Monetary stimulus in high-inflation regimes

In countries where inflation is high and highly variable, you would not expect that monetary policy is optimal in a social-welfare sense. After all, such inflation is a sign of political influence, and from politicians that do not have the good of the people in mind: strongly expansionary monetary policy before elections, financing government expenses with a hidden inflation tax instead of other visible taxes, and even just pocketing monetary injections. Still suppose that for some exogenous reason inflation is high and highly variable, is their still scope for optimal monetary policy (beyond working toward a long-term goal of getting this under control)?

Wojciech Charemza, Svetlana Makarova and Imran Shah claim that yes, the central bank still can do good. They claim that output can be stimulated with a monetary stimulus when inflation expectations are much higher than output-neutral inflation. The latter is obtained with a two variable VAR, and then the sign of the residuals is used to interpret asymmetric impulse responses. Like many VAR analyses, this is a little bit voodoo science, especially when you look at countries whose data records are poor if not manipulated. Of course, following this policy will not help in solving the inflation problem of these economies (defined as at least 4.8% inflation at least 25% of the time). But if expectations are much lower, then one can tighten monetary policy without big consequences. Unfortunately, a VAR cannot tell us why all this would be happening, only that there is a statistical coincidence.