WEBVTT

00:00:00.299 --> 00:00:04.644
因果推断之路径既黑暗又危险

00:00:05.139 --> 00:00:08.015
但是计量经济学是很厉害的武器

00:00:08.480 --> 00:00:11.734
当自然界给你带来偶然的随机分配时

00:00:11.734 --> 00:00:15.803
使用气势汹汹与灵活多變的
工具变量进行攻击

00:00:19.393 --> 00:00:21.094
[]

00:00:23.653 --> 00:00:26.362
随机试验是完成
“其他条件不变”的比较

00:00:26.362 --> 00:00:28.704
的最可靠途径

00:00:28.704 --> 00:00:32.640
但我们经常无法使用
这个功能强大的工具

00:00:33.224 --> 00:00:36.940
但是有时候，随机是偶然发生的

00:00:36.940 --> 00:00:40.592
这时候我们转向工具变量

00:00:40.592 --> 00:00:41.938
—简称IV

00:00:41.938 --> 00:00:44.508
工具变量

00:00:44.508 --> 00:00:48.186
今天的课堂是IV两节课的第一节

00:00:48.958 --> 00:00:52.801
我们的第一节IV课
从学校的故事开始

00:00:52.801 --> 00:00:54.348
[]

00:00:54.348 --> 00:00:56.138
特许学校是一些公立学校

00:00:56.138 --> 00:01:00.112
不受日常学区监督
与教师工会合同约束

00:01:00.895 --> 00:01:03.511
特许学校能否提高成绩

00:01:03.511 --> 00:01:05.161
是美国教育改革史上

00:01:05.161 --> 00:01:07.761
最重要的问题之一

00:01:08.145 --> 00:01:12.562
最受欢迎的特许学校的申请人数
远多于学位

00:01:12.562 --> 00:01:16.462
因此抽奖运决定了
谁家孩子可获录取

00:01:16.870 --> 00:01:20.695
在学生争夺机会时需要面对很多风险

00:01:20.695 --> 00:01:25.003
正如获奖纪录片“等待超人”中

00:01:25.003 --> 00:01:27.832
所描述的那样

00:01:27.832 --> 00:01:29.699
等待结果时会产生很多种情绪

00:01:30.258 --> 00:01:32.916
别哭，你会让妈妈哭的
好吗？

00:01:37.498 --> 00:01:40.618
特许学校真的能提供更好的教育吗？

00:01:40.948 --> 00:01:43.183
评论家肯定会说"不是的"

