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Are Open Market Operations wrong-signed when nominal rates are negative? (No)

Summary:
I'm going to start out with a silly unrealistic thought-experiment. Then I'm going to say why I think my silly unrealistic thought-experiment might matter. A central bank issue two types of money: notes; and 0 notes. The two types of money are not perfect substitutes: the notes are convenient for small purchases; the 0 notes are convenient for large purchases. The central bank is willing to exchange notes for 0 notes at a fixed exchange rate of 100 to 1. There are no other denominations, no other banks, and no other forms of money. The notes and 0 notes pay the bearer a nominal rate of interest that is chosen daily by the central bank. Those two rates of interest can be the same or different, and can be positive or negative. Suppose the central bank sets the

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I'm going to start out with a silly unrealistic thought-experiment. Then I'm going to say why I think my silly unrealistic thought-experiment might matter.

A central bank issue two types of money: $1 notes; and $100 notes. The two types of money are not perfect substitutes: the $1 notes are convenient for small purchases; the $100 notes are convenient for large purchases. The central bank is willing to exchange $1 notes for $100 notes at a fixed exchange rate of 100 to 1. There are no other denominations, no other banks, and no other forms of money.

The $1 notes and $100 notes pay the bearer a nominal rate of interest that is chosen daily by the central bank. Those two rates of interest can be the same or different, and can be positive or negative.

  1. Suppose the central bank sets the same rate of interest on both notes. What happens if the central bank cuts that rate of interest, holding the total $ value of the stock of notes constant? That's an easy question to answer. The opportunity cost of holding money increases, so the demand for money falls, the Velocity of circulation increases so MV rises, so Aggregate Demand increases. It's an "expansionary" monetary policy. It doesn't matter whether the interest rate is positive or negative.
  2. Suppose the central bank always sets the rate of interest on $1 notes at 0%. What happens if the central bank cuts the rate of interest on $100 notes, holding the total $ value of the stock of notes constant? That's a slightly harder question to answer, but I think the answer is qualitatively the same as in the previous question above. It's still an expansionary policy, because the opportunity cost of holding money has increased, on average, so the demand for money has decreased, though it's less expansionary than the first policy. But the answer is complicated by the fact that some $100 notes will be exchanged for $1 notes, so the composition of the money supply changes, even though the total stays constant.
  3. Suppose the central bank wants to change the composition of the money supply, so there are more $1 notes and fewer $100 notes in public hands, holding the total $ value of the stock of notes constant. And it adjusts the rate of interest on $100 notes, holding constant the rate of interest on $1 notes, to hit that new target for the composition of the money supply? The answer to question 3 is the same as the answer to question 2 above. It's the same question, except the exogenous and endogenous variables have been swapped in the central bank's targeting perspective. If the central bank buys $100 notes and sells $1 notes, and adjusts the rate of interest on $100 notes so the exchange rate stays at 100 to 1, it's an expansionary policy, even though the total money stock stays the same. Because the rate of interest on $100 notes will fall.

The above thought-experiment was a metaphor. The "$1 notes" in my thought-experiment stand for all central bank money (currency and reserves). The "$100 notes" in my thought-experiment stand for Treasury bills. My policy experiment 3 above stands for an Open Market Operation where the central bank buys Treasury bills.

And if my thought-experiment metaphor is correct, Open Market Operations still have the "right" sign, even if nominal interest rates on Tbills are negative, and even if Tbills are used as money, and even if those negative nominal interest rates on Tbills indicate that Tbills are more liquid (more money-like) than the money (currency and reserves) issued by the central bank.

Which might matter again soon, if pessimistic forecasts turn out to be right.

[Liquidity Preference is a bad theory of "the" rate of interest, but a good theory of interest rate differentials (people prefer more liquid to less liquid assets, other things equal). Silvio Gesell was right about interest on money being what matters for Aggregate Demand

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