Sumner's Monetary Theory--Long and Variable Leads

Scott Sumner argues that monetary policy operates with long and variable leads.   However, his reform proposal, index futures targeting, was initially developed years ago when Sumner took a more traditional approach.   Changes in the quantity of money today cause changes in spending on output and prices in the future.   How does futures targeting work?   Trading an index futures contract today, causes changes in the quantity of money today, which in turn impacts spending on output in the future.  It is that future level of spending that determines the payoffs on the futures contracts traded today.  

Suppose the central bank uses a different approach.   This quarter, quarter 1, it trades a futures contract defined on nominal GDP for  the next quarter, quarter 2.    It announces a tentative target for base money two quarters in the future, which is quarter 3.  

Depending on the trades of the future contract in quarter 1, it makes adjustments in that tentative target for base money in quarter 3.    If the market expects nominal GDP next quarter to be below target in quarter 2 and so has a short position on the contract, the Fed raises the tentative target for base money in quarter 3.   If, on the other hand, the market is long, because it expects nominal GDP to be above  target in quarter n quarter 2. the Fed lowers its tentative target for base money in quarter 3.

At the end of quarter 1, the target for base money for quarter 3 is determined.   During quarter 2, nominal GDP happens, and is measured.    Near the end of quarter 3, when the "final" results for nominal GDP in quarter 2 are calculated, and if nominal GDP deviated from its target, funds are shifted between those who traded the contract rewarding those who correctly predicted the deviation while imposing costs on those who got it wrong.  And also, during quarter 3, the central bank uses ordinary open market operations in bonds to reach the final target for base money, which was set back at the end of quarter 1.

So, in any given quarter t, contracts are being traded for nominal GDP in quarter t+1, the target for base money is being set for quarter t+2, contracts there were made during quarter t-2 are being settled according  to nominal GDP in quarter t-1, and open market operations in bonds are being made to implement the target for base money set in quarter t-2.

This system is based on Sumner's notion that nominal GDP today depends on expected nominal GDP tomorrow, and expected nominal GDP tomorrow depends on the expected quantity of money the day after. Unfortunately, the "long and variable" part of the leads suggest that today, tomorrow, and the next day, or this quarter, next quarter, and the subsequent quarter, might not be right.

I will try writing down what I think Sumner has in mind:

Nt  = f(ENt+1) = z(EBt+2)

Current nominal GDP is some function of expected nominal GDP next period which is some function of expected base money two periods into the future.

What are these functions represented by f and z?

The intuition behind the f function is that current spending will not deviate much from expected future spending.   It would relate to the permanent income hypothesis for consumption as well as some notion that current investment spending is driven by expected future sales.   However, I would think that deviations would be best represented by a random variable, and when it makes nominal GDP move away from the expected nominal GDP for next period, it is dampened in a way that depends on the interest rate.

The z function would presumably be some kind of equation of exchange.   The expectation of desired base money velocity in period 3 times the expected value of base money in period 3 determines expected nominal GDP in period 2.     Of course, that points to a equation of exchange determination of nominal GDP in period 3, which is inconsistent with the spirit of the approach outlined here.

Suppose spending on output falls below target in the current quarter.   Nothing can be done about that other than making sure that people believe that this will be temporary and spending on output will return to target next quarter.   This dampens any such deviations, though doesn't prevent them.

Why do people expect nominal GDP to be on target next quarter?   Because they believe that the Fed will create enough money the following quarter to keep nominal GDP on target next quarter.

Of course, it would seem to me that a simpler approach would be to have trades of the contract this quarter determine the quantity of base money next quarter according to expectations of nominal GDP next quarter.   However, along with any contemporaneous impact of base money next quarter on nominal GDP next quarter, there would be the indirect effect of base money in subsequent quarters impacting nominal GDP next quarter.

Anyway, I hope that this very preliminary analysis will trigger more discussion   Hopefully, Sumner will clarify his position.  (If no one else is interested in filling in model details, I guess I will keep on working on it.)