// Øktri eksamen 
//1.1
tabstat LTV Age HouseholdSize, statistics(mean min max count) by (Moved) nototal columns(statistics) longstub

twoway (histogram LTV, by(Moved, total cols(3) graphregion(color(white))))

//1.2
regress Moved LTV,r

//1.3
predict Moved_est, xb
hist Moved_est
summarize Moved_est

//2.1
gen Age2 = Age * Age
regress Moved LTV HouseholdSize Age Age2, r

//2.2
gen LTVo1 = 1 if LTV>1
replace LTVo1 = 0 if LTV < 1
gen LTVo1_LTV = LTVo1 * (LTV-1)
regress Moved LTV HouseholdSize Age Age2 LTVo1 LTVo1_LTV, r

//2.3


//3.1
ivregress 2sls Moved (LTV=LocalPriceChange) HouseholdSize Age Age2 LTVo1 LTVo1_LTV, r

//3.2
//first stage
ivregress 2sls Moved (LTV=LocalPriceChange) HouseholdSize Age Age2 LTVo1 LTVo1_LTV, r first

//reduceret form
regress Moved LocalPriceChange HouseholdSize Age Age2 LTVo1 LTVo1_LTV, r

//3.3
gen HouseholdSize2=0
replace HouseholdSize2=1 if HouseholdSize==2
gen HouseholdSize2_LTV=HouseholdSize2*LTV
gen HouseholdSize_inst=HouseholdSize2*LocalPriceChange


ivregress 2sls Moved (LTV HouseholdSize2_LTV=LocalPriceChange HouseholdSize_inst) HouseholdSize Age Age2 LTVo1 LTVo1_LTV, r


//5 MONTE CARLO
clear all
global numobs 500


set seed 38

program DGP, rclass
	drop _all
	
	set obs $numobs
	
	gen z = rnormal(0,1)
	gen u = rnormal(0,2)
	gen v = runiform(0,1)
	
	gen aA_0 = 1
	gen aA_1 = $aA_1_global
	gen betaA_0 = 1
	gen betaA_1 = 1
	
	gen aB_0 = 1
	gen aB_1 = 1
	gen betaB_0 = 1
	gen betaB_1 = 2
	
	gen x = aA_0 + aA_1 * z + u if v>=0.5
	replace x = aB_0 + aB_1 * z + u if v<0.5
	
	gen y = betaA_0 + betaA_1 * x + u if v >= 0.5
	replace y = betaB_0 + betaB_1 * x + u if v < 0.5

	ivregress 2sls y (x=z)
	return scalar betaIV = _b[x]
	return scalar betase = _se[x]
	
	
	gen sumBeta = betaA_1 if v >= 0.5
	replace sumBeta = betaB_1 if v < 0.5
	sum sumBeta
	return scalar beta_mean = r(mean)
	
	regress y z //reduced form til at sammenligne
	return scalar beta_reduced=_b[z]
	
end

global aA_1_global 0

//5A
simulate betaIV=r(betaIV) betase=r(betase), reps(1):DGP
summarize

//5B
simulate betaIV=r(betaIV) betaMean=r(beta_mean) beta_reduced=r(beta_reduced), reps(1000):DGP
summarize

//5C
global aA_1_global 1
simulate betaIV=r(betaIV) betaMean=r(beta_mean) beta_reduced=r(beta_reduced), reps(1000):DGP
summarize