st: First stage of panel IV

["Filippos Petroulakis" <petroulakis@econ.umd.edu>]

Hi all,

I am running a panel first differences (fixed effects) model. My regression is of the sort

y_it=b_0+b_1 x_it + b_k demographic_covariates + e_it

x_it is endogenous so I have an instrument z_it.

I essentially have 3 issues and I list them in descending order of importance.

1) xtivreg2 is running the first stage of x_it on z_it and the exogenous demographic covariates as OLS instead of fixed effects or first differences. I honestly do not know whether this is due to theory but it seems to be very odd, especially given the fixed effects is definitely the correct specification for the model as a whole, and so I would think it has to be the case for the first stage as well. I can do the 2 stages manually and correct the errors using the process outlined here (http://www.stata.com/support/faqs/stat/ivreg.html) and I presume the fact that I have a panel doesn't change much, but my issue is basically whether this is the correct thing to do.

2) xtivreg and xtivreg2 give me pretty different results, which is due to the fact that xtivreg drops about half of the observations in the first stage. I checked and the variable that is causing the dropping (for whatever reason) is the dependent variable. I am thus positive that xtivreg is the wrong one but am still worried. Anyone knows why this happens?

3) Finally, at some point I will need to include a further two variables, call them w_it and q_it, which are surely endogenous. I don't care about instrumenting for them as I am not interested in a causal interpretation, but the problem is that they are also endogenous to x_it. So my first stage will be regression x_it on variables that are endogenous to itself and to y_it. Is that an issue I should be concerned about?

Thank you very much in advance - answers to any or all of those issues will be immensely appreciated.

Best,

Filippos Petroulakis 

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