Introduction to Instrumental Variables (IV)

0:00  0:05 [Instructor] The path from cause
to effect is dark and dangerous. 
0:05  0:08But the weapons
of Econometrics are strong. 
0:08  0:12Attack with fierce
and flexible instrumental variables 
0:12  0:16when nature blesses you
with fortuitous random assignment. 
0:19  0:21[gong rings]

0:24  0:26Randomized trials
are the surest path 
0:26  0:29to ceteris paribus comparisons.

0:29  0:33Alas, this powerful tool
is often unavailable. 
0:33  0:37But sometimes, randomization
happens by accident. 
0:37  0:41That's when we turn
to instrumental variables  
0:41  0:42IV for short.

0:42  0:45 [Voice whispers]
Instrumental variables. 
0:45  0:48 [Instructor] Today's lesson
is the first of two on IV. 
0:49  0:53Our first IV lesson begins
with a story of schools. 
0:53  0:54[school bell rings]

0:54  0:56 [Josh] Charter schools
are public schools 
0:56  1:00freed from daily district oversight
and teacher union contracts. 
1:01  1:04The question of whether charters
boost achievement 
1:04  1:05is one of the most important

1:05  1:08in the history
of American education reform. 
1:08  1:13 The most popular charter schools
have more applicants than seats, 
1:13  1:16so the luck of a lottery draw
decides who's offered a seat. 
1:17  1:21A lot is at stake for the students
vying for their chance, 
1:21  1:25and waiting for the lottery results
brings up lots of emotions 
1:25  1:28as was captured
in the awardwinning documentary 
1:28  1:30"Waiting For Superman."

1:30  1:33 [Mother] Don't cry. You're gonna
make Mommy cry. Okay? 
1:37  1:41 Do charters really provide
a better education? 
1:41  1:43Critics most definitely say no,

1:43  1:47arguing that charters enroll
better students to begin with, 
1:47  1:50smarter or more motivated,
so differences in later outcomes 
1:50  1:52reflects selection bias.

1:53  1:55 [Kamal] Wait, this one seems easy.

1:55  1:58In a lottery, winners
are chosen randomly, 
1:58  2:00so just compare winners and losers.
 [Student] Obviously. 
2:00  2:02 On the right track, Kamal,

2:02  2:04but charter lotteries
don't force kids 
2:04  2:08into or out of a particular school.

2:08  2:11They randomize offers
of a charter seat. 
2:12  2:13Some kids get lucky.

2:13  2:15Some kids don't.

2:15  2:17If we just wanted
to know the effect 
2:17  2:19that charter school offers,

2:19  2:22we could treat this
as a randomized trial. 
2:23  2:25But we're interested
in the effects 
2:25  2:27of charter school attendance,

2:27  2:28not offers.

2:29  2:32And not everyone
who is offered, accepts. 
2:32  2:37IV turns the effect of being offered
a charter seat into the effect 
2:37  2:40of actually attending
a charter school. 
2:40  2:42 [Student] Cool.
 Oh, nice. 
2:46  2:49 Let's look at an example,
a charter school from 
2:49  2:52the Knowledge Is Power
Program, or KIPP for short. 
2:53  2:55This KIPP school is in Lynn

2:55  2:59a faded industrial town
on the coast of Massachusetts. 
2:59  3:02The school has
more applicants than seats 
3:02  3:06and therefore picks its students
using a lottery. 
3:06  3:12From 2005 to 2008,
371 fourth and fifth graders 
3:12  3:15put their names
in the KIPP Lynn lottery, 
3:15  3:19253 students won a seat at KIPP,

3:19  3:22118 students lost.

3:22  3:26A year later, lottery winners
had much higher math scores 
3:26  3:28than lottery losers.

3:28  3:30But remember,
we're not trying to figure out 
3:30  3:34whether winning a lottery
makes you better at math. 
3:34  3:38We want to know if attending KIPP
makes you better at math. 
3:39  3:46Of the 253 lottery winners,
only 199 actually went to KIPP. 
3:46  3:49The others chose
a traditional public school. 
3:50  3:56Similarly, of the 118 lottery losers,
a few actually ended up at KIPP. 
3:56  3:57They got an offer later.

