[Maxence Morlet]

Hi Joao Santos Silva, sorry for the delay; I was on annual leave.

Thank you very much for your recommendations.

I will give the papers you recommended a thorough read.

Concerning Johnston and DiNardo (1997), here is the reference:

Johnston, J., DiNardo, J., 1997. Econometric Methods. 4th Ed: McGraw Hill.

Page 438: "Consider ignoring the censoring problem and running OLS on all the observations. Then: plim B_hat_OLS = B * prob(y*>0)

Because prob(y*>0) < 1, OLS will be attenuated".

[Joao Santos Silva]

Dear Maxence Morlet,

Thanks for the quote, They are talking about censoring, which is not what you have. As you say, you essentially have count data so the zeros are true zeros, not censored observations.

Best wishes,

Joao

[Maxence Morlet]

Thank you very much for all your advice Joao Santos Silva !

One final question regarding PPML:

I have read you paper "The Log Gravity at 15" with great interest, as well as the paper by Weidner and Zylkin (2021), who stipulate that three-way FE-PPML is asymptotically biased (approaching the true value "at an angle"). The authors also indicate that they believe the IPP will be reinforced if additional fixed-effect dimensions are added (e.g. four-way fixed effects).

My question is: Correia et al. (2020) use iteratively reweighted least squares in combination with the FWL to "expurgate" the fixed-effects and make computation feasible.

Given the definition of the IPP given by Neyman and Scott (1948), does this "expurgation" of fixed-effects make the ppmlhdfe estimator of Correia et al. (2020) (mathematically) immune to the IPP, as fixed-effects are iteratively profiled out which should limit their ability to contaminate other parameter estimates?

[Joao Santos Silva]

Dear Maxence Morlet,

I do not believe that is the case, that is just a trick to facilitate the estimation rather than a proper elimination of the fixed effects. You may be aware that Tom Zylkin has written the ppml_bias_fe command to correct the asymptotic bias; in my limited experience it makes very little difference but it is useful to be able to check.

Best wishes,

Joao