Think globally, fit locally?

I made an offhand comment a few minutes ago about the information transfer model being a local approximation. In particular Canada and the US seem to show different segments of their economic history can be modeled by two or three separate fits. In the older posts I (rather impetuously) interpreted these changes as phase transitions or monetary policy shifts.

It is possible that the model represents a local approximation which are dislodged by extreme events such as inflation in Canada in the 1980s or the Great Depression in the US. The interest rate model for the US does appear to work really well across the entire domain 1920s to today so I don't want to give it up just because there seem to be some issues with Canada. Recall that the US model has two or three domains for the price level, not the interest rate. Essentially this is what gives me the idea that the quantity theory and the IS-LM model represent two different approximations to the same underlying model where the former is more accurate than the latter when the base is small relative to GDP, inflation is high but less accurate when the base is large and inflation is low.