Lecture 23 Comparison Groups Practice

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

1. Consider the problem
2. Think about what we think the data-generating process is
3. Draw a diagram
4. Figure out the method (we may have to control for some things for the usable diagram to emerge!)
5. 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

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

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

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

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