Gravity model with fixed effects and ppml

[Basile Feller]

Hello everyone,

Happy to have joined Statalist after being a long-time lurker.

I'm a Master's student estimating his very first gravity model. I'm looking at bilateral trade flows for 40 countries between 1999-2019. My regressors are gdp (both for origin and destination), distance between countries, classic binary variables (contiguity, common language, colonial links and rta). Finally, my main variable of interest is an index (0-6) called EPS which measures environmental policy stringency for both origin and destination country.

I have generated FE as follows:

egen exporters = group(exporter year)
egen importers = group(importer year)
quietly tabulate exporters, generate(exp_dum_)
quietly tabulate importers, generate(imp_dum_)

I then use the ppml command to estimate my model:

ppml trade ln_gdp_exp ln_gdp_imp eps_e eps_i ln_distance rta contig comlang_off exp_dum_* imp_dum_*, cluster(dist)

In many other posts about gravity models, the discussion was centred around multicollinearity caused by the FE and countries' characteristics (gdp, for example). It seems that you cannot estimate them when introducing FE, which would be a huge problem for me since I'm interested in this EPS index. Indeed, apparently Stata drops these variables automatically.

Since I'm quite new to this, I have a couple of questions:

1) In my case, and with the code I used, Stata does not drop any of my regressors (only a couple of dummies FE). Besides, I get significant coefficients that are in line with the relevant literature. So, is my code actually OK and are my coefficients reliable?
2) I have read many gravity papers that estimate a model using PPML with FE. Nonetheless, they still estimated countries' characteristics (GDP and so on). So, what am I missing? I'd be grateful if you could shed some light on this collinearity situation.

Many thanks for your help.

Basile Feller

[Joao Santos Silva]

Dear Basile Feller,

Welcome to Statalist!

Instead of using the ppml command, please use ppmlhdfe which is much better at dealing with the fixed effects. You probably want to let your importer and exporter FE vary by year and in that case things like GDP will drop out.

As for the second part of your question, it all depends on what fixed effects are included in the model, but I would not be surprised if some researchers report estimates of parameters that are not identified.

Best wishes,

Joao

[Basile Feller]

Dear Mr. Silva,

Thank you very much for your quick answer.

I tried the ppmlhdfe command with time-varying (importer and exporter) fixed effects and this time, variables like GDP were dropped out. If I may, I still have a couple of questions:

1) If I understand correctly, even though they're not dropped with the ppml command, the coefficients of country characteristics variables in the presence of FE are meaningless with the ppml command. Is that correct?
2) I realize that my variable of interest, EPS (environmental policy stringency for a given country at time t), is thus not identifiable in the presence of time-varying fixed effects. Thus, I'm not sure what to do... I tried generating a new variable, the difference between the two indicators (eps_diff = eps_exp - eps_imp), but the coefficient is not significant. Do you have any suggestions as to what I should do? Estimate without fixed effects?
3) When I mentioned some papers that still reported results on country characteristics in the presence of FE, you said that "it all depends on what fixed effects are included in the model". Could you please clarify? Under what conditions could these estimates be reliable?

Thank you very much for your valuable time.

Best regards,

Basile Feller

[Joao Santos Silva]

Dear Basile Feller,

1) That will depend on the FEs you use. For example, with importer and exporter FEs, that is true for characteristics like area that do not change over time. However, if you include time varying importer and exporter FEs, that is also true for characteristics that vary over time such as GDP and population. If you include pair FEs, then that would be true for distance.

2) Only you can answer that question.

3) Please see 1) above.

Best wishes,

Joao

[Basile Feller]

Dear Mr. Silva,

Again, thank you very much for your precious answers. I'm starting to understand these concepts better now.

I just have a last question if I may as I did not find an answer on the forum or in the relevant literature: You mentioned here 3 different types of FEs. Is it possible to implement any combination of FEs within the same estimation? For example, is it possible to implement importer and exporter FEs alongside pair FEs? Or do they not make sense together?

I really appreciate your time and reading all your other contributions in the forum.

Best regards,

Basile Feller

[Joao Santos Silva]

Dear Basile Feller,

It may make sense, but that depends on the application. That approach is often used when estimating the impact of free trade agreements.

Best wishes,

Joao

[Basile Feller]

Dear Mr. Silva,

Thank you for your help. I have made great progress in this topic and this makes me feel confident for my upcoming Master's thesis.

Wishing you the best,

Basile Feller