Statistics Definitions > Fixed Effects Models and Omitted Variable Bias

## What are Fixed Effects Models and Omitted Variable Bias?

Fixed effects are variables that are **constant across individuals**. These models remove omitted variable bias by measuring changes within groups across time, usually by including dummy variables for the missing or unknown characteristics.

In research, one way to control for differences between subjects is to randomly assign the participants to treatment groups and control groups. For example, one difference could be age, but by randomly assigning participants you control for age across groups. Sometimes, it’s difficult or impossible to randomly assign participants, so these variables (like age) must be measured instead. Ultimately, it’s not possible to control for *all *possible variables and research results can be contaminated with these hidden variables. This contamination of results is called **omitted variable bias**.

Some variables, like age, sex, or ethnicity, don’t change or change at a constant rate over time. These variables have fixed effects. Other variables are random and unpredictable. In a fixed effects model, these random variables are treated as though they were non random, or fixed.

Fixed effects models do have some **limitations**. For example, they can’t control for variables that vary over time (like income level or employment status). However, these variables can be included in the model by including dummy variables for time or space units. This may seem like a good idea, but the more dummy variables you introduce, the more the “noise” in the model is controlled for; this could lead to over-dampening the model, reducing the useful as well as the useless information.

## On Different Definitions

The definition above seems to be the most common, and it’s the one used by Kreft and De Leew (1998). But — like the word “average” — there are many different definitions, depending on who you are talking to. An economist might refer to “fixed effects” one way, a bio-statistician another way. Textbook authors vary in their treatment of the subject (like LaMotte (1983)) who states ” “If an effect is assumed to be a realized value of a random variable, it is called a random effect.” The debate about who is right (or wrong) is beyond the scope of this site, but if you want to read about it, hop over to Andrew Gelman’s blog.

**References**:

Kreft, I., and De Leeuw, J. (1998). {\em Introducing Multilevel Modeling}. London: Sage.

LaMotte, L. R. (1983). Fixed-, random-, and mixed-effects models. In {\em Encyclopedia of Statistical Sciences}, ed.\ S. Kotz, N. L. Johnson, and C. B. Read, {\bf 3}, 137–141.