Random or fixed?

[Petra]

Hi,

I am new to stata and have trouble with specifying my model. I have panel data for appr 11000 individuals and 3 years. My dependent variable is bivariate (but could be made into an ordered discrete variable with 3 values). I am now trying to choose between fixed and random effects. The Hausman test rejects the null hypothesis of non-systematic difference, so I guess that means I should use fixed. However, as I have understood it, running a fixed effect regression would disregard all individuals that show the same value all three years for any variable. Considering I do not have much variation in my dependent variable, isn't random effects to prefer so that I won't lose too many observations? If I use random effects, how do I motivate this? I have read that one could use "individual random effects" (e.g. Ferrer-i-Carbonel, 2005) and that this would be something "in between" fixed and random effects, where one can choose what independent variables that the error term is allowed to correlate with. Has anyone used this and what are your experiences with this? Moreover, would it be better to define my dependent variable as a 3-value ordered discrete variable in order to have more variation (still not much though)?

Thanks!

[Alfonso Sánchez-Peñalver]

Hola Petra,

I believe you may have misunderstood the implication of fixed effects with respect to what is included in the estimation or not. It's correct that if you specify fixed effects you cannot account for the effect of variables that just vary across individuals, and not years, but that just means that you cannot include those variables as explanatory variables, not that you lose observations. The problem, then, is that all the effects of those variables are captured by the fixed effects, and you cannot discern what specific effect each of those variables have. If you didn't have variability of the dependent variable across years, fixed effects would yield insignificant coefficients because it only measures the within variation, so that is not a problem in your case.

Having said that, I would do estimation of both and present results from both. This allows you to talk about the effects of those time invariant variables. You can then refer to the Hausman test to indicate that fixed effects are preferred because they are consistent, which random effects estimates are not. I am not familiar with what individual random effects are and how they differ from regular random effects, so I cannot comment on that. Finally, I believe that your thought of defining the dependent variable into a 3-value ordered discrete variable had to do with your confusion I addressed before. The only reason you ought to consider changing the variable should come from what you want to analyze.

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