* use "C:\data\STATA\participation.dta", clear
use "H:\Documents and Settings\Lee\My Documents\Document\stata\participation.dta", clear

gen A2 = A*A
gen one = 1

* Excersise 11.12 (w/o OPG based LM test)
* generate the squared variables
gen no2=no*no
gen nu2=nu*nu

* Restricted model
quietly probit lfp I A A2 E F no nu, technique(nr)
estimates store restrict

* Unrestricted model
quietly probit lfp I A A2 E F no no2 nu nu2, technique(nr)
estimates store unrestrict
estimates stats unrestrict restrict

* Wald test of restrictions
test nu2 no2

* The LR test for joint significance of the new variables
lrtest restrict unrestrict 

* An equivalent test based on Hausman.  Note:  you have to 
* manually set the degrees of freedom for the pvalue.
hausman unrestrict restrict, df(2)

quietly probit lfp I A A2 E F no nu, technique(nr)
predict index_r, xb
predict prb, pr

generate Ft = prb
generate ft = normalden(index_r)

/* variance */
gen vt = Ft*(1-Ft)

*  Transform variables for BRMR regression. 
*  Notice that I divided by sqrt(vt).  My previous advice
*  about using [aweight=1/vt] was not so good.
gen ystar=(lfp-Ft)/sqrt(vt)
gen Istar=ft*I/sqrt(vt)
gen Astar=ft*A/sqrt(vt)
gen A2star=ft*A2/sqrt(vt)
gen Estar=ft*E/sqrt(vt)
gen nustar=ft*nu/sqrt(vt)
gen nostar=ft*no/sqrt(vt)
gen Fstar=ft*F/sqrt(vt)
gen nu2star=ft*nu2/sqrt(vt)
gen no2star=ft*no2/sqrt(vt)
gen cons = ft/sqrt(vt)

/* BRMR */
quietly reg ystar cons Istar Astar A2star Estar nustar nostar Fstar nu2star no2star, noconst 
di "The BRMR test"  
scalar ess = e(mss)
scalar pval = chi2tail(2,ess)
scalar list ess pval

* OPG regression to generate the LM test statistic
drop index_r prb Ft ft vt Istar Astar A2star nostar nustar Fstar Estar ind nu2star no2star
quietly probit lfp I A A2 E F no nu, technique(nr)
predict index_r, xb
predict prb, pr 

generate Ft = prb
generate ft = normalden(index_r)

/* variance */
gen vt = Ft*(1-Ft)

gen ind=(lfp-Ft)*ft/vt
gen Istar=ind*I
gen Astar=ind*A
gen A2star=ind*A2
gen Estar=ind*E
gen nustar=ind*nu
gen nostar=ind*no
gen Fstar=ind*F
gen nu2star=ind*nu2
gen no2star=ind*no2

/* OPGR */
quietly reg one ind Istar Astar A2star Estar nustar nostar no2star nu2star Fstar, noconst 
di "The LM test from the OPGR regression"  
scalar ess = e(mss)
scalar pval = chi2tail(2,ess)
scalar list ess pval