It is done within the SAS/ETS proc model of GMM estimation.

data tmp;
do i = 1 to 300;
x=rannor(890);
x2=x+rannor(890);
x3=x+rannor(890);
x4=x+rannor(890);
y=1+1*x+rannor(890);
output;
end;
run;

proc model data=tmp;
y = a * x + b;
eq.two = resid.y**2 - sigma**2;
fit y two/ gmm;
instruments x x2 x3 x4;
run;
quit;

The reported value of OBJECTIVE*N is test statistics with chi-square distribution with df=r-p

Testing Over-Identifying Restrictions



Let r be the number of unique instruments times the number of equations. The value r represents the number of orthogonality conditions imposed by the GMM method. Under the assumptions of the GMM method, r-p linearly independent combinations of the orthogonality should be close to zero. The GMM estimates are computed by setting these combinations to zero. When r exceeds the number of parameters to be estimated, the OBJECTIVE*N, reported at the end of the estimation, is an asymptoticly valid statistic to test the null hypothesis that the over-identifying restrictions of the model are valid. The OBJECTIVE*N is distributed as a chi-square with r-p degrees of freedom (Hansen 1982, p. 1049).