# Lecture 25 Instrumental Variables in Action

## Causal Inference Midterm

• One week from today
• Similar format to the homeworks we’ve been having
• At least one question evaluating a research question and drawing a dagitty graph
• At least one question identifying the right causal inference method to use
• At least one question about the feature(s) of the methods
• At least one question carrying out a method in R

## Causal Inference Midterm

• Covers everything up to today (obviously, a focus on things since the Programming Midterm, but there is a little programming)
• No internet (except dagitty) or slides available this time
• One 3x5 index card, front and back
• You’ll have the whole class period so don’t be late!

## Recap

• Instrumental Variables is sort of like the opposite of controlling for a variable
• You isolate just the parts of `X` and `Y` that you can explain with the IV `Z`
• If `Z` is related to `X` but all effects of `Z` on `Y` go THROUGH `X`, you’ve isolated a causal effect of `X` on `Y` by isolating just the causal part of `X` and ignoring all the back doors!
• If `Z` is binary, get difference in `Y` divided by difference in `X`
• If not, get correlation between explained `Y` and explained `X`

## Recap

• In macroeconomics, how does US income affect US expenditures (“marginal propensity to consume”)?
• We can instrument with investment from LAST year.
``````library(AER)
#US income and consumption data 1950-1993
data(USConsump1993)
USC93 <- as.data.frame(USConsump1993)

#lag() gets the observation above; here the observation above is last year
IV <- USC93 %>% mutate(lastyr.invest = lag(income) - lag(expenditure)) %>%
group_by(cut(lastyr.invest,breaks=10)) %>%
summarize(exp = mean(expenditure),inc = mean(income))
cor(IV\$exp,IV\$inc)``````
``## [1] 0.9993985``

## Today

• We’re going to be looking at several implementations of IV in real studies
• We’ll be looking at what they did and also asking ourselves what their causal diagrams might be

## Today

• And whether we believe them! What would the diagram be for that expenditure/income example? Do we believe that there’s really no back door from last year’s investment to this year’s expenditure? Really?
• Every identification implies a diagram… and diagrams come from assumptions. We always want to think about whether we believe those assumptions
• Remember, in any case, each of these is just one study. I could cite you equally plausible studies on these topics that found different findings in different contexts

## College Remediation

• In most colleges, if you come unprepared to take first-year courses, you must first take remedial courses
• On one hand they can help ease you into the first-year courses
• On the other hand you might get discouraged and drop out

## College Remediation

• What’s our diagram? Include `Rem`ediation, `Pers`istence, other things.
• Keep in mind that many of the things that would cause you to take remediation in the first place are the same things that might lead you to drop out (difficulty with material, dislike for school, etc.)
• Sketch out a diagram

## College Remediation

• Bettinger & Long (2009) use data from Ohio and notice that the policy determining who goes to remediation varies from college to college
• And also, as is generally well-known, people tend to go to the college closest to them
• So for each student and each college, they calculate whether that student would be in remediation at that college
• And use “Would be in remediation at your closest college” (`RemC`) as an instrument for “Actually in remediation” (`RemA`)