# First Difference Estimator error autocorrelation

I am struggling to get the right covariance matrix for a Fixed Effects First Difference Panel data model.

I guess that there might be some problem of error autocorrelation ,$cov(\varepsilon_t,\varepsilon_{t-1})\neq0$ so the covariance matrix is not the correct one. I haven't found out how to derive the correct Covariance matrix because if I derive $Var(\hat{\beta_D})=E[\hat{\beta_D}^2]-E[\hat{\beta_D}]^2$ I get the same result as in the question but I can't really see how to see this error autocorrelation and get the right covariance matrix.

• $cov(\epsilon_t,\epsilon_{t-1})=0$ due to the independence property contained in $\epsilon_{t} \sim i.i.d(0, \sigma_\epsilon^2)$ – rapaio Dec 2 '16 at 12:30