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Selection Bias: Will You Make More Going to a Private University? - YouTube
Channel: Marginal Revolution University
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- [Josh] Welcome back.
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Today we continue our pursuit
of causal knowledge.
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Recall that private university alumni
earn wages 14% higher
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on average than the wages earned
by public university grads.
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Does that mean
private university education
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causes your wages to go up?
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As with most of the questions we ponder,
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the facts are not in dispute,
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rather it's the interpretation
that's contentious.
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- [Narrator] Let's compare
private school graduates
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with those who attended public schools.
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Private university grads differ
in a number of ways.
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For example, they have higher SAT scores.
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Attendees of private universities score
120 points higher on average.
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These SAT stars sport orange sweatshirts.
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Private university grads also come
from wealthier families --
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13% higher
than public university students.
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The rich kids have green pants.
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It would seem
that public/private comparisons
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are not apples to apples.
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Perhaps their 14% wage gain is caused
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by pre-existing differences
in earnings potential
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rather than
by private university attendance.
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- Like many who have walked before us
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in search of causal knowledge,
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we are waylaid here by selection bias.
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- [Narrator] Selection bias misleads us
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into interpreting naive comparisons
as causal effects.
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- [whisper] Come with me.
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- [Narrator] Here we see
selection bias tricking us
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by directing traffic.
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Those with higher test scores
go to the left
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towards private universities.
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Those with lower family incomes
go to the right
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towards public universities.
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Public/private comparisons
have causal force
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only when the groups compared
are otherwise identical on average.
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For then, we can happily say
ceteris paribus.
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But private schools are typically
more selective and more expensive
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than their public university counterparts.
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So those going left are not comparable
to those going right.
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This is how selection bias bewitches us.
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- Although colleges really do select
their applicants,
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the term selection bias refers
to any comparison plagued
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by systematic differences between groups
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other than the difference
we're focused on.
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When the groups being compared
differ in many ways,
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we've lost ceteris paribus.
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Selection bias is the principal enemy
facing metrics students
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and metrics masters alike.
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Our five most important weapons
in the fight against it
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are the Furious Five of Econometrics.
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- [whisper] The Furious Five.
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- [Josh] Selection bias is
insidious and pervasive,
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but our weapons are powerful,
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for we do not need to ensure
that the individuals
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to be compared are identical.
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We don't need virtual clones.
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Rather we need only ensure
that the groups compared
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be the same on average.
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Our most powerful weapon,
strong and dependable,
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is random assignment
of group membership.
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Imagine a secret experiment
in which applicants
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to public and private colleges
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are randomly assigned
to attend one or the other.
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Seems only fair.
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And maybe we'll learn something
from this too.
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In the interest of science,
I have proposed such an experiment
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at MIT where I teach econometrics.
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I'd like to replace our skilled
but well-paid admissions officers
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with a coin toss.
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Random assignment
of college admission ensures
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that when it comes
to cross school comparisons,
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ceteris is paribus on average.
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Unfortunately, for science,
I have not yet convinced MIT admissions
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to replace its staff
with a stack of pennies.
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- As we'll discuss later,
random assignment is often impossible
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or impractical so we must
look for practical
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and inexpensive strategies
that have the same
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ceteris paribus inducing power
as random assignment.
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Kamal, where should we look?
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- [Kamal] I don't know.
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If we could somehow control for...
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- Correct.
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- [whisper] What?
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- Metrics masters are control freaks.
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We implement statistical strategies
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that make the groups choosing
different paths as similar as possible.
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Rather than simply comparing wages
of public and private alums,
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we look within sets of alumni
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that have similar ability and background.
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Within these sets,
we make public/private comparisons
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but not across them.
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This strategy moves us one giant step
closer to ceteris paribus
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and apples to apples comparisons.
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Let's look again at the Furious Five.
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- [whisper] Furious Five.
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- [Josh] Our principal tool
in the struggle
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for control is regression.
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Regression is a neat way
to compare two groups
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while simultaneously holding
many differences
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between those in the groups fixed.
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- Do regression estimates show
that private university education
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is worth paying for?
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- [Man] Good question.
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- [Narrator] Using regression
to adjust for applicant ability
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and family background
and a few demographic characteristics
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like race and sex reduces
the private college premium
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from 14% to 9%.
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- Nine percent still seems pretty good.
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- [Man] Nine is legit.
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- [Narrator] But do we have
true ceteris paribus?
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Camilla?
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- [Camilla] Um... I'm not sure
we controlled for everything,
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Maybe private school students
are more ambitious or smarter
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in ways not fully captured
by test scores.
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If so, comparisons are not
apples to apples
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even after the adjustments you speak of.
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- Worrying indeed.
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The possibility that the variables
we've adjusted for
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using regression do not fully account
for group differences
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is called omitted variables bias or OVB.
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- [man] That's bad.
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- [Narrator] OVB is selection bias
in a regression context.
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- We suffer the effects of OVB
when the regression we've got
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is not the one we want.
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The regression we want,
the regression of our dreams,
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has more and better controls
than the one we've got.
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How can we control
for something like ambition?
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Is there an ambition index?
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It's not easy to produce
ceteris paribus comparisons.
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Regression is a tool.
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It's not magic.
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Yet sometimes the results unearthed
by this tool are striking.
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Masters of Econometrics
professor Stacy Dale
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and Alan Krueger faced the challenge
of selection bias and OVB.
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In a famous academic study,
Dale and Krueger controlled
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for the many possible differences
between students who've attended
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different types of schools.
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They had the insight that
selection bias in this context originates
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in two forces: student ambition
and college opportunity.
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Most students have a pretty good sense
of their own aptitude,
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inclination, and motivation
for school work.
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These forces are summarized
by the type of schools they apply to.
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At the same time,
college admissions offices invest
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massive hours and energy
into ascertaining
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who will succeed on campus.
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They evaluate and select for
academic ability and college commitment.
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What if we compare the outcomes
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of those who had the exact same
acceptances and rejections?
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Compare two high school students,
Maya and Mariana.
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Both admitted to UNC and Duke
but not to Yale.
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Similarly ambitious
and judged similarly capable
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by these three schools'
admissions offices,
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Maya opts for Duke
because a friend is going there,
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while Mariana heads
to UNC in Chapel Hill.
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- [woman] Come on, Heels!
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- [Josh] Maya and Mariana are
not clones of course,
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and they've chosen different types
of schools for personal reasons.
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But otherwise, they have a lot in common.
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The personal factors that drive them
to choose between the schools
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on their menu might not be closely related
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to their future earning power.
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Pooling many such comparisons
moves us one giant step closer
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to ceteris paribus.
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Remarkably, a regression model
that controls for the sets of schools
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to which applicants have applied
and been admitted
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shows almost no difference
in earnings between public
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and private graduates.
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In other words, averaging over
a large number
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of Maya to Mariana type comparisons,
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the private school premium falls
to nothing.
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Maya might have enjoyed
her expensive Duke education,
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but on average at least
students like her will do no better
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in the labor market
than comparable public school peers.
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That's quite a change
from our initial 14% earnings gap
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favoring elite school alumni.
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Regression has the power
to turn a clouded statistical night
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into a clear causal day.
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But you'll need to know a little more
before you can regress
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with skill and confidence.
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- [Narrator] You're on your way
to mastering econometrics.
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Make sure this video sticks
by taking a few quick practice questions.
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Or, if you're ready,
click for the next video.
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You can also check out MRU's website
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for more courses,
teacher resources, and more.
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