# Do the results show an omitted variable bias? How sizeable is the bias?

The question is more involved on how to calculate the omitted variable bias. We were given data and are supposed to use SAS to run regression models. First, how do you know if results suggests there was an omitted variable bias? Second, how do you estimate the different components of

Bias($\tilde{\beta_{1}}$)=$E(\hat{\beta_{1}})-\beta_{1}=\beta_{2} \tilde{\delta_{1}}$

since you don't know the true values of $\beta_{1}$ and $\beta_{2}$?

• Is the omitted variable unknown or do you have a candidate in mind? – Dimitriy V. Masterov Mar 26 '13 at 0:57

## 2 Answers

If you have data on an outcome and data on a response, only, you cannot determine the presence or magnitude of omitted variables bias numerically. For an analytical treatment of omitted variables bias, try Angrist & Pishke, Mostly Harmless Econometrics.

Detecting missing variables in full generality is impossible. However, something you can do is plot residuals. Specifically, you could try to plot $y_i - \hat{y}_i$ against each predictor $x_i$. If you observe any patterns (e.g. the residuals look U-shaped), then you are missing some predictors. If you do not observe any patterns, then you may or may not have omitted variables, but at least you can feel good about having looked for them!