The study of the first harmonic mode of the neutron spectrum in a boiling water reactor (BWR) yields the capability to assess the decay ratio for the harmonic mode and anticipate the impact on the fundamental mode when an out-of-phase oscillation is about to take place. In this work, the neutron spectrum for a BWR is approximated as a linear combination of the fundamental and first harmonic modes, and these two modes are studied applying reduced order modal models. A stability estimator is constructed to monitor the development of the harmonic mode instability through the calculation of the decay ratio. To achieve an estimation of the decay ratio for each mode, the estimator requires the separation of both modes from the neutron spectrum, and a method to obtain these modes based on a bare homogeneous reactor is presented. The Reduced Order Modal Estimator is tested with computer-generated data and with data from the Ringhals Stability Benchmark.