/* written paper 1 fall 2007 */

use earningsdata_males

gen gender = 1
append using earningsdata_females
replace gender = 2 if gender==.

label define genderlbl 1 "male" 2 "female"
label values gender genderlbl

/* inspect the data */
desc
summ

/* question 1 */

summ ln_y_ if gender==1
return list
gen mean_male 	= r(mean)
gen N_male    	= r(N)
gen sd_mean_male = r(sd)/sqrt(N_male)

summ ln_y_ if gender==2
return list
gen mean_female 		= r(mean)
gen N_female    		= r(N)
gen sd_mean_female   	= r(sd)/sqrt(N_female)

summ mean_* sd_* N_*

/* confidence intervals for the respective means */

gen ci_mean_male_lower = mean_male - 1.64*sd_mean_male
gen ci_mean_male_upper = mean_male + 1.64*sd_mean_male

disp "90% confidence interval for male log earnings is [" ci_mean_male_lower "," ci_mean_male_upper "]"

gen ci_mean_male_lower5 = mean_male - 1.96*sd_mean_male
gen ci_mean_male_upper5 = mean_male + 1.96*sd_mean_male

disp "95% confidence interval for male log earnings is [" ci_mean_male_lower5 "," ci_mean_male_upper5 "]"

gen ci_mean_female_lower = mean_female - 1.64*sd_mean_female
gen ci_mean_female_upper = mean_female + 1.64*sd_mean_female

disp "90% confidence interval for female log earnings is [" ci_mean_female_lower "," ci_mean_female_upper "]"

gen ci_mean_female_lower5 = mean_female - 1.96*sd_mean_female
gen ci_mean_female_upper5 = mean_female + 1.96*sd_mean_female

disp "95% confidence interval for female log earnings is [" ci_mean_female_lower5 "," ci_mean_female_upper5 "]"

/* test whether the means are different */

gen diff    = mean_male - mean_female
gen se_diff = sqrt((sd_mean_male^2)+(sd_mean_female^2))

gen t = diff/se_diff
disp t

/* p-value of test of equal means */

gen p = 2*normal(-abs(t))	/* norm in stata8 */
disp p

/* the p-value is less than 0.01, se we reject the H0 that the means are equal at the 1% level */

/************************************************************************************************************/
/* question 2 */

egen mean_sample = mean(ln_y_)
gen temp = exp(mean_sample)

gen earnings = exp(ln_y_)
egen mean_earnings = mean(earnings)

/* mean earnings are not equal to exp(ln(mean earnings)) since ln is not a linear operator */


/************************************************************************************************************/
/* question 3 */

reg ln_y_ s if gender==1

gen alpha_male = _b[_cons]
gen beta_male  = _b[s]
gen se_male  = _se[s]
ereturn list
gen r2_male = e(r2)

/* make graph */
twoway scatter ln_y_ s if gender==1||lfit ln_y_ s if gender==1, legend(off)

reg ln_y_ s if gender==2

gen alpha_female = _b[_cons]
gen beta_female  = _b[s]
gen se_female  = _se[s]
ereturn list
gen r2_female = e(r2)

/* make graph */
twoway scatter ln_y_ s if gender==2||lfit ln_y_ s if gender==2, legend(off)


/* OLS assumptions are: */
/* (1) E(ui|Xi)=0 	*/
/* (2) Xi, Yi for i = 1,...,n are iid draws from their joint distribution 	*/
/* (3) Large outliers are unlikely: 0<E(Xi^4)<infinity, 0<E(Yi^4)< infinity	*/


/************************************************************************************************************/
/* question 4 */

/* conditional expectations */

disp "the conditional expectation of E(lnY|S) for males is " alpha_male " + " beta_male "*S"
disp "the conditional expectation of E(lnY|S) for females is " alpha_female " + " beta_female "*S"

/* expected log earnings if 12 years of education (note: education here is defined as beyond 7th grade) */

disp "the expected log earnings of a male with 12 years of education is " alpha_male " + " beta_male "*5 = " alpha_male +  beta_male*5
disp "the expected log earnings of a female with 12 years of education is " alpha_female " + " beta_female "*5 = "alpha_female + beta_female*5

/* check the R-square to see the fit, i.e., the portion of the variation in ln_y explained by S */
disp "the R2 of the male wage regression is " r2_male
disp "the R2 of the female wage regression is "r2_female


/************************************************************************************************************/
/* question 5 */

/* 95% confidence interval for beta */

disp "95% confidence interval for beta for males is [" beta_male - 1.96*se_male "," beta_male + 1.96*se_male " ]"

disp "95% confidence interval for beta for females is [" beta_female - 1.96*se_female "," beta_female + 1.96*se_female " ]"

disp "the expected marginal return to schooling for males is " beta_male

disp "the expected marginal return to schooling for females is " beta_female

disp "the estimated percentage increase in income of one additional year of schooling for males is " beta_male*100 "%"

disp "the estimated percentage increase in income of one additional year of schooling for females is " beta_female*100 "%"


/************************************************************************************************************/
/* question 6 */

/* testing whether the returns to schooling are different for men and women */
/* run pooled regression and include a dummy for females*years of schooling and use t-statistics to test whether it's different from zero */

gen d_female = gender==2
gen s_female = d_female*s

reg ln_y_ d_female s s_female 


/* calculate p-value or compare t-statistic to the critical t-value */
/* reject equal effect of schooling for men and women if |t_female|>1.96 */

gen t_female = _b[s_female]/_se[s_female]
disp t_female

gen p_female = 2*normal(-abs(t_female))	/* norm in stata8 */
disp p_female

/* use an F-test for the two schooling coefficients being the same */
gen d_male = gender==1
gen s_male = s*d_male 
reg ln_y_ d_male d_female s_male s_female, noconst

test s_female = s_male


/************************************************************************************************************/
/* question 8 */

/* other specifications */

/* only experience */

reg ln_y_ e e_2 if gender==1


/* only private/public sector */
reg ln_y_ public servi if gender==1, noconst

/* only type of education */

reg ln_y_ unsp-serv if gender==1

/* only region */

reg ln_y_ ostf-finmark if gender==1