I am having a problem with estimation of a model using panel data in Stata. The dataset consists of 12 cross sectional units, each of these units has around 950 time periods (the panel is unbalanced). The issue is that usage of certain set of explanatory variables causes the value of "sigma_u" to be 0. Specifically, this problem arises if I add either three seasonal dummy variables or 4 weekday dummy variables to 9 other "normal" (non-dummy) variables. However, if I only use 8 of the normal variables, then the value of "sigma_u" is NOT 0 even if I add the seasonal dummy variables or the weekday ones (but not both of these groups). My question is: is "sigma_u = 0" a problem in the first place? If I undestand it corectly, RE estimation "only" degenerates to Pooled OLS - but if this happens, then there is probably something fundamentally wrong with the model's specification - maybe collinearity?
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$\begingroup$ What are "normal" variables? Can you give an example? $\endgroup$– AksakalCommented May 6, 2015 at 20:04
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$\begingroup$ Continuous variables like GDP or stock return. $\endgroup$– SkuminCommented May 6, 2015 at 20:56
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$\begingroup$ What are the "cross sectional" units? It's not something to do with 12 months? $\endgroup$– AksakalCommented May 6, 2015 at 21:06
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$\begingroup$ By "cross-sectional units" I meant number of panels, i.e. what Stata calls "Number of groups" when I run -xtreg-. $\endgroup$– SkuminCommented May 7, 2015 at 7:07
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You must be exhausting the between-panel space with your explanatory variables. I don't really know if there's any good collinearity-type diagnostics to detect that; you could try generating white noise and running a regression with that as the dependent variable to see if the issue with the regressors or with any weird patterns of variability in your dependent variable. Keep in mind that the traditional econometric asymptotics for panel data is $N \to \infty, T$ is small or fixed, and you have a flip of that.
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$\begingroup$ So, generally, if the structure of the dataset is opposite to the "traditional econometric asymptotics", i.e. $N$ is relatively small compared to $T$, is it more justified to use e.g. fixed effects? $\endgroup$– SkuminCommented May 6, 2015 at 19:50
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$\begingroup$ In the usual economic setting; when that is the case, you have no idea what is going on... The statistics have (usually) no known distribution, and things gets very complicated. $\endgroup$– RepmatCommented May 6, 2015 at 21:11