3:57  4:02So what was the effect on test scores
of actually attending KIPP? 
4:03  4:05 [Kamal] Why can't we just measure
their math scores? 
4:06  4:07 [Instructor] Great question.

4:07  4:09Who would you compare them to?

4:09  4:11 [Kamal] Those who didn't attend.

4:11  4:13 [Instructor] Is attendance random?

4:14  4:16 [Camilla] No.
 Selection bias. 
4:16  4:18 [Instructor] Correct.
 [Otto] What? 
4:18  4:22 [Instructor] The KIPP offers
are random so we can be confident 
4:22  4:26of ceteris paribus,
but attendance is not random. 
4:27  4:31The choice to accept the offer
might be due to characteristics 
4:31  4:33that are related
to math performance  
4:33  4:36say, for example,
that dedicated parents 
4:36  4:39are more likely
to accept the offer. 
4:39  4:43Their kids are also more likely
to do better in math, 
4:43  4:44regardless of school.

4:44  4:45 [Student] Right.

4:45  4:48 [Instructor] IV converts
the offer effect 
4:48  4:51into the effect of KIPP attendance,

4:51  4:53adjusting for the fact
that some winners go elsewhere 
4:53  4:57and some losers manage
to attend KIPP anyway. 
4:57  5:01Essentially, IV takes
an incomplete randomization 
5:01  5:03and makes the appropriate
adjustments. 
5:04  5:07How? IV describes a chain reaction.

5:08  5:10Why do offers affect achievement?

5:10  5:13Probably because they affect
charter attendance, 
5:13  5:17and charter attendance
improves math scores. 
5:17  5:21The first link in the chain
called the first stage 
5:21  5:24is the effect of the lottery
on charter attendance. 
5:24  5:28The second stage is the link
between attending a charter 
5:28  5:30and an outcome variable

5:30  5:32in this case, math scores.

5:33  5:36The instrumental variable,
or "instrument" for short, 
5:36  5:40is the variable
that initiates the chain reaction. 
5:41  5:44The effect of the instrument
on the outcome 
5:44  5:47is called the "reduced form."

5:48  5:52This chain reaction can be
represented mathematically. 
5:52  5:54We multiply the first stage,

5:54  5:56the effect of winning
on attendance, 
5:56  5:58by the second stage,

5:58  6:01the effect of attendance on scores.

6:01  6:03And we get the reduced form,

6:03  6:06the effect of winning
the lottery on scores. 
6:07  6:12The reduced form and first stage
are observable and easy to compute. 
6:12  6:15However, the effect of attendance
on achievement 
6:15  6:17is not directly observed.

6:17  6:20This is the causal effect
we're trying to determine. 
6:21  6:24Given some important assumptions
we'll discuss shortly, 
6:24  6:26we can find the effect
of KIPP attendance 
6:26  6:29by dividing the reduced form
by the first stage. 
6:29  6:33This will become more clear
as we work through an example. 
6:33  6:34 [Student] Let's do this.

6:37  6:39 A quick note on measurement.

6:39  6:42We measure achievement
using standard deviations, 
6:42  6:45often denoted
by the Greek letter sigma (σ). 
6:45  6:49One σ is a huge move
from around the bottom 15% 
6:49  6:52to the middle of most
achievement distributions. 
6:52  6:55Even a ¼ or ½ σ difference is big.

6:56  6:58 [Instructor] Now we're ready
to plug some numbers 
6:58  7:02into the equation
we introduced earlier. 
7:02  7:03First up, what's the effect

7:03  7:06of winning the lottery
on math scores? 
7:06  7:10KIPP applicants' math scores
are a third of a standard deviation 
7:10  7:12below the state average

7:12  7:14in the year before
they apply to KIPP. 
7:14  7:18But a year later, lottery winners
score right at the state average, 
7:18  7:21while the lottery losers
are still well behind 
7:21  7:25with an average score
around  0.36 σ. 
7:26  7:30The effect of winning the lottery
on scores is the difference 
7:30  7:33between the winners' scores
and the losers' scores. 
7:33  7:36Take the winners'
average math scores, 
7:36  7:38subtract the losers'
average math scores, 
7:38  7:42and you will have 0.36 σ.

