Normally we would want to use all the data we have available to us to perform our DID model. However, that type of analysis can be complex. To keep things simple, we are going to focus on a 2x2 analysis for our student wage data, which means we will look at differences in average wages from the year before the law went into effect (2016) and the year after (2017).
From this plot, we see that the Washington schools had a much smaller increase in average student wages from 2016 to 2017 than the California schools did. We assume that if the law had NOT been passed, the pattern of student wages for the California schools would have been similar to the pattern of wages for the Washington schools. In other words, we assume the slope of the California wages would be the same as that of the Washington wages, as illustrated by the dotted red line in the following plot.
With this new line based on Washington’s pattern, we have drawn our approximation of California’s counterfactual trend. The difference between California’s 2017 observed wages and its 2017 counterfactual wages will be our estimated ATT, as shown in the plot. In the next exercises, we will compute this treatment effect using the approximated counterfactual trend in two ways.
A new dataset called
tickets2 that only includes the data from 2018 and 2019 has been created for you in notebook.Rmd. Uncomment and run the code in the workspace to view a plot of average tickets sales for Sydney and Toronto in those two years.
Based on the plot, consider the following:
- Do you think average ticket sales for Sydney would have increased or decreased had their not been a new tax?
- What do you think the impact of the tax was on average ticket sales in Sydney?