Controlling for multilateral resistance in a psuedo-Gravity model for migration.

[Euan Newgreen]

Dear Statalist,

First post on here. I've read a lot of literature on the topic of controlling for multilateral resistance within a Gravity model for the application of migration. The econometric technique strongly mentioned is to 'include a time-fixed effect; and an origin time interaction term that captures multilateral resistance' (Arif 2022 - 'Educational attainment, corruption, and migration: An empirical analysis from a gravity model').

I have panel data across 20 years in 5-year intervals for migration flows by gender and educational attainment from 159 origin countries into 18 destinations.
When typing the following into the command window:

reghdfe lnhigh lndistw inequality comlang_off MPI unemployment average_income  if gender == "Female", absorb(o#year year) cluster(o#d)

All the year fixed effects are considered redundant by Stata.

I was wondering why is this case and what's the intuition behind this?
And also is there any way to control for both time-fixed effects and include the origin-time interaction term without all the time dummies falling out of the regression, as specified in the paper cited above?

Many thanks in advance for any time invested into an answer!

[Joao Santos Silva]

Dear Euan Newgreen

The time fixed effects are, by construction, collinear with the origin-time fixed effects, and therefore they are dropped because they are not needed. The reference you give apparently overlooked this. A good place to see what is the state-of-the-art is

Beine M, Bertoli S, Fernandez-Huertas Moraga J (2016) A practitioners guide to gravity models of international migration. The World Economy 39:496–512

Finally, I strongly recommend that you estimate your model in levels using PPML, rather than on logs using OLS. Check out the command ppmlhdfe.

Best wishes,

Joao

[Euan Newgreen]

Dear Joao Santos Silva

Thanks for your suggestions.

Following up my initial post, I have 3 more questions:
1) Under PPML the time-fixed effects do not get dropped when using origin-time fixed effects, is this because PPML is a non-linear estimator and so they can no longer be collinear?

2) I really appreciate your PPML findings and planned in my thesis to use OLS as a baseline estimator and PPML as the preferred estimator to allow for comparisons.
In your opinion, would the following code be deemed adequate in attempting to calculate the determinants of high-skilled immigration while controlling for multilateral resistance through origin-year fixed effects and year fixed effects?

ppmlhdfe high-skilledmigrationflow lndistw lnpop_d lngdp_d comlang_off inequalitygap MigrationPolicyIndex unemploymentgap average_income o#year if gender == "Female", absorb(year) cluster(o#d)

3) Would my panel data qualify for the 'high-frequency data' requirement for use with the CCE estimator? I assumed not because in most studies involving the CCE estimator the panel data seems to be yearly with migration flows into only one destination.

4) And finally, since PPML is carried out on levels how should one best interpret coefficients? My impression is that the resilience of independent variable significance of withstanding all the controls is a result in the migration decision process, but coefficient readability is limited.
Many many thanks!

[Joao Santos Silva]

Dear Euan Newgreen,

1) Being non-linear makes no difference. So, either the time FE or some of the interactions will be dropped.
2) I cannot comment on the model, but note that you can absorb the interaction o#year.
3) I am not familiar enough with the CCE estimator to comment.
4) Interpretation is exactly as in the model in logs.

Best wishes,

Joao