This represents the NGDP actual value minus the Fed guess squared, it is proportional to the liquidity cost of currency adjusting to past innovations.
It is a probability distribution.
Note that real growth is a variation about the implicate deflator, and the deflator is a lagged variable.
Under any of the inflation, output gap target systems, the Fed is guessing about what future data will hold, it is guessing across a lag. The point of NGDPLT it to let the market sort out the difference in deflator and output, the Fed just issues the currency according to contract.
In reality, pricing is ex post adjusted in the system, it is a derived quantity not an innovative quantity. Merchants set prices after they get measures of demand and supply. So all the accounting sheets have prices as current best estimate, past deviations have already entered the gain loss column. So it is a derived value that predicts the break even in supply/demand.
The Fed cannot target derived values it will loop. The Walmart checkout manager has a walkie talkie. As he changes item per basket to keep the queue properly structured, he tells the prices, in the shelves, to hold prices. And that message backs up into the stock room, and so one. It is an iterative, derived outcome, after the the fact. Treating it as an instantaneous innovation is incorrect. The instantaneous innovation is the relative congestion of clerks and customers at the constricted entry and exit point.
Look at Selgin's discussion of the loss function and see he has a three dimensional equilibrium surface. That surface is continuous, the descending path is observable everywhere. In reality, the currency banker's job is to set the axis so as to simulate that surface. It does so by enforcing a queues stability between different bids as to the direction of descent. It is executing a kind of double sided option market, making variance and trend look like a no arbitrage path, a continuously observable path. It does this by setting an interest swap whenever a better S/L ratio is observable, as soon as a descending jump is observable.
It is a dual independent queue system. The power of the currency banker is in its market making function, it has right of first observation, it runs the trading pit. The currency banker is actually comparing two Hayek triangles. A three sep prcoess. Each of the independent loan and deposit quuesmust be structured to balance tree by the market maker filling in, separately, bid in either queue. Then they are balanced Hayek triangles, filled in. The currency banker than scales the triangles by an interest swap, according to area until the currency contract is fulfilled, the ratio minimizes contract deviation. Sandbox is Hayek done right.
The result is that the Walmart manager can calculate customer transaction size compared to clerk labor costs, essentially, where all goods are transcribed into labor. Or customer transaction totaled equal department sales totaled, another form of velocity. Making the system linear is equivalent to making those 3-D charts appear path continuous, making velocity equation work.
The inherent implication of the contract
The Fed has to act as soon as the bids predict a smaller contract deviation. Consider a contract tht allows the currency banker to deviate, for some time. There is no set of satble rules that cannot be simplified to one simple rule, the market maker has to act immediately upon seeing a better contract path. This is the no arbitrage condition, a necessary condition for currency banker.
That is why I keep saying that all of the Taylor solutions cycle, they have the Fed taking a path not yet observable in the market. So, no matter your Fed rule, it is bound to be asynchronous action as needed. Betting time is out of the question, and betting rates means time is ultimately factored out anyway. Then time is re-inserted as an insurance function, not a currency function. Hence, leave it out all together at the currency function level.
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