I have a panel, and for simplicity lets say I want to find the correlation between x and y. Unfortunately, the x and the y for any given individual hardly changes throughout my panel. For example, one regressor is education and the education of an individual does not change very much.
When I use a random effect model, there is a significant relationship between x and y. The problem is, a certain test (the Hausman test) tells me I need to use fixed effects. Because the x and the y do not change over time, I do not get any significant relationship between x and y when I use fixed effects. Which is what I would expect.
Somebody mentioned that I should just average the values of x and y for all individuals for the whole time period. I guess this is what is usually done in practice. The only problem is, I have categorical data and when you take an average of categorical data the result is meaningless.
Has anybody encountered a similar problem. Can anybody point me to some method which can circumvent this? If any of this needs clarification please let me know. I can't tell you how much I would appreciate some help.
To sum up, I need to use fixed effects in a panel but people don't change over time. I want to use averages, but I have categorical data. I am hopelessly lost.
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