7:42  7:47Next up: what's the effect
of winning the lottery on attendance? 
7:47  7:49In other words,
if you win the lottery, 
7:49  7:52how much more likely
are you to attend KIPP 
7:52  7:53than if you lose?

7:54  7:58First, what percentage
of lottery winners attend KIPP? 
7:58  8:01Divide the number of winners
who attended KIPP 
8:01  8:05by the total number
of lottery winners  that's 78%. 
8:06  8:09To find the percentage
of lottery losers who attended KIPP, 
8:09  8:12we divide the number of losers
who attended KIPP 
8:12  8:17by the total number
of lottery losers  that's 4%. 
8:17  8:22Subtract 4 from 78, and we find
that winning the lottery 
8:22  8:26makes you 74%
more likely to attend KIPP. 
8:26  8:29Now we can find
what we're really after: 
8:29  8:35the effect of attendance on scores,
by dividing 0.36 by 0.74. 
8:35  8:38Attending KIPP raises math scores

8:38  8:42by 0.48 standard deviations
on average. 
8:42  8:45That's an awesome achievement gain,

8:45  8:47equal to moving
from about the bottom third 
8:47  8:50to the middle
of the achievement distribution. 
8:50  8:51 [Student] Whoa, half a sig.

8:51  8:54 [Instructor] These estimates
are for kids opting in 
8:54  8:55to the KIPP lottery,

8:55  8:58whose enrollment status
is changed by winning. 
8:58  9:01That's not necessarily
a random sample 
9:01  9:02of all children in Lynn.

9:03  9:05So we can't assume
we'd see the same effect 
9:05  9:07for other types of students.
 [Student] Huh. 
9:07  9:10 But this effect
on keen for KIPP kids 
9:10  9:13is likely to be a good indicator
of the consequences 
9:13  9:16of adding additional charter seats.

9:16  9:17 [Student] Cool.
 [Student] Got it. 
9:20  9:23 IV eliminates selection bias,
but like all of our tools, 
9:23  9:26the solution builds on a set
of assumptions 
9:26  9:28not to be taken for granted.

9:28  9:31First, there must be
a substantial first stage  
9:31  9:36that is the instrumental variable,
winning or losing the lottery, 
9:36  9:39must really change the variable
whose effect we're interested in  
9:39  9:41here, KIPP attendance.

9:41  9:45In this case, the first stage
is not really in doubt. 
9:45  9:48Winning the lottery makes
KIPP attendance much more likely. 
9:48  9:51Not all IV stories are like that.

9:51  9:54Second, the instrument
must be as good 
9:54  9:55as randomly assigned,

9:55  9:59meaning lottery winners and losers
have similar characteristics. 
9:59  10:02This is the independence assumption.

10:02  10:06Of course, KIPP lottery wins
really are randomly assigned. 
10:06  10:10Still, we should check for balance
and confirm that winners and losers 
10:10  10:11have similar family backgrounds,

10:11  10:14similar aptitudes and so on.

10:14  10:17In essence, we're checking
to ensure KIPP lotteries are fair 
10:17  10:20with no group of applicants
suspiciously likely to win. 
10:21  10:24Finally, we require
the instrument change outcomes 
10:24  10:26solely through
the variable of interest, 
10:26  10:28in this case, attending KIPP.

10:28  10:31This assumption is called
the exclusion restriction. 
10:33  10:38 IV only works if you can satisfy
these three assumptions. 
10:38  10:40 I don't understand
the exclusion restriction. 
10:41  10:44How could winning the lottery
affect math scores 
10:44  10:45other than by attending KIPP?

