0:00:00.299,0:00:04.644
因果推断之路径既黑暗又危险

0:00:05.139,0:00:08.015
但是计量经济学是很厉害的武器

0:00:08.480,0:00:11.734
当自然界给你带来偶然的随机分配时

0:00:11.734,0:00:15.803
使用气势汹汹与灵活多變的[br]工具变量进行攻击

0:00:19.393,0:00:21.094
[]

0:00:23.653,0:00:26.362
随机试验是完成[br]“其他条件不变”的比较

0:00:26.362,0:00:28.704
的最可靠途径

0:00:28.704,0:00:32.640
但我们经常无法使用[br]这个功能强大的工具

0:00:33.224,0:00:36.940
但是有时候，随机是偶然发生的

0:00:36.940,0:00:40.592
这时候我们转向工具变量

0:00:40.592,0:00:41.938
—简称IV

0:00:41.938,0:00:44.508
工具变量

0:00:44.508,0:00:48.186
今天的课堂是IV两节课的第一节

0:00:48.958,0:00:52.801
我们的第一节IV课[br]从学校的故事开始

0:00:52.801,0:00:54.348
[]

0:00:54.348,0:00:56.138
特许学校是一些公立学校

0:00:56.138,0:01:00.112
不受日常学区监督[br]与教师工会合同约束

0:01:00.895,0:01:03.511
特许学校能否提高成绩

0:01:03.511,0:01:05.161
是美国教育改革史上

0:01:05.161,0:01:07.761
最重要的问题之一

0:01:08.145,0:01:12.562
最受欢迎的特许学校的申请人数[br]远多于学位

0:01:12.562,0:01:16.462
因此抽奖运决定了[br]谁家孩子可获录取

0:01:16.870,0:01:20.695
在学生争夺机会时需要面对很多风险

0:01:20.695,0:01:25.003
正如获奖纪录片“等待超人”中

0:01:25.003,0:01:27.832
所描述的那样

0:01:27.832,0:01:29.699
等待结果时会产生很多种情绪

0:01:30.258,0:01:32.916
别哭，你会让妈妈哭的[br]好吗？

0:01:37.498,0:01:40.618
特许学校真的能提供更好的教育吗？

0:01:40.948,0:01:43.183
评论家肯定会说"不是的"

