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I am trying to familiarise myself with panel regression techniques and I would like to know how the parameter estimates obtained from a panel regression model differ from those obtained from multiple time series regressions. Are they ever the same under specific assumptions?

Constantin
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(I'm not an expert in time series methods, so take this with a grain of salt.) But if you fit a number of series separately, it should be like fitting fixed effects in a larger model. Whereas panel regression would have a random effect distribution that would 'borrow' information from other series to inform what a given series is doing. If we set the time series aspect aside, I cover these ideas in more detail in my answer here: Why do the estimated values from a Best Linear Unbiased Predictor (BLUP) differ from a Best Linear Unbiased Estimator (BLUE)?

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gung - Reinstate Monica
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