2SLS First Stage Fixed Effects

[guneet robin]

I have panel data for firms (belonging to 14 industries) over year-quarters (400 firms starting from Q2-1994 to Q4-2018). In the main model, I include firm and industry-year fixed effects. One of the Xs is endogenous and I use instrumental variable that stems from the peers of firms. In the first stage 2SLS regression, if I include firm fixed effects, the second stage regression does not show effects.

Can someone explain, what exactly is the technical issue here? In what cases, I can exclude firm-fixed effects in the first stage of 2SLS and include in 2nd stage?

[Andrew Musau]

What estimator are you using and what is your command? In the usual implementation, the fixed effects are included in both stages as exogenous RHS variables are instruments in the first-stage.

[guneet robin]

Dear Andrew,

Here are my commands:

xtset firm yq

xtreg x z1 z2 w1 w2 i.cat-yq, vce(robust)
predict x_hat, xb
xtreg y x_hat w1 w2 i.cat-yq i.firm, vce(robust)

[Andrew Musau]

Use xtivreg, otherwise even if you implemented the two-stages correctly but separately, the standard errors in the second-stage would still be wrong.

xtset firm yq
xtivreg y w1 w2 (x=z1 z2) i.cat-yq, fe cluster(firm) first

[Andrew Musau]

Note that the default in xtreg is random effects (RE), so you needed the option -fe- in #3 to include fixed effects.

[Jeff Wooldridge]

Here's a Twitter (X) link where I discuss this approach. It is difficult to justify.

Using FEs as IVs