00:01:43.413 --> 00:01:46.586
他们会争辩说特许学校
能夠招募更好

00:01:46.586 --> 00:01:50.164
更聪明或更主动的学生
因此以后结果的差异

00:01:50.164 --> 00:01:52.061
反映了选择性偏差

00:01:52.595 --> 00:01:54.729
等一下，这个似乎很容易

00:01:55.139 --> 00:01:57.639
在抽奖活动中
我们会随机选择优胜者

00:01:57.639 --> 00:02:00.083
因此只比较赢家和输家
很明显的

00:02:00.083 --> 00:02:01.784
在正确的轨道上，卡马尔

00:02:01.784 --> 00:02:04.375
但是特许学校的抽签安排

00:02:04.375 --> 00:02:07.560
不会强迫孩子们进入
或离开特定的学校

00:02:07.749 --> 00:02:10.667
他们随机分配了特许学校的学位

00:02:11.650 --> 00:02:13.449
有些孩子很幸运

00:02:13.449 --> 00:02:14.966
有些孩子不是

00:02:14.966 --> 00:02:17.235
如果我们只是想知道特许学校

00:02:17.235 --> 00:02:19.202
所带来的影响

00:02:19.202 --> 00:02:22.417
我们可以将其视为随机试验

00:02:22.717 --> 00:02:24.684
但是，我们只对特许学校
就学的影响

00:02:24.684 --> 00:02:27.042
感兴趣

00:02:27.042 --> 00:02:28.283
而对录取不感兴趣

00:02:28.568 --> 00:02:32.039
并非所有获录取的学生
都会接受学位

00:02:32.039 --> 00:02:37.234
IV将被录取为特许学校学生的影响

00:02:37.234 --> 00:02:40.367
转变为实际就读特许学校的影响

00:02:40.367 --> 00:02:42.344
- 太酷了
- 哦，太好了

00:02:45.925 --> 00:02:48.871
让我们看一个例子

00:02:48.871 --> 00:02:52.353
这是一所执行知识就是力量专案
的特许学校，或简称为KIPP

00:02:52.736 --> 00:02:54.937
这所KIPP特许学校位于林恩

00:02:54.937 --> 00:02:58.837
一座位于麻省海边的
褪色工业城镇

00:02:59.104 --> 00:03:01.886
这所学校的申请者多于学位

00:03:01.886 --> 00:03:05.620
因此他们要抽签来挑选学生

00:03:05.834 --> 00:03:11.854
从2005年到2008年
共有371名四年级以及五年级生

00:03:11.854 --> 00:03:15.350
参加了KIPP林恩的抽签

00:03:15.350 --> 00:03:18.805
当中253名学生KIPP获录取

00:03:18.805 --> 00:03:21.651
118名学生没有录取

00:03:21.967 --> 00:03:26.001
一年后，获录取者的数学分数

00:03:26.001 --> 00:03:27.852
比未获录取者更高

00:03:27.852 --> 00:03:30.466
我们并不是试图弄清楚

00:03:30.466 --> 00:03:33.803
获录取后是否会提高
你的数学水平

00:03:34.070 --> 00:03:38.471
我们想知道参加KIPP
是否会使你的数学成绩改进

00:03:39.041 --> 00:03:45.750
在253位获录取者中
实际上只有199位到KIPP上学

00:03:46.139 --> 00:03:48.804
其他学生选择了传统的公立学校

00:03:49.563 --> 00:03:55.536
同样，在118名未被录取的学生中
事实上有一些最终参加了KIPP

00:03:55.536 --> 00:03:57.452
他们后来也获录取

00:03:57.452 --> 00:04:00.044
那么，实际上参加KIPP

00:04:00.044 --> 00:04:02.377
对考试成绩有何影响呢？

00:04:03.109 --> 00:04:05.426
为什么我们不能只衡量
他们的数学成绩？

00:04:05.894 --> 00:04:07.235
这是很好的问题

00:04:07.235 --> 00:04:09.302
你将他们与谁进行比较呢？

00:04:09.302 --> 00:04:11.111
那些没有参加的学生

00:04:11.111 --> 00:04:12.944
上学率是随机的吗？

00:04:14.161 --> 00:04:16.177
- 不是啊
- 选择性偏差

00:04:16.177 --> 00:04:17.909
- 对啊
- 什么？

00:04:17.909 --> 00:04:21.826
KIPP的录取是随机的，因此我们
对“其他条件不变”的假设充满信心

00:04:21.826 --> 00:04:26.409
但上学率不是随机的

00:04:26.635 --> 00:04:30.626
选择接受录取通知

00:04:30.626 --> 00:04:32.984
可能是与数学成绩有关的特征

00:04:33.251 --> 00:04:36.157
例如，有奉献精神的父母

00:04:36.157 --> 00:04:38.957
更有可能接受录取

00:04:38.957 --> 00:04:42.646
无论上那间学校

00:04:42.646 --> 00:04:44.090
他们的孩子的数学成绩
也有可能更好

00:04:44.090 --> 00:04:45.114
对啊

00:04:45.114 --> 00:04:47.725
IV将录取的影响

00:04:47.725 --> 00:04:50.567
转化为KIPP上学率的影响

00:04:50.573 --> 00:04:53.371
并就一些获录取者到其他学校上学

00:04:53.371 --> 00:04:56.573
而一些未被录取者还是设法
参加了KIPP 而进行调整

00:04:56.950 --> 00:05:00.517
本质上，IV需要进行不完全的随机化

00:05:00.517 --> 00:05:03.007
并进行适当的调整

00:05:03.684 --> 00:05:07.107
怎么样？ IV描述了一种连锁反应

00:05:07.641 --> 00:05:10.343
为什么学校的录取会影响成绩？

00:05:10.343 --> 00:05:13.256
可能是因为这影响了
特许学校的上学率

00:05:13.256 --> 00:05:16.643
而特许学校的上学率
提高了数学成绩

00:05:16.643 --> 00:05:20.645
连锁反应的第一个环节
称之为“第一阶段”

