# ch14 - Fixed Effects Estimation When there is an observed...

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Economics 20 - Prof. Anderson 1 Fixed Effects Estimation When there is an observed fixed effect, an alternative to first differences is fixed effects estimation Consider the average over time of y it = β 1 x it1 +…+ β k x itk + a i + u it The average of a i will be a i , so if you subtract the mean, a i will be differenced out just as when doing first differences
Economics 20 - Prof. Anderson 2 Fixed Effects Estimation (cont) If we were to do this estimation by hand, we’d need to be careful because we’d think that df = NT – k , but really is N(T – 1 ) – k because we used up df s calculating means Luckily, Stata (and most other packages) will do fixed effects estimation for you This method is also identical to including a separate intercept or every individual
Economics 20 - Prof. Anderson 3 First Differences vs Fixed Effects First Differences and Fixed Effects will be exactly the same when T = 2 For T > 2, the two methods are different Probably see fixed effects estimation more

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