log using ht,replace
use phuz,clear
sort id

replace y=log(y)
gen exp=yr-phd
gen expsq=exp^2
gen ier=1/(exp*rphd)
gen d70=0
replace d70=1 if phd>70
quietly by id: gen y1=y[_n-1]
quietly by id: gen y2=y[_n-2]
drop if y2==.
* Why can't we ommitt the above command?
* Stata can handle missing obs, but here we will
* have problems if we let Stata do our work. Why?

PQ exp
PQ expsq
PQ ier
PQ y
PQ y1
PQ y2 
PQ d70
PQ sex
* Note that Pd70=d70, Psex=sex, Qd70=0, Qsex=0. 
* Nonetheless, we need Pd70 and Psex latter.
* Can you see where and why?

regress y y1 y2 exp expsq ier d70 sex (Qy1 Qy2 Qier Pexp Qexp Pexpsq Qexpsq d70 sex)
predict r,res
PQ r
gen Prsq=Pr^2

quietly by id: gen mark=_n
* What does mark do? (see the next regression)
quietly by id: gen T=_N
gen iT=1/T
        
regress Prsq iT if mark==1
matrix b=get(_b)
gen theta=sqrt(_b[iT]/(_b[iT]+_b[_cons]*T))

replace y=y-(1-theta)*Py
replace y1=y1-(1-theta)*Py1
replace y2=y2-(1-theta)*Py2
replace exp=exp-(1-theta)*Pexp
replace expsq=expsq-(1-theta)*Pexpsq
replace ier=ier-(1-theta)*Pier
replace d70=d70-(1-theta)*Pd70 
replace sex=sex-(1-theta)*Psex

regress y y1 y2 exp expsq ier d70 sex theta (Qy1 Qy2 Qier Pexp Qexp Pexpsq Qexpsq Pd70 Psex theta),noconst
* Why do we have theta as a variable and no intercept here? 
matrix list b 
summarize theta
log close