This paper introduces a model that addresses the key worldwide features of modern monetary policy making: the discreteness of policy interest rates both in magnitude and in timing, the preponderance of status quo decisions, monetary policy inertia and policy regime switching. We capture them by developing a new dynamic ordered-choice model with switching among three latent policy regimes (easing, neutral and tightening). The simulations and an application to the federal funds rate target demonstrate that ignoring these features leads to biased estimates, worse in- and out-of-sample predictions, and a qualitatively different inference. Using all Federal Open Market Committee’s (FOMC) decisions made both at scheduled and unscheduled meetings as sample observations, we model the Federal Reserve’s response to real-time data available right before each meeting. The new model, fitted for the Greenspan’s tenure, detects oscillating switches among latent regimes, identifies three types of status quo decisions, correctly predicts out of sample 90% of the next 111 FOMC decisions on the target rate, and clearly outperforms the linear models (including the Taylor rule), the conventional ordered probit and other discrete-choice models from the literature.