00:05:20.645 --> 00:05:24.478
是抽签对特许学校上学率的影响

00:05:24.478 --> 00:05:28.452
第二阶段是在特许学校学

00:05:28.452 --> 00:05:30.153
以及结果变量之间的关联

00:05:30.153 --> 00:05:32.261
在这情况下，数学分数

00:05:32.732 --> 00:05:36.441
工具变量或简称为“工具”

00:05:36.441 --> 00:05:40.246
是启动链式反应的变量

00:05:40.979 --> 00:05:43.993
工具变量对结果的影响

00:05:43.993 --> 00:05:46.631
称为简化式

00:05:48.143 --> 00:05:51.869
这个链式反应可以用数学表示

00:05:51.869 --> 00:05:54.241
我们乘以第一阶段

00:05:54.241 --> 00:05:56.349
即录取者对上学率的影响

00:05:56.349 --> 00:05:57.960
到第二阶段

00:05:57.960 --> 00:06:00.538
上学率对分数的影响

00:06:00.538 --> 00:06:02.713
我们得到简化式

00:06:02.713 --> 00:06:05.680
获录取对分数的影响

00:06:06.780 --> 00:06:11.566
简化式和第一阶段是可观察的
并且易于计算

00:06:11.752 --> 00:06:14.876
但是，上学率对成绩的影响

00:06:14.876 --> 00:06:17.093
并未能直接观察到

00:06:17.093 --> 00:06:20.360
这是我们试图确定的因果关系

00:06:21.043 --> 00:06:23.827
考虑到我们将在稍后进行讨论的
一些重要假设

00:06:23.827 --> 00:06:25.977
我们可以通过将简化式
除以第一阶段

00:06:25.977 --> 00:06:29.265
来找出KIPP上学率的影响

00:06:29.265 --> 00:06:32.910
通过示例，这点将会更加清楚

00:06:32.910 --> 00:06:34.207
让我们做吧

00:06:37.161 --> 00:06:38.728
有关衡量的简短笔记

00:06:38.728 --> 00:06:41.745
我们使用标准差来衡量成就

00:06:41.745 --> 00:06:44.728
通常用希腊字母sigma (σ) 表示

00:06:44.728 --> 00:06:48.862
一个σ是从大多数成就分配的
最低15％

00:06:48.862 --> 00:06:51.634
到中间位置的巨大变化

00:06:51.634 --> 00:06:55.412
甚至¼或½ σ 的差异也很大

00:06:56.262 --> 00:06:58.389
现在我们准备将一些数字

00:06:58.389 --> 00:07:01.655
插入到前面介绍的方程式中

00:07:01.655 --> 00:07:03.231
首先，获录取对数学成绩

00:07:03.231 --> 00:07:06.076
有何影响呢？

00:07:06.354 --> 00:07:10.421
KIPP申请人的数学成绩是

00:07:10.421 --> 00:07:11.835
申请KIPP之前一年中

00:07:11.835 --> 00:07:14.386
低于州平均值的标准差的三分之一

00:07:14.386 --> 00:07:18.320
但是一年后，获录取者得分
达到了州平均水平

00:07:18.320 --> 00:07:21.482
而未被录取者

00:07:21.482 --> 00:07:25.499
仍然落后于平均分数-0.36σ

00:07:25.834 --> 00:07:29.619
获录取者对分数的影响
是获录取者的分数

00:07:29.619 --> 00:07:32.819
与未被录取者的分数之间的差异

00:07:33.403 --> 00:07:35.784
获录取者的平均数学成绩

00:07:35.784 --> 00:07:38.269
减去未被录取者的平均数学成绩

00:07:38.269 --> 00:07:41.502
你的答案是0.36σ

00:07:41.908 --> 00:07:46.880
接下来：获录取对上学率
有什么影响呢？

00:07:46.880 --> 00:07:49.193
换句话说，如果你获录取

00:07:49.193 --> 00:07:52.257
与未被录取相比

00:07:52.257 --> 00:07:53.456
你参加KIPP的可能性有多大？

00:07:53.671 --> 00:07:57.798
首先，有多少百分比的获录取者
参加KIPP？

00:07:57.798 --> 00:08:00.774
用参加KIPP的获录取者的人数

00:08:00.774 --> 00:08:05.490
除以获录取者的总数—78％

00:08:05.810 --> 00:08:09.331
要找出参加KIPP
而未被录取者的百分比

00:08:09.331 --> 00:08:12.333
我们将参加KIPP的
未被录取者的人数

00:08:12.333 --> 00:08:16.865
除以未被录取者的总数—即4％

00:08:17.377 --> 00:08:21.597
从78减去4，我们发现获录取

00:08:21.597 --> 00:08:25.600
会使你参加KIPP的可能性
提高了74％

00:08:25.946 --> 00:08:28.532
现在我们可以找到真正想要的数据—

00:08:28.532 --> 00:08:34.551
用0.36除以0.74
以得到上学率对分数的影响

00:08:34.789 --> 00:08:37.585
Attending KIPP raises math scores

00:08:37.585 --> 00:08:41.606
by 0.48 standard deviations
on average.

00:08:42.126 --> 00:08:44.503
