"Tight money leads to lower expected future NGDP growth. I don’t think that can be disputed."
No, Scott, it really can't be disputed ... because you define "tight" money by lower future expected NGDP growth.
Coupled with my post on Wicksell earlier this week, Sumner's post made me think a bit about what I'll call the unobservables: a collection of macroeconomic properties that cannot be directly measured. This list is not meant to be exhaustive, but here are some key ones :
- The natural rate of interest
- The natural rate of unemployment/NAIRU
- The "stance" of monetary policy
- Inflation expectations
- The velocity of money
What do these all have in common? They're all directly linked to an observable: inflation. Scott Sumner does mix it up a bit by keying in on NGDP growth (= inflation + RGDP growth). So the unobservables are all linked to a specific mechanism of (accelerating) inflation:
- Interest rates too low (price of money too low)
- Unemployment too low (wage-price spiral)
- Expansionary monetary policy (supply and demand for money)
- Agents expect inflation (rational expectations, adaptive expectations)
- Money supply increases (at constant velocity)
This leaves out a couple of additional mechanisms like supply shocks (which aren't monetary policy and thus considered more "real") and the neo-Fisherite view that high interest rates lead to inflation (via a specific expectations mechanism). But essentially we have a list of ideas people had about what causes inflation combined with an unobservable factor that determines how/when the mechanism works. Here's a generic way of putting this:
We get a fire when temperature is above the natural temperature of phlogiston.How do we determine the natural temperature of phlogiston? We observe a fire.
That's how you get falling estimates of the natural rate of interest [pdf] or unemployment, or falling velocity. And that's how you get Scott Sumner calling monetary policy "tight" since the 2008 recession. I don't mean to say that is hasn't been "tight", just that "tight" is kind of a circular definition.
Of all of the mechanism/unobservable combinations above, only one rises a bit above the circular phlogiston example. That is inflation expectations -- purportedly measured by TIPS spreads (the difference between the interest rate on a regular treasury bond and its inflation-protected cousin). But the problem is that inflation expectations measured by TIPS spreads seem to be entirely backward looking (or see here) or at least strongly dependent on previous inflation when inflation isn't high (see e.g. here H/T Mark Thoma). The only unobservable that has at least a theoretical way to measure it turns out to get it wrong. So either inflation expectations don't have a strong effect on inflation or things like TIPS spreads don't measure inflation expectations correctly.
And really, when you're comparing your measure of inflation expectations to actual inflation to see how much of an impact inflation expectations had, you've basically started to measure the temperature of phlogiston.
Now don't get me wrong: I'm not against the idea of an unobservable! As a physicist, I've frequently used an unobservable: the wavefunction in quantum mechanics. However, you do not figure out what the wavefunction is by measuring an interference pattern and taking its square root. There is a very specific model for calculating the wavefunction (e.g. the Schrodinger equation).
And that's the issue with the macroeconomic unobservables. Most of the time there's no way to calculate them besides using the data you're trying to explain, and when you can calculate them, they turn out to be wrong (inflation expectations are backwards looking, money velocity isn't constant).
I like to think of the information transfer model as the analog of the Schrodinger equation for velocity. But really, it's the Schrodinger equation for all of these unobservables since it tells you what inflation and NGDP are going to be. "Tight" money is when interest rates are above the information equilibrium value, or when the economy is above the NGDP-M0 path (see here). The best measure of the natural rate of interest is the information equilibrium value. The best measure of the natural rate of unemployment can be calculated. Velocity is κP (though I like Cambridge k more). And κ is a measure of the relative information in a symbol of output (proportional to the log of output) to a symbol of money (proportional to the log of the amount of cash). Or (probably more accurately), the inverse of the ensemble average of all of the individual market relative growth rate factors a.
 I left out total factor productivity because I'm focusing on monetary policy.