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I gathered my data into a panel and ran some basic regressions. Most importantly, there is a big difference between the fixed and random effects models.

I used the Hausman test, got a very low p-value, and noted that one model was inconsistent. But which one is it? I like the one with random effects more as the coefficients are closer to my expectations, but is it a good reason to choose that model? What I am looking for is some objective criteria to choose the right approach.

Mikhail
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    The choice between including an effect as fixed or random really shouldn't be based on the data. See for example here for an explanation how they differ. Very briefly, is the effect relevant for your population (for example, a male/female dichotomization assuming there's only two sexes) or is it really just a random realization in your sample that might change when you'd repeat the study (for example repeated measures within a specific subject)? – PBulls Oct 18 '23 at 04:27
  • When the estimates differ a lot, that is evidence to go for the FE estimator. Under the null being tested, both are consistent, while only FE is under the alternative – Christoph Hanck Oct 18 '23 at 07:17
  • Thank you, this is very helpful. Let's consider places A and B. Place A is further away and residents commute to work over a longer distance. In both places people use either cars or bikes, and Y = cars/bikes is higher in place A. I am concerned that this could be due to some factors other than distance, and gather the data for 5 years. I see that the distance travelled by people from both places increases over time; people from place B solve this problem by buying more bikes, whilst people from place A prefer cars. What is the relationship between X which is distance and Y in fixed effects? – Mikhail Oct 18 '23 at 21:28

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