That's an awesome achievement gain,

00:08:44.503 --> 00:08:47.380
equal to moving
from about the bottom third

00:08:47.380 --> 00:08:49.925
to the middle
of the achievement distribution.

00:08:49.925 --> 00:08:51.085
- [Student] Whoa, half a sig.

00:08:51.085 --> 00:08:53.507
- [Instructor] These estimates
are for kids opting in

00:08:53.507 --> 00:08:54.781
to the KIPP lottery,

00:08:54.781 --> 00:08:57.762
whose enrollment status
is changed by winning.

00:08:57.985 --> 00:09:00.617
That's not necessarily
a random sample

00:09:00.617 --> 00:09:02.283
of all children in Lynn.

00:09:02.536 --> 00:09:05.035
So we can't assume
we'd see the same effect

00:09:05.035 --> 00:09:07.327
for other types of students.
- [Student] Huh.

00:09:07.327 --> 00:09:10.218
- But this effect
on keen for KIPP kids

00:09:10.218 --> 00:09:13.367
is likely to be a good indicator
of the consequences

00:09:13.367 --> 00:09:15.767
of adding additional charter seats.

00:09:15.767 --> 00:09:17.216
- [Student] Cool.
- [Student] Got it.

00:09:19.628 --> 00:09:23.352
- IV eliminates selection bias,
but like all of our tools,

00:09:23.352 --> 00:09:25.624
the solution builds on a set
of assumptions

00:09:25.624 --> 00:09:27.540
not to be taken for granted.

00:09:28.098 --> 00:09:31.463
First, there must be
a substantial first stage --

00:09:31.463 --> 00:09:35.565
that is the instrumental variable,
winning or losing the lottery,

00:09:35.565 --> 00:09:39.065
must really change the variable
whose effect we're interested in --

00:09:39.065 --> 00:09:41.031
here, KIPP attendance.

00:09:41.298 --> 00:09:44.594
In this case, the first stage
is not really in doubt.

00:09:44.594 --> 00:09:47.894
Winning the lottery makes
KIPP attendance much more likely.

00:09:48.386 --> 00:09:50.631
Not all IV stories are like that.

00:09:51.321 --> 00:09:53.698
Second, the instrument
must be as good

00:09:53.698 --> 00:09:54.931
as randomly assigned,

00:09:54.931 --> 00:09:58.716
meaning lottery winners and losers
have similar characteristics.

00:09:58.893 --> 00:10:01.559
This is the independence assumption.

00:10:01.977 --> 00:10:05.716
Of course, KIPP lottery wins
really are randomly assigned.

00:10:05.716 --> 00:10:09.656
Still, we should check for balance
and confirm that winners and losers

00:10:09.656 --> 00:10:11.493
have similar family backgrounds,

00:10:11.493 --> 00:10:13.590
similar aptitudes and so on.

00:10:13.590 --> 00:10:16.969
In essence, we're checking
to ensure KIPP lotteries are fair

00:10:16.969 --> 00:10:20.055
with no group of applicants
suspiciously likely to win.

00:10:21.373 --> 00:10:24.373
Finally, we require
the instrument change outcomes

00:10:24.373 --> 00:10:26.092
solely through
the variable of interest --

00:10:26.092 --> 00:10:28.100
in this case, attending KIPP.

