“双重差分法”之简介

从原因到结果的路径

既黑暗且危险的

但是计量经济学的武器非常强大

当目睹平行趋势时
我们掌握了双重差分法

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计量经济学大师在寻找

令人信服的
「其他条件不变的比较」

理想的对比是

看起来相似的处理组和对照组
形成对照

但有时这种可比性是难以捉摸的

在没有处理的情况下

当处理组及对照组类似地演变时

即使起点不同

也有望进行因果推断

针对平行演化的武器

大师说的「平行趋势」

叫做「双重差分法」…

- 双重差分法...

- ...或简称为DD
- 好的

- 现在让我们看看 DD

如何帮助我们了解美国历史上

最重要的经济事件之一

- 现在我们一起回顾大萧条的情況—

我国有史以来最严重的经济灾难

在 1933 年失业率达到 25%—

这是之前或之后从未见过的水平

数百万国民失去了家园或土地

Suicide spiked, and hungry families

relied on soup kitchens
and bread lines

to keep from starving.

- Economists argue fiercely

over the causes
of the Great Depression.

Most agree, however,
that a key piece of the puzzle

is an epidemic of bank failures.

This was before deposit insurance.

So if your bank went bankrupt,
your savings disappeared with it.

- [Cashier] Closing your account?

- [Customer] Yes, sir.
I'm closing my account.

I wouldn't leave a nickel
in this bank.

- Faced with a banking crisis,
the Central Bank has a choice:

lend freely to troubled banks

or stand aside and refuse to lend.

Lending freely to banks in trouble
is called "easy money."

Refusing to lend
is called "tight money."

- [Joshua] Monetarist masters
Milton Friedman and Anna Schwartz

famously called
the Great Depression

the "Great Contraction,"

accusing the Federal Reserve

of inflicting a misguided policy
of tight money

on the nation's teetering
financial institutions.

They argued that easy money

would have kept
many banks in business,

shortening the Great Depression.

But others disagree!

If banks are insolvent

because of unwise
lending decisions,

then bailouts just encourage
more foolishness.

Economists called this problem
"moral hazard."

The debate over bailouts
and moral hazard continues today.

Should financial behemoth
Lehman Brothers

had been allowed to fail
on the eve of the Great Recession,

in an ideal world,
we'd answer this question

by applying different Fed policies
to randomly selected regions.

But we can still learn a lot

by using differences-in-differences

to compare trends across areas
with different monetary policies.

- [Camilla] How's that even possible?

Don't the same Fed policies
apply to all banks in the U.S.?

- [Man] Yeah.
- Good question.

The Federal Reserve System
is divided into 12 districts,

each headed by a regional bank.

Today, Fed policy is set
at the national level.

But in the 1930s, regional Feds
could do pretty much as they liked.

- [Man] Ah, interesting.

- And here's what's
so awesome about that.

In 1930, the Atlanta Fed,
running the 6th district,

followed an easy money policy,

sending wheelbarrows of cash
to rescue insolvent institutions.

The St. Louis Fed,
running the 8th district,

followed a tight money policy.

"Let fail the foolish!"
they said in St. Louis.

And so a natural experiment
in monetary policy was born.

Even better, this is
a within-state experiment.

The border between the 6th
and the 8th districts

ran smack through
the middle of Mississippi.

So northern Mississippi
had tight money,

while southern Mississippi
had easy money,

but under the same state laws
and banking regulations in both.

- [Teacher] The treatment group

is the district 6 part
of Mississippi,

which had access to easy money
during the crisis.

The control group

is the district 8 part
of Mississippi,

which had tight money
during the crisis.

The key year
in our natural experiment

was 1930.

Caldwell & Company,

a massive financial empire
in the South,

came crashing down.

Banking is a business
built on confidence and trust.

The Caldwell meltdown
caused a panic

that led to a widespread
bank run all at once.

Depositors wanted their money back,

causing banks to go bankrupt
and shut their doors.

We'll use differences-in-differences

to measure the effect
of contrasting monetary policies

in response to the Caldwell crisis.

This figure plots the number
of banks in Mississippi by year,

for the 8th and 6th districts.

