Jian,
Pretend that your model is:
y2 = b*y1 + c*x + e
if you estimate by LS then std error for b and c
depend on the fit as well the std errors of y1 and x
(you can check Marteen's question around 08/15)
LS+robust you add some of the structure of e,
which makes the things more complex.
Alternative you can say that y1 is also endogenous
therefore a IV estimator will be more appropiated
you are adding some additional equation like
y1 = d1*z1 + d2*z2 + d3*z3 + w
Assuming that z's are valid instruments and taking
whatever method of IV (2SLS, GMM, Nagar, LIML,
Fuller, etc) your news std errors for b and c depend
on several statistics and the std erros of z's and x.
