Cosmic ray (CR) modulation is driven by both solar activity and drift effects in the heliosphere, although their role is only qualitatively understood as it is difficult to connect the CR variations to their sources. In order to address this problem, the Empirical Mode Decomposition technique has been applied to the CR intensity, recorded by three neutron monitors at different rigidities (Climax, Rome, and Huancayo-Haleakala (HH)), the sunspot area, as a proxy for solar activity, the heliospheric magnetic field magnitude, directly related to CR propagation, and the tilt angle (TA) of the heliospheric current sheet (HCS), which characterizes drift effects on CRs. A prominent periodicity at ∼six years is detected in all the analyzed CR data sets and it is found to be highly correlated with changes in the HCS inclination at the same timescale. In addition, this variation is found to be responsible for the main features of the CR modulation during periods of low solar activity, such as the flat (peaked) maximum in even (odd) solar cycles. The contribution of the drift effects to the global Galactic CR modulation has been estimated to be between 30% and 35%, depending on the CR particle energy. Nevertheless, the importance of the drift contribution is generally reduced in periods nearing the sunspot maximum. Finally, threshold values of ∼40 • , ∼45 • , and >55 • have been derived for the TA, critical for the CR modulation at the Climax, Rome, and HH rigidity thresholds, respectively.