0:01:43.413,0:01:46.586
他们会争辩说特许学校[br]能夠招募更好

0:01:46.586,0:01:50.164
更聪明或更主动的学生[br]因此以后结果的差异

0:01:50.164,0:01:52.061
反映了选择性偏差

0:01:52.595,0:01:54.729
等一下，这个似乎很容易

0:01:55.139,0:01:57.639
在抽奖活动中[br]我们会随机选择优胜者

0:01:57.639,0:02:00.083
因此只比较赢家和输家[br]- 很明显的

0:02:00.083,0:02:01.784
On the right track，卡马尔

0:02:01.784,0:02:04.375
但是特许学校的抽签安排

0:02:04.375,0:02:07.560
不会强迫孩子们进入[br]或离开特定的学校

0:02:07.749,0:02:10.667
他们随机分配了特许学校的学位

0:02:11.650,0:02:13.449
有些孩子很幸运

0:02:13.449,0:02:14.966
有些孩子不是

0:02:14.966,0:02:17.235
如果我们只是想知道特许学校

0:02:17.235,0:02:19.202
所带来的影响

0:02:19.202,0:02:22.417
我们可以将其视为随机试验

0:02:22.717,0:02:24.684
但是，我们只对特许学校[br]就学的影响

0:02:24.684,0:02:27.042
感兴趣

0:02:27.042,0:02:28.283
而对录取不感兴趣

0:02:28.568,0:02:32.039
并非所有获录取的学生[br]都会接受学位

0:02:32.039,0:02:37.234
IV将被录取为特许学校学生的影响

0:02:37.234,0:02:40.367
转变为实际就读特许学校的影响

0:02:40.367,0:02:42.344
- 太酷了[br]- 哦，太好了

0:02:45.925,0:02:48.871
让我们看一个例子

0:02:48.871,0:02:52.353
这是一所执行知识就是力量专案[br]的特许学校，或简称为KIPP

0:02:52.736,0:02:54.937
这所KIPP特许学校位于林恩

0:02:54.937,0:02:58.837
一座位于麻省海边的[br]褪色工业城镇

0:02:59.104,0:03:01.886
这所学校的申请者多于学位

0:03:01.886,0:03:05.620
因此他们要抽签来挑选学生

0:03:05.834,0:03:11.854
从2005年到2008年[br]共有371名四年级以及五年级生

0:03:11.854,0:03:15.350
参加了KIPP林恩的抽签

0:03:15.350,0:03:18.805
当中253名学生KIPP获录取

0:03:18.805,0:03:21.651
118名学生没有录取

0:03:21.967,0:03:26.001
一年后，获录取者的数学分数

0:03:26.001,0:03:27.852
比未获录取者更高

0:03:27.852,0:03:30.466
我们并不是试图弄清楚

0:03:30.466,0:03:33.803
获录取后是否会提高[br]你的数学水平

0:03:34.070,0:03:38.471
我们想知道参加KIPP[br]是否会使你的数学成绩改进

0:03:39.041,0:03:45.750
在253位获录取者中[br]实际上只有199位到KIPP上学

0:03:46.139,0:03:48.804
其他学生选择了传统的公立学校

0:03:49.563,0:03:55.536
同样，在118名未被录取的学生中[br]事实上有一些最终参加了KIPP

0:03:55.536,0:03:57.452
他们后来也获录取

0:03:57.452,0:04:00.044
那么，实际上参加KIPP

0:04:00.044,0:04:02.377
对考试成绩有何影响呢？

0:04:03.109,0:04:05.426
为什么我们不能只衡量[br]他们的数学成绩？

0:04:05.894,0:04:07.235
这是很好的问题

0:04:07.235,0:04:09.302
你将他们与谁进行比较呢？

0:04:09.302,0:04:11.111
那些没有参加的学生

0:04:11.111,0:04:12.944
上学率是随机的吗？

0:04:14.161,0:04:16.177
- 不是啊[br]- 选择性偏差

0:04:16.177,0:04:17.909
- 对啊[br]- 什么？

0:04:17.909,0:04:21.826
The KIPP offers are random so we can be confident

0:04:21.826,0:04:26.409
of ceteris paribus,[br]但上学率不是随机的

0:04:26.635,0:04:30.626
The choice to accept the offer[br]might be due to characteristics

0:04:30.626,0:04:32.984
that are related[br]to math performance --

0:04:33.251,0:04:36.157
say, for example,[br]that dedicated parents

0:04:36.157,0:04:38.957
are more likely[br]to accept the offer.

0:04:38.957,0:04:42.646
Their kids are also more likely[br]to do better in math,

0:04:42.646,0:04:44.090
regardless of school.

0:04:44.090,0:04:45.114
- [Student] Right.

0:04:45.114,0:04:47.725
- [Instructor] IV converts[br]the offer effect

0:04:47.725,0:04:50.567
into the effect of KIPP attendance,

0:04:50.573,0:04:53.371
adjusting for the fact[br]that some winners go elsewhere

0:04:53.371,0:04:56.573
and some losers manage[br]to attend KIPP anyway.

0:04:56.950,0:05:00.517
Essentially, IV takes[br]an incomplete randomization

0:05:00.517,0:05:03.007
and makes the appropriate[br]adjustments.

0:05:03.684,0:05:07.107
How? IV describes a chain reaction.

0:05:07.641,0:05:10.343
Why do offers affect achievement?

0:05:10.343,0:05:13.256
Probably because they affect[br]charter attendance,

0:05:13.256,0:05:16.643
and charter attendance[br]improves math scores.

0:05:16.643,0:05:20.645
The first link in the chain[br]called the first stage

0:05:20.645,0:05:24.478
is the effect of the lottery[br]on charter attendance.

