Future changes in the stratospheric circulation may significantly impact Northern winter tropospheric climate, as polar sea level pressure (SLP) varies in association with coupled annular variability in the troposphere-stratosphere circulation. Northern winter stratospheric change and its potential to influence surface climate change are assessed in the CMIP5 multi-model ensemble.  An easterly change in zonal-mean zonal wind occurs in the polar stratosphere for the majority of CMIP5 models under global warming scenarios,. This stratospheric change varies considerably among the models, however. The respective contributions of tropical upper troposphere warming, polar amplification and the stratospheric wind change toward future SLP change are quantified using linear statistics. We find that the inter-model spread in stratospheric wind change provides a substantial contribution to the inter-model spread in Arctic SLP change. The results indicate that a proper representation of stratosphere-troposphere coupling is essential in minimizing the uncertainty in projections of future tropospheric climate change.