I am running an analysis of impacts of immigration on natives' votes to anti-immigration parties, across municipalities.
The concern in this type of analysis is that location decisions of immigrants may be endogenous to natives' support to anti-immigration parties. This is because immigrants may decide to settle in municipalities that are friendlier to them. In a naïve regression, this would represent a downwards bias on the effect identified of immigration on natives' votes.
Due to this concern, the literature widely uses the Instrumental Variable approach of popularized by Card (2001). This uses past, historical settlements of immigrants across municipalities - to predict future immigration flows (following network effects among immigrants, e.g. due to information access). The assumption is that past historical settlements are not correlated with more recent political voting outcomes - i.e. exclusion restriction.
Now: my IV estimates suggest larger impacts of immigration, compared to OLS. This would be consistent with the story that immigrants settle in friendlier municipalities (i.e. less anti-immigration parties support by natives).
In order to test for the exclusion restriction, I am running a regression where I test if past anti-immigration voting is a significant predictor of future immigration flows. I test this both for actual immigration flows, and for the immigration flow instrument. My finding is that both actual and instrument immigration flows seem to be positively affected by past anti-immigration voting (and the magnitude of the effect seems similar). That is, immigrants seem to settle in areas that are more pro anti-immigration.
The fact that I get (1) different IV and OLS results; and (2) IV estimates higher than OLS - is puzzling to me.
I was wondering if anyone would have thoughts on this. Many thanks in advance!