This paper analyzes the performance of linearly precoded time division duplex based multi-user massive MIMO downlink system under joint impacts of channel non-reciprocity (NRC) and imperfect channel state information. We consider a generic and realistic NRC model that accounts for transceiver frequency-response as well as mutual coupling mismatches at both user equipment (UE) and base station (BS) sides. The analysis covers two most prominent forms of linear precoding schemes, namely, zero-forcing (ZF) and maximum-ratio transmission (MRT), and assumes that only the statistical properties of the beamformed channel are used at the UE side to decode the received signal. Under the approximation of i.i.d. Gaussian channels, closed-form analytical expressions are derived for the effective signal to interference and noise ratios (SINRs) and the corresponding capacity lower bounds. The expressions show that, in moderate to high SNR, the additional interference caused by imperfect NRC calibration can degrade the performance of both precoders significantly. Moreover, ZF is shown to be more sensitive to NRC than MRT. Numerical evaluations with practical NRC levels indicate that this performance loss in the spectral efficiency can be as high as 42% for ZF, whereas it is typically less than 13% for MRT. It is also shown that due to the NRC, the asymptotic large-antenna performance of both precoders saturate to an identical finite level. The derived analytical expressions provide useful tools and valuable technical insight, e.g., into calculating the NRC calibration requirements in BSs and UEs for any given specific performance targets in terms of effective SINR or the system capacity bound.