Differences-in-differences estimation

7 important questions on Differences-in-differences estimation

Formula ATET when flexible OLS

ATET = delta + 1/sum(Di)*sum(Di*(Xi-Xbar)'gamma)

Observed outcome in case flexible OLS:

Yi = Xi'beta + Di*(Xi-Xbar)'gamma + Di*delta + epsilon_i

Where does the differences-in-differences estimator look at?

Changes in outcomes between treatment group and control group.
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Formula DiD's estimator:

beta = (Ytreat,after - Ytreat,before) - (Ycontrol,after - Ycontrol,before)

How can you test the parallel trend assumption?

- Use data for previous periods and redo the DiD's estimation.
- When many years are available, it is useful to plot the series of average outcomes for treatment and control groups and see whether trends are parallel and whether there is a sudden change just after reform for treatment group.
- If we have at least 3 observations over time, we can add state specific time trends.

What can also be a source of bias for the DiD's estimator?

Compositional changes with repeated cross sections.

How to check for compositional changes?

Check if observed characteristics of treatment group and composition of control group is constant over time (or at least changes in the same way).

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