[Joao Santos Silva]

Dear Noemi Seng,

The variables that are dropped by ppmlhdfe should be dropped; the estimates of the coefficients you get for them with ppml are meaningless.

Best wishes,

Joao

[Joao Santos Silva]

Dear Noemi Seng,

The variables dropped by ppmlhdfe should be dropped because their effects are not identified. The coefficient estimates you get for those variables with ppml are meaningless; ppml will also drop these variables if you write the command including all fixed effects immediately after the dependent variable.

Best wishes,

Joao

[Narendra Maharjan]

Dear Joao Santos Silva
Hope you get this query,
I'm currently running the gravity model with five specifications with import data of a single commodity (HS-6 digit level), and I'm not able to perform Ramsey's RESET for the last specification, which is the strongest specification as per the literature. Also, the literature I've reviewed hasn't performed Ramsey's RESET. Can you suggest any method to conclude on the best specification statistically?
Note: Here, FTA are the dummy variables (=1 when the country joins the FTA)
1 Country-pair and time FE
ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 lgdp_* lpop* lEXR* , a(pairid year) keepsingletons vce(cluster pairid) d
predict yhat_xb, xb
gen yhat_xb2 = yhat_xb^2
quietly ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 lgdp_* lpop* lEXR* yhat_xb2, a(pairid year) keepsingletons vce(cluster pairid) d
test yhat_xb2
2. Importer-year and pairid FE
ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 lgdp_exporter lpop_exporter lEXR_exporter, a(pairid imptime) keepsingletons vce(cluster pairid) d
quietly ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 lgdp_exporter lpop_exporter lEXR_exporter yhat_xb2, a(pairid imptime) keepsingletons vce(cluster pairid) d
3. Exporter-year and pairid FE
ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 lgdp_importer lpop_importer lEXR_importer, a(pairid exptime) keepsingletons vce(cluster pairid) d
quietly ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 lgdp_importer lpop_importer lEXR_importer yhat_xb2, a(pairid exptime) keepsingletons vce(cluster pairid) d
4. Importer time exporter time FE
ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 ldistw_h contiguity common_ethno colony landlocked island region, a(exptime imptime) keepsingletons vce(cluster pairid) d
ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 ldistw_h contiguity common_ethno colony landlocked island region yhat_xb2, a(exptime imptime) keepsingletons vce(cluster pairid) d
5. Importer-year exporter-year and pairid FE
ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010, a(pairid imptime exptime) keepsingletons vce(cluster pairid) d
ppmlhdfe imports_1 FTA1ij FTA1_2008 FTA2ij FTA2_2004 FTA3ij FTA3_2020 FTA4ij FTA4_2000 FTA5ij FTA5_2010 yhat_xb2, a(pairid imptime exptime) keepsingletons vce(cluster pairid) d
note: 1 variable omitted because of collinearity: yhat_xb2note: 1 variable omitted because of collinearity: yhat_xb2

Thank you,
Best,
Narendra

[Joao Santos Silva]

Dear Narendra Maharjan,

The most likely reason for that is that you have a specification that only includes dummies and the cross products between them are always zero. For example, if you regress an outcome on a dummy for male and a dummy for female, without constant, you will not be able to perform the tests. This is as it should be because in such models we are just estimating means for different sub-populations, so there is no room for misspecification.

BTW, do not report that pseudo R2 value; see here.

Best wishes,

Joao
PS: To be clear, the squares of the fitted values used to compute the RESET are just a linear combination of the regressors and their squares and cross products. If you only have dummies, the squares are the dummies themselves, so they add noting. That means that in this case the test is just checking for the omission of the cross products. If these are zero, there is nothing to test.