ECON 120C --- HOMEWORK #2 Part II, DUE AT 9:35 AM, TUESDAY, MAY 19, 1998


This is Part II of the homework that deals with the Weighted Least Squares
(WLS) procedure for obtaining Feasible Generalized Least Squares (FGLS)
estimates when there is heterosceadasticity.

All references are only to the fourth edition.  The third edition will
not help you understand the methodologies.

First review the FGLS method described in Page 398 of the book and study
the computer output in Table 8.4.

FROM YOUR HOME COMPUTER

If you have already installed ESL in your computer, then exit
temporarily to DOS and type CD \ESL and press enter to change to the
directory in which the ESL program is stored.  DO NOT USE ESLWIN
BECAUSE SOMETIMES IT DOES NOT WORK VERY WELL.

FROM PC LAB IN ECON 100

First exit from Windows to DOS.  Then type  CD \PGMS\ESL  and press 
enter to change to the directory in which the ESL program is stored.
DO NOT USE ESLWIN BECAUSE SOMETIMES IT DOES NOT WORK VERY WELL.  Also
note that if you do this in parts, copy files to a floppy disk and
then copy them back to this directory later.

Part II (Estimation by FGLS/WLS)

Type:  esl  data1  
to run ESL with the data you created in Part I.

II.1
In the Glesjer test in Part I,  you generated absut = |u hat sub t| and
saved it.  Rerun the auxiliary regression for this (see your earlier
printout).  Next use the command   absuhat = absut - uhat
to generate the predicted absolute ut.  Then print it (print absuhat ;)
and note that all values are positive.  You can get the weigts for WLS
using the command   genr wt = 1/absuhat  and the WLS estimates by

wls wt 1 0 2 3 4 5 6 7 8 ;

II.2
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 u squared hatt.  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                    
genr  sgmasq = (d*usqhat) + ((1-d)*usq)

Next print sgmasq and note that all values are positive.

You can get the weigts for WLS using the command
genr wt = 1/sqrt(sgmasq)
and use that same wls command as above.

II.3
Repeat the procedure described in II.2 for the White's test and obtain
the WLS estimates similarly.
(caution:  the auxiliary regression here is very different.)

II.4
Do the same for the Harvey-Godfrey procedure but since antilog generates only
positive values, you need not create the dummy variable.  Again obtain
WLS estimates.

II.5
Prepare a table similar to Table 8.3 and identify the "best" model using the
model selection criteria.  Interpret the results of this model in terms of
signs of coefficients and whether they make sense.