1
00:00:00,299 --> 00:00:04,644
因果推断之路径既黑暗又危险

2
00:00:05,139 --> 00:00:08,015
但是计量经济学是很厉害的武器

3
00:00:08,480 --> 00:00:11,734
当自然界给你带来偶然的随机分配时

4
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

5
00:00:19,393 --> 00:00:21,094
[]

6
00:00:23,653 --> 00:00:26,362
随机试验是完成
“其他条件不变”的比较

7
00:00:26,362 --> 00:00:28,704
的最可靠途径

8
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

9
00:00:33,224 --> 00:00:36,940
但是有时候，随机是偶然发生的

10
00:00:36,940 --> 00:00:40,592
这时候我们转向工具变量

11
00:00:40,592 --> 00:00:41,938
—简称IV

12
00:00:41,938 --> 00:00:44,508
工具变量

13
00:00:44,508 --> 00:00:48,186
今天的课堂是IV两节课的第一节

14
00:00:48,958 --> 00:00:52,801
我们的第一节IV课
从学校的故事开始

15
00:00:52,801 --> 00:00:54,348
[]

16
00:00:54,348 --> 00:00:56,138
特许学校是一些公立学校

17
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

18
00:01:00,895 --> 00:01:03,511
特许学校能否提高成绩

19
00:01:03,511 --> 00:01:05,161
是美国教育改革史上

20
00:01:05,161 --> 00:01:07,761
最重要的问题之一

21
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

22
00:01:12,562 --> 00:01:16,462
因此抽奖运决定了
谁家孩子可获录取

23
00:01:16,870 --> 00:01:20,695
在学生争夺机会时需要面对很多风险

24
00:01:20,695 --> 00:01:25,003
正如获奖纪录片“等待超人”中

25
00:01:25,003 --> 00:01:27,832
所描述的那样

26
00:01:27,832 --> 00:01:29,699
等待结果时会产生很多种情绪

27
00:01:30,258 --> 00:01:32,916
别哭，你会让妈妈哭的
好吗？

28
00:01:37,498 --> 00:01:40,618
特许学校真的能提供更好的教育吗？

29
00:01:40,948 --> 00:01:43,183
评论家肯定会说"不是的"

