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I run the following model with TSLS. I have panel dataset and I use Random Effects and White cross-section correction

LNAFT = C + LNASSETS + STOCK + SINGLE + LIFE + CAPRQ (Eq. 1)

I conside CAPRQ endogenous, and I use two instruments so in the "instruments box" I write:

C LNASSETS STOCK SINGLE LIFE INSTR1 INSTR 2 (Eq. 2)

Before getting the results from the above, I would like to check if my instruments pass the rule of thumb saying that the F-stat of the first stage should be above ten.

So I run: CAPRQ = C + LNASSETS + STOCK + SINGLE + LIFE + INSTR1 + INSTR2 (Eq. 3) Correct?

I can then use: Coefficient Tests - Redudand Variables (LNASSETS, STOCK, SINGLE, LIFE), to get the F-stat that I need. Correct?

My question is: in the First stage regression - eq. 3 above (CAPRQ = C + LNASSETS + ....) should I use:

(i) Random effects without White
(ii) White correction without Random
(iii) Both Random effects and white correction ( i.e. this is similar to the specification used in TSLS)
(iv) Simple pooled OLS without Random effects or White correction

Many thanks in advance!

It's an interesting question.

Let's leave aside the White correction for the moment.

The projection in the random effects TSLS is in the GLS transformed space, which suggests that you should use a random effects specification for your first stage. The one fly in your ointment is that the random effects transform that you get by running a first stage regression won't be the same as the one you get in your main estimation since it's on the endogenous variable not the original dependent variable. You can certainly run that test and I think that it does give you a lot of information, but it won't be the same projection.

What you can do is to use the output from your original equation to transform all of your variables using the usual spectral decomposition (differencing off a fraction of the mean) and then simply run an OLS regression for your first stage. This is pretty straightforward using the series created by @meansby(). This first stage regression should be the one that you want.

As to whether to use the White correction, I don't think that there is a right answer to this question since it's a different specification. I will point out that the F-statistic on from the redundant variables test doesn't use the robust covariances so that the choice of White or not will not affect that statistic. Off the top of my head (so don't hold me to this), I would probably use the White correction in the first stage regression, and then use the robust Wald version of the F-statistic.

Then you for the reply. I will try that.

Just in case that someone will read this post, having had one more look I think that the correct for the Coefficient Tests - Redudand Variables is: (INSTR1, INSTR2) and not the one that I initially posted

Hi, this seems very interesting, I hope you don't mind me reviving this.

I take that the first post is the correct method to deal with 1SLS for F-stat - weak instrument test.

My question is regarding the redundant variable phase. I did the same thing as FOTIS did, however some of my data has N/A in it and it could not proceed with redundant variable test.

My quesiton is whether in that case to just run with:

Endogenous Variable = C INSTRUMENT1 INSTRUMENT2 and ignore the redundant variable test totally, would the F-stat in this case be different?

I am also wondering what should be done if there are 2 endogenous variables in my model?? Would appreciate any help! Thanks.