I am interested in using a spatial research design. Imagine a line, like a time zone line. For example, in the United States, the line that makes between Eastern Standard Time and Central Standard Time runs North to South through the U.S. (and other places), more or less.
Suppose the United States implemented a policy where, with respect to county boundaries, all counties west of the 75th longitude were to get a tax deduction. No counties to the right of it would. I want to evaluate the impacts of the this tax deduction on crime.
For the sake of argument, can we please assume that the discontinuity is valid. I am trying to understand this idea for spatial discontinuities, in general?
I can imagine proceeding one of two ways. One way would a regression discontinuity. Exploiting the distance of say a county from this line. The other way would be a matching of counties that straddle this line on opposite sides. Note that a county might appear more than once if it borders more than one county on the opposite side of the time zone line.
The regression discontinuity includes a larger sample because it may include counties that are not exclusively along the border. The matching hones in on counties that touch each other, whereas the regression discontinuity, at best, can partition the time zone into smaller segmented lines where segments likely include multiple pairs of counties along the time zone.
What are the trade-offs of the research design? Which is preferred? Does one offer something that the other doesn't?