st: xtivreg2 testing for regressor endogeneity

[Costas Lambrinoudakis <costas.lambrinoudakis@gmail.com>]

Dear all

I am using command xtivreg2. I have a couple of questions concerning
regressor endogeneity testing and I would be grateful if anyone could help me
with that.

I want to estimate the following equation:

y = b0 + b1x1 + b2x2 + b3x3 + u                         (1)

Say that x1 is endogenous, x2 and x3 exogenous and that z1 is a potential
instrument for x1. The dataset is panel and the errors are
heteroskedastic and clustered.

Given that my data is panel and the errors are not iid, I cannot use
ivendog, hausman or dmexogxt. The only choice I am left with is the option
endog(x1) in xtivreg2,
i.e. xtivreg2 y x2 x3 (x1=z1), fe endog(x1) cluster(id year)

My questions are the following:

1. Is it correct to use endog when I have only one endogenous variable and
one instrument? I may get a result from the option endog(x1) when running
xtivreg2 command, but I am wondering how are the Sargan statistics
calculated, given that my model is exactly identified?

2. I read in the paper accompanying ivreg2 (2003) that when errors are
iid, the estimated C statistic (from endog) coincides with the
Durbin-Wu-Hausman chi^2 statistic (the one reported by ivendog). Is it
correct to always interpret this C-test like the Durbin-Wu-Hausman test?
In particular, may I argue that the C-test actually tests the same null,
i.e. that the coefficients in equation (1) are not significantly different
when estimated by OLS and when estimated by IV? If not, what is the proper
non-technical definition of the null hypothesis of the C-test in the
option endog(.)?

Any help would be greatly appreciated!
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