The Blandford and K{o}nigl model of AGN jets predicts that the position of the apparent opaque jet base - the core - changes with frequency. This effect is observed with radio interferometry and is widely used to infer parameters and structure of the innermost jet regions. The position of the radio core is typically estimated by fitting a Gaussian template to the interferometric visibilities. This results in a model approximation error, i.e. a bias that can be detected and evaluated through simulations of observations with a realistic jet model. To assess the bias, we construct an artificial sample of sources based on the AGN jet model evaluated on a grid of the parameters derived from a real VLBI flux-density-limited sample and create simulated VLBI data sets at 2.3, 8.1 and 15.4 GHz. We found that the core position shifts from the true jet apex are generally overestimated. The bias is typically comparable to the core shift random error and can reach a factor of two for jets with large apparent opening angles. This observational bias depends mostly on the ratio between the true core shift and the image resolution. This implies that the magnetic field, the core radial distance and the jet speed inferred from the core shift measurements are overestimated. We present a method to account for the bias.
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