But there’s still only a small % of cars with the device. Car thieves might be less cautious if they don’t know about these devices, which might mean these thieves get caught, but how could this dramatically decrease overall theft rates?

We’re trying to explain how theft rates could have decreased. Whether theft rates started below, at, or above the average theft rates for cities doesn’t explain how those rates could have declined dramatically.

Even if we interpret this answer as suggesting thieves today are more frequently apprehended, wouldn’t we expect only a small proportion of thieves to be caught, since the device is installed in only a small proportion of cars? How could this significantly decrease cars stolen?

We know only a small % of cars have the device installed in the relevant cities. Whether thieves live in other cities doesn’t affect our expectation that a small % of cars with the device should have only a small impact on overall theft rate.

If only a few car thieves are responsible for a large portion of car thefts, catching only a few car thieves can lead to a dramatic decline in thefts. This is how the devices could decrease thefts significantly despite being in only a small % of cars.