On the Solution of Markov-switching Rational Expectations Models

This paper describes a method for solving a class of forward-looking Markov-switching Rational Expectations models under noisy measurement, by specifying the unobservable expectations component as a general-measurable function of the observable states of the system, to be determined optimally via stochastic control and filtering theory. Solution existence is proved by setting this function to the regime-dependent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight autoregressive Markov jump state motion. As the exact expression of the conditional (rational) expectations term is derived both in finite and infinite horizon model formulations, no (asymptotic) stationarity assumptions are needed to solve forward the system, for only initial values knowledge is required. A simple sufficient condition for the mean-square stability of the obtained rational expectations equilibrium is also provided.Rational Expectations, Markov-switching dynamic systems, Dynamic programming, Time-varying Kalman filter

Extremely low-frequency spectroscopy in low-field nuclear magnetic resonance

We demonstrate a new phenomenon in nuclear magnetic resonance spectroscopy, in which nuclear spin transitions are induced by radio frequency irradiation at extremely low frequencies (of the order of a few Hz). Slow Rabi oscillations are observed between spin states of different exchange symmetry. These “forbidden” transitions are rendered weakly allowed by differential electronic shielding effects on the radio frequency field. We generate coherence between the singlet and triplet states of 15N-labeled nitrous oxide in solution, and estimate the scalar coupling between the two 15N nuclei with a precision of a few mHz