Thesis: The dissertation focuses on the interplay of monetary policy, liquidity, and inflation dynamics from an empirical and theoritical point of view. The first chapter empirically investigates the role of financial liquidity in the monetary policy history of the US Federal Reserve Bank, It combines real-time data and Markov switching models to reproduce the Fed’s information set and studies regime changes. A liquidity augmented Taylor rule fits well the US data, but its estimates also contrasts the consensus on destabilising passive policy stances: passive regimes coexists with moderate inflation after controlling for liquidity. The second chapter extends a simple NKDSGE model to account for liquid assets. The central bank sets total nominal liquidity and targets interest rates on liquid assets. Passive reactions to expected inflation do not trigger indeterminacy, but entail more persistent and volatile inflation. Moreover, passive policies slow down the recovery from a recession. The third chapter investigates how inflation persistence varied over time in the US macroeconomy. It adapts deep-learning methods besides more standard ones, to address this question, and consistently finds the inflation inertia has significantly decreased from its peak around 1995. Inflation currently behaves similarly to a memoryless white noise. Policy changes, international trade, or volatile commodities do not seem to determine such decrease, which predates all of those.