Confused interpretation with correlated explanatory variables

[Xavier Pedros]

Hi,

I study the effect of immigration on political voting with municipality data. I specifically study the effect of immigration on the voting of Natives. Immigrants cannot vote in my data.

I have a first differenced model of the form:

ΔY_it = a*ΔImmigration_it + b*ΔPopulationUnder25_it + c*ΔPopulationOver65_it + Δe_it

where Y is the vote share of a political party, in municipality i, in election year t. Immigration are the number of immigrants, over total population, in municipality i in election year t.

In order to control for demographic changes among the native population, and their impact on political voting, I have two variables for the share of population under 25, over total population; and the share of population over 65, over total population. These are not calculated among native population, but among population including immigrants.

My question is: because immigrants tend to affect the demographic structure of a municipality, likely by making it younger, do I have to worry that part of the immigration effect on political voting might be somewhat absorbed/captured in the two demographic variables?

I am not keen on interpreting the coefficients for these control variables (whose effect on political voting could be biased as it does not capture actual native demographics). I am just keen on the immigration estimate.

Many thanks!

[Maarten Buis]

I think you are right to be worried about that. It does not have to be a big problem, but there is a good chance that it might be. What you are doing is basically a fixed effects model, so any baseline differences in age structure between municipalities are already absorbed. So your age structure variables are not there to control for differences between municipalities in the baseline age structure, but only there to control for differences between communities in changes in the age structure. There are really two ways in which the age structure of a municipality can change:

1) Every year everyone gets one year older as long as they haven't died in that year.
2) People move into and out of that municipality.

Reason 1) is normally slow and very predictable. The predictable part (every year you get one year older) is absorbed by the fixed effects as long as the birthrate (and child mortality) has been fairly constant for a very long time. There could be a sudden change in those variables if in a electoral cycle the babyboom generation moved across the 65 year threshold. I think that that sudden change in the ΔPopulationOver65_it variable would exaggerate the importance of that event; it is no surprise that the boomers are getting old... The sudden change in that variable is just an artifact of the artificial threshold of 65. There could be a sudden change in the birthrate. That does not have a direct effect on voting, as it takes typically 18 years before they can vote. However, drastic changes in birthrate are typically a consequence of pretty dramatic changes in that community, that would also influence voting behavior. An example would be the drop in birthrate after the fall of the DDR. But I would want to capture those changes directly, rather than indirectly through the age structure. That leaves sudden changes in the age structure due to deaths. Sudden changes in the age structure for this reason could be something like an outbreak of a really serious disease that affects people of different ages differently. However, such an event would have all kinds of consequences on voting behavior on their own, and again I would want to capture that directly rather than indirectly through the changes in the age structure. So in short I don't think these variables are appropriate to capture changes in the age structure due to births and deaths.

Reason 2) Migration in and out of a municipality could be international migration or just movement within the country. Usually national migration is much higher than international migration; there are a lot less barriers to moving within a country compared to moving between countries. If that is the case in your country for the period you are studying, then you might use that as an imperfect justification for using that variable. However, if there are sudden international migration movement to your country within the time frame of your study, like Syrian refugees to Europe in 2015, then I would just leave the age structure out of your model.

So in short: just thinking about what a variable is supposed to capture and the mechanisms involved often tells you a lot about whether to include that variable or not, and how to include it.

[Xavier Pedros]

Thanks Marteen.

On Reason 2, let us assume that the age structure is very much affected by immigrants (international and/or moving within the country). Do you have a sense of how this would affect the immigration estimate?

I am personally thinking: the model holds changes in age structure constant (whether induced by immigration or for other reasons unrelated to immigration). Holding the latter constant, the model then evaluates the effect of an increase in immigration, on political voting of natives.

The immigration estimate is all I care.

Having said that, the theoretical justification for adding age structure is that the age of natives matters for their political voting, and that the age structrue change in a municipaltiy might also be a determinant of immigration flows. So I guess that its addition to the model assumes the idea that my age structure variables are mostly capturing changes in age structure due to natives motiving in and out.

[Maarten Buis]

If changes in the age structure are primarily due to international migration, and you keep the age structure constant, then you are filtering a part of the effect of migration out. That is bad. In that case the benefits of including that variable no longer outweigh the cost, and I would leave it out of the model.

[Xavier Pedros]

Agreed Maarten - Thanks!