The rate regions of half- and full-duplex links using the orthogonal frequency division multiplexing (OFDM) technique are analyzed after taking into account the non-ideality of practical transceivers. The non-ideality is quantified by a measure named error vector magnitude (EVM) level in practical systems. It is approximated as a Gaussian noise added to the original signal by the transmitter. The assumed full-duplex transceiver suppresses the self-interference via a three-stage process. The stages are antenna isolation, RF cancellation, and digital baseband cancellation. The self-interference caused by the EVM noise and the original signal are suppressed differently in the three-stage process. The optimal power allocation algorithms are developed to maximize the rates of the half- and full-duplex OFDM links under two different strategies. The first one aims at a low complexity design, where each node uniformly allocates the power over sub-carriers, whereas the second one adaptively allocates the power over sub-carriers to achieve the largest rate. Using the developed algorithms, the achieved rate regions under frequency-flat and frequency-selective environments are compared.