Review Question for No Endogeneity lecture
The review answer states that "The easiest way to detect an omitted variable bias is through the error term".
In the lecture, it mentions that "The error is correlated with the independent values" but does not elaborate on how this is done
Can someone elaborate on how this is done?
Omitted variable bias occurs when a relevant variable is left out of a statistical model. This omission can lead to a correlation between the error term and the independent variables, which can affect the accuracy of the model.
Let me break it down a bit. When you have an omitted variable, it means there's something important that you haven't included in your analysis. This missing variable could be influencing both the dependent variable (what you're trying to explain) and the independent variable(s) you've included in your model.
Now, if this omitted variable is correlated with the independent variable(s) in your model, it messes things up. The error term, which represents the difference between the actual and predicted values of the dependent variable, ends up carrying the influence of that missing variable. So, the error term becomes correlated with the independent variables, violating one of the assumptions of regression analysis.
To put it simply, if you see a correlation between your error term and your independent variables, it's a red flag. It suggests that there might be an omitted variable bias, and your model might be providing inaccurate or biased estimates. That's why keeping an eye on the error term is a handy way to sniff out potential issues in your statistical model.