Information equivalence among transformations of semiparametric nonlinear panel data models

This paper considers transformations of nonlinear semiparametric mean functions that yield moment conditions for estimation. Such transformations are said to be information equivalent if they yield the same asymptotic efficiency bound. I derive a unified theory of algebraic equivalence for moment conditions created by a given linear transformation. The main equivalence result states that under standard regularity conditions, transformations that create conditional moment restrictions in a given empirical setting need only to have an equal rank to reach the same efficiency bound. Examples are included, where I compare feasible and infeasible transformations of both nonlinear models with multiplicative heterogeneity and linear models with arbitrary unobserved factor structures.