Roughly two-thirds of the observed sudden stratospheric warming (SSW) events are followed by an equatorward shift of the tropospheric jet in the North Atlantic, while the other events generally show a poleward shift. It is however not resolved which drivers lead to the large inter-event variability in the surface impact. Using an intermediate complexity atmospheric model, we analyze the contribution of different factors to the downward response: polar cap geopotential height anomalies in the lower stratosphere, downstream influence from the northeastern Pacific, and local tropospheric conditions in the North Atlantic at the time of the initial response. As in reanalysis, an equatorward shift of the North Atlantic jet is found to occur for two-thirds of SSWs in the model. We find that around 40% of the variance of the tropospheric jet response after SSW events can be explained by the lower stratosphere geopotential height anomalies, while around 25% can be explained by zonal wind anomalies over the northeastern Pacific region. Local Atlantic condi- tions at the time of the SSW onset are also found to contribute to the surface response. To isolate the role of the strato- sphere from tropospheric variability, we use model experiments where the zonal mean stratospheric winds are nudged toward climatology. When stratospheric variability is suppressed, the Pacific influence is found to be weaker. These findings shed light on the contribution of the stratosphere to the diverse downward impacts of SSW events, and may help to im- prove the predictability of tropospheric jet variability in the North Atlantic.