have significant
      coefficients at the 10 percent level.  If, at any time, you want
      to see a list of variables, simply, type: list and press enter
      key.  To scroll for previous results, type: scroll.  Semicolon
      is needed only for open-ended items such as the ols command above.
      When you are finished with the session type: quit to exit ESL.  View
      the output file from the editor and make sure that you have not
      made any mistakes.  If everything is OK, use the File, Print
      commands from Notepad to print the file.  Be sure to edit the
      font size to point size 10.  Higher sizes will make the lines too
      long.

      If you made a mistake, you can use Notepad to change the input
      command file saved in the previous session, and then use the run
      command within ESL.

I.3   Using model selection statistics, significance of coefficients, 
      and the danger of omitted variable bias, choose the "best" model. 
      Carefully justify your choice.

      Be sure to submit your ORIGINAL computer printouts with
      annotations on the margin, justifying each step and answering the
      above questions.  Submitting Xerox copies of another person's
      outputs will be treated as cheating and the penalty is the same
      as before.

II.   After I cover the LM test for model specification, study Section
      6.14 on simple to general modeling.  Next review the LM test and
      Examples 6.7 and 6.8.  IN PARTICULAR, STUDY THE COMPUTER OUTPUT
      IN PAGES 289-293.

II.1  As before, load DATA4-15 and generate the squares of the variables
      using the square command given above.  Next estimate by ols the
      basic model (ols 1 0 2 ...  8 ;).  Then save the residual
      by the command: genr ut = uhat.

II.2  Estimate the auxiliary regression to carry out the LM test to
      test whether the square terms should be added to the model or
      not.  Think carefully before you do this because, as the cliche
      goes, "garbage in, garbage out."  Table 6.3 can show you the
      correct way to do this.

II.3  Write down the null hypothesis, compute the test statistic, and
      indicate its distribution including d.f.  Then test it at the 5
      percent level.  What do you conclude?

II.4  Use the auxiliary regression to select new variables to be added
      to the model estimated in II.1 using the 0.5 pvalue cut off rule
      discussed in Example 6.7.  Be sure to justify how you selected
      the variables.  Then estimate that model.  Here too, be careful in
      specifying the model.  In particular, note that the dependent
      variable will again be Gini and not uhat.

II.5  Choose the variable (ignore the constant term in all this) that
      has the least significant coefficient (two-sided alternative) and
      use the omit command to exclude it and reestimate the new model. 
      Repeat this process until all variables have significant
      coefficients at the 10 percent level.  Then quit twice to exit
      ESL and follow the previous directions to get the printed output.

II.6  Using model selection statistics, significance of coefficients, 
      and the danger of omitted variable bias, choose the "best" model. 
      Carefully justify your choice.

II.7  Are the models you chose in I.3 and II.6 the same?  If not,
      choose the better of the two, justifying your choice.  Call this
      the "final best model".

II.8  In the final model chosen in II.7, derive the expressions for the
      partial derivatives of Gini with respect to each of the
      explanatory variables and use this to graph the shape of the
      relationship between Gini and each of the independent variables,
      HOLDING OTHER THINGS CONSTANT.  Note that you cannot do this
      graph on the computer; just a free hand drawing along the lines I
      presented in class when discussing the quadratic model.  Use the
      graphs to explain whether the partial relations between Gini and
      the explanatory variables make intuitive sense.  Identify any
      "wrong" signs.  The summary command output will come in handy in
      answering this part.

Be sure to submit your ORIGINAL computer printouts with annotations on
the margin justifying each step and answering the above questions.

III.  Answer question 6.14 of the book on Page 306 (fourth edition 
      only).