Why sometimes we have trouble getting the PPML estimator to converge
Suppose that a country (say, Reunion) has zero recorded exports to every other country in the sample for a given year (say, 1996). That means that the multiplicative fixed effect for Reunion in 1996 is estimated as zero, that is, as the exponential of minus infinity. Of course, this cannot be estimated and the algorithm should never converge because STATA (or any other software) does not see the problem and tries to estimate the parameter anyway. If the problem is not addressed, (spurious) convergence can only be achieved if the algorithm is relatively crude. Note that this is an issue if the country did not trade at all in a given year; if it had traded with some partners but not with others, the effect can be identified and estimated without the need for any correction.
To solve the issue, we use a short code that first identifies and drops the problematic regressors, and then performs the usual PPML estimation.