How to include first-differenced variable into fixed-effects model?

[Sang Won Han]

Hi. I have a panel data set and the variables are the firm's asset, ROA, and so forth, as follows:

Year	GVKEY	Asset	ROA
2010	10456	13.4	0.99
2011	10456	10.5	0.82
2012	10456	12.1	0.75

The issue that I have is I have a first-differentiated variable that measures the change of the firm's position in vector space from one year to the next year, ranging from 0 to 1 (e.g., 0.84 from 2010 to 2011 for GVKEY 10456; 0.79 from 2011 to 2012 for GVKEY 10456) with information about the baseline levels for next year and previous year but not in a subsequent format (e.g., for 2010 to 2011, 0.92 - 0.08 = 0.84; for 2011 to 2012, 0.89 - 0.10 = 0.79).

I am now using the conventional fixed-effects model with year and GVKEY fixed-effects, but I am wondering how to include the above firm's position change variable into the model, given that other variables are level ones, not first-differenced one. Do I just include the firm's position change like 0.84 for Year 2010 for GVKEY 10456 and 0.79 for Year 2011 for GVKEY 10456? Or do I need to use first-difference regression? I have been trying to find an answer from this forum, but could not find anything meaningful. Thank you in advance!

[Carlo Lazzaro]

Sang:
I'd go first difference using the -D- operator available from -fvvarlist- notation when necessary.

[Sang Won Han]

Dear Carlo,

What do you mean by your comment above? Do I need to first difference onto all the variables other than already-first-differenced variable like below? Thanks!

reg D.ROA D.asset position_change i.year i.gvkey

[Carlo Lazzaro]

Correct.
I'd also use clustered standard errors (-vce(cluster gwkey)-).

[Maxence Morlet]

DEar Sang,

Carlo is absolutely right, simply one remark: in your model in #3, you are including a time trend by allowing a constant. In a "pure" FD model, there is no constant (you can implement this by using the "nocons" option).

[Jeff Wooldridge]

It's important to distinguish between the model and estimation method. FE and FD are different estimation methods. If the original model is in the the levels of everything and positionchange happens to be a difference, there is no problem with applying fixed effects. In fact, that's what should be done. If the other variables are differenced then the original model did NOT have positionchange in it; rather, it had the level of the position, which does not seem to be what Sang Won wanted. If you've already created the variable positionchange, as it appears you have, then just use fixed effects:

xtset id gvkey year
xtreg ROA asset position_change i.year, vce(cluster gvkey)

This means that you think it is the change in the position that affects ROA.

[Sang Won Han]

Thank you so much, Professor Wooldridge!