Dummy Endogenous Variables in a Simultaneous Equation System
联立方程系统中的内生虚拟变量AI 解读 ↓
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联立方程系统中的内生虚拟变量
- 研究问题
- 如何构建同时包含离散与连续内生变量的联立方程模型，并区分内生虚拟变量作为潜变量代理和行为方程移位项的作用？
- 方法与思路
- 作者把内生虚拟变量作为潜变量代理或行为方程的直接移位项，构建离散与连续内生变量并存的联立模型，并讨论多种估计。
- 材料陈述的贡献
- 摘要称，所提框架涵盖连续型与纯离散型联立模型；对其中最一般的混合模型，通过证明一致估计量存在来讨论识别与估计。
- 阅读关注点
- 核对两种虚拟变量角色如何进入结构方程、识别与一致性所需条件，以及最大似然和替代估计方法的具体构造。
- 阅读边界
- 所给文本有明显转录错误与缺损，未完整列出模型假设和估计细节；统一框架及一致性结论仍需结合原文条件核验。
原文摘要
This paper considers the formulation and estimation of simultaneous equation models with both discrete and continuous endogenous variables.The statistical model proposed here is sufficiently rich to encompass the álassjcai simultaneous equation model for continuous endogenous variables and more recent models for purely discrete endogenous variables as special cases of a more general model.Interest in discrete data has been ftsledby a rapid growth in the availability of microeconomic data sets coupled with a growing awareness of the importance of discrete choice models for the analysis of uiicroeconomic problems (see McFadden, 1976).To date, the only available statistical models for the analysis of discrete endogenous variables have been developed for the purely discrete case.The log-linear or logistic model of Goodman (1970) as expanded by Raberman (1974) and Nerlove and Press (1976) is one Vol.II, 1967; Lord and Novick, cbs.16-20, 1967.)It is argued in this paper that this class of statistical models provides a natural framework for generating simultaneous equation models with both discrete and continuous random variables.In contrast, the framework of Goodman, while convenient for formulating descriptive models for discrete data, offers a much less natural apparatus for analyzing econometric structural equation models.This is so primarily because the simultaneous equation model is inherently an unconditional representation of behavioral equations while the model of Goodman is designed to facilitate the analysis of conditional representations, and does not lend itself to the unconditional formulations required in simultaneous equation theory.The structure of this paper is in four parts.in part one general models are discussed.Dummy endogenous variables are introduced in two distinct roles: (1) as proxies for unobserved latent variables and (2) as direct shifters of behavioral equations.Five models incorporating such dummy variables are discussed.Part two, also the longest section, presents a complete analysis of the most novel and most general of the five models presented in part one.This is a model with both continuous and discrete endogenous variables.The issues of identification and estimation are discussed together by proving the existence of consistent estimators.Maximum likelihood estimators and alternative estimators are discussed.In part three, a brief discussion of a multivariate probit model with structural shift is presented.Part four presents a comparison between the models developed in this paper and the models of Goodman and Nerlove and Press.