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Those deviations from the normal look like they are largely driven by a few outliers. See what happens when you trim those, and look closely at them to see whether they belong in your model in the first place. They may have high leverage and thereby drive your estimates. If you know why they are what they are, and have data on the mechanism, you should ...

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One solution would be to create a location variable that has four levels: Urban-urban, urban-rural, rural-urban and rural-rural. Then this would only get an i subscript.

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Building upon Arne's answer, there's a very interesting paper by Bell/Jones (2012), mentioned in this post Panel regression: what to do when Hausman test fails and want to keep time invariant regressors?. They argue in favor of an RE model to capture both within and between variance by 'Within-Between transformation', essentially building upon Mundlak ...

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You can account for certain unobserved heterogeneity in panel, called correlated random effects, if you are willing to make certain assumptions about the correlation of the unobserved heterogeneity with the observed regressors. Let us say $y_{it}$ is your outcome of interest (perhaps a binary variable), $X_{it}$ are observable individual characteristics, ...

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