<p>If immigration were randomly assigned and would affect the demographic structure, which in turn affects voting, then this would be an example of overcontrol bias. Lagging the demographic variables could address this issue?</p>
<p><a href="https://i.sstatic.net/ItG6I.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ItG6I.png" alt="enter image description here" /></a></p>
<p>If, however, the demographic structure affects both immigration and voting, then it would block back door paths and be a good control.</p>
<p><a href="https://i.sstatic.net/sDFVO.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/sDFVO.png" alt="enter image description here" /></a></p>
<p>Bottomline: it depends what you assume about the causal relationship between the variables, not only whether they correlate.</p>
<p>The images (and content) are taken from the incredible <a href="https://ftp.cs.ucla.edu/pub/stat_ser/r493.pdf" rel="nofollow noreferrer">A Crash Course on Good and Bad Controls</a></p>

CC BY-SA 4.0
2022-10-07T07:24:15.197Z
2022-10-07T07:24:15.197Z
Papayapap
<p>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.</p>
<p>I have a first differenced model of the form:</p>
<p>ΔY_it = a<em>ΔImmigration_it + b</em>ΔPopulationUnder25_it + c*ΔPopulationOver65_it + Δe_it</p>
<p>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.</p>
<p>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.</p>
<p>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?</p>
<p>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.</p>
<p>Many thanks!</p>

<econometrics>
Confused interpretation with correlated explanatory variables
Padarapla
# Confused interpretation with correlated explanatory variables

(Asked by: username_0 on 2022-10-07)

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!

**Tags:** econometrics


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## 1 answers

### Answer by username_1 on 2022-10-07. Score: 1

If immigration were randomly assigned and would affect the demographic structure, which in turn affects voting, then this would be an example of overcontrol bias. Lagging the demographic variables could address this issue?

[![enter image description here](https://i.sstatic.net/ItG6I.png)](https://i.sstatic.net/ItG6I.png)

If, however, the demographic structure affects both immigration and voting, then it would block back door paths and be a good control.

[![enter image description here](https://i.sstatic.net/sDFVO.png)](https://i.sstatic.net/sDFVO.png)

Bottomline: it depends what you assume about the causal relationship between the variables, not only whether they correlate.

The images (and content) are taken from the incredible [A Crash Course on Good and Bad Controls](https://ftp.cs.ucla.edu/pub/stat_ser/r493.pdf)


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