# How to motivate a POLS?

How would you justify the usage of Pooled OLS regression instead of Fixed effects?

If I am calculating just correlation between two phenomena, may I get rid of these fixed effects? May I choose to ignore them?

Not using FE when they matter, let omitted variable bias arise determining a correlation between the error term and regressors. Can we accept this in the same way we accept autocorrelation in the residuals (that is highlighting the fact that even though it cannot be interpreted as a causal relationship, it can still be a valid correlation)?

In your case, if we look at it from the predictive inference perspective, you are trying to understand the association between two variables (assume binary). You could do this with 2x2 tables, but then you think that variable $$Z$$ would change the observed distribution of this 2x2 table so you segment and run again. You could do this kind of bivariate and multivariate analysis all day to draw a picture of the associations. Eventually, though, the associations become too complex and you decide to run a model which will summarize all of these tables for you. From what I understand, this is where you are at.