Poisson regression (xtpoisson) requires the dependent variable to be a non-negative count variable. However, in some cases one may need to take the first difference of the dependent variable to deal with, for example, reverse causality of the regressors. My question is how can one take the first difference of the count variable in Stata while making sure that the resulting difference stays non-negative so that it can be used in poisson regression. Cameron and Trivedi's Microeconometrics using Stata outline a transformation $(\frac{\lambda_{i,t-1}}{\lambda_{i,t}) * y_{i,t} - y_{i,t-1}$ where $\lambda_{i,t}=exp(x_{it}'\beta)$ which, they state, can be used to eliminate the FE and as the basis for estimation of dynamic panel count models. My question is how can one actually estimate $\lambda_{it}$ in Stata so that it can then be used to create first differences?