Satellite instruments show a cooling of global stratospheric temperatures over the whole data record (1979-2014). This cooling is not linear, and includes two descending steps in the early 1980s and mid-1990s. The 1979-1995 period is characterized by increasing concentrations of ozone depleting substances (ODS) and by the two major volcanic eruptions of El Chichón (1982) and Mount Pinatubo (1991). The 1995-present period is characterized by decreasing ODS concentrations and by the absence of major volcanic eruptions. Greenhouse gas (GHG) concentrations increase over the whole time period. In order to isolate the roles of different forcing agents in the global stratospheric temperature changes, we performed a set of AMIP-style simulations using the NASA Goddard Earth Observing System Chemistry-Climate Model (GEOSCCM). We find that in our model simulations the cooling of the stratosphere from 1979 to present is mostly driven by changes in GHG concentrations in the middle and upper stratosphere and by GHG and ODS changes in the lower stratosphere. While the cooling trend caused by increasing GHGs is roughly constant over the satellite era, changing ODS concentrations cause a significant stratospheric cooling only up to the mid-1990s, when they start to decrease because of the implementation of the Montreal Protocol. Sporadic volcanic events and the solar cycle have a distinct signature in the time series of stratospheric temperature anomalies but do not play a statistically significant role in the long-term trends from 1979 to 2014. Several factors combine to produce the step-like behavior in the stratospheric temperatures: in the lower stratosphere, the flattening starting in the mid 1990's is due to the decrease in ozone depleting substances; Mount Pinatubo and the solar cycle cause the abrupt steps through the aerosol-associated warming and the volcanically induced ozone depletion. In the middle and upper stratosphere, changes in solar irradiance are largely responsible for the step-like behavior of global temperatures anomalies, together with volcanically induced ozone depletion and water vapor increases in the post-Pinatubo years.