This incentive program was predicted to be popular with drivers, and cities were eager to

implement it$.$ Cities were told that they would be given a date on which they could start enrolling

drivers in the program, and were sent a SQL query that identified qualified drivers from their city.

Drivers qualify based on a number of criteria, the most important of which was how active they

had been in the preceding month. So$,$ for example, a driver would only qualify if they were in the

top quartile of their city$$s distribution of minutes driven in the last month.

On their assigned date $($staggered across cities$),$ a city would begin enrolling drivers by taking all

qualified drivers $($as of that day$),$ and stratifying them based on minutes driven in the last month.

On each subsequent day a city could add more drivers to the experiment by re$-$running the SQL

query, and taking drivers who now qualified $($but hadn$$t before$),$ stratifying them, and adding

them to the experiment. $$Treated$$ drivers would be sent an email explaining the new incentive,

and containing instructions as to how they could apply $/$ enroll in the program $($acceptance was

not automatic, and was based on meeting several financial conditions$).$Control$$ drivers were

sent an email with the same information, but told that the incentive would be coming soon.

For your Analysis:

$1)$ Use files Driver$\_$Days $($days a driver drove$)$ and Driver$\_$Condition $($drivers$$ experimental

details$).$ The quantities we are interested are: minutes driven per day, probability of driving

per day, and earnings per day. What is the intent$-$to$-$treat effect $($i$.$e$.$ effect of the treatment

group$)$ on these variables when expressed in levels? What is it when expressed as a percent?

How statistically confident are we in these effects? Make sure to succinctly justify your

empirical approach $/$ defend your empirical design