Terminology of fixed vs random effects panel data?

Question

In short, in a fixed effects model, the individual effect is correlated with the regressors, while in the random effects model it is uncorrelated.

But what does "fixedness" have to do with the fact that the regressors are uncorrelated with the individual effects? similarly, "randomness" and "uncorrelated" are not the same concept. So why then are these models called "fixed effects" and "random effects", if they are instead about correlatedness vs uncorrelatedness? Is there some history behind this?

Answer 1

The main difference between fixed and random effects are as follows:

• Fixed Effects: Effects that are independent of random disturbances, e.g. observations independent of time.
• Random Effects: Effects that include random disturbances.

The effects are referred to as "fixed", due to the fact that individual-specific effects are not correlated with the independent variables. The issue is not necessarily correlation, but rather how fixed and random effects interact with other data in the regression model.

When conducting a study, fixed effects are often used when looking to compute effect size for one population in particular, and not generalize results for other populations.

This source illustrates a good example on comparing effects of drugs vs. placebos, which should shed more light on why the terms "fixed" and "random" are so-called.