The claim has been made that the Generalized Maximum Entropy (GME) estimator of Golan, Judge and Miller is not sensitive to variations in the support bounds of either the parameters or the error terms. In this paper, we scrutinized this claim by means of Monte Carlo experiments and found that the parameter estimates are impacted in a substantial way by these changes. We also analyzed the famous data sample on the US manufacturing industry used by Cobb and Douglas in 1934 and found that the GME estimator is very sensitive to changes in support bounds. We conclude with a general result by Caputo and Paris according to which any support bound variation produces unexpected responses in the parameter estimates.