Taylor series-based flexible forms cannot be interpreted as Taylor series approximations unless all data used in estimation lie in a region of convergence. When flexible forms lose their Taylor series interpretation, elasticity estimates will be biased. When the flexible form is a translog, Rotterdam, or AIDS model, the region of convergence is shown to be the entire positive orthant. Regions of convergence associated with quadratic, Leontief, and any flexible form that does not employ logged arguments are smaller and may not encompass the entire data set. Implications for production and demand analyses and experimental design are discussed.