Dynamic panel bias - FE pooled sandwich

[Michael Makovi]

I am estimating a dynamic panel, and I am seeking to avoid IV-type estimators, such as Arellano-Bond. I am currently having what appears to be success with xtbcfe and xtdpdbc.

But I want to try estimating OLS FE and OLS pooled, which have opposite biases, so that I can sandwich the estimate between two bounds.

My question is: should the OLS pooled include my time-invariant variables? Conceptually, am I . . .

(1) Starting with OLS pooled with time-invariant variables, and then adding FE which wipe out those variables, or


(2) Starting with OLS FE and then removing the FE without doing anything else to the variable list?

My estimate of OLS pooled with time-invariant variables is almost identical to OLS FE, whereas my OLS pooled without time-invariant variables is quite different.

Obviously, OLS pooled with more variables is less biased than OLS pooled with fewer variables. But I don't know if that means that OLS pooled with time-invariant variables is the proper estimator to compare to FE for the purposes of sandwiching my dynamic panel Nickell bias.

Thank you.

[Jared Greathouse]

I have a few thoughts: To the first point, any FE estimator can't include time invariant variables. Or it can in the sense that Stata won't issue an error (I don't know this for fact, I haven't tried this), but the real issue is that they'll just drop out. You can certainly begin with the pooled model and extend from there, in fact, that's what I'd advise you to do.

Removing the (unit?) FE from OLS is just pooled OLS again (presuming there are no time FE here).

My bigger point, is that if you have multiple units observed across time, then the OLS-FE approach is where you'd like to focus your analysis on. I'm curious though, how were you originally connecting this to your sandwich SEs?

[Michael Makovi]

Jared Greathouse,

Thank you. Let me clarify.

I agree with everything you say.

But I am not talking about a sandwich standard error, such as White heteroskedastic standard errors.

Rather, I am talking about sandwiching the true estimate of beta between two biased estimates of beta that each have biases in the opposite direction. Thus, the true beta is expected (with repeated sampling) to lie between the upper bound estimate and the lower bound estimate.

So of course OLS-FE is preferred if we think that there unit-specific, time-invariant variables that are omitted from the model. Omitting FE is omitted variables bias.

But what I want to exploit is the fact that even though FE is biased when there is a lagged dependent variable, the bias is the opposite of the bias from omitting the FE. So if we estimate OLS FE and OLS pooled, we can get an upper bound and a lower bound estimate.

What I don't know is whether the OLS pooled can include time-invariant variables.

Obviously, if we are just comparing two OLS pooled models, the one with more variables is less biased (although possibly less efficient). But I don't want to compare two pooled models. I want to compare FE to pooled so that I can sandwich the estimate, and I don't know which of the two pooled models to use.

[Sebastian Kripfganz]

For the pooled OLS estimator with time-invariant variables, it is not immediately obvious in which direction the bias goes. It could still go in the same direction as the pooled OLS estimator without time-invariant variables, or it could go in the same direction as the FE estimator. For the purpose of "sandwiching" the estimates, I would argue that you should therefore use the pooled OLS estimator without time-invariant variables.

Btw: Since you mentioned my xtdpdbc command, I have just released an update to the command.