ECON 120C --- HOMEWORK #2, DUE AT 11:10 AM, TUESDAY, NOVEMBER 17, 1998
This assignment consists of three parts and will be worth 5 percent for
all the parts combined. LATE PAPERS WILL NOT BE ACCEPTED. As before,
you may form a team of no more than three members.
START THIS RIGHT AWAY BECAUSE THE METHODOLOGY IS VERY COMPLICATED
AND YOU NEED PLENTY OF LEAD TIME.
All references are only to the fourth edition. The third edition will not
help you understand the methodologies.
Part I (Testing for heteroscedasticity)
First review the four tests for heteroscedasticity (HSK) described in
Section 8.2 (ignore the Goldfeld-Quandt test). In particular, study
Examples 8.3 and 8.5, the computer printout in Table 8.1, Example 8.4, and
Table 8.6. You are going to carry out similar tests using the data in the
file data7-4 described in Appendix D.
FROM YOUR HOME COMPUTER
If you have already installed ESL in your computer, then use the class Web
page link to download a revised version of esl.exe to C:\ESL. Use ESLWIN,
interactive, text-book data set data7-4, and give different names for
input and output files in each session.
FROM PC LAB IN ECON 100
Choose the ESLWIN, interactive, text-book data set data7-4, and give
different names for input and output files in each session.
When the ? prompt appears, type the following commands one at a time.
DO NOT use variable numbers in the genr statements.
genr D90YF = D90 * YF
genr D90UE = D90 * UE
genr D90MR = D90 * MR
square YF EDUC UE MR DR URB WH D90YF D90UE D90MR ;
The model you will be using is
WLFP = b1 + b2 YF + b3 EDUC + b4 UE + b5 MR + b6 DR + b7 URB
+ b8 WH+ b9 D90YF + b10 D90UE + b11 D90MR + u
Study the definitions of variables in Appendix D. The reason for not
including all the variables in the data set and other shift variables such
as D90YM, etc. is that these variables have been found to be statistically
insignificant.
Next estimate by ols the above model (ols WLFP 0 YF ... D90MR ;) and save
the residuals and their squares using the commands
genr ut = uhat
genr usq = ut * ut
Run the auxiliary regression for the Breusch-Pagan test only, that
is, skip the Glesjer, Harvey-Godfrey, and White tests. The auxiliary
equation for the error variance is
sigma sub t squared = a1 + a2 sq_YF + .... a11 sq_D90MR
and usq is an estimate of the left hand side. Follow the directions in
class to see how the auxiliary regression is run. If you missed the
class, get someone else's notes and follow the directions. DO NOT ASK THE
TAs OR ME FOR HELP UNTIL YOU HAVE FOLLOWED THE DIRECTIONS AND FOUND
PROBLEMS. IF YOU FOUND PROBLEMS, YOU MUST BRING THE PRINTOUT FOR US TO
TROUBLE SHOOT, i.e. type quit to exit ESL and print the output by
following the screen directions.
Next carry out the LM test for heteroscedasticity at the 1 percent level.
To do this, first state the null hypothesis, compute the LM test
statistics, state its distribution and d.f., and the decision rule. If
you follow the class directions, you can get the p-values using ESL. When
you are done, type
store hw2data ;
quit
to store all the original and transformed variables in the file hw2data
and exit ESL. Follow screen directions to obtain the printed output.
If you did the above in the Econ 100 lab, be sure to copy the files
hw2data, hw2data.hdr, inp.txt, and out.txt from the workarea folder to a
floppy and take it with you.
In the computer output either write on the margin or import the output
file into MSWord and insert annotations as in the book describing step by
step what you did and why. What do you conclude? Does the test indicate
significant HSK or not?
Keep the above with you for reference when you do Part II which will cover
the estimation procedure. Do not turn it in yet. Turn in answers only
when all three parts are done. KEEP A COPY OF THE PAPERS FOR YOUR
REFERENCE BECAUSE THEY WON'T BE RETURNED BEFORE THE EXAM.
Part II (Weighted Least Squares Estimation)
Here you will use the Weighted Least Squares (WLS) procedure to obtain
Feasible Generalized Least Squares (FGLS) estimates when there is
heteroscedasticity.
First review the FGLS method described in Page 398 of the book and study
the computer output in Table 8.4.
Run ESLWIN again using the same procedure as in Part I. If you are at
home, choose the data file hw2data from the \esl\user folder. If you are
in Econ 100, choose the same data from the \workarea folder.
II.1
For the Breusch-Pagan test, you generated usq = uhat squared and saved it.
Rerun the auxiliary regression for this (see your earlier printout).
Next use the command genr usqhat = usq - uhat
to generate the predicted uhat squared. Then print it and note that some
of the values are negative and hence unacceptable. In these cases you
should replace them by the original usq values. This is done with the
following commands explained in class (use parentheses exactly as shown).
genr d = (usqhat > 0.0)
genr sgmasq = (d*usqhat) + ((1-d)*usq)
Next use the command print usq usqhat sgmasq -o ;
and verify that sgmasq is the same as usqhat if the latter is positive but
is equal to usq when the latter is negative. You can get the weigts for
WLS using the command
genr wt = 1/sqrt(sgmasq)
and the wls command as
wls wt WLFP 0 YF ... D90MR ; (do not use squares here)
to get the WLS(FGLS) estimates. Use the p-values to choose a variable to
omit and omit that. Repeat this process until all coefficients (exclude
the constant term) are significant at 10 percent. When finished, type
quit to exit ESL and print the output file.
As before, either write on the margin of the computer output or import the
output file into MSWord and insert annotations as in the book describing
step by step what you did and why.
II.2
Using the significance of coefficients, omitted variable bias, and model
selection statistics, select the best final model. Carefully explain why
you chose the particular model.
II.3
Write down the estimated relations separately for 1980 and 1990 (see Pages
347, 348, and 350 for guidance on this). Interpret the results using the
description in Page 350 as an example. For expected signs of coefficients,
see the description in Pages 192-193. FOR EACH EXPLANATORY VARIABLE, explain
whether your observed signs agree with what is discussed in Page 192.
III. After Chapter 9 is covered, answer Exercise 9.6 on Page 478 of
the book.