10:45  10:47 [Student] Yeah.
 [Instructor] Great question. 
10:47  10:51Suppose lottery winners
are just thrilled to win, 
10:51  10:55and this happiness motivates them
to study more and learn more math, 
10:55  10:57regardless of where
they go to school. 
10:57  11:00This would violate
the exclusion restriction 
11:00  11:04because the motivational effect
of winning is a second channel 
11:04  11:07whereby lotteries
might affect test scores. 
11:07  11:10While it's hard
to rule this out entirely, 
11:10  11:13there's no evidence
of any alternative channels 
11:13  11:14in the KIPP study.

11:18  11:21 IV solves the problem
of selection bias 
11:21  11:25in scenarios like the KIPP lottery
where treatment offers are random 
11:25  11:27but some of those offered opt out.

11:28  11:32This sort of intentional
yet incomplete random assignment 
11:32  11:33is surprisingly common.

11:33  11:36Even randomized clinical trials
have this feature. 
11:37  11:40IV solves the problem
of nonrandom takeup 
11:40  11:43in lotteries or clinical research.

11:43  11:47But lotteries are not the only
source of compelling instruments. 
11:47  11:49Many causal questions
can be addressed 
11:49  11:51by naturally occurring

11:51  11:54as good as randomly
assigned variation. 
11:55  11:57Here's a causal question for you:

11:57  11:59Do women who have children
early in their careers 
11:59  12:02suffer a substantial earnings penalty

12:02  12:03as a result?

12:03  12:05After all, women earn less than men.

12:06  12:09We could, of course, simply compare
the earnings of women 
12:09  12:11with more and fewer children.

12:11  12:14But such comparisons are fraught
with selection bias. 
12:15  12:17If only we could
randomly assign babies 
12:17  12:19to different households.

12:19  12:22Yeah, right,
sounds pretty fanciful. 
12:22  12:27Our next IV story  fantastic
and not fanciful  
12:27  12:30illustrates an amazing,
naturallyoccurring instrument 
12:30  12:32for family size.

12:33  12:35♪ [music] ♪

12:35  12:38 [Instructor] You're on your way
to mastering Econometrics. 
12:38  12:40Make sure this video sticks

12:40  12:43by taking a few
quick practice questions. 
12:43  12:46Or, if you're ready,
click for the next video. 
12:47  12:50You can also check out
MRU's website for more courses, 
12:50  12:52teacher resources, and more.

12:52  12:54♪ [music] ♪
 Title:
 Introduction to Instrumental Variables (IV)
 Description:

MIT's Josh Angrist introduces one of econometrics most powerful tools: instrumental variables.
Instrumental variables (IV, for those in the know), allow masters of econometrics to draw convincing causal conclusions when a treatment of interest is incompletely or imperfectly randomized.
For example, arguments over American school quality often run hot, boiling over with selection bias. See a school with strong graduation rates and enticing test scores? Is that a good school or just an ordinary school fortuitously located in a good neighborhood?
Lotteries that randomize offers of a school seat at indemand schools should unravel the school quality conundrum. But lotteries only offer seats. Families are free to accept or go elsewhere and these choices are far from random.
IV provides a path to causal conclusions even in the face of this sort of incomplete randomization.
In this video, we cover the following:
 Incomplete random assignment
 IV terminology: first stage, second stage, instrument, reduced form
 Three key IV assumptions: substantial first stage, independence assumption, exclusion restriction
***INSTRUCTOR RESOURCES***
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More from Marginal Revolution University: https://mru.io/4my  Video Language:
 English
 Team:
 Marginal Revolution University
 Project:
 Mastering Econometrics
 Duration:
 12:57
Theresa Ranft edited English subtitles for Introduction to Instrumental Variables (IV)  
Theresa Ranft edited English subtitles for Introduction to Instrumental Variables (IV)  
Theresa Ranft edited English subtitles for Introduction to Instrumental Variables (IV)  
Kirstin Cosper edited English subtitles for Introduction to Instrumental Variables (IV)  
Kirstin Cosper edited English subtitles for Introduction to Instrumental Variables (IV)  
Kirstin Cosper edited English subtitles for Introduction to Instrumental Variables (IV)  
Kirstin Cosper edited English subtitles for Introduction to Instrumental Variables (IV)  
Kirstin Cosper edited English subtitles for Introduction to Instrumental Variables (IV) 