# Can we use pooled ols on dynamic panel without individual fixed effect (but with group fixed effects) and no serial correlation in error

Is it correct that dynamic panel without individual fixed effect (but with group fixed effects), no serial correlation in error can be estimated consistently through pooled ols?

For example, suppose we have $$y_{it} = \rho y_{it-1} + \beta x_{it}+v_g+\epsilon_{it}$$ where $$E(x_{it}\epsilon_{it})=0$$ and $$E(y_{it-1}\epsilon_{it})=0$$.

Do we need to use Arellano and Bond's GMM method in the above case?

• Is $y_{it}$ on the right-hand side a lag of your outcome? – Thomas Bilach Jul 25 '20 at 16:46
• @ThomasBilach It's a typo. I have corrected it. – chuck Jul 25 '20 at 16:47