Une belle vulgarisation. Faudrait que quelqu'un l'explique encore plus simplement à Poilievre.
Let me clatify this problem for everyone.
MV = PY is an identity. It simply states that you need enough money to cover all transactions. The theory is about how you think money M, velocity V, prices P, and output Y interact.
The intuition behind monetarism is often conveyed to undergraduates by saying that if you hold V and Y constant, then changes in M will be reflected in changes in P. That is the simplest way to say that printing money causes inflation. The problem is that this isn't the actual theory and it glances over important nuances.
For starters, in the theory behind all of this, 1/V is money demand and that thing varies over time. The grown-up version of V is constant is V is covariance stationary meaning that it fluctuates around a stable mean. That is precisely what people debated in the 80s and 90s, and more recently in the 2010s using a different way to measure money in the US (specifically, the latter research used Divisia indexes).
One reason this matters is that if money demand and money supply both increase, M rises and V falls, so there need not be a rise in prices. Intuitively, people have to use the money to bid up prices. Nothing happens if everyone sits on it.
The other reason this is important is the nature of the signal you get from variations in M to predict variations in P. What theory gives you is a long-run relationship between M, P, and Y: if V fluctuates around a stable mean, then M, P, and Y have to "grow together" and, if they break apart too much, they get pulled back in. The technical term is that M, P, and Y share a stochastic trend -- they are cointegrated. So, what the theory buys you is what we call an "error correction" mechanism that keeps everything together over long periods of time. It's not nothing. To first order and with some assumptions, it says that 2% inflation and 2% real GDP growth requires 4% money growth over the long-run. But it's not clear that it's a great signal to forecast inflation -- other things besides monetary policy moves stuff in that equation.
Now, back to policy. Monetary policy in Canada only engaged in quantitative easing during the pandemic. Otherwise, the Bank of Canada usually works by setting a short term interest rate, not by targetting changes in the money supply. So, it's hard to measure those things just for Canada, but one can try.
To do it, you have to ask yourself what happened between March 2020 and the peak of inflation in June 2022 (healine CPI peaked there year-over-year). Can you really attribute all or even most of this to unconventional monetary policy? Because there were massive fiscal expansions in both Canada and the US, lockdowns and subsequent easing of punlic health policy, disruptions in shipping, energy and commodity markets, and the Canadian labor market was extraordinarily tight for a while... Where does any of this figure in your analysis?
I am working on a project specifically on that inflation episode for the US and Canada using a model estimated before the pandemic (partly to see if "old" explanations are enough). I don't explicitly treat unconventonal monetary policy like QE and FG, but it would probably show up as demand shocks in my model. And I also have some policy counterfactuals to think about the cost of moving to hike rates earlier when inflation started rising. I'll be sharing preliminary results in two weeks at the SCSE conference in Quebec City. Feel free to follow my work and take a look later this year when we have a full working paper ready.