(Recentered IV x High Ag Indicator) does not predict pre-Interstate county characteristics
For \(x_{c} \in \{ \text{Population Density}_{c, 1940}, \text{Log House Value}_{c, 1940}, \text{Market Potential}_{c, 1950}\}\)
\[ x_{c} = \beta_{0} + \beta_{1}(\text{RecenteredIV}_{c}\times \text{High Ag}_{c}) + \beta_{2}\text{RecenteredIV}_{c} + \varepsilon_{c} \]
Note: I am not worried about that \(*\). If the interacted instrument is truly uncorrelated with counties’ potential outcomes, 1 in 10 tests for this will be rejected at the 10% significance level, by construction of hypothesis testing.
(Recentered IV x High Ag Indicator) does not pre-Interstate employment growth
\[\small \log(\text{Employment}_{c, 1950}) - \log(\text{Employment}_{c, 1930}) = \beta_{0} + \beta_{1}(\text{RecenteredIV}_{c}\times \text{High Ag}_{c}) + \beta_{2}\text{RecenteredIV}_{c} + X_{c}\gamma + \varepsilon_{c} \]
