- [Instructor] The path from cause
to effect is dark and dangerous.
But the weapons
of Econometrics are strong.
[Attack] with fierce
and flexible instrumental variables
when nature blesses you
with fortuitous random assignment.
[gong rings]
Randomized trials are the surest
path to ceteris parabus comparisons.
Alas, this powerful tool
is often unavailable.
But sometimes, randomization
happens by accident.
That's when we turn
to instrumental variables,
IV for short.
- [Voice whispers] Instrumental
variables.
- [Instructor] Today's lesson
is the first of two on IV.
Our first IV lesson begins
with a story of schools.
- [Josh] Charter schools
are public schools
freed from daily district oversight
and teacher union contracts.
The question of whether charters
boost achievement
is one of the most important
in the history
of American education reform.
- The most popular charter schools
have more applicants
so the luck of the lottery draw
decides who's offered a seat.
A lot is at stake for the students
vying for their chance.
Waiting for the lottery results
brings up lots of emotions
as was captured
in the award-winning documentary
"Waiting For Superman."
- [Mother] Don't cry.
You're gonna make Mommy cry.
Okay?
- Do charters really provide
a better education?
Critics most definitely say no,
arguing that charters enroll
better students to begin with,
smarter or more motivated
so differences in later outcomes
reflects selection bias.
- [Kamal] Wait, this one seems easy.
In a lottery, winners
are chosen randomly,
so just compare winners and losers.
- [Student] Obviously.
- On the right track, Kamal,
but charter lotteries
don't force kids into
or out of a particular school.
They randomize offers
of a charter seat.
Some kids get lucky.
Some kids don't.
If we just wanted to know
the effect of charter school offers,
we could treat this
as a randomized trial.
But we we're interested
in the effects
of charter school attendance,
not offers.
And not everyone
who is offered, accepts.
IV turns the effect of being offered
a charter seat into the effect
of actually attending
a charter school.
- [Student] Cool.
- Oh nice.
- Let's look at an example,
a charter school from
the Knowledge Is Power
Program, or KIPP for short.
This KIPP school is in Lynn,
a faded industrial town
on the coast of Massachusetts.
The school has
more applicants than seats
and therefore picks its students
using a lottery.
From 2005 to 2008,
371 fourth and fifth graders
put their names
in the KIPP/Lynn lottery,
253 students won a seat at KIPP,
118 students lost.
A year later, lottery winners had
much higher match scores
than lottery losers.
But remember,
we're not trying to figure out
whether winning a lottery
makes you better at math.
We want to know if attending KIPP
makes you better at math.
Of the 253 lottery winners,
only 199 actually went to KIPP.
The others chose
a traditional public school.
Similarly of the 118 lottery losers,
a few actually ended up at KIPP.
They got an offer later.
So what was the effect of test scores
of actually attending KIPP?
- [Student] Why can't we just
measure their math scores?
- [Instructor] Great question.
Who would you compare them to?
- [Student] Those who didn't attend.
- [Instructor] Is attendance random?
- [Camilla] No.
- Selection bias.
- [Instructor] Correct.
- [Otto] What?
- [Instructor] The KIPP offers
are random so we can be confident
of ceteris parabus,
but attendance is not random.
The choice to accept the offer
might be due to characteristics
that are related
to math performance.
Say, for example,
that dedicated parents
are more likely
to accept the offer.
Their kids are also more likely
to do better in math,
regardless of school.
- [Student] Right.
- [Instructor] IV converts
the offer effect
into the effect of KIPP attendance,
adjusting for the fact
that some winners go elsewhere
and some losers manage
to attend KIPP anyway.
Essentially, IV takes
an incomplete randomization
and makes the appropriate
adjustments.
How? IV describes a chain reaction.
Why do offers affect achievement?
Probably because they affect
charter attendance
and charter attendance
improves math scores,
the first link in the chain
called the first stage
is the effect of the lottery
on charter attendance.
The second stage is the length
between attending a charter
and an outcome variable,
in this case, math scores.
The instrumental variable
or instrument for short
is the variable
that initiates the chain reaction.
The effect of the instrument
on the outcome is called
the reduced form.
This chain reaction can be
represented mathematically.
We multiply the first stage,
the effect of winning
on attendance, by the second stage,
the affect of attendance on scores.
And we get the reduced form,
the effect of winning
the lottery on scores.
Reduced form and first stage
are observable and easy to compute.
However, the effect of attendance
on achievement
is not directly observed.
This is the causal effect
we're trying to determine.
Given some important assumptions
we'll discuss shortly,
we can find the effect
of KIPP attendance
by dividing the reduced form
by the first stage.
This will become more clear
as we work through an example.
- [Student] Let's do this.