0:05:24.478,0:05:28.452
The second stage is the link[br]between attending a charter

0:05:28.452,0:05:30.153
and an outcome variable --

0:05:30.153,0:05:32.261
in this case, math scores.

0:05:32.732,0:05:36.441
The instrumental variable,[br]or "instrument" for short,

0:05:36.441,0:05:40.246
is the variable that initiates[br]the chain reaction.

0:05:40.979,0:05:43.993
The effect of the instrument[br]on the outcome

0:05:43.993,0:05:46.631
is called the reduced form.

0:05:48.143,0:05:51.869
This chain reaction can be[br]represented mathematically.

0:05:51.869,0:05:54.241
We multiply the first stage,

0:05:54.241,0:05:56.349
the effect of winning[br]on attendance,

0:05:56.349,0:05:57.960
by the second stage,

0:05:57.960,0:06:00.538
the effect of attendance on scores.

0:06:00.538,0:06:02.713
And we get the reduced form,

0:06:02.713,0:06:05.680
the effect of winning[br]the lottery on scores.

0:06:06.780,0:06:11.566
The reduced form and first stage[br]are observable and easy to compute.

0:06:11.752,0:06:14.876
However, the effect of attendance[br]on achievement

0:06:14.876,0:06:17.093
is not directly observed.

0:06:17.093,0:06:20.360
This is the causal effect[br]we're trying to determine.

0:06:21.043,0:06:23.827
Given some important assumptions[br]we'll discuss shortly,

0:06:23.827,0:06:25.977
we can find the effect[br]of KIPP attendance

0:06:25.977,0:06:29.265
by dividing the reduced form[br]by the first stage.

0:06:29.265,0:06:32.910
This will become more clear[br]as we work through an example.

0:06:32.910,0:06:34.207
- [Student] Let's do this.

0:06:37.161,0:06:38.728
- A quick note on measurement.

0:06:38.728,0:06:41.745
We measure achievement[br]using standard deviations,

0:06:41.745,0:06:44.728
often denoted[br]by the Greek letter sigma (σ).

0:06:44.728,0:06:48.862
One σ is a huge move[br]from around the bottom 15%

0:06:48.862,0:06:51.634
to the middle of most[br]achievement distributions.

0:06:51.634,0:06:55.412
Even a ¼ or ½ σ difference is big.

0:06:56.262,0:06:58.389
- [Instructor] Now we're ready[br]to plug some numbers

0:06:58.389,0:07:01.655
into the equation[br]we introduced earlier.

0:07:01.655,0:07:03.231
First up, what's the effect

0:07:03.231,0:07:06.076
of winning the lottery[br]on math scores?

0:07:06.354,0:07:10.421
KIPP applicants' math scores[br]are a third of a standard deviation

0:07:10.421,0:07:11.835
below the state average

0:07:11.835,0:07:14.386
in the year before[br]they apply to KIPP.

0:07:14.386,0:07:18.320
But a year later, lottery winners[br]score right at the state average,

0:07:18.320,0:07:21.482
while the lottery losers[br]are still well behind

0:07:21.482,0:07:25.499
with an average score[br]around -0.36 σ.

0:07:25.834,0:07:29.619
The effect of winning the lottery[br]on scores is the difference

0:07:29.619,0:07:32.819
between the winners' scores[br]and the losers' scores.

0:07:33.403,0:07:35.784
Take the winners'[br]average math scores,

0:07:35.784,0:07:38.269
subtract the losers'[br]average math scores,

0:07:38.269,0:07:41.502
and you will have 0.36 σ.

0:07:41.908,0:07:46.880
Next up: what's the effect[br]of winning the lottery on attendance?

0:07:46.880,0:07:49.193
In other words,[br]if you win the lottery,

0:07:49.193,0:07:52.257
how much more likely[br]are you to attend KIPP

0:07:52.257,0:07:53.456
than if you lose?

0:07:53.671,0:07:57.798
First, what percentage[br]of lottery winners attend KIPP?

