Efficient Estimation Using Panel Data
利用面板数据进行有效估计AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要直接讨论个体效应与解释变量相关的面板回归，以及多种工具变量估计量的构造与效率比较，故归入面板数据。
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利用面板数据进行有效估计
- 研究问题
- 面板回归中，部分解释变量与个体效应相关时，HT、AM 与 BMS 工具变量估计量如何联系，效率改善又依赖哪些额外条件？
- 方法与思路
- 作者比较 HT 的均值与去均值工具、AM 的逐期工具扩展，并将相关变量的去均值项拆为线性独立的工具，构造 BMS 估计量。
- 材料陈述的贡献
- 摘要称，文章澄清 HT 与 AM 的工具构造及效率条件，给出标准两阶段最小二乘实现形式，并提出在更强假设下更有效率的 BMS 估计量。
- 阅读关注点
- 重点核对三种估计量的工具集合、逐期正交条件及效率比较前提，尤其检查去均值是否足以消除相关来源，以及 BMS 工具的合法性。
- 阅读边界
- 摘要中的效率排序以逐步增强的假设为前提；变量与个体效应相关的成因影响工具合法性，仅凭摘要不能确认这些条件在具体数据中成立。
原文摘要
IN AN IMPORTANT RECENT PAPER, Hausman and Taylor (1981)-hereafter HT-considered the instrumental-variable estimation of a regression model using panel data, when the individual effects may be correlated with a subset of the explanatory variables. They provided a simple consistent estimator and an efficient estimator. More recently, Amemiya and MaCurdy (1986)-hereafter AM-have suggested an alternative estimator which is more efficient than the HT estimator, under certain conditions and given stronger assumptions than HT made. However, the relationship between the HT and AM papers is less clear than it might be, in part because of notational differences between the two papers. In this paper we clarify the relationship between the HT and AM estimators, and we show that the difference between these estimators lies in the treatment of the time-varying explanatory variables which are uncorrelated with the effects: HT use each such variable as two instruments (means and deviations from means), while AM use such variables as T + 1 instruments (as deviations from means and also separately for each of the T available time periods). This enables us to make clear the conditions under which the AM estimator is more efficient than the HT estimator. We also present each estimator in a form which allows it to be calculated using standard instrumental-variables (two-stage least squares) software. Following the AM path one step further, we then define a third (BMS) estimator which, under yet stronger assumptions, is more efficient than the AM estimator. Both HT and AM use as instruments the deviations from means of the time-varying variables which are correlated with the effects. A more efficient estimator may be obtained by using separately the (T - 1) linearly independent values of these deviations from individual means. Consistency requires that these be legitimate instruments, and whether this is so depends on why these time-varying variables are correlated with the effects. For example, if such correlation arises solely because of a time-invariant component which is removed in taking deviations from individual means, these instruments are legitimate.