Interpreting Sargan-Hansen Tests

[Jaspal Channa]

Hi all,

I am running diff GMM using Sebastian's xtdpdgmm command. However, I am not sure how to interpret the 2 different Sargan-Hansen tests that are produced when I run "estat overid". Is one more important than the other? What range should the p-values both be in?

Note that my instrument count is between 20-30, the number of groups I have is 52, I have about 1200 observations and 32 time periods. Instruments are collapsed.

I have tried looking at older threads to find the answer, but could not see one.

Best,
Jaspal

[Sebastian Kripfganz]

The two tests reported by estat overid after xtdpdgmm are asymptotically equivalent. Ideally, they should give you very similar results. The second test is based on another updating round for the weighting matrix. Any substantial difference between the two tests serves as a warning signal. It is an indication that the weighting matrix might be poorly estimated. A solution in this case might be to use the iterated GMM estimator instead of the two-step estimator. Since a poor estimation of the weighting matrix is often due to many or weak instruments, it may also help to reduce the number of instruments, if possible, in particular if your number of groups is relatively small. (52 groups could still be seen as rather small, in particular given that 32 time periods is already relatively large.)

In principle, the same rules apply to the p-values as for other hypothesis tests. That is, at a 5% significance level you would reject the null hypothesis of no model misspecification if the p-value is smaller than 0.05. However, in particular in relatively small samples, the test can suffer from size and power problems. A cautious approach might thus be to choose a larger nominal size (i.e. a larger significance level) than you would usually do.

If there are many instruments, a very large p-value close to 1 may also sometimes indicate a problem with a poor estimation of the weighting matrix. But as long as you ensure that the number of instruments is reasonably small, this is not too much of a concern.