A quick addendum to the previous post; I tried using M1 in the interest rate model, but it didn't work. However, it didn't work in an interesting way:
The vertical line represents the point where NOW accounts were introduced nationally in 1981 (here is the NY Fed and here is the NY Times), which should represent a big influx of money (and thus lower interest rates in the model since it depends on NGDP/M1). Starting in the 1990s, M1 is significantly lower than interest rates would suggest (if the model was correct). Maybe this has something to do with the reserve requirements on M2 components dropping to zero (which I learned from Tom Brown in comments), making banking products that are part of M2 more attractive than those that are part of M1 -- hence moving money out of being measured by the M1 aggregate and into being measured by the M2 aggregate.