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
自杀率飙升
贫困的家庭依靠施食处和面包生产线
来避免挨饿
- 经济学家们
就大萧条的原因展开了激烈的争论
然而，大多数经济学家都同意 这个难题的关键部分
是银行大规模倒闭
这是施行存款保险制度之前的年代
因此，如果银行破产 你的储蓄也会化为乌有
- 取消你的帐户？
- 对啊，我想取消我的帐户
我不会在这家银行留下一分钱
- 面对银行业危机，央行有一项选择
随意地放贷给陷入困境的银行
或者袖手旁观拒绝贷款
借钱给有困难的银行叫「易钱」
拒贷叫「紧钱」
- 货币学派的代表人物 米尔顿弗里德曼和安娜施瓦茨
把大萧条称为
「大收缩」
指责美联储
就国家摇摇欲坠的金融机构 实施紧缩政策
是一项错误的政策
他们争辩说
易钱可让许多银行继续营业
从而缩短大萧条的时期
但其他人不同意
如果银行因为其不明智的贷款决定
而资不抵债
那么救助只会鼓励更多的愚蠢行为
经济学家把这个问题称为「道德风险」
今天人们仍就救助和道德风险 继续进行辩论
如果金融巨头雷曼兄弟
被允许在大衰退前夕倒闭
在理想的世界里 我们将会通过对随机选择的地区
应用不同的美联储政策 来回答这个问题
但是通过使用双重差分法
来比较不同货币政策的跨领域趋势
我们仍然可以学到很多事情
- 这怎么可能呢？
所有美国银行不是实施 相同的美联储政策吗？
- 对啊 - 好问题
联邦储备系统分为 12 个区
由12家地区性的联邦储备银行组成
今天，美联储政策是在国家层面制定的
但在 1930 年代，地区性的 联邦储备银行几乎可以随心所欲
- 啊，真有趣
- 这就是最棒的地方
在1930 年代，管理第六区的 亚特兰大联邦储备银行
遵循「易钱」政策
用手推车运送现金 去拯救破产的金融机构
而管理第八区的 圣路易斯联邦储备银行
则采取了紧缩的资金政策
「让愚蠢的人倒下吧！」 他们在圣路易斯说
因此，货币政策的自然实验诞生了
更好的是，这是州内的实验
第 6 区和第 8 区之间的边界
穿过密西西比州中部
密西西比北部实施紧钱政策
而密西西比南部则实施易钱政策
但是两个地区施行相同的 州法律和银行法规
- [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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