Let's start in 1929,

a year before the Caldwell crash.

There are 169 banks
open in the 8th,

and 141 banks open in the 6th.

Over the next year,

we see a similar handful
of banks fail, in both districts.

The change in the number
of banks in operation

is remarkably similar --

that's what parallel trends look like.

In November 1930, Caldwell crashes,

and the panic begins.

Banks failed frequently
in the 8th district,

which had tight money.

But the decline is slower
in the 6th district,

which had easy money.

Diverging trends in this period

might be attributable
to easy versus tight money.

In July of 1931, the 8th district
abandons tight money,

so now both districts are easy.

Parallel trends are restored.

In a counterfactual world,

where the 6th district
follows a tight money policy,

what might have happened?

If we extrapolate the trend
of the 8th district to the 6th,

it would look like this.

So the treatment-effective
easy money

is how much the 6th district
deviated from the path

implied by the 8th district trend.

How many banks
did the easy money treatment save?

This table reports data
for the treatment group, district 6,

in the first row,

and data for the control group,
district 8, in the second row.

The first column shows
the number of banks in business

before the crisis began in 1930.

The second column shows 1931.

This is the key period

when each district
had differing monetary policies

during the crisis.

The rightmost column
reports changes within the district.

District 6 lost 14 banks,
while district 8 lost 33.

The mathematical formula
for the treatment effect is simple.

We subtract the change in banks
in operation in the 8th district

from the change in banks
in operation in the 6th.

Hence, the name
"differences-in-differences."

-14 minus -33 equals 19.\]

We estimate that 19 banks
were saved by easy money.

In practice, tables and figures
like those shown here

are the beginning
rather than the end

of a DD analysis.

The problem of how to gauge

the statistical significance
of DD estimates

turns out to be exceedingly tricky,

and a regression is typically
part of the solution.

The key assumption
behind a valid DD analysis

is that of parallel trends.

Recall the principle
of ceteris paribus.

Our ideal comparison
would have the two districts

experience an identical
business environment,

except for one factor:

easy or tight money.

Both districts would have
identical types of customers

who would go bankrupt
at exactly the same rate.

The skill of their employees
would be equal, and so on.

Perfect ceteris paribus comparisons
would allow us to clearly see

the causal effect
of different Fed policies.

In this case, that's not possible.

But the idea of parallel trends
is based on a similar concept.

If we see that the two regions
experience similar trends

in the number of banks over time,

in the absence of treatment,

we can assume
they are good comparisons.

We see that the two districts
move in parallel,

both before the crisis and after,

when they have the same Fed policy.

The only time the districts
behave differently

is when the Fed policy is different.

In view of this,

Fed policy is a likely cause
of diverging trends

from 1930 to 1931.

But we should also check
for other changes

unique to northern Mississippi.

- [Man] Huh?
- What do you mean?

- [Teacher] Imagine that bad tornadoes

hit northern but not
southern Mississippi in 1930.

These tornadoes devastate farms,

causing farmers
to default on loans,

which drives their banks
out of business.

Then the 6th and 8th districts

would differ in not one
but two ways:

Fed policy and weather.

And we'd have trouble
identifying Fed policy

as the causal factor
behind increased bank failures

in the 8th.

- [Man] Ceteris is not paribus.

- DD credibility lives or dies

with the claim that the only reason

northern Mississippi
was special in 1930

is differing regional Fed policy.

We're in DD heaven with strong,
visual evidence of parallel trend.

- In general, the first step
in evaluating whether to use DD

is usually this type of visual
confirmation of parallel trends

outside of the period,

when we expect to see
a treatment effect.

The treatment in our example

is easy money
in the face of bank failures.

Metrics masters use DD
to explore effects of many policies,

like the minimum legal drinking age,

and environmental changes,
like access to clean water.

In our next video,

we'll see an example
of how regression is used

to implement a DD approach.

- [Narrator] Are you a teacher?

Click to explore ways
to use these videos in class.

If you're a learner,
make sure this video sticks

by taking a few quick
practice questions.

Or if you're ready,
click for the next video.

You can also check out
MRU's website

for more courses,
teacher resources, and more.

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