# PS8.7, for Example 8.8 -- estimation of model by FGLS
open data8-1 
genr LNSALARY=ln(SALARY)
# generate powers of YEARS for the various tests 
genr YRS2 = YEARS*YEARS
genr YRS3 = YEARS*YRS2
genr YRS4 = YRS2*YRS2
# estimate log quadratic model by OLS 
ols LNSALARY const YEARS YRS2 
# save absolute value of uhat and uhat squared 
genr absuhat=abs($uhat)
genr usq=$uhat*$uhat
# compute weights using the Glesjer test approach 
ols absuhat const YEARS YRS2 
# predict uhat as observed minus residual stored as uhat 
genr absuhat1=absuhat-$uhat
print absuhat1 
# luckily all estimated sigmas are positive and so apply WLS 
genr wt1=1/(absuhat1^2)
wls wt1 LNSALARY const YEARS YRS2 
# compute weights using the Breusch-Pagan test approach 
ols usq const YEARS YRS2 
/* predict uhat squared as observed uhat square minus residual
   stored under the name uhat.  Note that even though labelled as uhat, 
   it is really the residuals for uhat squared model */
genr usqhat1=usq-$uhat
# print estimated variance and note that 3 observations have negative 
# values, which are unacceptable 
print usqhat1 
# replace these negative values with the original uhat squared values 
genr d1=(usqhat1>0.0)
genr usqhat2=(d1*usqhat1) + ((1-d1)*usq)
print usqhat2 
# compute weights and use FGLS which is also WLS 
genr wt2=1/usqhat2
wls wt2 LNSALARY const YEARS YRS2 
# compute weights using the White's test approach 
ols usq const YEARS YRS2 YRS3 YRS4 
genr usqhat3=usq-$uhat
# print estimated variance and note that this also has negative 
# values, which are unacceptable 
print usqhat3 
# replace these negative values with the original uhat squared values 
genr d2=(usqhat3>0.0)
genr usqhat4=(d2*usqhat3) + ((1-d2)*usq)
print usqhat4 
# compute weights and use FGLS which is also WLS 
genr wt3=1/usqhat4
wls wt3 LNSALARY const YEARS YRS2 
# compute weights using the Harvey-Godfrey test approach 
genr lnusq=ln(usq)
ols lnusq const YEARS YRS2 
# save estimated ln(sigma square) and take antilog 
genr lnusq1=lnusq-$uhat
genr usqhat5=exp(lnusq1)
# compute weights and use FGLS which is also WLS 
genr wt4=1/usqhat5
wls wt4 LNSALARY const YEARS YRS2