Should we control for variables
to close as many backdoors as
possible in our diff-in-diff model?

How does moving time back
let us check for parallel trends?'

Can you conduct diff-in-diff
with a binary outcome?

I keep reading about estimates, estimands, and estimators.
What are these and are they the same thing?

Tell us more about
the final project!

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.

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

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

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

What are random effects?

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?