The weighted least squares (WLS) estimator is commonly employed to solve the state estimation problem in today's power systems, which are primarily measured by SCADA measurements, including bus power injection, branch power flow and bus voltage magnitude measurements. Despite being widely used, WLS estimator remains to be non-robust, i.e., it fails in the presence of bad measurements. The so called least absolute value (LAV) estimator is more robust, but is not widely used due to its higher computational cost. LAV estimator has the desirable property of automatic bad-data rejection provided that the measurement set does not include any "leverage measurements."There will be two important advantages to using LAV estimator when systems are observed by phasor measurements: 1) if the measurement set consists of only phasors, the leveraging effect of measurements can be easily eliminated by strategic scaling; 2) computational performance of LAV estimator will become competitive with that of WLS due to the linearity of the estimation problem for phasor measurements. This paper demonstrates these advantages and argues that the LAV estimator will be a statistically robust and computationally competitive estimator for those power systems that will be measured entirely by PMUs.