30
00:01:43,413 --> 00:01:46,586
他们会争辩说特许学校
能夠招募更好

31
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

32
00:01:50,164 --> 00:01:52,061
反映了选择性偏差

33
00:01:52,595 --> 00:01:54,729
等一下，这个似乎很容易

34
00:01:55,139 --> 00:01:57,639
在抽奖活动中
我们会随机选择优胜者

35
00:01:57,639 --> 00:02:00,083
因此只比较赢家和输家
很明显的

36
00:02:00,083 --> 00:02:01,784
在正确的轨道上，卡马尔

37
00:02:01,784 --> 00:02:04,375
但是特许学校的抽签安排

38
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

39
00:02:07,749 --> 00:02:10,667
他们随机分配了特许学校的学位

40
00:02:11,650 --> 00:02:13,449
有些孩子很幸运

41
00:02:13,449 --> 00:02:14,966
有些孩子不是

42
00:02:14,966 --> 00:02:17,235
如果我们只是想知道特许学校

43
00:02:17,235 --> 00:02:19,202
所带来的影响

44
00:02:19,202 --> 00:02:22,417
我们可以将其视为随机试验

45
00:02:22,717 --> 00:02:24,684
但是，我们只对特许学校
就学的影响

46
00:02:24,684 --> 00:02:27,042
感兴趣

47
00:02:27,042 --> 00:02:28,283
而对录取不感兴趣

48
00:02:28,568 --> 00:02:32,039
并非所有获录取的学生
都会接受学位

49
00:02:32,039 --> 00:02:37,234
IV将被录取为特许学校学生的影响

50
00:02:37,234 --> 00:02:40,367
转变为实际就读特许学校的影响

51
00:02:40,367 --> 00:02:42,344
- 太酷了
- 哦，太好了

52
00:02:45,925 --> 00:02:48,871
让我们看一个例子

53
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

54
00:02:52,736 --> 00:02:54,937
这所KIPP特许学校位于林恩

55
00:02:54,937 --> 00:02:58,837
一座位于麻省海边的
褪色工业城镇

56
00:02:59,104 --> 00:03:01,886
这所学校的申请者多于学位

57
00:03:01,886 --> 00:03:05,620
因此他们要抽签来挑选学生

58
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

59
00:03:11,854 --> 00:03:15,350
参加了KIPP林恩的抽签

60
00:03:15,350 --> 00:03:18,805
当中253名学生KIPP获录取

61
00:03:18,805 --> 00:03:21,651
118名学生没有录取

62
00:03:21,967 --> 00:03:26,001
一年后，获录取者的数学分数

63
00:03:26,001 --> 00:03:27,852
比未获录取者更高

64
00:03:27,852 --> 00:03:30,466
我们并不是试图弄清楚

65
00:03:30,466 --> 00:03:33,803
获录取后是否会提高
你的数学水平

66
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

67
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

68
00:03:46,139 --> 00:03:48,804
其他学生选择了传统的公立学校

69
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

70
00:03:55,536 --> 00:03:57,452
他们后来也获录取

71
00:03:57,452 --> 00:04:00,044
那么，实际上参加KIPP

72
00:04:00,044 --> 00:04:02,377
对考试成绩有何影响呢？

73
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？

74
00:04:05,894 --> 00:04:07,235
这是很好的问题

75
00:04:07,235 --> 00:04:09,302
你将他们与谁进行比较呢？

76
00:04:09,302 --> 00:04:11,111
那些没有参加的学生

77
00:04:11,111 --> 00:04:12,944
上学率是随机的吗？

78
00:04:14,161 --> 00:04:16,177
- 不是啊
- 选择性偏差

79
00:04:16,177 --> 00:04:17,909
- 对啊
- 什么？

80
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

81
00:04:21,826 --> 00:04:26,409
但上学率不是随机的

82
00:04:26,635 --> 00:04:30,626
选择接受录取通知

83
00:04:30,626 --> 00:04:32,984
可能是与数学成绩有关的特征

84
00:04:33,251 --> 00:04:36,157
例如，有奉献精神的父母

85
00:04:36,157 --> 00:04:38,957
更有可能接受录取

86
00:04:38,957 --> 00:04:42,646
无论上那间学校

87
00:04:42,646 --> 00:04:44,090
他们的孩子的数学成绩
也有可能更好

88
00:04:44,090 --> 00:04:45,114
对啊

89
00:04:45,114 --> 00:04:47,725
IV将录取的影响

90
00:04:47,725 --> 00:04:50,567
转化为KIPP上学率的影响

91
00:04:50,573 --> 00:04:53,371
并就一些获录取者到其他学校上学

92
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

93
00:04:56,950 --> 00:05:00,517
本质上，IV需要进行不完全的随机化

94
00:05:00,517 --> 00:05:03,007
并进行适当的调整

95
00:05:03,684 --> 00:05:07,107
怎么样？ IV描述了一种连锁反应

96
00:05:07,641 --> 00:05:10,343
为什么学校的录取会影响成绩？

97
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

98
00:05:13,256 --> 00:05:16,643
而特许学校的上学率
提高了数学成绩

99
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”

100
00:05:20,645 --> 00:05:24,478
是抽签对特许学校上学率的影响

101
00:05:24,478 --> 00:05:28,452
第二阶段是在特许学校学

102
00:05:28,452 --> 00:05:30,153
以及结果变量之间的关联

103
00:05:30,153 --> 00:05:32,261
在这情况下，数学分数

104
00:05:32,732 --> 00:05:36,441
工具变量或简称为“工具”

