Fixed-effects regression

If I have panel data over a long period of time, am I allowed slight variation in my “fixed” effects, or must they remain exactly constant?

For example, say I have three areas with populations of 10M, 50M, and 80M, respectively. But across a period of 20 years, the populations change, but overall trends remain the same. By the end of my data, say the populations are 23M, 56M, 90M. Do I want to take the average across all years and repeat for each area, or am I allowed slight variation over time within each area?

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Nevin Manimala

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