Exam 1 Review

Question 1

What is a mediator? Explain and draw the DAG

Answer 1

X > M > Y
Mediation is the process by which a third vari-
able (i.e., the mediator) transmits the effect of an independent variable on a dependent variable
* 𝑋: Attending an elite high school (main independent variable/treatment/exposure)
* 𝑌 : Going to an elite university (dependent variable/outcome)
* 𝑀 : Better teacher in the elite high school (mediator)

Question 1

Draw a fork DAG. Label the variables and explain the essence of a fork DAG with an example

Answer 1

Z
↓↘
X >Y

Question 2

What is a direct effect, and how does it relate to mediation?

Answer 2

A direct effect refers to the mediation effect produced every other mediator except 𝑀 .
In the example from question 2, it would be the every other reason besides good teachers
why going to an elite high school helps with getting into an elite university.

Question 3

In the language of DAGs, what does it mean to close all relevant backdoor
paths?

Answer 3

It means to only close the backdoor paths associated with confounders, not colliders or
mediators — i.e., assuming an interest in some form of an average treatment effect as
the estimand

Question 4

What is a collider? Draw the DAG and explain.

Answer 4

C
↗ ↑
X Y
Colliders (𝐶) are variables that, if adjusted for, can introduce a spurious relationship
between 𝑋 and 𝑌

Question 5

What is selection bias and how do you indicate it in a DAG?

Answer 5

Selection bias is when you have of availability of data in your sample that does not rep-
resent the population for which you are making your inference. You indicated selection
bias with a boxed S

Question 6

Draw a DAG with selection bias on the dependent variable. What can we learn in such instances? Explain with an example.

Answer 6

In our smoking example, sample selection bias on the dependent variable (𝑌 ) entails
having a sample of either people mostly with lung cancer or mostly without lung cancer.
In either case, it is difficult to make any within-sample inference with respect to causality
or prediction, because there is not enough variation in people. For external validity, we
can’t make inferences to a larger population if we don’t have (1) data representative
of that population; or (2) variables in our sample to adjust for the sample-population
differences

Question 7

You are presented with a regression in which the author uses female literacy as the independent variable (𝑋) and overall literacy (𝑌 ) as the dependent
variable. Does this seem like a valid set up? Why or not?

Answer 7

No, it is not a valid set up. Clearly, female literacy is part and parcel of overall literacy.
Accordingly, there is no point in running a regression of something that already partly
explains something else by design.

Question 8

What is positivity in the context of internal validity? Provide an example to show that you understand it. It may also be helpful to draw something.

Answer 8

Whether the different manifestations of the independent variable (𝑋)
overlap across subgroups/strata of the treatment and control, taking into account selec-
tion bias ( 𝑆 ) that can result in under- or over-coverage

Question 9

What is positivity in the context of external validity? Provide an ex-
ample to show that you understand it. It may also be helpful to draw
something

Answer 9

Whether the different manifestations of the independent variable (𝑋)
and effect modifiers (𝑉 ) overlap across the sample and population, taking into account
selection bias ( 𝑆 ) that can result in under- or over-coverage.

Question 10

What are generalizability and transportability?

Answer 10

Generalizability is when the sample is embedded within the population of interest, and
transportability is when the sample corresponds to another population of interest

Question 11

What is an Intent to Treat (ITT) effect?

Answer 11

The effect of assigning the treatment, even if people did not comply with their treatment
assignment. The ITT is often a very conservative estimand.

Question 12

What are the treatment (𝑋), instrument (𝑄), dependent variable (𝑌 ),
and confounder (𝑍) in Column (2) of Table 4 of Acemoglu, Johnson, and
Robinson (2001)? Also, draw the DAG.

Answer 12

• 𝑋: average protection against expropriation risk (quality of institutions)
• 𝑄: settler mortality in colonial era
• 𝑌 : log GDP per capita
• 𝑍: latitude

Question 13

What is the exclusion restriction in Acemoglu, Johnson, and Robinson
(2001)?

Answer 13

Settler mortality at the time of colonization (𝑄) must not be directly related to current
GDP per capita (𝑌 ). If settler mortality at the time of colonization were related to current GDP, it would violate the exclusion restriction assumption.