0:07:57.798,0:08:00.774
Divide the number of winners[br]who attended KIPP

0:08:00.774,0:08:05.490
by the total number[br]of lottery winners -- that's 78%.

0:08:05.810,0:08:09.331
To find the percentage[br]of lottery losers who attended KIPP,

0:08:09.331,0:08:12.333
we divide the number of losers[br]who attended KIPP

0:08:12.333,0:08:16.865
by the total number[br]of lottery losers -- that's 4%.

0:08:17.377,0:08:21.597
Subtract 4 from 78, and we find[br]that winning the lottery

0:08:21.597,0:08:25.600
makes you 74%[br]more likely to attend KIPP.

0:08:25.946,0:08:28.532
Now we can find[br]what we're really after --

0:08:28.532,0:08:34.551
the effect of attendance on scores,[br]by dividing 0.36 by 0.74.

0:08:34.789,0:08:37.585
Attending KIPP raises math scores

0:08:37.585,0:08:41.606
by 0.48 standard deviations[br]on average.

0:08:42.126,0:08:44.503
That's an awesome achievement gain,

0:08:44.503,0:08:47.380
equal to moving[br]from about the bottom third

0:08:47.380,0:08:49.925
to the middle[br]of the achievement distribution.

0:08:49.925,0:08:51.085
- [Student] Whoa, half a sig.

0:08:51.085,0:08:53.507
- [Instructor] These estimates[br]are for kids opting in

0:08:53.507,0:08:54.781
to the KIPP lottery,

0:08:54.781,0:08:57.762
whose enrollment status[br]is changed by winning.

0:08:57.985,0:09:00.617
That's not necessarily[br]a random sample

0:09:00.617,0:09:02.283
of all children in Lynn.

0:09:02.536,0:09:05.035
So we can't assume[br]we'd see the same effect

0:09:05.035,0:09:07.327
for other types of students.[br]- [Student] Huh.

0:09:07.327,0:09:10.218
- But this effect[br]on keen for KIPP kids

0:09:10.218,0:09:13.367
is likely to be a good indicator[br]of the consequences

0:09:13.367,0:09:15.767
of adding additional charter seats.

0:09:15.767,0:09:17.216
- [Student] Cool.[br]- [Student] Got it.

0:09:19.628,0:09:23.352
- IV eliminates selection bias,[br]but like all of our tools,

0:09:23.352,0:09:25.624
the solution builds on a set[br]of assumptions

0:09:25.624,0:09:27.540
not to be taken for granted.

0:09:28.098,0:09:31.463
First, there must be[br]a substantial first stage --

0:09:31.463,0:09:35.565
that is the instrumental variable,[br]winning or losing the lottery,

0:09:35.565,0:09:39.065
must really change the variable[br]whose effect we're interested in --

0:09:39.065,0:09:41.031
here, KIPP attendance.

0:09:41.298,0:09:44.594
In this case, the first stage[br]is not really in doubt.

0:09:44.594,0:09:47.894
Winning the lottery makes[br]KIPP attendance much more likely.

0:09:48.386,0:09:50.631
Not all IV stories are like that.

0:09:51.321,0:09:53.698
Second, the instrument[br]must be as good

0:09:53.698,0:09:54.931
as randomly assigned,

0:09:54.931,0:09:58.716
meaning lottery winners and losers[br]have similar characteristics.

0:09:58.893,0:10:01.559
This is the independence assumption.

0:10:01.977,0:10:05.716
Of course, KIPP lottery wins[br]really are randomly assigned.

0:10:05.716,0:10:09.656
Still, we should check for balance[br]and confirm that winners and losers

0:10:09.656,0:10:11.493
have similar family backgrounds,

0:10:11.493,0:10:13.590
similar aptitudes and so on.

0:10:13.590,0:10:16.969
In essence, we're checking[br]to ensure KIPP lotteries are fair

0:10:16.969,0:10:20.055
with no group of applicants[br]suspiciously likely to win.

0:10:21.373,0:10:24.373
Finally, we require[br]the instrument change outcomes

0:10:24.373,0:10:26.092
solely through[br]the variable of interest --

0:10:26.092,0:10:28.100
in this case, attending KIPP.

