In this paper, we analyze the error rate degradation caused by the finite-precision extrinsic log-likelihood ratio (LLR), i.e., demapper output, for multiple-input multiple-output (MIMO) bit-interleaved coded modulation with iterative decoding (BICM-ID). A closed-form expression for the probability density function (pdf) of the metric difference with finite precision is derived. This pdf is well-approximated by two approaches, namely the pseudo quantization noise (PQN) model and the pdf tail truncation. Moreover, we interpret such performance degradation as an additional signal-to-noise ratio (SNR) loss. As validated by Monte Carlo simulations, this SNR loss can be directly applied at the first iteration, extending our analysis to non-iterative scenario. This work provides a convenient indicator for deciding the LLR precision in real implementations.