/* PREDICTING MALE WAGES */

/* Load Data and Define Variables */

load path=c:\gauss35\classes\econ5340\data\;
load x[1001,12]=cps88.asc;
data = x[2:1001,.];

age = data[.,1];
age2 = age^2;
grade = data[.,3];
lnwage = data[.,6];
potexp = data[.,9];
married = data[.,5];
union1 = data[.,10];
nobs = rows(data);
constant = ones(nobs,1);

xmat = constant~age~age2~grade~married~union1;
k = cols(xmat);

/* Least Squares Estimation */

urb = inv(xmat'*xmat)*(xmat'*lnwage);
urerr = lnwage - xmat*urb;
s2 = (urerr'*urerr)/(nobs - k);
varb = s2*inv(xmat'*xmat);

/* Predicting the Wage */

xo = {1 34 1156 22 1 0};
lnwagehat = xo*urb;
wagehat = exp(lnwagehat);
print "Predicted ln(wage) = " lnwagehat;
print "Predicted wage = " wagehat;

/* Confidence Interval for the Forecast */
tcrit = 1.96;
varwagehat = s2*(1+ xo*inv(xmat'*xmat)*xo');
lb = lnwagehat - tcrit*sqrt(varwagehat);
ub = lnwagehat + tcrit*sqrt(varwagehat);
print "Lower Bound of 95% Confidence Interval for ln(wage) = " lb;
print "Upper Bound of 95% Confidence Interval for ln(wage) = " ub;