Monetary Policy and Zero Rates, A Thought Experiment

As always when I think about money and interest rates, I'd like to start with the Fisher equation, which says the nominal interest rate is equal to the real interest rate plus expected inflation. Lets imagine that in a closed economy, the market for loanable funds clears at a 5% real rate of interest, and the money supply is expected to grow 5% while real output grows 3%, giving 2% inflation. The nominal interest rate observed in credit markets would then be 7%. Simple enough. At a 7% nominal interest rate no one would argue that the monetary authority could "cut" interest rates by buying bonds, hence raising their price and lowering their yields. That's because the expansionary stance of policy (5% money growth) has kept them decisively positive, thus giving the impression that their is room to be "more" expansionary. At the margin, the central bank can exchange non-interest bearing  base money for interest bearing bills, altering the portfolio structutre of the economy and temporarily lowering short-term rates (before the increased money supply pushes up nominal spending and prices and financial markets price in the increase in inflation.)

But let's imagine a scenario where the stance of policy is not expansionary, but contractionary. Let's say the money supply is growing at 2% per year, real output at 1%, but the income elasticity of demand for base money is more than unity so that it rises 2% for a 1% rise in income. This gives us a -1% rate of inflation, or a 1% rate of deflation even though the money supply is growing at 2%. Now let's say weak growth has depressed the demand for loanable funds and households and businesses are saving more so the equilibrium real interest rate has collapsed to one percent. Going back to the Fisher equation, this means the nominal interest rate in the short-term money market is...zero. By standard Keynesian monetary theory, we are in a liquidity trap, and the central bank is out of ammo. On the margin, bonds and money are perfect substitutes, so expanding the money supply will do nothing.

The implication of this is that all the hemming and hawing about how monetary policy is ineffective when nominal rates are zero has bizarre implications. When money has been loose, the thinking goes, more expansion will have traction. When money has been tight and the economy is weak, expansionary policy will do nothing. I don't buy it.