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Provided that the specification is right, will these two different ways of removing the cross sectional bias result in the exactly same result (contrasting to first difference which will result in different coefficients)? Here is how I have defined the terms, just to be clear:

Fixed effects with demeaning = demean variables and run regression on the demeaned data to calculate the coefficient.

LSDV = Create dummy variables for each cross section except for one and run the regression to calculate the coefficient.

Tony
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    Yes, the coefficients are the same (but the standard errors using the demeaning approach need to be adjusted). See this Stata note that shows the equivalence. – Andy W Mar 05 '15 at 12:52
  • @AndyW does this apply to VAR models as well? I tried it and so far I am getting a different result. IE. I transformed the variables in a panel and ran a normal unrestricted VAR and got a different result than a pvar package claiming to use the same method. All overlapping lags from one cross section to the next were removed. Is there something extra that needs to be done? – Tony Mar 05 '15 at 16:41
  • Generally for more complicated models it is possible to see differences. It isn't clear to me how you can estimate a VAR using the fixed effects approach (fixed effects and lags in dynamic panel models don't really go together). Maybe try some simpler reduced form equations to see if you can fit equivalent models. – Andy W Mar 05 '15 at 17:03
  • @AndyW Do you know if the relationship holds if OLS is employed though? I was under the impression that VARs are often estimated by taking the first differences, demeaning, using the LSDV method or taking the Helmert transform on panel data and then running regular VAR with some sort of GMM (that maybe the reason for different result - I am using OLS). – Tony Mar 05 '15 at 19:42

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