Assume a dataset that has a time series of a dependent variable for a number of stocks, and then a time series of an independent variable over time.
Would applying a fixed effects model on this mean that all unobserved characteristics of the stocks would be included in the intercepts, and all changes should therefore be due to changes in the independent variable(s)? With the assumption that the unobserved characteristics stay stable over time. What if an unobserved thing affects all the stocks and is thus not a characteristic of a specific stock?
The model would look like this for example:
dependent(i,t) ~ a(i) + b1*independent(i,t)
where i is the specific stock.
Someone presented me this about fixed effects models and I'm trying to understand whether this really is true. For example, if I was to examine whether $X$ affects e.g. the liquidity of the market in general, would a fixed effects model rule out anything else than omitted things about the specific stocks? What if there is $Y$ that also affects all the stocks, I believe this would still be considered omitted variable bias?
The story behind here is that this someone argues that all changes can be said to be result of $X$ thanks to using a fixed effects model. But if there is also $Y$ that has a similar effect on all stocks as $X$, would omitting $Y$ here overestimate the effect of $X$?
Hopefully someone understands my questions, it is basically about the general characteristics of a fixed effects model, and what exactly can be omitted and what not.
