Explain difference-in-differences with an example

Question

Explain difference-in-differences in simple terms and provide a concrete example.

Codemia · Accepted Answer

To illustrate the difference-in-differences (DiD) method, let's say Grubhub wants to evaluate the impact of a new marketing campaign in a specific city, City A. The analytical question is: **Did the new marketing campaign lead to an increase in order volume compared to a control city, City B, which did not receive the campaign?**

We would need the following data:
- Order volume data for City A and City B, both before and after the marketing campaign.
- Demographic information to ensure cities are comparable.
- Any external factors that might influence order volume (like local events or seasonality).

The difference-in-differences approach involves comparing the change in order volume in City A (treatment group) before and after the campaign to the change in order volume in City B (control group) over the same time periods.

1. **Calculate the average order volume for both cities pre- and post-campaign.** 
2. **Compute the difference in order volume for both cities:**
   - For City A: $ 	ext{Post}_{A} - 	ext{Pre}_{A} $
   - For City B: $ 	ext{Post}_{B} - 	ext{Pre}_{B} $
3. **The DiD estimator is then:**
   - $ (	ext{Post}_{A} - 	ext{Pre}_{A}) - (	ext{Post}_{B} - 	ext{Pre}_{B}) $

Assume:
- City A (Pre): 1000 orders, City A (Post): 1500 orders
- City B (Pre): 1200 orders, City B (Post): 1300 orders

Now, calculate:
- City A Change: $ 1500 - 1000 = 500 $
- City B Change: $ 1300 - 1200 = 100 $

Using the DiD formula:
- DiD = $ 500 - 100 = 400 $

This result implies that the marketing campaign is associated with an increase of 400 orders in City A, above and beyond the change seen in City B.

The DiD result of 400 suggests that the marketing campaign effectively increased order volume in City A by 400 orders compared to City B, controlling for other variables. However, it’s crucial to interpret this result cautiously:
- Consider external factors that might have influenced both cities during the study period.
- Ensure the assumption of parallel trends holds; that is, the order volumes in both cities would have followed the same trend over time in the absence of the campaign.

Common mistakes in implementing DiD include:
- **Ignoring parallel trends:** If the two cities had different trends before the campaign, it could bias results.
- **Not adjusting for confounding variables:** External factors can skew results if not accounted for. 
- **Overlooking network effects:** For instance, if customers in City B are influenced by the marketing in City A, it can lead to interference in the treatment effects.
- **Small sample sizes:** Not ensuring a large enough sample size can lead to unreliable estimates and reduce the power of the analysis.

Explain difference-in-differences with an example

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