Recentered IV does not predict counties pre-Interstate employment growth
For \(\text{Interstate Variable}_{c} \in \{ \text{Treatment}_{c}, \text{Recentered IV}_{c}\}\), I run the following regression:
\[ \log(\text{Employment}_{c, 1950}) - \log(\text{Employment}_{c, 1930}) = \beta_{0} + \beta_{1}\,\text{Interstate Variable}_{c} + X_{c}\gamma + \varepsilon_{c} \]
When I regress employment growth from 1930 to 1950 on the recentered instrument, the coefficient is zero.
