A bit of cheating Scott Sumners

It’s still true that a permanent, exogenous, one-time doubling of the monetary base will cause the price level and NGDP to double in the long run.

In the long run means we will eventually get an ex post view of the entire economy. That is the relativity error.

To predict the long run you need to predict the behavior of stopping points along the way. There is nothing in your philosophies of NGDP targeting that gets us to the definition of permanent, not in a double entry accounting system. You need a change in procedure to get anything permanent, and even then the new procedure carries a renewal limiting your ability to see a smooth long run. You are trying to invent the ergodic model then insert uncertainty. You mention your own flaw in 'exogenous', that means unhedged in the banking system.  The currency banker cannot create hedges.

Then what is the long run? It is what comes after we invent an exogenous possibility by assigning devaluation rates to the original party, let Treasury worry about long run, direct inflation. Treasury has that right, the right to coin, they are in charge of expanding money supply. Then the central banker can target NGDP all it wants, under zero mean price volatility, if it wants. 

To be exogenous the event must be unexpected.  In the normal automated S/L, the borrowers and depositors reveal their own exogenous bets to each other, the pit boss is flow neutral on the loss/gain market account. These depositors and borrowers are intended to be distribution matched, ex post, as soon as the currency banker sees any skew. 

The central banker is what it is because its main borrowers are Treasury, and its main depositors are member banks with restricted entry and exit.  Under those condition, the Fed is mostly targeting the solvency of government bonds.

But you know this Scott, it is slightly hiding under your occasional sarcasm. Your long run will happen, as you expect, but it takes a lot of turbulent Coasian negotiating in the Senate among folks who are mostly dim bulbs. And it is not a certainty that we can figure this out. So your long run could include a huge, overnight and sudden devaluation among panicked senators. That would be like making a one time, 6 trillion NGDP bet for fifty years out.

My plan targets the New Fed contract renewal, it estimates the amount of devaluation we might get from Treasury when we renew the current devaluation contract, in about 15 years. Otherwise, direct NGDP injections are the business of the Senate and Treasury, and you should know all this Scott.