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"if the government eschews "helicopter money" forever? It ends in communism, of course, because the government will eventually own everything!"

If the CB targets a growth in NGDP less than or equal to the growth in RGDP (an average inflation rate of less than or equal to 0) we can avoid eventual communism as the real value of the government balance sheet will not increase over time. Is that correct ?

MF: I don't think that's correct. Seigniorage is still positive, and is growing with GDP.

Plus, the lower the inflation target, the lower the opportunity cost of holding 0% nominal interest currency, the larger the demand to hold that currency, and the larger the central bank's balance sheet. In the limit, as currency yields the same rate of return as all other assets, yet is more liquid that all other assets, the central bank owns everything. And since the government owns the central bank, that means communism!


I've always noticed that notwithstanding your occasional displeasure with the accounting perspective, you consistently employ the usual definition of seigniorage, which is very much a de-consolidated accounting construction.

The consolidated interpretation is one of opportunity cost, right? The seigniorage exists as a reduction in interest cost.

In that view, you can end up in the same place through a different route. Unless the government in effect spends currency demanded into existence as a deficit (i.e. helicoptering) then it must create it by acquiring private sector assets.

JKH: There are two ways of calculating seigniorage income:

1. (M/P) times the interest rate differential between central bank assets and liabilities.

2. (dM/dt)/P

If you assume that central bank money pays no interest, you should eventually get the same answer either way, but one method uses...errr....accrual(???) accounting, and the other method uses....a different form of accounting. (You explained this to me once before, but I keep forgetting the accounting terms. The first records interest income as it is earned, and the second treats the purchase of an asset as income, if it's financed with an interest-free loan. Something like that.) I mentally switch back and forth between the two methods. In an evenly growing economy, it should make no difference which way we do the accounting.

I think I am agreeing with you.

JKH: Ah! But you are talking about the distinction between consolidating or not consolidating the central bank + government balance sheets. In this case, yes, it shouldn't matter. We end up with the same result either way. Either the government spends (or cut taxes) with seigniorage, or else it buys assets (either government bonds, or something else) from private agents.

Citing Nick: "There are two ways of calculating seignorage income:

1. (M/P) times the interest rate differential between central bank assets and liabilities.

2. (dM/dt)/P.

In an evenly growing economy, it should make no difference which way we do the accounting."

Nick, this is the first time I believe you are outright wrong. Assume an efficient steady state, so r > g. Assume also (which is immaterial but makes the argument easier) that P is constant, hence i = r.

#1 yields seigniorage M/P times i.

#2 yields seigniorage M/P times g.

As i > g, seigiorage is LARGER in the first case.

"MF: I don't think that's correct. Seigniorage is still positive, and is growing with GDP."

OK, But what about the case when the CB targets NGDPT = 0? There will be deflation to match RGDP growth - and this will be reflected in the nominal interest rate. But I'm not seeing why this will cause the currency/NGDP ratio to change (beyond what happens when the new target is first adopted). (I think I can see why this would be the case if deflation exceeded RGDP growth.

Herbert, and MF: I had to think about this.

Take a simple case where NGDP growth is zero, and the nominal interest rate is positive.

Suppose I start a central bank de novo. In the first year I print M dollars, and the price level is P, so that's M/P real dollars. I print nothing in subsequent years.

#2 gives a one-shot seigniorage of M/P, and nothing thereafter.

#1 gives a constant annual flow of seigniorage of (M/P)i. But the present value of that annual flow of seigniorage is (M/P)i/i = (M/P)

So we get the same answer either way. It's just that the #2 method capitalises the future flow of seigniorage from the current real dollars printed, and the #1 method only counts the interest income as it is received.

Something like that.

Suppose the central bank were run on a break-even basis by paying interest on money, including paper money. Would the demand for money inevitably go to infinity ("communism"), or would it stabilize at some higher level?

Nick, I agree with your argument that a one-shot of seigniorage (#2) and a constant annual flow of seigniorage (#1) have the same present value.

Therefore, the two specifications lead to identical conclusions in a Ricardian model, where the time profile of seigniorage payments plays no role.

But you often argue with overlapping generations models. Here, the two specifications entail different steady state capital stocks. In a sense, the one-shot seigniorage is similar to government debt. It depresses the capital stock.

A thought-provoking, if somewhat over-complicated, post. As a former central banker, I prefer to think of seigniorage as the interest rate (strictly "return" to allow for other types of assets such as equities) pick up between a central bank's assets and its liabilities, which proceeds whether the nominal economy grows or not.

Isn't the issue simple? The difference between normal monetary policy and a helicopter drop is that in normal monetary policy, the central bank's balance sheet is always balanced. In other words, the central bank only creates money to transfer to the government to the extent that the value of its assets has been increased over and above the value of its liabilities by interest. Given a bit of capital, this leaves the central bank in independent control of the base money stock. In a helicopter drop, however, the central bank is required to create money to transfer to the government regardless, and most likely in excess of, the value of its assets. Indeed in my view, this is the defining feature of a helicopter drop - a free transfer of central bank money to the government without any asset backing - not permanence or a change in the inflation target, such as the academics like to emphasise.

Central banks have run with negative net worth at times (eg the Czech Republic and Chile), but not in situations where they might come into conflict with their government over inflation, in which case the central bank's ability to independently control the base money stock matters. I therefore agree with Tony.

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