Gravity model of migration: ppml vs. ppmlhdfe

[Sarah Braas]

Dear all,

I'm working on a gravity model of migration for my thesis. My data contains 28 EU countries as destination countries, 130 non-EU countries as origin countries and spans 10 years.
My dependant variable is the number of first-time issued residence permits for employment for any given courtrypair (as I'm focussing on work-related migration) and I want to interpret the influence of different migration policies. Due to the large number of zeros in the dependant variable, I want to use the PPML estimator as described by Santos Silva & Tenreyo (2006) and used in most gravity-related literature in the recent years.

I want to run the following command:

ppml permits_all lgdp_o lgdp_d ldist contig comlang_off colony comcol market_test shortage_list point_system job_offer dFE_ot*, cluster(dist)

market_test, shortage_list, point_system and job_offer are dummy variables for the different migration policies, dFE_ot* are origin*time FE that I want to include

As I'm using Stata 15.1 IC, I can't run the code because 1300 origin*time dummies are too much for the IC version. Before buying a new licence (poor student here), I checked for alternatives and found the following three commands:
1. xtpoisson, fe
2. ppml_panel_sg
3. ppmlhdfe

I'm (theoretically) abel to use xtpoisson, fe and ppml_panel_sg, but since they are set in regards to the kinds of fixed effects they use, they are not practical for me.
I like ppmlhdfe, as I can decide which fixed effects to add (as with ppml), but don't need to inflate my modell with the manually added FE dummy variables (and thus can run the regression in Stata IC).

Now to my question:
Is my understanding correct, that the following to codes would produce the same output?

ppml permits_all lgdp_o lgdp_d ldist contig comlang_off colony comcol market_test shortage_list point_system job_offer dFE_ot*, cluster(dist)

ppmlhdfe permits_all lgdp_o lgdp_d ldist contig comlang_off colony comcol market_test shortage_list point_system job_offer, a(i.origin#i.year)

Best regards,
Sarah

[Joao Santos Silva]

Dear Sarah Braas,

That looks fine to me, but I suggest that you experiment with a subset of your data to confirm it; I always like to experiment :-)

Best wishes,

Joao

[Sarah Braas]

Dear Joao Santos Silva,

Thank you very much for the quick reply (and for all your replies on other posts that helped me a lot to even get to this point)!

I will try the commands with half the origin countries as to fit the origin*time dummy variables of the ppml command within the restrictions of Stata IC.
I really don't know how I haven't thought about that before. Thanks a lot for the pointer!

Best regards,
Sarah

[Jorge Vera]

Dear Joao Santos Silva,

I am currently facing a similar situation, since I am working on a gravity model of migration in the EU using PPMLHDFE. I was wondering if you would be so kind to let me know if my interpretations are correct or if I'm missing something. Below are my regression and results:

Regression:
ppmlhdfe Flow_d ln_Pop_o ln_Pop_d BCFS_diff ln_Distance Contig Law Religion Language EtnoLang ln_gdpcap_ppp_d ln_gdpcap_ppp_o ln_Unemployment_o ln_Unemployment_d BothEU, a(country_origin country_destination year) cluster(country_origin country_destination year)

The variable BCFS_diff refers to the absolute difference in the levels of specialization in blue-collar activities measure by an RCA-like index (based on Timmer et al., 2019) that takes between 0 and infinite, where values over 100 indicate specialization. Contig, Law, Language and BothEU are dummies to check matching characteristics. Religion is a Religious proximity index (Disdier and Mayer, 2007) that takes values from 0 to 100.

Results:

Flow_d	Coef.	St.Err.	interpretation
ln_Pop_o	-2,374	5,619	-2,37%
ln_Pop_d	8,537	3,777	+8,53%
BCFS_diff	0,005	0,015	+0,5%
ln_Distance	0,350	0,549	+0,35%
Contig	0,237	0,678	26,74%
Law	-0,171	0,677	-15,72%
Religion	0,001	0,012	+0,1%
Language	1,504	1,255	+349,97%
ln_gdpcap_ppp_d	-2,137	4,325	-2,137%
ln_gdpcap_ppp_o	-2,219	1,286	-2,219%
ln_Unemployment_o	1,535	0,472	+1,535%
ln_Unemployment_d	-0,196	0,590	-0,196%
BothEU	-0,232	1,122	-20,71%

Interpretation:
+1% pop at origin is associated with a reduction in the expected migration flow of 2,37%.
+1% pop at destiny is associated with an increment in the expected migration flow of 8,53%.
+1% BCFS_diff is associated with an increment in the expected migration flow of 0,5%.
+1% distance is associated with an increment in the expected migration flow of 0,35%.
Sharing borders is associated with an increment in the expected migration flow of 26,74%.
Sharing laws is associated with a reduction in the expected migration flow of 15,72%.
+1% religion similarity is associated with a reduction in the expected migration flow of 0,1%.
Sharing language is associated with an increment in the expected migration flow of 349,97%.
+1% gdpcap (ppp) at destiny is associated with a reduction in the expected migration flow of 2,137%.
+1% gdpcap (ppp) at origin is associated with a reduction in the expected migration flow of 2,219%.
+1% unemployment rate at origin is associated with an increment in the expected migration flow of 1,535%.
+1% unemployment rate at destiny is associated with a reduction in the expected migration flow of 0,196%.
Being both countries EU members is associated with a reduction in the expected migration flow of 20,71%.


Thank you very much in advance for your help!

Best regards,
Jorge

[Joao Santos Silva]

Dear Jorge Vera,

I do not think your interpretations are totally correct, but I may be missing something. Your interpretation of the dummies as semi-elasticities looks OK, and so does the interpretation of the effect of the variables in logs. However, I think there is a problem with the variables that are not in logs. For example, for Religion, it should be that an increase of 1 point in the index (not 1%) implies an increase of 0.1%. The same goes for BCFS_diff, what you estimate is the effect of changing the difference by 1, not by 1%.

On a different note, I find your results difficult to believe. For example, distance has a positive effect?

Hope this helps,

Joao

[Jorge Vera]

Dear Joao Santos Silva.

Thank you very much for your corrections, it is most helpful. Regarding my results, I agree with your concern. In fact, these are not statistically significant, however, I still wanted to make sure that I fully understood them. Thank you very much for your time.

Kind regards,
Jorge