How can I estimate a pseudo-gravity equation

[Lakshmi Castillo]

Hello everyone I a little bit new with Stata and now I am using the pseudo-gravity equation from the paper of Bacardio-Colom (2013) to study the efectts of the FTA of Perú and China ONLY in the Peruvian exports, that's why the name es PSEUDO-gravity equation. For my estimation I use 60 countries including China from the period 1994 to 2017. The FTA starts in 2000.

There is how I order mi panel data base:

This pseudo-Gravity equation takes this form:

where:
X_ijt : Exports for country i (Perú un this case) to country f in time t
PBI_ij : GDP of the country j in time t
DIST_ij: Distance from the capital of country i to country j
Z_ijt: Dummy variable that takes the valué of 1 if in the time t country i and j share a diplomatic relationship and 0 if they don't.
TLCCHINA_ijt : Dummy variable that takes the value of for China 1 when the FTA agreements starts.

I also use other dummy variables like same continent, lenguaje, colony.

My biggest problema starts with the method I have of estimation, when I estimate by OLS-pooled all my results are okay, then I estimate by FE or RE and it make that my variable of FTA not significant that is totally wrong because many studies find that this FTA make the export from Perú grow very much.

I`ll post my code here:

cls
clear all
set more off
import excel using "", firstrow
egen CountryNumber = group (Country)
destring Year, replace

gen log_y_j = log(PBIj)
gen log_y_i = log(PBII)
gen exp = log(ImportExport)
gen log_dis = log(Distancia)

xtset CountryNumber
xtset CountryNumber Year, yearly

Ols-Pooled:

reg exp log_y_j log_dis TLCCHINA Colonia Lenguaje Continuo i.Year, r
reg exp log_y_j log_dis TLCCHINA Relacionesdiplomticas Colonia Lenguaje MismoContinente, r

FE:
xtreg exp log_y_j log_y_i log_dis TLCCHINA Relacionesdiplomticas Colonia Lenguaje, fe
xtreg exp log_y_j log_dis TLCCHINA Colonia Lenguaje i.Year, fe


* I also add year fixed effects
* And I have another question how can I add country-time fixed effects

I deeply appreciate any help or comments you can give me.