st: xtivreg predictions from first stage

[Tunga Kantarcı <tungakantarci@gmail.com>]

Hi,

I would like to ask a simple question.

xtivreg first runs a fixed effects regression and then uses the
predictions from the first stage as instruments in the second stage.

But what are precisely the predictions in the first stage ?

Suppose the auxiliary regression in the first stage is the fixed
effects estimation of the following model:

y_it = b_0 + b_1 * x_it + n_i + u_it

So what are the predictions used in the second stage?

estimated_b_0 + estimated_b_1 * x_it + estimated_n_i (prediction of y_it) ?

or

estimated_b_1 * (x_it - mean_x_i) (prediction of y_it - mean_y_i) ?

My guess is that it is the second.

Thanks in advance.
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