Lecture 23 Comparison Groups Practice

Nick Huntington-Klein

March 20, 2019

Recap

We’ve been going over ways in which we can isolate causal effects
We can select similar control groups using matching or controlling (what economists call “selection on observables”)
We can use a group at a different time as its own control with fixed effects
Or, “natural experiments”:
When a treatment is applied at a particular time, we can select a reasonable control to account for the effects of time using difference-in-difference
When the treatment is assigned according to a cutoff in a running variable, we can use regression discontinuity

Today

We’re going to be trying to apply these methods
Given a real-world causal statement, how can we go about selecting a method?
We can follow the steps we’ve been taking all along!

Our Approach

Consider the problem
Think about what we think the data-generating process is
Draw a diagram
Figure out the method (we may have to control for some things for the usable diagram to emerge!)
Actually implement the method

Think about the Data-Generating Process

Our example from last time was corporate social responsibility
We think that CSR might affect stock prices, and we know that CSR resolutions are taken up by winning vote
Of course, the vote share might be related to a million different things about the company, or about the company at that time

Draw a Diagram

comp is “company”, c.t is company at a particular time

Figure out a Method

What back doors do we have? (CSR <- win <- vote <- comp/c.t -> price)
Can we measure enough variables to control/match to close them all?
Are they all individual-level or time-level variables so that we can do a diff-in-diff with panel data?
Do we have a running variable and assign the treatment with a cutoff so we can do regression discontinuity?

Implement the Method

#I don't actually have this data but we can pretend
data(CSRdata)

bandwidth <- .02
cutoff <- .5
CSRdata %>% 
  #Limit to just the area around the cutoff
  filter(abs(vote - cutoff) < bandwidth) %>%
  #Then, compare winning votes to losing votes
  mutate(win = vote > cutoff) %>%
  group_by(win) %>%
  summarize(price = mean(price))

Let’s do More

Let’s focus on the topic of real importance:
How can we build a research design based on our causal question of interest and what we know about the world?
I have five questions and topics, let’s work together to build diagrams and pick a research design
Don’t look ahead in the slides!

Fishery Sustainability

We don’t want to overfish the oceans! However, common economic logic dictates that fish stocks are a “common good” likely to be overharvested if without restrictions
One way of restricting fishing is to implement a transferable quota (ITQ) - a “cap and trade” basically
This limits the allowable catch, and by allowing people to trade their allotment, ensures that the most efficient boats do the catching
But does it work? Does ITQ affect next year’s fishing stock?

Fishery Sustainability

Draw the diagram! To consider:

Some countries implement ITQs, others don’t. We can observe countries both before and after the ITQ
Certain characteristics of the country, like size, coastline, politics, etc., might be related to the decision to implement
ITQ doesn’t affect stock directly, but by reducing this year’s catch
The global economy changes over time, and affects fish demand and thus catch

Fishery Sustainability

coun = country characteristics, econ = world economy

Fishery Sustainability

This is a clear case for applying difference-in-differences!
Do we need to worry about that econ back door?
Nope! Note that all back doors through econ either go through time (which we control for naturally without DID) or through ITQ -> catch <- econ in which catch is a collider and we’re already closed.

Financial Reports

Do financial statements, required to be released annually, affect a firm’s stock price?
You might expect them to! After all, this contains important information about the company
But maybe not - these reports just say what the company’s financial health is, and investors paying attention may already know that so it would already be baked into the price.
What is the effect of the financial report on stock price?

Financial Reports

Draw the diagram! To consider:

The govt requires reports be released at a certain time, so there’s a particular time at which the report goes from being unknown to known
A firm’s health will change over time and also affect the price
The overall economy will also change over time, and affect firm health
Firm health is too complex to be measured and controlled for

Financial Reports

This is a case for a regression discontinuity with time as the running variable
When an RDD uses time as a running variable it’s called an “interrupted time series”
Generally not considered quite as trustworthy as other RDDs, since it’s more likely that other stuff changes across the before/after barrier than across the below cutoff/above cutoff barrier

Medicare and Retirement

Does having health insurance encourage you to take more risks? Like quitting your job?
Many people in the US get health insurance through their employer and have no realistic way of paying for it otherwise
At age 65 you become eligible for Medicare
Does Medicare make people quit their jobs?

Medicare and Retirement

Draw a diagram! To consider:

You become eligible for medicare at exactly the day you turn65.
Your overall age, and your decision to quit, may be related in different ways to many things like race, gender, before-age-65 health, and income. Some of these things may also affect each other
Your income may also determine whether or not you choose to use Medicare (or go with something private instead)

Medicare and Retirement

Regression discontinuity again, this time with age as running variable
Lots of back doors! But no need for controls, the RDD isolates just our path of interest here
As long as the treatment is “turning 65” - if the treatment is “receives Medicare” we still need to control for income - why?
Note: how can age “cause” race or gender? Why, differential mortality rates of course!

Monetary Policy

A standard economics result is that monetary policy - putting more money into the economy, which the Federal Reserve does by buying treasury bonds (“monetary policy”) - leads to more inflation
Of course, there might be other reasons why we see monetary policy linked to inflation
Perhaps, for example, the kinds of things that make the Fed respond by buying bonds happen to lead to inflation on their own?

Monetary Policy

Draw a diagram! To consider:

Buying/selling bonds (monetary policy, MP) changes the amount of money in the economy
Inflation comes from the amount of money there is relative to the amount of stuff there is, which comes from economic productivity and unemployment
Money in the economy is also affected by the amount of money tied up in investments
And your country characteristics affect everything too!

Monetary Policy

For this one we need lots of controls!
We have back doors through unemp, inv, prod, and coun
So we control for all of them with controlling or matching. For coun we need fixed effects.

The Minimum Wage

A classic causal question is “what is the effect of the minimum wage on employment?”
Principles of econ classes point out that raising the minimum wage (like raising the price on anything) should reduce the number of people employed
However there are other wrinkles: what if people take that money and spend it, improving the economy and increasing employment that way-
Or what if the labor market isn’t competitive, meaning that increasing wages might actually encourage more employment?

The Minimum Wage

Draw a diagram! To consider:

In 1992 (i.e. in a certain year), New Jersey increased their MW from $4.25 to $5.05
Neighboring Pennsylvania didn’t. So the MW differs by state
We can look at fast food restaurants (most likely to be affected) just around the border
It’s possible that the two states had different trends in terms of how their labor markets were changing
The national economy might have also had an effect on unemployment
What is the effect of the MW increase on unemployment?

The Minimum Wage

A good spot for difference-in-differences!
We need to control for trends too - DID won’t handle that on its own as it has to do with changes in the gap BETWEEN the two states over time.
No need to control for econ - the DID adjustment for year handles that back door

Research Design Assignment

Not long: 1-2 pages.
Ask a causal question (“How does X affect Y?”)
Draw a causal diagram in dagitty. Justify your diagram (both your choice of variables and your arrows)
Explain whether or not it’s possible to identify your effect of interest and how you’d do it
You may have to pick a particular context (like Penn vs. NJ) to make your approach work, that’s fine