Summary: A comparison among Ordinary Least Squares (OLS), Weighted Symmetric (WS), Modified Weighted Symmetric (MWS), Maximum Likelihood (ML), and our new modification for Modified Weighted Symmetric (NMWS) estimators for the first-order autoregression are studied in the case of unit roots by using Crude Birth Rate (CBR) data from 1900 to 2003 in Egypt. We found that all previous estimators lead to accept the null hypothesis of a unit root at 5\% level of significance. We also obtained the cumulative distribution of NMWS $τ$ for unit roots by using Monte Carlo methods.