I am trying to model Foreign Direct Investment (FDI) flows and am facing several issues;
There is the well-known condition that under heteroskedasticity log-linearized OLS models are biased and inconsistent. Santos-Silva and Tenreyro (2006) suggest using Poisson pseudo-maximum-likelihood (PPML) to overcome this, and subsequently PPML, negative binomial and Poisson modeling became commonplace in the literature, but...
... FDI flows are often negative (divestment), which cannot be accommodated by count data models or PPML. Negative flows are economically meaningful and therefore cannot just be dropped without loss of consistency. An alternative is to use stocks rather than flows, but this does not seem to fit very well with the theory of gravity equations which seem to me to inherently deal with flow concepts.
Can anyone suggest an appropriate estimator? I have heard the suggestion of multinomial logit (where dep.var. is share of global FDI flows) but this would also seem to falter in the case of a negative flow.