Estimation of the input parameters of the stochastic (leaky) integrate-and-fire neuronal models is studied. It is shown that the presence of the firing threshold brings a systematic error to the estimation procedure. The analytical formulae of the bias are given for two, the randomized random walk and the perfect integrator, models. For the leaky integrate-and-fire model the study is performed by using Monte-Carlo simulated trajectories. The bias is compared with other errors appearing during the estimation and it is documented that the effect of the bias has to be taken into account in the experimental studies.