Information Equivalence among Transformations of Semi‐parametric Nonlinear Panel Data Models*
研究非线性半参数均值函数的变换如何产生用于估计的矩条件，证明在标准正则条件下，只要变换的秩相等，就能达到相同的渐近效率界，并比较了含乘性异质性的非线性模型和含未观测因子结构的线性模型中的可行与不可行变换。
Abstract This paper considers transformations of nonlinear semi‐parametric 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. I compare feasible and infeasible transformations of both nonlinear models with multiplicative heterogeneity and linear models with unobserved factor structures.