105
00:05:36,441 --> 00:05:40,246
是启动链式反应的变量

106
00:05:40,979 --> 00:05:43,993
工具变量对结果的影响

107
00:05:43,993 --> 00:05:46,631
称为简化式

108
00:05:48,143 --> 00:05:51,869
这个链式反应可以用数学表示

109
00:05:51,869 --> 00:05:54,241
我们乘以第一阶段

110
00:05:54,241 --> 00:05:56,349
即录取者对上学率的影响

111
00:05:56,349 --> 00:05:57,960
到第二阶段

112
00:05:57,960 --> 00:06:00,538
上学率对分数的影响

113
00:06:00,538 --> 00:06:02,713
我们得到简化式

114
00:06:02,713 --> 00:06:05,680
获录取对分数的影响

115
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

116
00:06:11,752 --> 00:06:14,876
但是，上学率对成绩的影响

117
00:06:14,876 --> 00:06:17,093
并未能直接观察到

118
00:06:17,093 --> 00:06:20,360
这是我们试图确定的因果关系

119
00:06:21,043 --> 00:06:23,827
Given some important assumptions
we'll discuss shortly,

120
00:06:23,827 --> 00:06:25,977
we can find the effect
of KIPP attendance

121
00:06:25,977 --> 00:06:29,265
by dividing the reduced form
by the first stage.

122
00:06:29,265 --> 00:06:32,910
This will become more clear
as we work through an example.

123
00:06:32,910 --> 00:06:34,207
- [Student] Let's do this.

124
00:06:37,161 --> 00:06:38,728
- A quick note on measurement.

125
00:06:38,728 --> 00:06:41,745
We measure achievement
using standard deviations,

126
00:06:41,745 --> 00:06:44,728
often denoted
by the Greek letter sigma (σ).

127
00:06:44,728 --> 00:06:48,862
One σ is a huge move
from around the bottom 15%

128
00:06:48,862 --> 00:06:51,634
to the middle of most
achievement distributions.

129
00:06:51,634 --> 00:06:55,412
Even a ¼ or ½ σ difference is big.

130
00:06:56,262 --> 00:06:58,389
- [Instructor] Now we're ready
to plug some numbers

131
00:06:58,389 --> 00:07:01,655
into the equation
we introduced earlier.

132
00:07:01,655 --> 00:07:03,231
First up, what's the effect

133
00:07:03,231 --> 00:07:06,076
of winning the lottery
on math scores?

134
00:07:06,354 --> 00:07:10,421
KIPP applicants' math scores
are a third of a standard deviation

135
00:07:10,421 --> 00:07:11,835
below the state average

136
00:07:11,835 --> 00:07:14,386
in the year before
they apply to KIPP.

137
00:07:14,386 --> 00:07:18,320
But a year later, lottery winners
score right at the state average,

138
00:07:18,320 --> 00:07:21,482
while the lottery losers
are still well behind

139
00:07:21,482 --> 00:07:25,499
with an average score
around -0.36 σ.

140
00:07:25,834 --> 00:07:29,619
The effect of winning the lottery
on scores is the difference

141
00:07:29,619 --> 00:07:32,819
between the winners' scores
and the losers' scores.

142
00:07:33,403 --> 00:07:35,784
Take the winners'
average math scores,

143
00:07:35,784 --> 00:07:38,269
subtract the losers'
average math scores,

144
00:07:38,269 --> 00:07:41,502
and you will have 0.36 σ.

145
00:07:41,908 --> 00:07:46,880
Next up: what's the effect
of winning the lottery on attendance?

146
00:07:46,880 --> 00:07:49,193
In other words,
if you win the lottery,

147
00:07:49,193 --> 00:07:52,257
how much more likely
are you to attend KIPP

148
00:07:52,257 --> 00:07:53,456
than if you lose?

149
00:07:53,671 --> 00:07:57,798
First, what percentage
of lottery winners attend KIPP?

150
00:07:57,798 --> 00:08:00,774
Divide the number of winners
who attended KIPP

151
00:08:00,774 --> 00:08:05,490
by the total number
of lottery winners -- that's 78%.

