st: ivreg2, cluster vs. state fixed effects

[Nirina F <fstata@gmail.com>]

Dear all,
I am estimating a 2SLS for the following equation from a microdata at
individual level:

Y = b0+ b1*X1 +X2 ' *b2
where Y and X1 are dummy variables and X1 is endogenous and will be
instrumented with Z. X2 is a vector of control variables.

I only have one instrument and it is from a state level data because
it is the number of hospitals that the individual has in her state.
Therefore, I cannot use state-fixed effects anymore as otherwise, Z
will get dropped automatically due to collinearity.
Therefore, the model isn't identified with state effects, because
implicitly, I am using state as IV.
I am thinking of clustering the standard errors on state, so am I
right to just run the following?

ivreg2 y (x1=z) x2, cluster (state)

I tried to put under cluster state dummies but  I realized that I can
only put one variable under cluster.
So I am wondering how do people cluster by region-year level? because
if we just  gen a variable
gen regyr=region*year and then put that variable under cluster then we
might get trapped in the magic of multiplication.
suppose my region is coded from 1 to 4 and year from 1 to 5, then
2*3=3*2=6 therefore I cannot say those who are from region 2 and born
in 3 are in the same group as those who are from region 3 and born in
year 2.

 Also, after clustering my coefficient on b1 became insignificant and
decreased in value.

This is the results I get from loneway of x1 against z (as may be you
have other suggestions for me on how to deal with this identification
problem?)

loneway x1 z

                  One-way Analysis of Variance for x1:

                                              Number of obs =     33385
                                                  R-squared =    0.1178

    Source                SS         df      MS            F     Prob > F
-------------------------------------------------------------------------
Between z           903.19067     23    39.269159    193.61     0.0000
Within z            6766.5203  33361    .20282726
-------------------------------------------------------------------------
Total                  7669.7109  33384    .22974212

         Intraclass       Asy.
         correlation      S.E.       [95% Conf. Interval]
         ------------------------------------------------
            0.12599     0.04266       0.04237     0.20961

         Estimated SD of z effect             .1709937
         Estimated SD within z                .4503635
         Est. reliability of a z mean          0.99483
              (evaluated at n=1336.11)

Thank you in advance for your time and for your help,

Nirina
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