The Identification Problem in Systems Nonlinear in the Variables
仅在变量上非线性的方程系统的识别问题AI 解读 ↓
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仅在变量上非线性的方程系统的识别问题
- 研究问题
- 在参数线性、仅变量非线性的联立方程系统中，单个方程系数何时可识别，观测等价又如何刻画识别障碍？
- 方法与思路
- 作者以观测等价构建识别框架，在扰动独立于外生变量的要求下推导识别的充要条件，并与既有判据及线性秩条件比较。
- 材料陈述的贡献
- 摘要称得到识别的充要条件，指出 Fisher 的方法提供充分但非必要条件，并说明若干常见特殊情形可简化为线性模型的秩条件。
- 阅读关注点
- 核对“仅变量非线性”的模型边界、观测等价的定义、扰动独立性在证明中的作用，以及哪些特殊情形可化为线性秩条件。
- 阅读边界
- 摘要未列出充要条件的具体形式及完整限制；不能据此将结论推广至参数非线性、仅要求均值独立或其他未讨论的模型。
原文摘要
This paper examines the identifiability of the coefficients of a single equation in a simultaneous equation model which is nonlinear only in the variables. The concept of identifiability in this model is motivated and developed using the closely related concept of observational equivalence. This framework is then utilized to develop necessary and sufficient conditions for identifiability when the disturbances are required to be independent of the exogenous variables. The approach recommended by Fisher is shown to yield sufficient but not necessary conditions for identifiability. For several relatively common special cases the necessary and sufficient conditions are found to simplify to the familiar rank condition for identifiability in the linear model. THE SIMULTANEOUS EQUATION MODEL that is nonlinear only in the variables has enjoyed widespread application in economics. Such models are linear in the parameters and typically seem to be linear in the variables as well, when viewing a single equation. In many models the nonlinearity in the variables arises due to endogenous variables entering in different forms in different equations (logged and unlogged form, for example). In macroeconometric models nonlinearity in the variables arises when the model includes endogenous real, nominal, and price variables, which are nonlinearly related.2 Whatever the reason for the nonlinearity in the variables, it is important to determine the conditions under which the equations of such models can be identified.