00:10:28.299 --> 00:10:31.367
This assumption is called
the exclusion restriction.

00:10:32.951 --> 00:10:37.500
- IV only works if you can satisfy
these three assumptions.

00:10:38.033 --> 00:10:40.418
- I don't understand
the exclusion restriction.

00:10:40.917 --> 00:10:43.599
How could winning the lottery
affect math scores

00:10:43.599 --> 00:10:45.244
other than by attending KIPP?

00:10:45.244 --> 00:10:47.230
- [Student] Yeah.
- [Instructor] Great question.

00:10:47.230 --> 00:10:50.536
Suppose lottery winners
are just thrilled to win,

00:10:50.536 --> 00:10:55.045
and this happiness motivates them
to study more and learn more math,

00:10:55.045 --> 00:10:57.285
regardless of where
they go to school.

00:10:57.285 --> 00:10:59.901
This would violate
the exclusion restriction

00:10:59.901 --> 00:11:03.787
because the motivational effect
of winning is a second channel

00:11:03.787 --> 00:11:06.569
whereby lotteries
might affect test scores.

00:11:06.865 --> 00:11:09.546
While it's hard
to rule this out entirely,

00:11:09.546 --> 00:11:12.650
there's no evidence
of any alternative channels

00:11:12.650 --> 00:11:14.108
in the KIPP study.

00:11:17.817 --> 00:11:20.700
- IV solves the problem
of selection bias

00:11:20.700 --> 00:11:25.051
in scenarios like the KIPP lottery
where treatment offers are random

00:11:25.051 --> 00:11:27.083
but some of those offered opt out.

00:11:28.451 --> 00:11:31.700
This sort of intentional
yet incomplete random assignment

00:11:31.700 --> 00:11:33.367
is surprisingly common.

00:11:33.367 --> 00:11:36.318
Even randomized clinical trials
have this feature.

00:11:37.134 --> 00:11:40.053
IV solves the problem
of non-random take-up

00:11:40.053 --> 00:11:42.534
in lotteries or clinical research.

00:11:43.054 --> 00:11:46.725
But lotteries are not the only source
of compelling instruments.

00:11:46.915 --> 00:11:49.124
Many causal questions
can be addressed

00:11:49.124 --> 00:11:50.758
by naturally occurring

00:11:50.758 --> 00:11:53.831
as good as randomly
assigned variation.

00:11:54.731 --> 00:11:56.915
Here's a causal question for you:

00:11:56.915 --> 00:11:59.450
Do women who have children
early in their careers

00:11:59.450 --> 00:12:01.647
suffer a substantial earnings penalty

00:12:01.647 --> 00:12:02.648
as a result?

00:12:02.648 --> 00:12:04.970
After all, women earn less than men.

00:12:05.573 --> 00:12:08.506
We could, of course, simply compare
the earnings of women

00:12:08.506 --> 00:12:10.891
with more and fewer children.

00:12:10.891 --> 00:12:14.190
But such comparisons are fraught
with selection bias.

00:12:14.806 --> 00:12:17.401
If only we could
randomly assign babies

00:12:17.401 --> 00:12:19.089
to different households.

00:12:19.089 --> 00:12:22.131
Yeah, right,
sounds pretty fanciful.

00:12:22.470 --> 00:12:26.714
Our next IV story -- fantastic
and not fanciful --

00:12:26.714 --> 00:12:30.234
illustrates an amazing,
naturally occurring instrument

00:12:30.234 --> 00:12:31.918
for family size.

00:12:33.317 --> 00:12:34.551
♪ [] ♪

00:12:34.551 --> 00:12:38.202
- [Instructor] You're on your way
to mastering econometrics.

00:12:38.202 --> 00:12:40.170
Make sure this video sticks

00:12:40.170 --> 00:12:42.636
by taking a few
quick practice questions.

00:12:42.886 --> 00:12:46.336
Or, if you're ready,
click for the next video.

00:12:46.529 --> 00:12:50.204
You can also check out
MRU's website for more courses,

00:12:50.204 --> 00:12:52.027
teacher resources, and more.

00:12:52.289 --> 00:12:53.772
♪ [] ♪