Tony Yates is arguing with Willem Buiter about helicopter money. Willem says that helicopter money increases aggregate demand even in a liquidity trap, because helicopter money increases net wealth, because money is irredeemable. Tony says that if money is irredeemable, the existence of an equilibrium in which intrinsically worthless money has positive value becomes problematic. And if money is redeemable, and is therefore a liability of the government, it is not net wealth.
I am going to use Tony's argument for my own ends. It helps me illustrate my own argument that what matters is the monetary policy target. "Helicopter money" with no change in the monetary policy target is not like helicopter money with a change in the target. Willem Buiter does not need to assume irredeemable money. But he does need to assume that helicopter money is accompanied by a change in the monetary policy target.
And by changing the monetary policy target the central bank can convert some of the existing money into helicopter money. It doesn't even need the helicopter.
Let us suppose, with Tony, that the government will eventually redeem all the money it has issued in the past, for real goods, and will re-start the monetary system anew.
Specifically, in the year 2525 the government will redeem all the money at a price Pm, so every $1 will be redeemed for Pm units of real goods, and people know this in 2014. What this also means is that the price of real goods in terms of money, at the beginning of 2525, will be 1/Pm, and people know this in 2014 too.
Now suppose that in 2014 the government doubles the supply of base money, by helicopter, and at the same time halves the 2525 redemption price Pm. The net result of doubling M and halving Pm is that real government liabilities MPm are unchanged. At the previously existing price level for 2014, the real value of the stock of money is doubled by the helicopter drop, and net wealth is increased. We get Willem Buiter's result, that helicopter money increases net wealth at the previously existing price level, without needing to make Willem's assumption, that money is irredeemable.
If we remember that 2x0=0, and the stock of dollars will be zero after 2525 (they will give the new money a new name), we can see that my thought-experiment is compatible with a permanent doubling of the dollar money supply, relative to what it would otherwise have been.
We also know that the halving of Pm in 2525 will double the price level in 2525. Which in turn will increase the price level in 2524 relative to what it would have been. Because if the 2524 price level were to remain unchanged, the expected inflation rate in 2524 would increase by 100%[percentage points], which would cause upward pressure on the price level in 2524. And so on, by backwards induction, all the way back to 2014.
Halving Pm in 2525 is like doubling the target price level for 2525. But there is nothing special about the year 2525. We could suppose that the central bank has a target price level P*(t) for every year between 2014 and 2525. And when it doubles the money supply by helicopter drop, it also doubles P*(t) for all t between 2014 and 2525. Doing this ensures that the helicopter drop is compatible with a permanent doubling of the money supply.
"Helicopter money", with no change in the price level target P*(t), will eventually need to be redeemed, at some future time, to prevent the future price level rising above the future target.
And it doesn't need to be a price level path target. It could be an NGDP level path target instead, or any nominal variable.
What makes helicopter money truly helicopter money -- a permanent increase in the money supply that does not imply increased tax liabilities or future government spending cuts -- is the announced increase in the price level target or NGDP level path target that accompanies the helicopter. "Helicopter money" with no change in the target is not like Willem Buiter's helicopter money, because that extra "helicopter money" will need to be redeemed at some (unknown) time in the future, at the same future price level as before, and so the "helicopter" increases the real value of government liabilities.
Furthermore, if the central bank announces an increase in the NGDP level path target, that reduces the real value of government liabilities, and this converts some of the previously existing money into helicopter money ex post facto. You don't need the helicopter. If the government halves Pm, it converts half the money that already exists into helicopter money.
When Willem Buiter is talking about helicopter money he is really talking about a permanent increase in the NGDP level path target.