Instrumental variable is a fraction

[Ivan Ivanov]

Hello everybody, I am looking for help in creating my instrumental variable.

I am doing research in which I am trying to look at how change in minorities influence voting results. Since there is possibility of endogeneity, I decided to use IV regression. I have present data for the elections that I am covering, including results and data regarding population.
I also have the past data regarding population. My instrument therefore is based on the past share of minorities. So, I am trying to predict a present share of minorites with the past ones.

My instrument should be calculated as:

predicted change in minority share = (predicted minority population_t / predicted populatiomn_t) - (predicted minority population_t-1 / predicted population_t-1).

Can somebody help me out with this.
Thank you.

[Jeff Wooldridge]

Ivan: The problem in my view is not that the IV is a fraction. It's more that you're using a lagged value of a variable you think is endogenous and assumption it's exogenous. If you write down an unobserved effects model, where the error term is c(i) + u(i,t) then assumption past minority share is uncorrelated with c(i) is a strong assumption. I think more convincing is to use fixed effects to eliminate c(i). If you can find an external instrument that predicts minority share then you can combine FE and instrumental variables. But finding an exogenous instrument that is also sufficiently strong is a tall order for this kind of application.

[Ivan Ivanov]

Hi Jeff, thank you for your reply. I will take into consideration what have you written. The paper that I took the idea from is the Immigration and electoral support for the far-left and the far-right (Edo et al., 2019).