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In Koop's Bayesian Econometrics, the author states that in a panel data model, where the slope is constant, but the intercept is allowed to change with the individuals being studied, if we impose:

  • Hierarchical prior on the intercept, the resulting panel data model will be equivalent to the frequentist random-effects model.
  • Non-hierarchical prior on the intercept, the resulting panel data model will be equivalent to the frequentist fixed-effects model.

What's the intuition for this?

Note: the random effects model is where the unobserved individual intercept is independent of individual explanatory variables for all observations. The fixed effects model allows the individual intercept to be correlated with the individual explanatory variables for all observations.

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    $\begingroup$ @RichardHardy Hi Richard, you're right. Is it better now? $\endgroup$ – An old man in the sea. Jan 1 at 13:24
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    $\begingroup$ Yes, thank you. $\endgroup$ – Richard Hardy Jan 1 at 13:39

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