We consider a dynamic panel AR(1) model with fixed effects when both n and T are large. Under the “T fixed n large” asymptotic approximation, the ordinary least squares (OLS) or Gaussian maximum likelihood estimator (MLE) is known to be inconsistent due to the well-known incidental parameter problem. We consider an alternative asymptotic approximation where n and T grow at the same rate. It is shown that, although OLS or the MLE is asymptotically biased, a relatively simple fix to OLS or the MLE results in an asymptotically unbiased estimator. Under the assumption of Gaussian innovations, the bias-corrected MLE is shown to be asymptotically efficient by a Hajék type convolution theorem.