To achieve a higher inflation target of 4% the central bank has to stimulate harder than to achieve a 2% target. This entails a higher growth rate of the MB and higher demand for bonds by the central bank. Therefore credit is stimulated to a greater degree than under a lower inflation target while achieving the same level of real GDP growth.
Greater credit stimulus grows the financial sector and speculation more which generates more volatility and therefore you hit the ZLB more often. So on the one hand a higher inflation target means the central bank has more room to move should rates need to decline but on the other hand it is contributing to what creates volatile business cycles to a greater extent.