Reference Category for PPML hdfe

[Chinmay Sharma]

Hi All,

I am making use of the wonderful command

ppmlhdfe

which is used to estimate models with a large number of fixed effects using Poisson pseudo ML. One issue from the documentation (http://scorreia.com/help/ppmlhdfe.html) is that I am unable to find what the normalization was done for the reference category. I cannot tell, if a category is automatically dropped, or if there is some other constraint imposed, such as the sum of the fixed effects equalling 0. Any help on this is much appreciated.


Best,
CS

[Chinmay Sharma]

Sergio Correia

[Chinmay Sharma]

any suggestions? many thanks!

[Tom Zylkin]

Hi Chinmay,
The fixed effects are normalized so that their weighted sums add to zero, weighting by the conditional mean (which can be obtained using predict, mu).

Note that in general the fixed effects are not uniquely identified. You may need to apply additional normalizations if you want to be able to interpret their magnitudes.

Hope this helps.

Regards,
Tom

[Chinmay Sharma]

Hi Tom,

Many thanks. Yes, that makes sense. Is there a no-constant option equivalent for ppmlhdfe? If the FE are already normalized such that their (weighted) sum equals 0, there seems to be no reason to drop the constant (except if there are bi-directional FE (like importer and exporter FE where two normalizations will be required)).

Let me be more specific. Suppose we have a set of fixed effects (just identifiers for countries). We decide to leave one out. Now, the FE are not collinear, and should be identified relative to the left out country. In this case, we do not need the normalization you mention anymore.

Thank you for this wonderful command. It has saved me a lot of time.

Best,
Chinmay

[Tom Zylkin]

Hi Chinmay,
No there is no "no constant" option. We report a constant to be consistent with what reghdfe does. But you should interpret it only as reflecting the scale of the dependent variable. Really you should ignore it for estimation purposes, since the results for non-FE parameters do not depend on the normalization.

If you are interested in the fixed effects estimates, what I would recommend is saving the fixed effects estimates into memory as variables and then applying the appropriate normalizations as needed. I'm attaching a .do file that does this for a trade model with exporter-time, importer-time, and exporter-importer fixed effects. Thus it is more complicated than the models you have in mind, but the steps can be reduced to simpler cases as needed. Trade economists looking to use our command to estimate technology levels, multilateral resistances, etc., may also find it useful.

Regards,
Tom

[Chinmay Sharma]

Hi Tom,

This is incredible. Thank you so much for the detailed exposition! This do file is extremely useful. Thank you once again for this great command- it has saved me countless hours..


Thanks,
CS