ECON 120C, SPRING 1998  --  HOMEWORK #1


This assignment is due no later than 9:35 am on Tuesday, April 21, 1998
(late papers will have a 25% penalty PER DAY).  It will carry a weight of
5% towards the grade.  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 SECOND MID-TERM EXAM.  If your name
appears on more than one paper, the LOWER score will be recorded.


I.  This and the next part requires you to run things on the computer. 
    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.

    If you have your own copy of esl installed at home, exit
    temporarily to DOS, then type CD \ESL  to enter the ESL
    subdirectory, then type:  esl data4-7 and .
    
    If you want to use the Econ 100 Lab, use CD \PGMS\ESL to enter
    the ESL subdirectory and type the ESL command above.

I.1.  When you get the ? prompt, use the command: logs 2 3 4 5 6 7 8 9 ;
      to generate the logs of the independent variables.  To see the
      definitions of these variables, see DATA4-7 in Appendix D (4/e
      only).  Next estimate by ols the most general model with the
      linear and logs terms (ols 1 0 2 3 ...  17 ;).

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.  Then quit twice to get
      back to DOS and follow the screen directions to get the printed
      output. (say YES to overwriting the inp file).

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

      Be sure to submit your 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.  Estimate by ols the basic model (ols 1 0 2 ...9 ;).  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 log 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 10
       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 chd 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 get
       back to DOS and follow the screen directions to get the printed
       output.

II.6.  Using significance of coefficients, model selection statistics, 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.

II.8.  In the final model, derive the expressions for the partial
       derivatives of chd with respect to each of the explanatory
       variables and use this to graph the shape of the relationship
       between chd 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 chd and the
       explanatory variables make intuitive sense.  Identify any
       "wrong" signs.

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