工具变量与两阶段最小二乘法.

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 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。
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？ 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

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 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
Instrumental Variables & 2SLS 工具变量与两阶段最小二乘法
y = b0 + b1x1 + b2x2 + . . . bkxk + u x1 = p0 +ຫໍສະໝຸດ Baidup1z + p2x2 + . . . pkxk + v
Intermediate Econometrics, Yan Shen
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 That is, when Cov(x,u) ≠ 0 即，Cov(x,u) ≠0时

Intermediate Econometrics, Yan Shen
7
Instrumental Variable: Who qualifies? 什么样的变量可以作为IV？



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 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, 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， 我们不得不 依赖于常识和经济理论。
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? 如果一些重要的变量被遗漏，我们应当怎 么办？
Intermediate Econometrics, Yan Shen
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 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
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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。