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* Advanced Applied Econometrics
* Jakub Muck 
* Exercise 8

* (i) and (ii) importing data, generating variables of interest and regression
clear all 
use "http://e-web.sgh.waw.pl/jmuck/AAE/Datasets/cps.dta"
gen lwage=ln(wage)
gen exper2=exper^2

reg lwage educ exper exper2 female 

* (iii) Testing slope on the eduction 
local t_stat=(_b[educ]-.1)/_se[educ] 
local df=e(df_m)
local t_crit=invt(`df',.95)
local pval=1-t(`df',`t_stat')
disp "t statistic:   	" `t_stat' 
disp "critical value:	" `t_crit'  
disp "p-value:       	" `pval'

* (v) Example hypothesis 
test (3*educ=-female)

* (vi) Experience 
test(exper=0) (exper2=0)

* (vii) The extreme point of experience at which wages are the highest
nlcom(exper_star:_b[exper]/(-2*_[exper2]))