工具变量与两阶段最小二乘法

Yan Shen
4
The ways out 一些办法
Ignore the problem, pretend that it does not exist 忽略这个问题，假装这个问题并不存在
Find and use a suitable proxy 使用代理变量
Uses an estimation method that recognizes the presence of the omitted variable 使用一种对遗漏变量稳健的估计方法。
IV solutions to errors-in-variables problem 用工具变量解决测量误差问题
Testing for endogeneity… 检验内生性
Intermediate Econometrics,
Yan Shen
2
Lecture Outline 本课提要
Motivation: Why using IV? 出发点：为何用工具变量？
Intermediate Econometrics,
Yan Shen
5
Why Use Instrumental Variables? 为何使用工具变量？
Instrumental Variables (IV) estimation is used when your model has endogenous x’s 当模型解释变量具有内生性时，使用工具 变量估计
Sometimes we refer to this regression as the first-stage regression. 有时我们将这个回归称为第一阶段回归。
In order for a variable, z, to serve as a valid instrument for x, the following must be true 针对内生变量 x 的一个有效的工具变量 z 应当满 足如下条件
The instrument must be exogenous 工具变量应为外生
Additionally, IV can be used to solve the classic errors-in-variables problem 而且，IV可用来解决经典的测量误差问题
Intermediate Econometrics,
Yan Shen
7
Instrumental Variable: Who qualifies? 什么样的变量可以作为IV？
That is, Cov(z,x) ≠ 0 (15.5)
Intermediate Econometrics,
Yan Shen
9
About Cov(z,u) 关于Cov(z,u)
We have to use common sense and economic theory to decide if it makes sense to assume Cov(z,u) = 0 为了判断Cov(z,u) = 0这一假定是否合理，
1
Chapter Outline 本章提要
Omitted Variables in a simple regression model 简单回归中的遗漏变量
IV estimation of the Multiple Regression 多方程回归中的工具变量估计
Two Stage Least Squares 两阶段最小二乘法
That is, Cov(z,u) = 0 (15.4) 即Cov(z,u) = 0
Intermediate Econometrics,
Yan Shen
8
Instrumental Variable: Who qualifies? 什么样的变量可以作为IV？
The instrument must be correlated with the endogenous variable x 工具变量应与内生变量 x 相关
That is, when Cov(x,u) ≠ 0 即，Cov(x,u) ≠0时
Intermediate Econometrics,
Yan Shen
6
Why Use Instrumental Variables? 为何使用工具变量？
Thus, IV can be used to address the problem of omitted variable bias 所以，IV可以用来解决遗漏变量偏差
Statistical Inference with the IV estimator IV 估计中的统计推断
Properties of IV with a poor IV “坏”工具变量的性质
Computing R squares after IV 计算IV估计的R方
IV estimation of the multiple regression model 多方程回归的IV估计
我们不得不 依赖于常识和经济理论。
Intermediate Econometrics,
Yan Shen
10
About Cov(z,x)
We can test if Cov(z,x) ≠ 0 我们可以检验是否Cov(z,x) ≠ 0
Just testing H0: p1 = 0 in x = p0 + p1z + v 只需检验 H0: p1 = 0 in x = p0 + p1z + v
Instrumental Variables & 2SLS 工具变量与两阶段最小二乘法
y = b0 + b1x1 + b2x2 + . . . bkxk + u x1 = p0 + p1z + p2x2 + . . . pkxk + v
Intermediate Econometrics,
Yan Shen
Intermediate Econometrics,
Yan Shen
3
Problem to start with 从这个问题出发…
If important variables are omitted, what should we do? 如果一些重要源自文库变量被遗漏，我们应当怎 么办？
Intermediate Econometrics,