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* Advanced Applied Econometrics
* Jakub Muck 
* Exercise 17

* importing data
clear all 
use http://e-web.sgh.waw.pl/jmuck/AAE/Datasets/InternationalTradePoland.dta

* data preperation 
gen im_pl=ln(IM_PL)
gen ex_pl=ln(EX_PL)
gen dd_pl=ln(DD_PL)
gen dd_eu=ln(DD_EU)
gen reer=ln(REER)

*(ii) estimated demand on imported goods 
reg im_pl dd_pl reer

*(iv) estimated demand on exported goods
reg ex_pl dd_eu reer

*(iv) testing symmetric effect of real achange rate 

reg3 (import: im_pl  dd_pl reer) ///
	(export: ex_pl  dd_eu reer), ///
	ols endog(im_pl ex_pl)

test ([import]reer=-[export]reer)

* constrained estimation 

cons 1 [import]reer=-[export]reer

reg3 (import: im_pl  dd_pl reer) ///
	(export: ex_pl  dd_eu reer), ///
	ols endog(im_pl ex_pl) constraints(1)

* (x) 2SLS estimation of SEM  
reg3 (import: im_pl ex_pl dd_pl reer) ///
	(export: ex_pl im_pl dd_eu reer), ///
		2sls endog(im_pl ex_pl) 

* (xi) Testing symmetric effect 

test ([import]reer=-[export]reer)

* (xii) 3SLS estimation of SEM 
* Motivating 3SLS -- cross-equation correlation of residuals
predict r1,res eq(#1)
predict r2,res eq(#2)

corr r*

* 3SLS estimation 
reg3 (import: im_pl ex_pl dd_pl reer) ///
	(export: ex_pl im_pl dd_eu reer), ///
		2sls endog(im_pl ex_pl)