new;
cls;


/***** Step 1: DGP *****/
b1=1;
b2=5;
b3=4;
sig2=2;

Tru_b=b1|b2|b3; @ True parameters @

T=200;        @ # of observations @
k=3;            @ # of regressors    @
x2=rndu(T,1)*2;  
x3=rndu(T,1)*2;

emat=rndn(T,1)*sqrt(sig2); @ Error term @

ymat=b1+x2*b2+x3*b3+emat;  


/***** Step 2: Estimation(OLS) *****/

X=ones(T,1)~x2~x3; @ T by 3, Independent variables @
Y=ymat;             @ T by 1 @
b_hat=inv(X'*X)*X'*Y;   @ 3 by 1, Estimates for b1 and b2  @
Y_hat=X*b_hat;  @ T by 1, fitted data @
e_hat=Y-Y_hat;  @ T by 1, residuals @
sig2_hat=e_hat'e_hat/(T-k); @ Estimates of variance @ 


/*****  Step 3: Simple Hypothesis Test   *****/
cov=sig2_hat*inv(X'*X); @ 3 by 3, variance-covariance matrix @ 
stde=sqrt(diag(cov)); @ 3 by 1, standard deviation @
t_val=b_hat./stde;  @ t values @


/***** Step 4: Joint Hypothesis Test  *****/
/* Test 1: b1=b2=b3=0 */
R1=1~0~0|0~1~0|0~0~1;
L1=3;      @ # of Restrictions @
gam1=0|0|0;
F1=(R1*b_hat- gam1)'inv(R1*inv(X'X)*R1')*(R1*b_hat-gam1)/(L1*sig2_hat); @ F statistic @


/* Test 2: b1+b2=1 and b2=b3 */
R2=1~1~0|0~1~-1;
L2=2;        @ # of Restrictions @
gam2=1|0;
F2=(R2*b_hat - gam2)'inv(R2*inv(X'X)*R2')*(R2*b_hat-gam2)/(L2*sig2_hat); @ F statistic @


"----------------------------------------------";
"       True values      Estimates  ";
Tru_b~b_hat;
"----------------------------------------------";
"----------------------------------------------";
" Ho            t value         ";
"b1=0";;t_val[1];
"b2=0";;t_val[2];
"b3=0";;t_val[3];
"----------------------------------------------";
"----------------------------------------------";
"        Ho                             F value         ";
"b1=b2=b3=0             ";;F1;
"b1+b2=1 and b2=b3 ";;F2;
"----------------------------------------------";

end;