Hi everyone,
I analyze the impact of an agreement concluded between 4 countries on the mobility of people in these 4 countries. The agreement came into force and the same time for the 4 countries in 1995. In addition to these 4 countries, I added another 15 countries as a control group. I use a matrix of 19 countries of origin and 19 countries of destination (matrix 19 * 19).
The database covers the periods from 1990 to 2000.

lnN(ijt) : number of people from country i who go to country j to time t
lngdp(it) : log of gdp (constant 2000 US$) in the country of origin
lngdp(jt): log of gdp (constant 2000 US$) in the country of destination
lndist(ij): Log of distance between origin and destination countries
contig(ij): common border between origin and destination countries
lang(ij): common language in origin and destination countries
lnstock1990(ij): stock of migrants from country i and country j at year 1990
bothcountry1995 = 1 if i and j are both members of agreement at time t and 0 otherwise
onecountry1995 = 1 if the country (i) belongs to agreement but the country (j) does not
l(it): time-varying origin-country dummies which control for multilateral resistances
l(jt): time-varying destination-country dummies that account for multilateral resistances
l(ij): captures the country-pair fixed effects

The augmented gravity equation is:
LnN(ijt) = bo + b1lngdp(it) + b2lngdp(jt) + b3lndist(ij) + b4conti(ij) + b5lang(ij)+ b6stock(ij) +b7bothcountry1995(ijt) + b8onecountry1995(ijt) + e(ijt)

The variables created in stata are the following:
gen logN_ij=log(N_ij)
gen loggdp_i=log(gdp_i)
gen loggdp_j=log(gdp_j)
gen logdist_ij=log(dist_ij)
gen logstock1990_ij=log(stock1990_ij)
egen orig_time= group(origin year)
tabulate orig_time, generate(ORIGIN_TIME_FE)
egen dest_time = group(destination year)
tabulate dest_time, generate(DESTINATION_TIME_FE)
egen pair_id = group(origin destination)
tabulate pair_id, generate(PAIR_FE)
egen id = group(origin destination)
tsset id year

1) To solve the problem of endogeneity of the agreement, should I include time-varying origin-country dummies which control for multilateral resistances, time-varying destination-country dummies that account for multilateral resistances and the country-pair fixed effects ? or , should I include country-pair fixed effects and year effects ?
2) Do I use vce (robust) or cluster (pair_id)?

xi:xtreg logN_ij
loggdp_i
loggdp_j
logstock1990_ij logdist_ij lang_ij contig_ij bothcountry1995 onecountry1995 ORIGIN_TIME_FE* DESTINATION_TIME_FE*, fe vce (robust)

reg logN_ij bothcountry1995 onecountry1995 PAIR_FE* ORIGIN_TIME_FE* DESTINATION_TIME_FE*, cluster(pair_id)

xi:xtreg logN_ij
loggdp_i
loggdp_j
logstock1990_ij logdist_ij lang_ij contig_ij bothcountry1995 onecountry1995 i.year, fe vce (robust) (country-pair fixed effects and year effects)

reg logN_ij bothcountry1995 onecountry1995 PAIR_FE* i.year, cluster(pair_id) (country-pair fixed effects and year effects)

Thank you so much for your help in advance