Methods based on psychoacoustical forward masking have been proposed to estimate the local compressive growth of the basilar membrane (BM). This results from normal outer hair cells function, which leads to level-dependent amplification of BM vibration. Psychoacoustical methods assume that cochlear processing can be isolated from the response of the overall system, that sensitivity is dominated by the tonotopic location of the probe and that the effect of forward masking is different for on- and off-characteristic frequencies (CF) maskers. In the present study, a computational model of the auditory nerve (AN) in combination with signal detection theory was used to test these assumptions. The underlying idea was that, for the BM compression to be estimated using psychoacoustics, enough information should be preserved at the level of the AN, because this forms an information bottleneck in the ascending auditory pathway. The simulated AN responses were quantified in terms of rate and synchrony for different types of AN fibers and CFs. The results show that, when using a low-intensity probe, local activity at the tonotopic location of the probe frequency is the dominant contributor to sensitivity in the healthy auditory system. However, on- and off-CF maskers produced similar forward masking onto the probe, which was mainly encoded by high- and to little extent by medium-spontaneous rate fibers. The simulation results suggested that the estimate of compression based on the behavioral experiments cannot be derived from sensitivity at the level of the AN but may require additional contributions, supporting previous physiological studies.