What do we (not) know about the effectiveness of the monetary policy tools in the modern world?

Monetary policy played a dominant role in ensuring macroeconomic stability in the advanced economies for two decades, from the mid-1980s to 2007, and appeared to be a very effective tool for smoothing economic cycles and maintaining price stability. After the global financial crisis of 2007-2009 the effectiveness of monetary policy was put under question, since it did not succeed in ensuring rapid economic recovery in the advanced economies despite massive use of both conventional and unconventional monetary tools. The paper addresses the factors which are responsible for the weakening of the monetary policy effectiveness including global disinflation, the Phillips curve flattening, the effective lower bound problem and the neutral real rate decline. Unconventional monetary policy tools, such as the "helicopter money", targeted refinancing and other prospective tools, are analyzed. We critically assess recommendations of the Modern Monetary Theory (MMT) as the most consistent heterodox theory. Based on the analysis, we draw conclusions about the possibility of monetary policy weakening in Russia in the foreseeable future and desirability of the implementation of the hybrid fiscal-monetary measures.