This Monte Carlo study compares the performance of a recently proposed multiprocess mixture model and a more traditional random walk time-varying parameter model in the face of structural shifts and outliers. The mixture model performs well and the latter model performs poorly. This finding is of general interest since investigators often adopt random-walk time-varying parameter models to accommodate potential regime shifts in regression relationships. The findings suggest that the time-varying parameter estimation procedure is unlikely to find abrupt shifts, since the time-varying parameter estimates are contaminated by the outliers and regime shifts.