We noted that Toronto may be a good control group for Sydney because the trends in ticket sales follow a similar pattern. This is actually a necessity of DID called the parallel trends assumption: trends between the control and treatment groups should be similar prior to the start of treatment.
The specific values between groups do not need to be the same, but the two groups should have the same change over time. We can check this visually by plotting the data by group and verifying that the general trends are similar, as we saw in the previous exercise. A disadvantage to DID is the difficulty of meeting the parallel trends assumption: we need pre-treatment data for both groups AND the data has to show similar trends before treatment.
Another assumption for DID is that the treatment group was selected for the treatment by a factor that is independent of the outcome. This assumption is met for our example: the treatment is determined by state, which is independent of the overall average student wages.
Finally, the assumptions for DID also include the normal assumptions for all causal inference methods:
- Conditional exchangeability
- Stable Unit Treatment Value Assumption (SUTVA)
The learning environment shows your plot from the ticket sales data in the previous exercise. Take a look at the lines for Toronto and Sydney covering the time from 2012 to 2018, just before the new tax was implemented. Both lines follow a similar trend going up and down slightly each year but with a particular dip in 2016.
Do you think Toronto will make a good approximation of Sydney’s counterfactual even though its line is lower on the plot?
Do you think we’ve met the other assumptions of DID in this case?