152
00:08:05,810 --> 00:08:09,331
To find the percentage
of lottery losers who attended KIPP,

153
00:08:09,331 --> 00:08:12,333
we divide the number of losers
who attended KIPP

154
00:08:12,333 --> 00:08:16,865
by the total number
of lottery losers -- that's 4%.

155
00:08:17,377 --> 00:08:21,597
Subtract 4 from 78, and we find
that winning the lottery

156
00:08:21,597 --> 00:08:25,600
makes you 74%
more likely to attend KIPP.

157
00:08:25,946 --> 00:08:28,532
Now we can find
what we're really after --

158
00:08:28,532 --> 00:08:34,551
the effect of attendance on scores,
by dividing 0.36 by 0.74.

159
00:08:34,789 --> 00:08:37,585
Attending KIPP raises math scores

160
00:08:37,585 --> 00:08:41,606
by 0.48 standard deviations
on average.

161
00:08:42,126 --> 00:08:44,503
That's an awesome achievement gain,

162
00:08:44,503 --> 00:08:47,380
equal to moving
from about the bottom third

163
00:08:47,380 --> 00:08:49,925
to the middle
of the achievement distribution.

164
00:08:49,925 --> 00:08:51,085
- [Student] Whoa, half a sig.

165
00:08:51,085 --> 00:08:53,507
- [Instructor] These estimates
are for kids opting in

166
00:08:53,507 --> 00:08:54,781
to the KIPP lottery,

167
00:08:54,781 --> 00:08:57,762
whose enrollment status
is changed by winning.

168
00:08:57,985 --> 00:09:00,617
That's not necessarily
a random sample

169
00:09:00,617 --> 00:09:02,283
of all children in Lynn.

170
00:09:02,536 --> 00:09:05,035
So we can't assume
we'd see the same effect

171
00:09:05,035 --> 00:09:07,327
for other types of students.
- [Student] Huh.

172
00:09:07,327 --> 00:09:10,218
- But this effect
on keen for KIPP kids

173
00:09:10,218 --> 00:09:13,367
is likely to be a good indicator
of the consequences

174
00:09:13,367 --> 00:09:15,767
of adding additional charter seats.

175
00:09:15,767 --> 00:09:17,216
- [Student] Cool.
- [Student] Got it.

176
00:09:19,628 --> 00:09:23,352
- IV eliminates selection bias,
but like all of our tools,

177
00:09:23,352 --> 00:09:25,624
the solution builds on a set
of assumptions

178
00:09:25,624 --> 00:09:27,540
not to be taken for granted.

179
00:09:28,098 --> 00:09:31,463
First, there must be
a substantial first stage --

180
00:09:31,463 --> 00:09:35,565
that is the instrumental variable,
winning or losing the lottery,

181
00:09:35,565 --> 00:09:39,065
must really change the variable
whose effect we're interested in --

182
00:09:39,065 --> 00:09:41,031
here, KIPP attendance.

183
00:09:41,298 --> 00:09:44,594
In this case, the first stage
is not really in doubt.

184
00:09:44,594 --> 00:09:47,894
Winning the lottery makes
KIPP attendance much more likely.

185
00:09:48,386 --> 00:09:50,631
Not all IV stories are like that.

186
00:09:51,321 --> 00:09:53,698
Second, the instrument
must be as good

187
00:09:53,698 --> 00:09:54,931
as randomly assigned,

188
00:09:54,931 --> 00:09:58,716
meaning lottery winners and losers
have similar characteristics.

189
00:09:58,893 --> 00:10:01,559
This is the independence assumption.

190
00:10:01,977 --> 00:10:05,716
Of course, KIPP lottery wins
really are randomly assigned.

191
00:10:05,716 --> 00:10:09,656
Still, we should check for balance
and confirm that winners and losers

192
00:10:09,656 --> 00:10:11,493
have similar family backgrounds,

193
00:10:11,493 --> 00:10:13,590
similar aptitudes and so on.

194
00:10:13,590 --> 00:10:16,969
In essence, we're checking
to ensure KIPP lotteries are fair

195
00:10:16,969 --> 00:10:20,055
with no group of applicants
suspiciously likely to win.

