EMET8002 Chap.9 Difference-in-Differences and Event Studies
Difference-in-Differences and Event Studies
Comparing changes
Causal questions compare what happened with an unobserved counterfactual.
Difference-in-differences estimates it by subtracting a control group's change from a treated group's change, which removes both fixed group differences and common time trends, under the parallel trends assumption.
Cases and best practice
The chapter works the estimator and its regression form, then follows the lecture's cases: Card and Krueger's minimum wage study, John Snow's cholera data and the Medicaid expansion event study, ending with the checks that make a design credible.
What makes a DiD design persuasive
A proposal or report that uses difference-in-differences is judged on the credibility of its control group and on how well it argues the assumptions.
The Week 7 lecture names three: parallel trends, no anticipation, and the stable unit treatment value assumption. It adds the practices that persuade a reader, namely verifying the first stage, plotting event-study coefficients for the years before the policy, and clustering standard errors at the level of the group that was treated.
What this chapter covers
- 01
Correlation and causation
- 02
Counterfactuals and randomised trials
- 03
Quasi-experiments
- 04
The two by two estimator
- 05
The interaction regression
- 06
Parallel trends, anticipation and SUTVA
- 07
Snow's cholera study
- 08
Event studies with leads and lags
Worked example · free
Reading an event-study plot
- 1The pre-policy coefficients all lie within 0.5 of zero, so there is no sign of divergence before the policy.
- 1That supports parallel pre-trends, the evidence a DiD design needs.
- 1From the first year after, the coefficients rise from 1.2 to 2.1 with intervals above zero, so the effect grows over time.
Key terms
- Counterfactual
- The outcome that would have occurred without the intervention, with everything else the same.
- Quasi-Experiment
- An event that assigns treatment as if at random, used when a randomised trial is infeasible.
- Event Study
- A design that estimates one treatment coefficient for each period before and after a policy.
- Anticipation Effect
- A change in behaviour before a treatment starts because it was expected.
Difference-in-Differences and Event Studies FAQ
What is the parallel trends assumption?
It assumes that, had the treatment never happened, the treated group's outcome would have changed by the same amount as the control group's. It cannot be tested directly, because the counterfactual is unobserved, but parallel pre-treatment trends in an event study support it.
How did John Snow use difference-in-differences?
He compared cholera deaths for households supplied by Lambeth, which moved its water intake upstream, with those supplied by Southwark and Vauxhall, which did not. Deaths per 10,000 households fell from 85 to 19 for Lambeth and rose from 135 to 147 for the other company, a difference of 78.
Where should DiD standard errors be clustered?
At the group level at which treatment is assigned, such as the state when a policy switches on state by state. Individual-level errors would treat a handful of state-level comparisons as if they were many independent observations.
Why can't I just compare the treated group before and after?
A before-and-after comparison of the treated group alone mixes the treatment effect with everything else that changed over the same period. The control group's change estimates that common time trend, and subtracting it isolates the effect of the treatment, provided the trends would have been parallel.
What did Card and Krueger study?
They examined the employment effect of a 1992 minimum wage increase in New Jersey, using neighbouring Pennsylvania, where the minimum wage did not change, as the control. The policy change was treated as if randomly assigned with respect to other determinants of employment over that period.
What are the coefficients in the DiD regression?
In the regression with a treatment dummy, a post-period dummy and their interaction, the intercept is the control group's baseline, the treatment dummy is the pre-existing gap between the groups, the post dummy is the common trend, and the interaction coefficient is the treatment effect.
Assessment move
For any DiD you read, write the four group means, the two changes and the double difference, then name the control group and the most plausible way parallel trends could fail. Then write the regression version of the same estimate and check that the four coefficients reproduce the treated group's mean after the policy.
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