Instrumental Variable?

#1
So i have a bunch of variables: religious beliefs (how religious you are) and religious participation (how often you go to church), and demographic variables like age, gender, income, education, etc. if i want to find out the casuality between religious beliefs and religious participation, how should i use instrumental variables to construct the model?


*i posted this under statistic help as well cuz i realized it fits my question better... apologies for the double posting
 
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#2
So i have a bunch of variables: religious beliefs (how religious you are) and religious participation (how often you go to church), and demographic variables like age, gender, income, education, etc. if i want to find out the casuality between religious beliefs and religious participation, how should i use instrumental variables to construct the model?


*i posted this under statistic help as well cuz i realized it fits my question better... apologies for the double posting
The goal of Instrumental Variables (IV) regression is to sidestep the endogeneity problem and provide the researcher with consistent estimates. In your problem, if you try to explain religious participation (the dependent variable) as a function of religious beliefs, age, gender, income, education, etc., you have a problem since religious participation is not really exogenous (i.e., independent) but is likely endogenous. You could make the case that someone's religious faith is in turn strengthened by their religious participation. In that case, your variable "religious participation" is correlated with the error term, and the ordinary assumptions of OLS are violated.

One solution is IV. The essential step here is to find a variable X that is correlated with both religious beliefs and religious participation, but affects religious participation only through its affect on religious beliefs. In that way, it is exogenous to the dependent variable. This is a VERY important step, since you need a good (well correlated and exogenous) instrument to provide useful results. In the example data you provide, I couldn't find a suitable instrument, but if you give some more examples we can come up with one.

Once you've completed that step, the rest is cake. You can write down a 2SLS model, obtain predicted values of the endogenous variable, and estimate the IV results. If your instrument is good, you will have some idea of the true effect.