This study showed that using bands can increase muscle force production during the squat – especially during the second half of the positive portion. This is probably because bands add tension during the second half of the lift which forces the lower body muscles to continue producing force instead of allowing momentum to take over.
Reference: Wallace, B. J., Winchester, J. B., & Mcguigan, M. R. (2006). Effects of elastic bands on force and power characteristics during the back squat exercise. The Journal of Strength & Conditioning Research, 20(2), 268-272.