In the recent monthly bulletin of the German Bundesbank, researchers present and discuss the modelling and the use of Dynamic Stoachstic Equilibrium Models for Germany. One estimation and simulation result of this model is presented in the following figure.
It shows dynamic responses (back to equilibrium) of key macro variables to an oil price shock. In particular, the Bundesbank identifies that an oil price shock delivers a transitory negative effect on potential production (since the model works with constant steady state values, this effect is only temporary). In addition, the more world-demand-driven oil price shocks tend to be, the less severe the impact on domestic real production tends to appear. However, it implies that a domestic reduction of aggregate demand will not trigger price dynamic moderations if oil price shocks are demand driven rather than supply-driven due to supply shortages.