196
00:10:21,373 --> 00:10:24,373
Finally, we require
the instrument change outcomes

197
00:10:24,373 --> 00:10:26,092
solely through
the variable of interest --

198
00:10:26,092 --> 00:10:28,100
in this case, attending KIPP.

199
00:10:28,299 --> 00:10:31,367
This assumption is called
the exclusion restriction.

200
00:10:32,951 --> 00:10:37,500
- IV only works if you can satisfy
these three assumptions.

201
00:10:38,033 --> 00:10:40,418
- I don't understand
the exclusion restriction.

202
00:10:40,917 --> 00:10:43,599
How could winning the lottery
affect math scores

203
00:10:43,599 --> 00:10:45,244
other than by attending KIPP?

204
00:10:45,244 --> 00:10:47,230
- [Student] Yeah.
- [Instructor] Great question.

205
00:10:47,230 --> 00:10:50,536
Suppose lottery winners
are just thrilled to win,

206
00:10:50,536 --> 00:10:55,045
and this happiness motivates them
to study more and learn more math,

207
00:10:55,045 --> 00:10:57,285
regardless of where
they go to school.

208
00:10:57,285 --> 00:10:59,901
This would violate
the exclusion restriction

209
00:10:59,901 --> 00:11:03,787
because the motivational effect
of winning is a second channel

210
00:11:03,787 --> 00:11:06,569
whereby lotteries
might affect test scores.

211
00:11:06,865 --> 00:11:09,546
While it's hard
to rule this out entirely,

212
00:11:09,546 --> 00:11:12,650
there's no evidence
of any alternative channels

213
00:11:12,650 --> 00:11:14,108
in the KIPP study.

214
00:11:17,817 --> 00:11:20,700
- IV solves the problem
of selection bias

215
00:11:20,700 --> 00:11:25,051
in scenarios like the KIPP lottery
where treatment offers are random

216
00:11:25,051 --> 00:11:27,083
but some of those offered opt out.

217
00:11:28,451 --> 00:11:31,700
This sort of intentional
yet incomplete random assignment

218
00:11:31,700 --> 00:11:33,367
is surprisingly common.

219
00:11:33,367 --> 00:11:36,318
Even randomized clinical trials
have this feature.

220
00:11:37,134 --> 00:11:40,053
IV solves the problem
of non-random take-up

221
00:11:40,053 --> 00:11:42,534
in lotteries or clinical research.

222
00:11:43,054 --> 00:11:46,725
But lotteries are not the only source
of compelling instruments.

223
00:11:46,915 --> 00:11:49,124
Many causal questions
can be addressed

224
00:11:49,124 --> 00:11:50,758
by naturally occurring

225
00:11:50,758 --> 00:11:53,831
as good as randomly
assigned variation.

226
00:11:54,731 --> 00:11:56,915
Here's a causal question for you:

227
00:11:56,915 --> 00:11:59,450
Do women who have children
early in their careers

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suffer a substantial earnings penalty

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as a result?

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After all, women earn less than men.

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We could, of course, simply compare
the earnings of women

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with more and fewer children.

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But such comparisons are fraught
with selection bias.

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If only we could
randomly assign babies

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to different households.

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Yeah, right,
sounds pretty fanciful.

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Our next IV story -- fantastic
and not fanciful --

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illustrates an amazing,
naturally occurring instrument

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00:12:30,234 --> 00:12:31,918
for family size.

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♪ [] ♪

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- [Instructor] You're on your way
to mastering econometrics.

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00:12:38,202 --> 00:12:40,170
Make sure this video sticks

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00:12:40,170 --> 00:12:42,636
by taking a few
quick practice questions.

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00:12:42,886 --> 00:12:46,336
Or, if you're ready,
click for the next video.

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00:12:46,529 --> 00:12:50,204
You can also check out
MRU's website for more courses,

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00:12:50,204 --> 00:12:52,027
teacher resources, and more.

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00:12:52,289 --> 00:12:53,772
♪ [] ♪