What type of graph can be hepful to explain the type of errors that should be used?

Question

I have a regression of wage on several variables, such as education, marriage and so on. I want to explain that it would be a better idea to use cluster errors, since we expect the wage to be correlated with abilities for each person, but I want to do so using a graph, what graph would you recommend me to use and why? When you have one regressor it is obvious, but here how to decide what variables to plot?

Since I am using stata I would appreciate if you could help me with an example of the code for the graph.

Answer 1

You are saying: $y$ is regressed on $x_1$ and $x_2$, say, and you think it would be better to use cluster errors since you expect $y$ is correlated with abilities for each person.

First, $y$ is naturally correlated with the error term $u$ (if you mean the error term by "abilities") because $u$ is a part of $y$. You have no problems with that; $y$ is always strongly correlated with $u$. It also has nothing to do with cluster errors.

If you happen to mean cluster standard errors (SE) by "cluster errors", and if you are saying that you would use cluster SE because $x_1$ is correlated with $u$, I would say that the regressor-error correlation (endogeneity) has nothing to do with cluster SE, what so ever. Cluster SE provides valid inference when the the error term show within-cluster (auto)correlation.

Please enlighten me if I misinterpreted your question.