|Shhh...I told you *nothing!*
Let's start with something that most people find uncontroversial, the Fisher equation:
[FE] R(t) = r(t) + Π (t+1)
where R is the gross nominal interest rate, r is the gross real interest rate, an Π is the expected gross inflation rate (all variables logged).
I like to think of the Fisher equation as a no-abitrage condition, where r represents the real rate of return on (say) a Treasury Inflation Protected Security (TIPS) and (R - Π) represents the expected real rate of return on a nominal Treasury. If the two securities share similar risk and liquidity characteristics, then we'd expected the Fisher equation to hold. If it did not hold, a nimble bond trader would be able to make riskless profits. Nobody believes that such opportunities exist for any measurable length of time.
Let me assume that the real interest rate is fixed (the gist of the argument holds even if we relax this assumption). In this case, the Fisher equation tells us that higher nominal interest rates must be associated with higher inflation expectations (and ultimately, higher inflation, if expectations are rational). But association is not the same thing as causation. And the root of the controversy seems to lie in the causal assumptions embedded in the Neo-Fisherite view.
The conventional (Monetarist) view is that (for a "stable" demand for real money balances), an increase in the money growth rate leads to an increase in inflation expectations, which leads bond holders to demand a higher nominal interest rate as compensation for the inflation tax. The unconventional (Neo-Fisherite) view is that lowering the nominal interest leads to...well, it leads to...a lower inflation rate...because that's what the Fisher equation tells us. Hmm, no kidding?
The lack of a good explanation for the economics underlying the causal link between R and Π is what leads commentators like Nick Rowe to tear at his beard. But the lack of clarity on this dimension by a some writers does not mean that a good explanation cannot be found. And indeed, I think Nick gets it just about right here. The reconciliation I seek is based on what Eric Leeper has labeled a dirty little secret; namely, that "for monetary policy to successfully control inflation, fiscal policy must behave in a particular, circumscribed manner." (Pg. 14. Leeper goes on to note that both Milton Friedman and James Tobin were explicit about this necessity.)
The starting point for answering the question of how a policy affects the economy is to be very clear what one means by policy. Most people do not get this very important point: a policy is not just an action, it is a set of rules. And because monetary and fiscal policy are tied together through a consolidated government budget constraint, a monetary policy is not completely specified without a corresponding (and consistent) fiscal policy.
When Monetarists claim that increasing the rate of money growth leads to inflation, they assert that this will be so regardless of how the fiscal authority behaves. Implicitly, the fiscal authority is assumed to (passively) follow a set of rules: i.e., use the new money to cut taxes (via helicopter drops), finance government spending, or pay interest on money. It really doesn't matter which. (For some push back on this view, see Price Stability: Is a Tough Central Banker Enough? by Lawrence Christiano and Terry Fitzgerald.)
When Neo-Fisherites claim that increasing the nominal interest rate leads to inflation, the fiscal authority is also implicitly assumed to follow a specific set of rules that passively adjust to be consistent with the central bank's policy. At the end of the day, the fiscal authority must increase the rate of growth of its nominal debt (for a strictly positive nominal interest rate and a constant money-to-bond ratio, the supply of money must be rising at this same rate.) At the same time, this higher rate of debt-issue is used to finance a higher primary budget deficit (just think helicopter drops again).
Well, putting things this way makes it seem like there's no substantive difference between the two views. Personally, I think this is more-or-less correct, and I believe that Nick Rowe might agree with me. I hestitate a bit, however, because there may be some hard-core "Neo-Wicksellians" out there that try to understand the interest rate - inflation dynamic without any reference to fiscal policy and nominal aggregates. (Not sure if this paper falls in this class, but I plan to read it soon and comment on it: The Perils of Nominal Targets, by Roc Armenter).
If the view I expressed above is correct, then it suggests that just limiting attention to (say) the dynamics of the Fed's balance sheet is not very informative without reference to the perceived stance of fiscal policy and how it interacts with monetary policy. Macroeconomists have of course known this for a long time but have, for various reasons, downplayed the interplay for stretches of time (e.g., during the Great Moderation). Maybe it's time to be explicit again. Let's help Nick keep his beard.