/* TESTING LINEAR RESTRICTIONS */

/* Load Data and Define Variables */

load path=c:\gauss\classes\econ5340\;
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);
rb = inv(constant'*constant)*(constant'*lnwage);
urerr = lnwage - xmat*urb;
rerr = lnwage - constant*rb;
s2 = (urerr'*urerr)/(nobs - k);
print "Unrestricted Coefficient Vector = " urb;
print "Restricted Coefficient Vector = " rb;

/* Testing Restriction #1 */

R1 = {0 0 0 1 0 0};
q1 = 0;
F1 = (R1*urb - q1)'*inv(R1*inv(xmat'*xmat)*R1')*(R1*urb - q1)/s2;
print "F statistic for Restriction #1 = " F1;

/* Testing Restriction #2 */
J = k - 1;
urerrsq = urerr'*urerr;
rerrsq = rerr'*rerr;
F2 = ((rerrsq - urerrsq)/J)/(urerrsq/(nobs - k));
print "F statistic for Restriction #2 = " F2;