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Wooldridge Test and Serial Correlation Question

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Hello,

I have TSCS data set (11 groups, 6 years each) and I am using a random effects OLS model with a discrete dependent variable. I have a time variable measuring the number of years since each group's last conflict. I know that when you have binary dependent variables, you can use a cubic spline or include squared and cubic transformations to account for serial correlation of the time variable. However, I am not sure what is the preferred method for a model with a discrete dependent variable? Is it a GLS model, or in this case xtgls? Perhaps more importantly, the Wooldridge test reveals no significant first-order autocorrelation in my model, so do I even need to worry about this?

Thank you!!

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