Selection into treatment bias in panel fixed effects model

[Leon Schmidt]

Dear all,

I have a conceptual question that I hope somebody can help me with.

My question is whether panel data two-way fixed effects models control for selection into treatment if this selection is due to initial differences between units?

For example, I study how the effect of adopting a new process (a dummy) is on the size of firms (proxied by number of workers). As such, I could run something like

xtset firm year
xtreg number_workers i.process i.year, fe robust

But what if larger firms are more likely to adopt the process in the first place?

My hunch is that this initial difference in size would be constant within firms, so fixed effects should control for such type of bias. But I am not sure if this is correct, hence the question.

Thank you very much for your time!

[Carlo Lazzaro]

Leon:
being unfamiliar with your research filed, what I would investigate is the risk of reverese causation (endogeneity): does the number of workers influence the likelihhod of adopting the process you mention?

[Maxence Morlet]

A very pertinent question in 2.

How about matching on firm size and then looking at the difference? The drawback is that is there are unobservable differences, the difference iwll be biased (matching is only possible on observables).

[Fei Wang]

A short answer: If you truly believe the selection into treatment solely depends on the level of firm size in a particular previous year (or the level of any firm characteristics in a particular previous year), then firm fixed effects would fully account for that. But if selection depends on the change in firm characteristics (for example, firms with faster size growth are more likely to adopt the process), then firm-specific trends may need to be included.

[Leon Schmidt]

Thank you all very much, it is much clearer to me now!