*==============================================================================*
* Advanced Applied Econometrics
* Jakub Muck 
* Exercise 12

* (i) 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

* In the code below there will be genereated marginal effects (mf), elasticities (el)

*---------------------------------
* Linear model 
reg wage educ exper exper2 female 
estimates store model1
predict ehat1 

* Marginal effect
gen mf_educ1=_b[educ]
gen mf_exper1=_b[exper]+2*_b[exper2]
gen mf_female1=_b[female]

* Elasticity 
gen el_educ1=_b[educ]*educ/wage
gen el_exper1=(_b[exper] +2*_b[exper2])*exper/wage 
*gen el_female1=_b[female]*female/wage
* Technically it could be clacualted. But the above commented line does not make sense.
* But we can calaculate semi-elasticities in this case. 


*---------------------------------
* Log-linear model
reg lwage educ exper exper2 female 
estimates store model2
predict ehat2

* Marginal effect
gen mf_educ2=_b[educ]*wage 
gen mf_exper2=(_b[exper]+2*_b[exper2])*wage 
gen mf_female2=_b[female]*wage 

* Elasticity 
gen el_educ2=_b[educ]*educ
gen el_exper2=(_b[exper] +2*_b[exper2])*exper 
*gen el_female2=_b[female]*female


* Comparison of marginal effects 
sum mf*
* Comparison of elasticities
sum el_*



* (ii) Histogram of residuals
hist ehat1
hist ehat2

* (iii) Test for normality of the error term
sktest ehat*, noadjust 

* (iv) Histogram of dependent variables 
hist wage
hist lwage
sktest wage lwage 

* (v) Testing colinearity 
cor educ exper exper2 female 
estimates replay model1
estat vif

*(vi) Adding interaction 
gen female_educ=female*educ 
reg lwage educ exper exper2 female female_educ
* alternatively, instead of generating new variable one might use expression "c.female##c.educ"