0:10:28.299,0:10:31.367
This assumption is called[br]the exclusion restriction.

0:10:32.951,0:10:37.500
- IV only works if you can satisfy[br]these three assumptions.

0:10:38.033,0:10:40.418
- I don't understand[br]the exclusion restriction.

0:10:40.917,0:10:43.599
How could winning the lottery[br]affect math scores

0:10:43.599,0:10:45.244
other than by attending KIPP?

0:10:45.244,0:10:47.230
- [Student] Yeah.[br]- [Instructor] Great question.

0:10:47.230,0:10:50.536
Suppose lottery winners[br]are just thrilled to win,

0:10:50.536,0:10:55.045
and this happiness motivates them[br]to study more and learn more math,

0:10:55.045,0:10:57.285
regardless of where[br]they go to school.

0:10:57.285,0:10:59.901
This would violate[br]the exclusion restriction

0:10:59.901,0:11:03.787
because the motivational effect[br]of winning is a second channel

0:11:03.787,0:11:06.569
whereby lotteries[br]might affect test scores.

0:11:06.865,0:11:09.546
While it's hard[br]to rule this out entirely,

0:11:09.546,0:11:12.650
there's no evidence[br]of any alternative channels

0:11:12.650,0:11:14.108
in the KIPP study.

0:11:17.817,0:11:20.700
- IV solves the problem[br]of selection bias

0:11:20.700,0:11:25.051
in scenarios like the KIPP lottery[br]where treatment offers are random

0:11:25.051,0:11:27.083
but some of those offered opt out.

0:11:28.451,0:11:31.700
This sort of intentional[br]yet incomplete random assignment

0:11:31.700,0:11:33.367
is surprisingly common.

0:11:33.367,0:11:36.318
Even randomized clinical trials[br]have this feature.

0:11:37.134,0:11:40.053
IV solves the problem[br]of non-random take-up

0:11:40.053,0:11:42.534
in lotteries or clinical research.

0:11:43.054,0:11:46.725
But lotteries are not the only source[br]of compelling instruments.

0:11:46.915,0:11:49.124
Many causal questions[br]can be addressed

0:11:49.124,0:11:50.758
by naturally occurring

0:11:50.758,0:11:53.831
as good as randomly[br]assigned variation.

0:11:54.731,0:11:56.915
Here's a causal question for you:

0:11:56.915,0:11:59.450
Do women who have children[br]early in their careers

0:11:59.450,0:12:01.647
suffer a substantial earnings penalty

0:12:01.647,0:12:02.648
as a result?

0:12:02.648,0:12:04.970
After all, women earn less than men.

0:12:05.573,0:12:08.506
We could, of course, simply compare[br]the earnings of women

0:12:08.506,0:12:10.891
with more and fewer children.

0:12:10.891,0:12:14.190
But such comparisons are fraught[br]with selection bias.

0:12:14.806,0:12:17.401
If only we could[br]randomly assign babies

0:12:17.401,0:12:19.089
to different households.

0:12:19.089,0:12:22.131
Yeah, right,[br]sounds pretty fanciful.

0:12:22.470,0:12:26.714
Our next IV story -- fantastic[br]and not fanciful --

0:12:26.714,0:12:30.234
illustrates an amazing,[br]naturally occurring instrument

0:12:30.234,0:12:31.918
for family size.

0:12:33.317,0:12:34.551
♪ [music] ♪

0:12:34.551,0:12:38.202
- [Instructor] You're on your way[br]to mastering econometrics.

0:12:38.202,0:12:40.170
Make sure this video sticks

0:12:40.170,0:12:42.636
by taking a few[br]quick practice questions.

0:12:42.886,0:12:46.336
Or, if you're ready,[br]click for the next video.

0:12:46.529,0:12:50.204
You can also check out[br]MRU's website for more courses,

0:12:50.204,0:12:52.027
teacher resources, and more.

0:12:52.289,0:12:53.772
♪ [music] ♪