PPML Gravity Model - Comparison of Coefficients

[Michael Lieberman]

Dear colleagues,

I am augmenting a gravity model and estimate it with PPML (Common Language, Contiguity, GDP)

In my model, I have three indicators (Institutional Quality) and I want to estimate (among other controls such as Regional Trade Agreements) the bilateral trade effects (e.g. measured by exports):

EX = ß0 + ß1 * ln(GDPR) + ß2*Contiguity + ß3*CommonLanguage + ß4+InstitutionalQuality1+ß5*InstitutionalQuality2 +ß6*InstitutionalQuality3
for country i and country j.

I assume country-specific and time-specific fixed effects.

How can I compare the coefficients of the variables InstitutionalQuality I II and III? They are all significant for both countries, e.g.
InsitutionalQuality1i = 0.003***
InsitutionalQuality1j = 0.001***
InsitutionalQuality2i = 0.303***
InsitutionalQuality2i = 0.503***

Can I say that the effects of InstiutionalQuality2 for both countries i and j are significantly positive and way larger than InstiutionalQuality1?
Is it possible to compare these coefficient from the regression output as long as they are in the same dimension (e.g. three indicators ranging all three from 0 to 3.)

Is there a statistical method to compare the effects coefficients after running the regression? Or any other approach to draw a conclusion about the relative strength of the effect suggested by the model?

Thanks a lot!

[Joao Santos Silva]

I suggest you use these variables as binary indicators and interpret them as usual.

Best wishes,

Joao

[Michael Lieberman]

Dear Joao,

thanks for reaching out so quickly! I try to be more specific.

The "Institutional Quality" Indicators (INST*) I work with (Kuncic, 2014), seek to measure the quality of the institutional frameworks on three different levels (Economic, Legal and Political Institutional framework). All three indicators are normalized between 0 (worst) to 3 (best).

The model seeks to measure whether there is a significant effect of the quality of the institutional framework on trade respectively exports (for the importing country j as well as for the exporting country i).
I am interested whether the coefficients are significant and also which direction they take (positive / negative).

During the analysis and plenty of research I was not sure whether I could compare the "strength" of the INST* indicators and thus include a discussion into the analysis e.g. that InstEcon* (Quality of the Economic institutional framework) has a value of 0.543*** (p-value < 0,01) while InstPolit* (i.e. the quality of the Political institutional framework) has a coefficient of 0.111*** (p-value < 0,01)

Is it possible to compare these coefficient, hence say that InstEcon* might have a stronger (even fivefold) effect thant InstPolit*? Hence, is it possible to compare coefficient not only by their signficance or direction (plus/minus) in a ppml model as long as the compared coefficients have the same dimension (in my case normalized indicators between 0 and 3)?
If not, are there any other statistical methods / approaches to compare the "contribution" of the different coefficients on the depended variable?

Thanks a lot and best regards,
Michael

[Joao Santos Silva]

Dear Michael,

Given that the variables are in the same scale, I see no problem in using the size of the coefficients to compare the strength of the effects.

Best wishes,

Joao

[Jane Quan]

Dear Joao Santos Silva ,

In my study, I want to compare two coefficients in four subsamples of the same model with the command ppmlhdfe.
I initially included cluster in the estimation, but the suest" command told me to reestimate without cluster() and specify the cluster() option with suest.

I followed this instruction, but STATA reported that I was estimating with a non-standard vce(robust). My codes are as follows:

use data, clear
xtset iso3num_o year
egen exporter = group(iso3num_o)

ppmlhdfe realanimal logdist logecondist logwgigap logexrate logarea logimmi, a(year)
estimates store Y1
ppmlhdfe realvegetable logdist logecondist logwgigap logexrate logarea logimmi, a(year)
estimates store Y2
ppmlhdfe realoilwax logdist logecondist logwgigap logexrate logarea logimmi, a(year)
estimates store Y3
ppmlhdfe realprocessedfood logdist logecondist logwgigap logexrate logarea logimmi, a(year)
estimates store Y4

suest Y1 Y2 Y3 Y4, cl(exporter)
test [Y1_mean = Y2_mean = Y3_mean = Y4_mean]:logimmi

Is there something wrong in my code?
Thank you very much for your help.

Best regards

[Joao Santos Silva]

Dear Jane Quan,

I am afraid I am not familiar with the suest command; hopefully others will be able to help. Meanwhile, given that you are estimating relatively simple models, you may want to try estimating using Stata's built-in poisson command rather than ppmlhdfe.

Best wishes,

Joao

[Fred Lee]

Dear Joao Santos Silva ,

In my study, I want to compare two coefficients in four subsamples of the same model with the command ppmlhdfe.
I initially included cluster in the estimation, but the suest" command told me to reestimate without cluster() and specify the cluster() option with suest.

I followed this instruction, but STATA reported that I was estimating with a non-standard vce(robust). My codes are as follows:

use data, clear
xtset iso3num_o year
egen exporter = group(iso3num_o)

ppmlhdfe realanimal logdist logecondist logwgigap logexrate logarea logimmi, a(year)
estimates store Y1
ppmlhdfe realvegetable logdist logecondist logwgigap logexrate logarea logimmi, a(year)
estimates store Y2
ppmlhdfe realoilwax logdist logecondist logwgigap logexrate logarea logimmi, a(year)
estimates store Y3
ppmlhdfe realprocessedfood logdist logecondist logwgigap logexrate logarea logimmi, a(year)
estimates store Y4

suest Y1 Y2 Y3 Y4, cl(exporter)
test [Y1_mean = Y2_mean = Y3_mean = Y4_mean]:logimmi

Is there something wrong in my code?
Thank you very much for your help.

Best regards

Dear,
have you solved the problem?

[Maxence Morlet]

I think PPML by definition integrates an adjustment to palliate the failure of the information matrix equality, hence the "PML" in "PPML", or at least that is my understanding. Try with just

poisson

and see what happens?