Recentered IV is uncorrelated with latitude and longitude
For \(\text{Interstate Variable}_{c} \in \{ \text{Treatment}_{c}, \text{Recentered IV}_{c}\}\), I run the following regression:
\[\text{Interstate Variable}_{c} = \beta_0 + \beta_1 \frac{\text{Latitude}_c}{100} + \beta_2 \frac{\text{Longitude}_c}{100} + \epsilon_c\]
When I regress latitude and longitude on the recentered instrument, the coefficients are zero.
