Omitted variables due to collinearity in PPMLHDFE regressions

[Giang Lie]

Dear All,

I am trying to run gravity regressions on the impact of the difference between policies of countries on their bilateral trade, with the exporter-year fixed effect, importer-year fixed effect and importer-exporter-industryimport- industryexport fixed effect. The distinction between ndustryimport (A) and industryexport (B) is that importer imports goods from sector B in the exporting country to use for sector A in importing country. I use command ppmlhdfe as following but the main variable is dropped.

Could anyone know how this issue can be fixed? Thanks a lot in advance.

[Joao Santos Silva]

Do you really want to use importer-exporter-industryimport-industryexport fixed effects? That is a lot of fixed effects and that is what makes your policy variable redundant.

[Giang Lie]

Dear Silva,

I need importer-exporter-industryimport-industryexport fixed effects to control for time-invariant components of bilateral trade, as exporter fixed effects and importer fixed effect only control for time-variant exporter and importer terms.

[Joao Santos Silva]

Then I do not think you can estimate the effect of your variable of interest...

[Jane Quan]

Dear Joao Santos Silva,

I ran into the similar problem in my analysis when I used the "ppmlhdfe" command in STATA. Hopefully I can get some advice from you, because you are the expert in this field.
My problem is as follows:

Data: China's agricultural imports from over 170 countries, 2009-2021.
Dependent variable: real import values (I adjusted it using CPI)
Independent variables (taking logs):
distance (since I applied gravity model),
economic distance (China's per capita GDP/exporter's per capita GDP),
institutional distance (China's governance indicator /exporter's governance indicator),
real exchange rate (proxied by china's ppp / exporter's ppp, and I also converted it using CPI),
land size of exporter,
STATA code:
ppmlhdfe realagritotal logdist logecondist logwgigap logexrate logarea , a(year) cl(countrycode)

my problem: in other post, you said that "No tests are essential, but it is useful to perform a RESET" (pls. see https://www.statalist.org/forums/for...44-ppml-method)

Therefore, I ran a RESET test using following code:
predict XB,xb
qui su XB
gen XB2 = (XB-r(mean))^2
quietly ppmlhdfe variety logdist logecondist logwgigap logexrate logarea logimmi XB2, a(year) cl(countycode)
test XB2 = 0

Unfortunately, p-value( Prob > chi2 = 0.0000) reject the null hypothesis.
So I respecified my model, used real GDP and population of the China instead of economic distance:
ppmlhdfe realagritotal logdist logrealgdp_d logpop_d logwgigap logexrate logarea logimmi, a(year) cl(countycode)

but the result shows ommited for replaced independent variables.
also, in all regressions, it shows such warnings: "warning: dependent variable takes very low values after standardizing (5.2639e-09)"

Wondering if you have any comments for this problems. And thank you for your time

Best regards.

[Joao Santos Silva]

Dear Jane Quan,

I am not sure if I understand what you are doing, but it looks that the two variables you added are collinear with the year fixed effects and therefore do not contribute to explain the dependent variable. I suggest that you consider using other kinds of fixed effects instead of including those variables. Also, I think you can ignore the warning message.

Best wishes,

Joao

[Jane Quan]

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[Jane Quan]

Dear Joao Santos Silva ,
I thank you very much for your answer. And as you suggested, I did consider an individual (country-specific) fixed effect as well as a time and an individual fixed effect, rather than just a time (year) fixed effect. However, distance and land area are collinear with the individual fixed effect, so the coefficients were omitted.

My concern is that if I drop these two variables, especially distance, it would not be a gravity model. Have I coded something wrong?

ppmlhdfe agritotal logdist logecondist logwgigap logexrate logarea logimmi, a(countrycode) cl(countrycode)
or
ppmlhdfe agritotal logdist logecondist logwgigap logexrate logarea logimmi, a(year countrycode) cl(countrycode)

Thank you so~~~oo much for your time!

Best regards.

[Joao Santos Silva]

Dear Jane Quan,

The fact that log-distance drops is not a problem; its effect is still accounted for by the fixed effect.

Best wishes,

Joao