Lord help me, I've been looking at vaccine data to see what the impact of the $100 incentive is.
If you look
at the AB website, you can see that the vaccine doses have been pretty flat since the start of August; they were up to 50-60K per weekday in May and June, then declined substantially in July to around 10K per day. Here's the four weeks of daily vaccine totals before the incentive was announced on September 3; first dose in red second dose in blue (not stacked):
There's a clear day of week effect (Sundays are particularly low), but there's also something of a trend; the first dose is increasing through time and the second dose is decreasing. The overall total is remarkably constant the three weeks before the announcement, but it hides these two trends.
I've estimated a fairly simple model (log-linear form) with parameters for the days of the week and a trend parameter for both the first and second dose using the three weeks of data before the announcement; not all parameters are statistically signific
ant, but I kept them all anyways. ¯\_(ツ)_/¯ Here's the model with the observed data; it's a pretty good fit. (It should be; there's 21 observations and 8 parameters.)
One challenge with the announcement is that not only are there underlying trends, but it was made the day before a holiday weekend. I assumed that the holiday is better treated as another Sunday than a typical Monday; this is consistent with the August civic holiday where the Sunday had 1232 first doses and 3804 second, and the holiday Monday had 1230 firsts and 3355 second (the Tuesday after the holiday had 2997 firsts and 8449 seconds).
The Alberta website has vaccines through the 8th, but the numbers on the 8th seem a little low so perhaps there's some straggling data reporting. Here's the first five days with the incentive versus the model:
There is a clear spike in both first and second doses, especially the first couple of days after the announcement, this is consistent with more people hearing about the incentive and getting their shots.
This final chart shows the difference between the model and the observed data:
The model is a pretty good fit, and there's a clear bump of several hundred more vaccines per day in the days after the announcement. The filled area represents my best quick estimate of the additional people who got vaccines after the 3rd, and it's probably fair to say most of these are due to the incentive.
Overall, in the first five days there seems to have been roughly 4500 more vaccines provincewide than would be expected based on recent trends; around 3000 more first vaccines and 1500 more second vaccines. (This is consistent with what I would expect; the incentive would be more likely to bring people off the fence than to accelerate people who already found the time for their first shot.)
Unfortunately, because of the free rider problem, everybody who was getting a vaccine in this time period is getting paid -- and remember there are 50,000 vaccines per week. Over these five days -- assuming everyone collects -- there was $1.6 million for first doses and $1.8 million for second doses. That works out to roughly $530 per new (marginal) first dose and $1150 per new second dose, or $740 per new dose (ignoring first or second status). More unfortunately, I'm guessing that the response to the incentive will drop off over time (it seems to in the five days of data we have), so this will likely only get more expensive and less effective.