# Concepts behind fixed/random effects models

1. Can someone help me to understand fixed/random effect models? You may either explain in your own way if you have digested these concepts or direct me to the resource (book, notes, website) with specific address (page number, chapter etc) so that I can learn them without any confusion.
2. Is this true: “We have fixed effects in general and random effects are specific cases”?
I would especially be grateful to get help where the description goes from general models to specific ones with fixed and random effects

This seems a great question as it touches a nomenclature issue in econometrics that disturbs students when switching to statistic literature (books, teachers, etc). I suggest you http://www.amazon.com/Econometric-Analysis-Cross-Section-Panel/dp/0262232197 chapter 10.

Assume that your variable of interest $y_{it}$ is observed in two dimensions (e.g. individuals and time) depends on observed characteristics $x_{it}$ and unobserved ones $u_{it}$. If $y_{it}$ are observed wages then we may argue that it’s determined by observed (education) and unobserved skills (talents, etc.). But it’s clear that unobserved skills may be correlated with educational levels. So that leads to the error decomposition:
$u_{it} = e_{it}+v_i$
where $v_i$ is the error (random) component that we may assume to be correlated with the $x$‘s. i.e. $v_i$ models the individual’s unobserved skills as a random individual component.

Thus the model becomes:

$y_{it} = \sum_j\theta_jx_j + e_{it}+ v_{i}$

This model is usually labeled as a FE model, but as Wooldridge argues it would be wiser to call it a RE model with correlated error component whereas if $v_i$ is not correlated to the $x's$ it becomes a RE model. So this answer your second question, the FE setup is more general as it allows for correlation between $v_i$ and the $x's$.

Older books in econometrics tend to refer to FE to a model with individual specific constants, unfortunately this is still present in nowadays literature (I guess that in statistics they never have had this confussion. I definitevely suggest the Wooldridge lectures that develops the potential missunderstanding issue)