Design-based vs.
model-based inference

Special situations vs. controlling for stuff

How would you know when it is appropriate to use a quasi-experiment over an RCT?

Which is better or more credible?
RCTs, quasi experiments,
or DAG-based models?

There's no hierarchy!

Can we talk more about interaction terms and how to interpret them?

Are interaction effects in regression always more accurate of a difference than running a "regular" regression without them?

Regression is just fancy averages!

When doing your subtracting to get
your differences in the matrix, is it better
to do the vertical or horizontal subtractions?

Are there situations where
one is preferable to the other?

Why are we learning
two ways to do diff-in-diff?
(2x2 matrix vs. lm())

What happened to confounding??

Now we're only looking
at just two "confounders"?

What group level is best for comparison? For example, if we are looking at policy change in NJ, is it best to compare with just one or two similar states? How similar do the populations need to be?

Wouldn't matching be better?

Do we have to think about balance when dealing with observational data in diff in diff?

Two-way fixed effects (TWFE)

Minimum legal drinking age

MLDA reduction

Two states: Alabama vs. Arkansas

$$\begin{aligned} \text{Mortality}\ =&\ \beta_0 + \beta_1\ \text{Alabama} + \beta_2\ \text{After 1975}\ + \\ &\ \beta_3\ (\text{Alabama} \times \text{After 1975}) \end{aligned}$$

Organ donations

Two states: California vs. New Jersey

$$\begin{aligned} \text{Donation rate}\ =&\ \beta_0 + \beta_1\ \text{California} + \beta_2\ \text{After Q22011}\ + \\ &\ \beta_3\ (\text{California} \times \text{After Q22011}) \end{aligned}$$

Two states: Alabama vs. Arkansas

$$\begin{aligned} \text{Mortality}\ =&\ \beta_0 + \beta_1\ \text{Alabama} + \beta_2\ \text{After 1975}\ + \\ &\ \beta_3\ (\text{Alabama} \times \text{After 1975}) \end{aligned}$$

All states: Treatment == 1
if legal for 18-20-year-olds to drink

$$\text{Mortality}\ =\ \beta_0 + \beta_1\ \text{Treatment} + \beta_2\ \text{State} + \beta_3\ \text{Year}$$

$$\begin{aligned} \text{Mortality}\ =&\ \beta_0 + \beta_1\ \text{Alabama} + \beta_2\ \text{After 1975}\ + \\ &\ \color{red}{\beta_3}\ (\text{Alabama} \times \text{After 1975}) \end{aligned}$$

vs.

$$\text{Mortality}\ =\ \beta_0 + \color{red}{\beta_1}\ \text{Treatment} + \beta_2\ \text{State} + \beta_3\ \text{Year}$$

$$\begin{aligned} \text{Mortality}\ =&\ \beta_0 + \beta_1\ \text{Alabama} + \beta_2\ \text{After 1975}\ + \\ &\ \color{red}{\beta_3}\ (\text{Alabama} \times \text{After 1975}) \end{aligned}$$

vs.

$$\text{Mortality}\ =\ \beta_0 + \color{red}{\beta_1}\ \text{Treatment} + \beta_2\ \text{State} + \beta_3\ \text{Year}$$

vs.

$$\begin{aligned} \text{Mortality}\ =\ & \beta_0 + \color{red}{\beta_1}\ \text{Treatment} + \beta_2\ \text{State} + \beta_3\ \text{Year}\ +\\ &\beta_4\ (\text{State} \times \text{Year}) \end{aligned}$$

$$\begin{aligned} \text{Donation rate}\ =&\ \beta_0 + \beta_1\ \text{California} + \beta_2\ \text{After Q22011}\ + \\ &\ \beta_3\ (\text{California} \times \text{After Q22011}) \end{aligned}$$

vs.

$$\begin{aligned} \text{Donation rate}\ =\ & \beta_0 + \color{red}{\beta_1}\ \text{Treatment}\ + \\ & \beta_2\ \text{State} + \beta_3\ \text{Quarter} \end{aligned}$$

What about this
staggered treatment stuff?

See this

How do we know when we've got
the right confounders in our DAG?

How do we solve the fact that
we have so many unknowns in our DAG?