This situation is analogous to what happens in binary choice
models when there is complete separation or quasi-complete
separation, as described by Albert and Anderson (1984) and Santner
and Duffy (1986). Moreover, it is clear that it can also occur in any
other regression model where the conditional mean is specified in
such a way that its image does not include all the points in the support
of the dependent variable. Therefore, this problem can occur not only
in the Poisson regression model but whenever y is non-negative and
the conditional mean is specified as E(yi|xi)=exp(xi′β).