I regularly hear that our expedition into the lands of quantitative easing and monetization will inevitably cause a rise in the dollar value of goods and services. That makes a lot of sense intuitively: more dollars chasing fewer things. It's certainly true in extremis. But outside of that extreme, there's a wide variety in behavior.
Multiple authors have found that for US data series prior to 1961, there is, as expected, a strong positive correlation between M2 growth and inflation. But after that, the relationship broke down, and an even stronger negative correlation emerged.
This breakdown makes little sense with money supply held as an independent variable. We would expect more money to consistently lead to higher prices modulo GDP growth, by definition, but the opposite has clearly happened for half a century.
A strong inverse correlation is still correlation, so there's probably a good reason.
Perhaps we could invert the causality to make money supply a function of the inflation rate, and hence nominal interest rates. A fall in interest rates would lead to a rise in credit outstanding as entities sought to maintain financial obligation ratios. This would make sense in a world with a great deal of callable debt, e.g. mortgages.
This could also be a result of financial deepening and counter-cyclical monetary policy. Agents would seek to lever up when inflation and interest rates are low, typically during recessions, anticipating future rises. During a boom, higher inflation and interest rates deter borrowing in anticipation of rate cuts later.
These ideas are just stabs into a nebulous dark thus far, and I'd appreciate reader thoughts.
Does forcible money creation exhibit a different relationship? Theoretically, to the extent that people believe quantitative easing will cause inflation during a liquidity trap, it could. In practice, the inverse relationship seems to linger. We might also see the inverse relationship persist, or suffer a strong snap back to monetaristic normalcy. As M2 growth rates stab to new highs, the response in inflation and interest rates is unpredictable.