The omitted variable bias is a common and serious problem in regression analysis. Generally, the problem arises if one does not consider all relevant variables in a regression. In this case, one violates the third assumption of the assumption of the classical linear regression model. The following series of blog posts explains the omitted variable bias and discusses its consequences.
In case you have never heart of the omitted variable bias before, it is a good idea to start with the introductory post. This post explains the omitted variable bias in general words and tries to be as non-technical as possible. Even if you already heart of the omitted variable bias it might still be a good idea to have a quick look at the introduction as I introduce the example that we will be using throughout the entire series.
The second post describes the nature of the omitted variables bias by the means of a Venn-Diagram. This post really tries to increase the general understanding of the bias and to provide an deeper intuition on the dynamics of the bias.
The third post continues to work on understanding of the bias. While the third post provides an understanding in more general terms, this post addresses the omitted variable bias in formal way. Using our working example, the post will detail what exactly happens to our estimates when we neglect a variable.
The fourth post elaborates the consequences of the omitted variable bias. That is, the post shows that omitting a variable form the regression model violates the third OLS assumption and discusses what will happen if this assumption is violated. Moreover, this additional post presents a simulation exercise to demonstrate what happens if we omit a relevant variable from our regression model.
By now you should know more about the consequences of the omitted variable bias. You should know that omitting a relevant variable form your regression model can cause your estimates to be biased and your standard errors to be way off. Naturally, you will ask yourself the question what you can do against the omitted variable bias. This question will be at the center of the following post. The fifth post discusses what one can do in the light of an omitted variable bias. The post presents several measures to address a potential omitted variable bias.
The last post concludes. It provides a short summary of the omitted variable bias and presents a list of questions, regarding the omitted variable bias, which one should answer before conducting a linear regression analysis.